Structure determination of biologically relevant molecules and their van der Waals complexes using Fourier-transform microwave spectroscopy

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STRUCTURE DETERMINATION OF BIOLOGICALLY RELEVANT MOLECULES
AND THEIR VAN DER WAALS COMPLEXES
USING FOURIER-TRANSFORM MICROWAVE SPECTROSCOPY
A dissertation submitted to Kent State University
in partial fulfillment of the requirements for the
degree of Doctor of Philosophy
by
Richard J. Lavrich
May 2002
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UMI Number. 3057401
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Dissertation written by
Richard J. Lavrich
B.S., The Ohio State University, 1994
Ph.D., Kent State University, 2001
Approved by
$ / '<O fa c u l
—
Chair, Doctoral Dissertation Committee
Members, Doctoral Disseration Committee
Accepted by
w JL
f f r
- Chair, Department of Chemistry
Dean, College of Arts and Sciences
u
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TABLE OF CONTENTS
LIST OF FIGURES......................................................................................... vi
LIST OF TABLES........................................................................................... ix
Chapter 1 Theory
1.1 Introduction....................................................................................1
1.2 Angular Momentum...................................................................... 3
1.3 Moment of Inertia Tensor............................................................. 14
1.4 Solution of the Hamiltonian......................................................... 16
1.4.1 Linear Molecules.............................................................19
1.4.2 Symmetric Tops.............................................................. 22
1.4.3 Asymmetric Tops............................................................ 25
1.5 Structure Determination from Rotational Spectroscopy............... 32
Chapter 2
Experimental
2.1 Instrumentation............................................................................. 38
2.2 Synthesis.......................................................................................42
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Chapter 3 Amino Acid derivatives
3.1 Introduction................................................................................. 51
3.2 Alaninamide................................................................................ 54
3.2.1 Ab initio.........................................................................54
3.2.2 Experimental Data......................................................... 59
3.2.3 Structural Information.................................................... 64
3.2.4 Discussion......................................................................67
3.3 Valinamide..................................................................................77
3.3.1 Ab initio.........................................................................77
3.3.2 Experimental Data......................................................... 81
3.3.3 Discussion......................................................................88
Chapter 4 Alaninamide-H20
4.1.1 Introduction....................................................................92
4.1.2 Ab initio......................................................................... 93
4.1.3 Experimental.................................................................. 95
4.1.4 Structure......................................................................... 97
4.1.5 Discussion......................................................................103
iv
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Chapter 5
Ring Systems
5.1 3-Hydroxytetrahydrofuran.......................................................... 111
5.1.1 Introduction...................................................................I l l
5.1.2 Ab initio........................................................................114
5.1.3 Results.......................................................................... 116
5.1.4 Structure........................................................................121
5.1.5 Discussion.....................................................................125
5.2 3-Hydroxytetrahydrofuran- H20 ................................................ 127
5.2.1 Introduction...................................................................127
5.2.2 Ab initio........................................................................128
5.2.3 Results.......................................................................... 130
5.2.4 Structure........................................................................136
5.2.5 Discussion.....................................................................140
v
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LIST OF FIGURES
Figure
1.
The instantaneous position of a particle denoted by a vector r in
a Cartesian coordinate system..............................................................4
Figure
2.
The orientation of two coordinate systems described by a set of
Euler angles......................................................................................... 9
Figure
3.
Principal inertial axes of linear, symmetric top, and asymmetric
top molecules...................................................................................... 17
Figure
4.
Rotational energy levels of a rigid linear molecule..............................21
Figure
5.
A prolate-oblate correlation diagram................................................... 28
Figure
6,
Hamiltonian matrix for an asymmetric top.......................................... 30
Figure
7.
Potential energy surface illustrating zero-point vibrations.................. 34
Figure
8.
Circuit diagram for microwave spectrometer...................................... 41
Figure
9.
General reaction scheme for converting an amino acid into an
amino amide...................................................................................... 43
Figure
10. Infrared spectrum of N-CBZ-DL-valine..............................................45
Figure
11. Infrared spectrum of N-CBZ-DL-valine p-nitrophenol ester...............48
Figure
12. Infrared spectrum of N-CBZ-DL-valinamide...................................... 50
Figure
13. Conformations of glycine....................................................................52
vi
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Figure
14. Ab initio conformations of alaninamide................................................55
Figure
15. Labeling scheme for alaninamide......................................................... 65
Figure
16. Ab initio conformations of valinamide................................................. 78
Figure
17. Newman projections of the ab initio conformations within
the amide-to-amine intramolecular hydrogen bonding scheme........... 79
Figure 18.
Newman projections of the ab initio conformations within
the bifurcated amine-to-carbonyl intramolecular hydrogen
bonding scheme.................................................................................. 80
Figure 19.
Ab initio conformations of the alaninamide-H20 van der Waals
complex............................................................................................. 94
Figure 20.
Fitting parameters of the alaninamide-H20
van der Waals complex....................................................................... 99
Figure 21.
Barriers to the flapping motion of the free proton in the
alaninamide-H20 complex.................................................................106
Figure 22.
Barrier to the internal rotation of the water molecule in the
alaninamide-H20 complex.................................................................107
Figure 23.
Furanose ring with a nucleotide and 3-hydroxytetrahydrofuran......... 108
Figure 24.
Ab initio conformations of 3-hydroxytetrahydrofuran.......................115
Figure 25.
Ab initio conformations of 3-hydroxytetrahydrofuran-H20 .............. 129
Figure 26.
Fitting parameters in 3-hydroxytetrahydrofuran-H20 .........................137
vii
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Figure 27.
Barriers to the flapping motion of the free proton in the
3-hydroxytetrahydrofuran-H20 ...........................................................143
Figure 28.
Barrier to the internal rotation of the water molecule in the
3-hydroxytetrahydrofuran-H20 ...........................................................144
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LIST OF TABLES
Table
1.
Matrix elements of angular momentum operators.................................13
Table
2.
Principal axis atomic coordinates (A) of ab initio conformer I
of alaninamide.................................................................................... 56
Table
3.
Principal axis atomic coordinates (A) of ab initio conformer II
of alaninamide.................................................................................... 57
Table
4.
Principal axis atomic coordinates (A) of ab initio conformer 01
of alaninamide.....................................................................................58
Table
5.
Frequencies (MHz) of the assigned nuclear quadrupole hyperfine
transitions of the normal isotopomer of alaninamide...........................60
Table
6.
Spectroscopic constants of the normal and nitrogen isotopomers
of alaninamide.................................................................................... 62
Table
7.
Spectroscopic constants of the l3C isotopomers of alaninamide........... 63
Table
8.
Heavy-atom bond lengths (A), angles (°), and torsional angles (°)
from the least-squares fit and ab initio conformer I
of alaninamide.................................................................................... 66
ix
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Table
9.
Atomic coordinates (A ), of the heavy atoms of alaninamide
determined from Kraitchman’s equations, least-squares fit, a
and the lowest energy ab initio model................................................. 68
Table
10.
Frequencies (MHz) of the assigned nuclear quadrupole hyperfine
transitions of ^N’-alaninamide...........................................................71
Table
11.
Frequencies (MHz) of the assigned nuclear quadrupole hyperfine
transitions of ISN2-alaninamide...........................................................72
Table
12.
Frequencies (MHz) of the assigned transitions of
l5N‘, I5N2-alaninamide........................................................................73
Table
13.
Frequencies (MHz) of the assigned nuclear quadrupole hyperfine
transitions of l5Nl , 13C’ -alaninamide.................................................. 74
Table
14.
Frequencies (MHz) of the assigned nuclear quadrupole hyperfine
transitions of l5N‘, I3Ca-alaninamide.................................................. 75
Table
15.
Frequencies (MHz) of the assigned nuclear quadrupole hyperfine
transitions of 15N‘, l3Cp-alaninamide.................................................. 76
Table
16.
Approximate center frequencies of the rotational transitions of the
normal isotopomer of valinamide........................................................82
Table
17.
Spectroscopic constants of the isotopomers of valinamide...................84
Table
18.
Approximate center frequencies of the rotational transitions of
l5N‘- valinamide................................................................................. 85
x
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Table 19.
Approximate center frequencies of the rotational transitions of
15N2- valinamide...................................................................................86
Table 20.
Least-squares fit, Kraitchman, and ab initio coordinates ( A )
of the nitrogen atoms in valinamide......................................................89
Table 2 1.
Parameters used in the least-squares fit of valinamide........................... 91
Table 22.
Approximate center frequencies of the rotational transitions of the
Normal isotopomer of alaninamide-H20 .............................................. 96
Table 23.
Spectroscopic constants of the isotopomers of alaninamide-H20 ..........98
Table 24.
Values of the fitting parameters of alaninamide-H20 .......................... 100
Table 25.
Atomic coordinates on the nitrogen atoms in alaninamide-H20
calculated from the Kraitchman analysis, least-squares fit, and
ab initio structure................................................................................. 102
Table 26.
Approximate center frequencies of the rotational transitions of the
I5N‘ -alaninamide-H20 ......................................................................... 108
Table 27.
Approximate center frequencies of the rotational transitions of the
ISN2-alaninamide-HzO......................................................................... 109
Table 28.
Approximate center frequencies of the rotational transitions of the
15N‘ ,'5N2-alaninamide-H20 .................................................................. 110
Table 29.
Spectroscopic constants of 3-hydroxytetrahydrofuran
isotopic species.................................................................................... 117
xi
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Table 30.
Frequencies (MHz) of the assigned transitions of
3-hydroxytetrahydrofuran..................................................................... 118
Table 31.
Frequencies ( MHz) of the assigned transitions of
d-3-hydroxytetrahydrofuran.................................................................. 119
Table 32.
Frequencies ( MHz) of the assigned transitions of the >3C isotopic
species of 3-hydroxytetrahydrofuran................................................... 120
Table 33.
Bond lengths ( A ), angles ( degrees), and torsional angles ( degrees)
of the C4- endo conformation of 3-hydroxytetrahydrofuran from
the least-squares fit and ab initio structures......................................... 123
Table 34.
Atomic coordinates ( A ) of the ring carbons of
3-hydroxytetrahydrofuran from the Kraitchman analysis, best-fit
structure, and ab initio structure........................................................... 124
Table 35.
Frequencies of the assigned transitions of
3-hydroxytetrahydrofuran-H20 .............................................................131
Table 36.
Frequencies of the assigned transitions of
3-hydroxytetrahydrofuran-H2 lsO.......................................................... 132
Table 37.
Spectroscopic constants for the isotopic species of
3-hydroxytetrahydrofuran-H20 ............................................................. 134
Table 38.
Comparison of the observed and calculated stark effects for
3-hydroxytetrahydrofuran-H20 .............................................................135
xii
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Table 39.
Principal axis system coordinates (A) of the isotopically labeled
atoms in 3-hydroxytetrahydrofuran-H20 from the Kraitchman
analysis and the ab initio calculations....................................................139
Table 40.
Kraitchman coordinates (A) of the hydroxyl and water hydrogens
in principal axis coordinate systems of additional isotopic species
Table 41.
141
Frequencies of the assigned transitions of
d-3-hydroxytetrahydrofuran-H20 ...........................................................146
Table 42.
Frequencies of the assigned transitions of
3-hydroxytetrahydrofuran-DOH............................................................ 147
Table 43.
Frequencies of the assigned transitions of
d-3-hydroxytetrahydrofuran-DOH..........................................................148
Table 44.
Frequencies of the assigned transitions of
3-hydroxytetrahydrofuran-HOD.............................................................149
Table 45.
Frequencies of the assigned transitions of
d-3-hydroxytetrahydrofiiran-HOD..........................................................150
Table 46.
Frequencies of the assigned transitions of
3-hydroxytetrahydrofiiran-D20 .............................................................. 151
Table 47.
Frequencies of the assigned transitions of
d-3-hydroxytetrahydrofuran-D20 ............................................................152
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CHAPTER 1
1.1 Introduction
Molecular shape and conformation play a critical role in the selectivity and
function of biologically active molecules.1 This effect of structure on function has
been implicated in such diverse processes as transport through membranes,2
neurotransmission,3drug-receptor interactions,4 and enzyme catalysis.3 The basis of
this selectivity is believed to lie in the conformational flexibility of the biomolecules
involved. The detailed structural analysis of simple biologically relevant molecules is an
important pursuit. An examination of the preferred conformations in simple systems may
lend insight into the conformational preferences of larger and more biochemically
important molecules. The research pursued for this dissertation grew out the lack of
accurate structural information for even the simplest biomolecules. The conformational
structures of two general classes of systems have been investigated: amino acid
derivatives and ring compounds.
Amino acids are the smallest and simplest biomolecules; they are the building
blocks of the more complex peptides and proteins. Detailed structural analysis of this
important class of molecules has been hampered by difficulties obtaining suitable gas
phase concentrations. In the solid state amino acids exist as zwitterions,6 having a
1
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2
positively charged protonated amino group (-NH3+) and a negatively charged carboxylate
anion (COO ). The interaction of neighboring charges stabilizes the crystal resulting in
high temperatures needed for vaporization. Furthermore the amino acids are thermally
unstable typically decomposing as they melt.
We have chose to investigate the amide derivatives of amino acids. There are
two motivations for this choice. The first is a substantial reduction in melting point. The
conversion of the carboxylic acid into an amide group removes the capability of the
biomolecule to form a zwitterion. The melting point of the amino acid alanine is 230 °C;
the melting point of the corresponding amino amide alaninamide is 70 °C. The second
motivation for studying the amide derivative is that it can be considered as a very simple
model of a peptide. Peptides are formed when the amino group of one amino acid reacts
with the carboxylic acid of another to form a peptide linkage. This peptide linkage is an
amide bond and therefore the amide group in the amino amides can be thought of as the
simplest peptide linkage.
The second class of systems considered involve ring containing compounds. Due
to ring strain caused by eclipsing methylene groups, five membered rings adopt a
conformation that contains a pucker.7 This pucker serves to alleviate the ring strain by
orienting the methylene groups in a staggered arrangement. The position of the pucker on
the ring as well as its magnitude is heavily influenced by the nature of the ring atoms and
any substituents attached to the ring.8 Due to this conformational flexibility, these ring
containing compounds offer attractive systems for accurate structural determination.
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1.2
Angular Momentum
The concept of angular momentum plays a fundamental role in the physics of
rotation. The Hamiltonian operators that describe the rotational energy states between
which transitions occur are constructed with angular momentum operators.9 It will
therefore be necessary to define these important operators as well as to examine their
interrelationships. Furthermore it will be advantageous to have a knowledge of angular
momentum in two different coordinate systems; a space fixed laboratory frame
designated by uppercase X, Y, and Z axes and a molecule fixed frame originating at the
center of mass of the system designated by lowercase x, y, and z axes.
Classical expressions for angular momentum and its components are derived by
considering a moving particle of mass m within a space fixed coordinate system.10 The
instantaneous position of the particle from the origin of the coordinate system is given by:
(1.1)
r = Xi + Y j + Zk
where X, Y and Z are the coordinates of the particle and f, j , and k represent unit vectors
along the X, Y, and Z space fixed axes; Figure 1. The coordinates of the particle are a
function of time, the velocity being defined by:
3
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4
z
X
Figure 1: The instantaneous position of a particle denoted by
the vector r in a Cartesian coordinate system. The unit vectors
i, j, and k lie along the X, Y, and Z axes respectively
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5
( 1.2)
v = dr
dt
• dX . dY
, dZ
' ¥ + ' * + ‘ *
with the components of velocity along the space fixed axes given as:
(1.3)
vx = <*
dt
vv _= dY
dt
_ dZ
dt
The angular momentum P of the system with respect to the coordinate origin is defined as
the cross product of the position of the particle r with its linear momentum p=mv:10
(1.4)
P = rx p
Expansion of the cross product yields:
(1.5)
P=
•
i
J
k
X
Y
Z
Px
Py
Pz
From this definition the components of angular momentum are given as:
(1.6)
Px =Ypz -Zpy
(1.7)
PY=Z px-X pz
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6
(1.8)
Pz —XpY - Ypx
The total angular momentum P in a space fixed axis system ( X, Y, Z) can be written in
terms of its components as:
(1.9)
P = iP x+ j P Y+ k P z
Explicitly expressing the components of angular momentum in Equation 1.9 with those
given in Equations 1.6 -1.8 yields:
(1.10)
P = i(Y pz-ZpY) +j(Z px-X pz) +k(X pY- Ypx)
The transformation from classical to quantum mechanics occurs by replacing the
coordinates and momenta by their corresponding operators,11 for example
(1.11)
X -X
(1 .1 2 )
P„ -
-ii i
The components of quantum mechanical angular momentum operators are then expressed
as:
(1 .1 3 )
P-
=
« I V
^ - Z
| Y ]
with similar expressions for PY and Pz formed by a cyclic permutation of the variables.
A spherical polar coordinate system is a more natural choice when discussing angular
momentum; the total angular momentum and its components expressed in that system
are:12
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7
Px - - i* [*
(1.15)
PY
(1.17)
) - c o te c o s*
-iH [ ’ cos ‘H
{jf,)1
I - cote sin * ( ^ ) 1]
s jl
=
II
1
d*
N
(1.16)
*0
(1.14)
P2 ” - H l [- . ft(
sin0 ' do'
sra0(
d_
d§) + sin-e^ d<J>*
As mentioned earlier there is a second reference frame from which to consider
angular momentum; a molecule fixed coordinate system fixed at the molecules' center of
mass. The relative orientation of the two coordinate systems with respect to one another
are related by a set of Euler angles. The two coordinate systems can be related by a
transformation matrix S.13 This relationship is expressed as:
/x ’
= s
y
(118)
X
Y
, Z;
U;
with the elements of the transformation matrix S consisting of direction cosines <&jo
<
^&
iX
(119)
S
=
**
^iZ
&yY
**
O lV
**
The direction cosines describe the orientation of the x, y, and z molecule fixed axes in the
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XYZ coordinate frame. The relationship between the molecule fixed x-axis with respect
to the space fixed X, Y, and Z axes is illustrated in Figure 2. The molecule fixed y and z
axes have been omitted for clarity. The direction cosines describing the orientation of the
x axis to the XYZ coordinate frame make up the top row of the transformation matrix S
and have the form:
(1.20)
$ xX= cos a,
$ xY= cos p,
$ xZ= cosx,
Similar expressions exist relating the y and z axes to the space fixed frame. The
conversion of angular momentum between the two reference frames is accomplished
through the relations:
(1.21)
Px= * * Px + ^ XYPy +
Pz
Py^yxPx+fcyYPy + ^yzPz
P ,» « * P x+ * * P y + * * P z
One of the important principles of quantum mechanics is that operators which
commute have a common set of eigenfunctions." This becomes very useful when
seeking expressions which describe the rotational motion of molecules. The commutator
among operators is defined as:
(1.22)
[ A, B ] = AB - BA
When this expression is zero the two operators are said to commute and share a common
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9
Z
X
Figure 2: The orientation of two coordinate systems is described
by a set of Euler angles a , p, and x which the describes the angular
orientation of an axis of one system to the axes of the other.
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10
set of eigenfunctions. It can be shown that P2, the square of the total angular momentum,
commutes with one of its components.11 The choice of which component is arbitrary with
the z-component being the conventional choice. This relationship is expressed as:
(1.23)
[ P 2,P z] = 0
The components of angular momentum do not commute amongst themselves. Their
relationship can be expressed as:
(1.24)
[P x PY] = ihPz
The commutation relationships of the other combinations are achieved once again by
cyclic permutation of the variables.
As indicated above, two operators that commute share a common set of
eigenfunctions. The operators P2 and Pz meet this criterion. The common set of
eigenfunctions of P2 and Pz can be expressed as YJMor in the more compact <bra/ket>
notation as IJ M>.14 Their eigenvalue equations are written as:
(1.25)
P2IJM > = c IJM >
(1.26)
Pz IJ M> = b IJ M>
where c and b represent general forms of the eigenvalues of the operators. It is possible
to express the operators in their differential form and solve the resulting differential
equations to determine the eigenvalues. However there is a more simple and elegant way
that involves the commutation relations. The derivation requires the definition of a new
type of operator, the shift operators P+and P..11 These operators are defined as:
(1.27)
P+= Px + iP Y
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11
(1.28)
P. = P x -iP Y
and have the following commutation properties:
(1.29)
[ P +,P Z] = ->>P+
(1.30)
[ P ., P z ] = t>P.
(1.31)
[P 2 ,P +J = 0
The shift operators provide a very useful method of generating eigenfunctions of angular
momentum. Application of the shift operators to an eigenfunction of Pz results in a new
eigenfunction having the z-projection increased by one unit. That is, when the raising
operator P+ is applied to an eigenfunction of Jz with eigenvalue b, a new eigenfunction is
generated having eigenvalue b + h. The same holds true for the lowering operator P.; the
application of P. to an eigenfunction of Pz with eigenvalue b results in a new
eigenfunction with eigenvalue b - h.
The explicit values of the eigenvalues b and c of Pz and P2 are found by setting
boundary conditions on the shift operators;
(1.32)
P+1J Mmax> = 0
(1.33)
P. IJ Mmin> = 0
Equations 1.32 and 1.33 require that when the raising and lowering operators act on the
upper and lower bounds of the eigenfunctions IJ M >, the eigenfunctions are annihilated.
These boundary conditions lead to a system of equations
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12
(1.34)
c = b2max+>i b ^
^
^ mm ~ ^ ^min
that are solved to produce the eigenvalues of Pz and P2
(1.35)
P2IJM > = J(J+1)>,2IJM>
(1.36)
Pz IJ M> = M>i IJ M>
The preceding derivation of the eigenvalues of the operators P2 and Pz introduced
the shift operators P+ and P.. The matrix elements of these operators were never explicitly
used in the derivation, instead their commutation properties were utilized. The shift
operators involve expressions which depend upon Px and PYand as a result they can be
used to determine the matrix elements of these operators. The matrix elements of the
operators Px and PYare found by setting up eigenvalue expressions and utilizing the
normalization condition as well as the orthonormality of the eigenfunctions.
(1.37)
P+ IJ M> = C+ I J, M+l>
(1.38)
P. I JM > =C. I J, M-l>
This results in the following eigenvalue relations for the raising and lowering operators:
(1.39)
C+ = 'ih [J(J+1) - M (M +l)f
C. =-iM J(J+D -M (M -l)f
which are used along with Equations 1.27 and 1.28 to determine the matrix elements of
Px and PY The determination of the frequencies of the transitions between rotational
eigenstates relies on the nonvanishing matrix elements of the operators P2, Pz, Px, Py,
and the shift operators P+and P.. These matrix elements are summarized in Table 1.
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<
j k m i p
2i
j k m
>
H* J(J+1)
< J K M I P, IJ K M>
*K
< J K M I P z IJ K M>
•fiM
< J K t 1 M I P, I J K M>
I J(J-t-l) - K (K ± 1
< J K t l M I P yI J K M >
[ J ( J + 1 ) - K ( K ± 1 )]”
<JKM+1 I P JJK M >
i -h [ J (J + 1 ) -M ( M + 1 ) ] ,/J
< J K M- l I P. IJ K M>
- i "h [ J(J+1) - M (M -1)]I/J
Table 1: Matrix elements of angular momentum operator?
)]'n
13
Moment of inertia tensor
Molecules are made up of a collection of nuclei. A convenient way of describing
the angular momentum of a molecule is to describe its constituent nuclei in terms of a
moment of inertia.13 The moment of inertia describes the distribution of mass about the
axes of rotation. The angular momentum of a collection of a nuclei of mass mathat are
located at positions rBrelative to some Cartesian coordinate system is given as the cross
product of the positions of the nuclei with their linear momentum:
(1.40)
P
= I« ra X pa
= Za rna ra X (w X rJ
Using the relation:
(1.41)
A x ( B x C ) = B(A*C)-C(A*B)
allows P to be rewritten as:
(1.42)
P = I« ma [ <•>( ra • ra ) - rB( rB• a>) ]
=
me [ 0 ) ( xa2 + yB2 + zB2) - ra ( xBwx+ yBa>y + xBwz )
Further expansion of this expression by explicitly writing components of the remaining
vector quantities and grouping in a more compact matrix notation gives:
14
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15
y^ + z^1) *
= - Z m .y .x .
Zma(xaI +zj)
(
Px
Pv
(1.43)
Px
I
\
-
ZmKzBx0
■ £ in,,
y«
1
- Z m ^z.
<0.
- £ m* yBz„
“r
£!«*( x„2 +yal )
In symbolic form, Equation 1.43 is written as:
(1.44)
P =
I • <D
The 3X 3 matrix of Equation 1.43 represents the moment of inertia tensor. This tensor
plays a crucial role in rotational spectroscopy from an understanding of the observed
spectrum to the determination of structural information. The elements of the moment of
inertia tensor that lie along the diagonal are referred to as the moments of inertia while off
diagonal elements are referred to as the products of inertia. For a moment of inertia
tensor with its origin at the center of mass of the body it is always possible to diagonalize
the matrix, that is a similarity transformation is performed which makes all of the off
diagonal elements zero. Such a transformation puts the molecule in the principal axis
system and greatly simplifies later analysis. The axes of the principal axis system are
given the labels a, b, and c. The diagonal elements of the diagonalized matrix are referred
to as the principal moments of inertia and are given the symbols L,, Ib , and ^ By
convention I, £ I,, £ I,..
For the technique of rotational spectroscopy it is advantageous to classify
molecules according to the relationship between their principal moments of inertia.
The following classifications exist:15
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16
(1.45)
Linear Molecules
(1.46)
Symmetric Tops
I. = 0
Ib= Ic
Prolate
Oblate
(1.47)
Ia = Ib<Ic
Asymmetric Tops
Examples of each of these are given in Figure 3. The appearance of the rotational
spectrum as well as the solution of the rotational Hamiltonian depends upon these
relationship between the moments of inertia. Each class of molecules will therefore be
considered.
1.4
Solution of the Hamiltonian
An understanding of the rotational spectrum of a molecule requires a knowledge
of the rotational eigenstates between which transitions may occur. The general approach
to calculating the allowed rotational energy states of a molecule involves the solution of
the eigenvalue equation;
(1.48)
Hr IY> = E l*P>
where HRis the rotational Hamiltonian and I7> the appropriate rotational eigenfunctions
of the system. The Hamiltonian describing molecular rotation is given as:16
(1.49)
Hr = APa2+ BPb2+ CPc2
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17
a)
b)
c
c
,.c
b
c)
b
b
d)
b
Figure 3: Principal inertial axes of a) Linear molecule
b) prolate symmetric top c) oblate symmetric top and
d) asymmetric top
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18
The J,2 terms represent angular momentum about each of three molecule fixed principal
axes and the coefficients A, B, and C are rotational constants defined as:
(1 J# )
A
B
=
8jc2I„
Jh
C
81c2 Ic
From these expressions it can be seen that the rotational constants are inversely
proportional to the moments of inertia that result from the diagonalization of the moment
of inertia tensor.
The solution of the eigenvalue expression of equation 1.48 requires the
determination of the matrix elements of HRin the appropriate representation
(1.51)
< 7 iIHRl 7 i >
The resulting matrix must be diagonal to yield the allowed rotational energy states. If it is
not already diagonal a new set of functions must be determined which are. This is
accomplished by defining a new set of functions that are linear combinations of the
original basis functions:
(1.52)
l * > = E a iI T i >
The coefficients a; describe the amount of each I Yj > contained in the new basis function
I $ >. These new basis functions must satisfy the eigenvalue equation
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19
(1.53)
Hr I«&> = E(<& )!<&>
where E ( $ ) is the energy of the rotational state I $ >.
1.4.1
Linear molecules
For the case of a linear molecule the angular momentum about the intemuclear
axis is zero and equal about the other two. With these constraints the rotational
Hamiltonian of equation 1.49 reduces to;
(154)
Hr
21
using
(1.55)
P2= P ,2+Pb2+Pc2
and the definition of the rotational constants given in Equation 1.50. The Hamiltonian for
a rigid linear molecule contains only the operator J 2 and as a result has spherical
harmonics as eigenfunctions. The spherical harmonics are generated using the following
relationships:"
(1.56)
Yjm = (-1)M [
(2J+1)(J-M)!
PMj(cos 0 ) eiM*
(1.57)
(1.58)
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20
Solution of the eigenvalue equation;
(1.59)
Hr Y = E Y
using the spherical harmonics as the wavefunction T leads to the quanitized energies
given by:
(1.61)
E, = B J ( J+l)
J = 0,1,2,..
The selection rules governing transitions between rotational energy states are given as:
(1.62)
AJ = ± 1
(1.63)
AM = 0 , ± 1
The frequencies of the transitions are determined by calculating the energy difference
between states;
(1.64)
AE = EJ+, - E,
The energy separation between states J and J+l is:
(1.65)
AE = B(J+l)(J+2) - BJ(J+1)
= B(J2+3J +2) - B(J2+J)
= 2B(J + 1)
This expression illustrates that the lowest energy transition, from J=0 to J=l, occurs at a
frequency of 2B and that in the absence of centrifugal distortion the transitions are
equally spaced by multiples of 2B as illustrated in Figure 4.
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21
J
/
/
T
0
I
frequency
Figure 4: a) Rotational energy levels of a rigid linear molecule
b) The resulting stick spectrum
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1.4.2
Symmetric Tops
In a symmetric top one of the principal axes of inertia lies along the molecular
axis of symmetry. The principal moments of inertia which have their axes perpendicular
to this axis are equal. As discussed earlier in the derivation of the moment of inertia,
symmetric tops are further subdivided based upon which moments of inertia are equal.
When the axis of least moment of inertia, defined as the a axis, lies along the symmetry
axis, Ib and I,, are equal and the top is classified as a prolate symmetric top. When the
axis of greatest moment of inertia, the c axis, lies along the symmetry axis, L, and ^ are
equal and the top is classified as an oblate symmetric top
The general form of the rotational Hamiltonian is given by:
(1.66)
H = APa2+ BPb2+ CPc2
Noting that the square of the total angular momentum P in terms of its components is
given as:
(1.67)
P2= P a2+ P b2+ P c2
and considering thecase of the prolate symmetric top in which:
(1-68)
Ib = Ic
the Hamiltonian forthe prolate symmetric top can be expressed as:
22
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23
An analogous expression can be derived for the oblate symmetric top by performing a
cyclic permutation of the variables a, b, and c.
An examination of the rigid rotor symmetric top Hamiltonian in Equation 1.69
shows that it contains operators for the square of the total angular momentum P2 as well
as a component of this angular momentum in the molecule fixed axis system Pa . It has
been shown previously that P2 commutes with one of its components in the space fixed
axis system and as a result there is a common set of eigenfunctions of these operators
labeled IJ M >. P2 and Pz also commute with Pa the component of angular momentum
in the molecule fixed axis system, and as result symmetric top wavefimctions have an
additional quantum number K designating the component of the total angular momentum
in this molecule fixed axis system.16 The wavefunctions are the symmetric tops are
labeled as IJKM>.
Eigenvalues for the operators P2, Pa , and PA, have been shown in a Table 1 to be:
(1.70)
< J K M I P2I J K M > = b2 J(J+1)
(1.71)
< J K MI PzIJ K M > = bK
(1.72)
< J KM I Pzl J K M > = hM
with the restrictions that:
(1.73)
J =0, 1,2,
(1.74)
K = -J, -J+l
0....+J
(1.75)
M = -J, -J+l
0 ....+J
The allowed energies are determined by calculating the matrix elements:
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24
(1.76)
EJIC = < J K MI Hrl J K M>
J L j(j+ i) + J L ( J —
8*1!.
8b 1 ' I.
L )k !
I. '
Using the expressions for the rotational constants:
(1-77)
A
=
8ji%
(1.78)
B
=
h2
8tc2I„
the energy expression of Equation 1.76 is reduced to:
(1.79)
EJIC= h[BJ(J+1) + (A-B)K2]
Due to the presence of the K2 in the energy expression, all K levels except K=0 are
doubly degenerate. This K degeneracy can not be removed by either external or internal
fields. There is also a 2J+1 degeneracy in M in the Held free symmetric rotor. This
degeneracy can be lifted by the application of an external electric or magnetic field. The
application of an electric field to remove the degeneracy of the M lobes is used to
determine the dipole moment of the molecule. The selection rules for the symmetric top
are:
(1.80)
AJ = 0, ±1
(1.81)
AK = 0 ± 1
(1.82)
AM = 0
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25
The frequencies of allowed transitions between rotational energy levels can be calculated
using the energy expressions of Equation 1.79. The frequency of a transition is given by:
(1 .8 3 )
v
=
AE
------
h
The difference between energy levels with AJ = 1 and AK = 0 is
( 1.84)
AE = Ej+i, k • Ej K
= h[B(J+1 )(J+2) + (A-B)K2] - h[BJ(J+1) + (A-B)K2]
= h[B(J2+3J+2)] - h[B(J2+ J)]
= hB[J+l]
The frequency of transitions within a given K stack is given as:
(1.85)
v = 2B(J+1)
The spacing between rotational energy levels in the absence of centrifugal distortion is
the same as that determined for linear molecules.
1.4.3 Asymmetric Tops
In an asymmetric top molecule none of the moments of inertia are equal. As a
result the Hamiltonian has the form:
(1.86)
H = AP.1 +BP>* +CPc*
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26
For an asymmetric top molecule it is no longer possible to describe the rotational motion
in terms of conserved motion about a particular axis of the molecule. In other words
there is no component of the angular momentum that is a constant of motion and as a
result Pz no longer commutes with H, and only J and M are “good” quantum numbers
The frequencies of transitions between rotational states of asymmetric top
molecules can no longer be described in terms of closed form expressions like in the case
of linear and symmetric top molecules. The asymmetric top wavefunctions are best
described by expanding them in terms of those for the symmetric top. The details of the
solution of the asymmetric top Hamiltonian depend upon the degree of asymmetry. The
Hamiltonian is constructed to take advantage of any near symmetric top character. The
degree of deviation from the limiting cases of the oblate and prolate symmetric tops has
been formalized in the asymmetry parameter k.16 This parameter is defined as:
(1.87)
K =
(2B-A-C)
(A-C)
with A, B, and C the rotational constants of the molecule of interest. For the case of a
prolate symmetric top B=C and k in Equation 1.87 reduces to:
(2B-A-B)
( '- 88)
K =
= •'
For the oblate limit A=B and k approaches +1. A value of zero represents the highest
degree of asymmetry.
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27
A double subscript notation developed by King et al is a convenient way to
characterize the energy levels of an asymmetric top.17 This notation is written as J ^ .
The Kp subscript represents the K value of the limiting prolate top with which the
asymmetric top connects to as k - -1. The K„ term represents the K value of the limiting
oblate top when tc - +1. A prolate-oblate correlation diagram is shown in Figure S. The
prolate-oblate correlation diagram gives a qualitative description of the asymmetric top
wavefunctions. The outer edges of the diagram represent the limiting prolate, k - -1, and
oblate,
k —+1,
limits. The asymmetric top wavefunctions are made up of a linear
combination of symmetric top wavefunctions. The coefficients describing the amount of
oblate and prolate character in the asymmetric wavefunction are determined by the
relative position along the x-axis of the diagram as determined by the value of the
asymmetry parameter.
The general procedure for obtaining the allowed energy levels of an asymmetric
top involves expressing the asymmetric top wavefunctions as a superposition of
symmetric top wavefunctions and solving the eigenvalue equation:
(1.89)
Hr IY> = EIY>
The asymmetric top wavefunctions are given as:
(1.90)
T = S c nt|tn
where i|rn is a member of the set of symmetric top wavefunctions and the coefficients c„
describe the amount of t|t„ in the asymmetric top wavefunction Y. Substitution of the
expressions for 7 given in Equation 1.90 into the eigenvalue equation of Equation 1.89
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28
J=0 0
---------------------------------- Ooo--------------------------Kp
K = -l
0J=0
K„
K= 0
Prolate
K = +1
Oblate
Figure S: A prolate-oblate correlation diagram
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29
yields:
(1.91)
Zn c„Hi|in = E I„cnt|rn
Multiplication by the complex conjugate t|r* mand integration over all space results in:
(1.92)
I n cn < ijrj HI i|rn> = E I ncn < i|rm I i|rn>
Using the orthonormality of the symmetric top wavefunctions and rearranging results in:
(1.93)
cn [< i|rml HI i|rn> - E 5mn ] = 0
Equation 1.93 describes a set of 1 linear equations with 1unknowns. The nontrivial
solution of Equation 1.93 occurs when:
(1.94)
[<i|rmIHIt|rn> - E 5 mn] = 0
If the matrix elements <i|rJ HI t|r„> can be determined this equation can be solved for the
values E, the roots of the secular equation.
The Hamiltonian operator can be represented in matrix form, the diagonalization
of the resulting matrix produces the eigenvalues E. A general Hamiltonian matrix is
shown in Figure 6. The matrix elements < J KI H I J K’ > have been designated as HKK
for convenience. The matrix is not diagonal due to the nonvanishing elements of
K’=K± 2 resulting from the Px and Py operators in the asymmetric top Hamiltonian.
The matrix of Figure 6 can be solved algebraically only for low values of J. As J
increases it can be solved only with approximation methods and the use of computers. As
an example of the solution of the matrix of Figure 6 consider the simple case where J=1.
This simplified matrix is shown in Figure 6b. Solution of the resulting cubic equation
produces the roots of the secular equation:
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30
J-2
J-l
J-2
H ',-E
J-l
J-2
J-3
J-3
M
,1-2
1-2
i-}
A-B
(A+B) - E
A-B
Figure 6:
A+B
a) General Hamiltonian matrix for an asymmetric rotor
b) For the case when J = 1
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31
(1.95)
Eo=A+B
(1.96)
E+= B+C
(1.97)
E = A+C
These are the eigenvalues of the asymmetric top Hamiltonian for the case when J=l.
They represent the energy levels between which rotational transition occur.
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1.5
Structure Determination From Rotational Spectroscopy
The structural information obtained from rotational spectroscopy is contained in
the moments of inertia. The 3x3 moment of inertia tensor was derived in Section 1.3. It
is compactly written as:
(1.98)
I
=
The diagonal elements are referred to as the moments of inertia and have the form:
(1.99)
I» = Z m ^ + Zi2)
while the off diagonal elements, referred to as the products of inertia have the form
(1.100)
Iiy = - Z m ixjyi
An examination of these elements show that they contain the x, y, and z coordinates of
the molecule of interest and therefore can be used to determine structure.
The process of obtaining structural information from rotational spectroscopy
begins with finding rotational transitions for the species of interest. The quantum
numbers of the upper and lower energy states between which the transitions occur must
32
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33
be correctly assigned. When this is accomplished the A, B, and C constants of the
rotational Hamiltonian are obtained which can be seen from Equation 1.50 to be related
to the moments of inertia. This analysis of the rotational spectrum provides principal
moments of inertia. As described in Section 1.3, in order to relate the experimental
moments of inertia to structure, the moment of inertia tensor needs to be in diagonalized
form.
Because of the accuracy of the experimental measurements, moments of inertia
may be obtained to six or more significant figures. It is not always possible to obtain this
level of accuracy when structural parameters are calculated with these highly accurate
moments of inertia. The difficulty arises because of vibrational averaging. The zero
point vibrations of molecules affect their dimensions. As the nuclei vibrate their
distances change. This puts limitations on the usefulness of the moments of inertia
calculated from these distances. The potential well illustrated in Figure 7 demonstrates
this point. The wavefunction of the zero point vibrational energy level has a finite
probability over a range of intemuclear distances. The measured rotational constant
represents an average of these intemuclear separations. This average intemuclear
distance does not necessarily correspond to the equilibrium position of the vibrationless
state at the bottom of the well. The more asymmetric the potential function, the more the
experimental and equilibrium geometries will deviate.
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E
v=0
Q
Figure 7: Potential energy surface illustrating the difference between
equilbrium ( re) and average ( r„) structural parameters
resulting from vibrational averaging
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35
Despite these difficulties that arise form vibrational averaging it is still possible to obtain
accurate structural information using rotational spectroscopy. Bond distances can
typically be determined to less than 0.01
A, bond angles to within 0.1°, and dihedral
angles to within a few degrees.16 Furthermore the technique is ideally suited for the
current research. The biologically relevant molecules studied have been shown to have
numerous low energy structures due to conformational flexibility and stabilization from
intramolecular hydrogen bonding. These structures will have vastly different moments of
inertia and therefore will be easily distinguishable.
There are two independent methods of structural analysis that can be performed
using the moment of inertia data obtained from microwave spectroscopy, a least-squares
fitting procedure18and a Kraitchman analysis.16-19 Both of these methods rely on having
moments of inertia from a number of isotopomers of the species of interest. In some
cases it is possible to obtain spectra for >3C isotopomers in natural abundance but in the
vast majority of cases it is necessary to have isotopically enriched samples.
The least-squares fitting procedure18 begins with some reasonable starting
structure. Typically this would be one obtained from the ab initio calculations. The ab
initio structure is referred to as an equilibrium structure. The distances and angles
determined for this structure are those at the “vibrationless” state at the bottom of the
potential well shown in Figure 7. For the least-squares fit, structural parameters within
the starting structure are varied. Throughout this process the moments of inertia of the
adjusted structure are compared to those obtained from experiment. The goal of the least-
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36
squares fit procedure is to minimize the difference between the observed and adjusted
moments.
The structure obtained for the least-squares fit is referred to as an effective
structure. It uses the experimental rotational constants and as a result the structural
parameters calculated are from the zero point vibrational level. These parameters are
subject to the vibrational effects and as a result represent averages.
The second method of structure determination involves Kraitchman’s equations of
single isotopic substitution.16,19 This method allows for the determination of the principal
axis coordinates of the substituted atom. By isotopically labeling several atoms in the
molecule, a structure can be generated. The method relies on the differences between
moments of inertia of the normal and substituted isotopomers. Equations have been
developed by Kraitchman which relate the moments of inertia of the substituted species in
terms of the corresponding moments for the normal, the reduced mass of the system, and
coordinates. Solution of these equations gives the principal axis coordinates of the
substituted atom. The expression for the x coordinate of an asymmetric top is given as:
where
(1.102)
AP, = {
(- A I . + A ^ + A I J
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37
and AI, is the difference between the x component of the moments of inertia of the normal
and substituted species. Analogous expressions exist for the y and z coordinates
The structure obtained from the Kraitchman method is referred to as a substitution
structure. It partially accounts for the effects of vibrational averaging because as can be
seen in Equation 1.01 the coordinates calculated from this method are the result of
differences in the experimental moments of inertia. As a result the vibrational
contributions are subtracted from one another reducing their magnitude.
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CHAPTER 2
2.1
Instrumentation
Rotational spectra were measured on a custom built microwave spectrometer
designed by Michael J. Tubergen. The spectrometer is based on the Balle-Flygare system
developed in the 1980's.20 The benefits of the Balle-Flygare type spectrometer arise from
two factors; a highly reflective Fabry-Perot cavity and a pulsed supersonic jet expansion
system for sample introduction. The spectrometer is controlled by a home built circuit
and a windows based graphical user interface.
The heart of the spectrometer is the Fabry-Perot cavity21 established by two 36 cm
diameter concave mirrors. The mirrors have a spherical radius of curvature of 84 cm. The
highly polished mirrors result in a cavity with high Q. The quality factor Q22 is a measure
of the radiation loss of the cavity; the higher the Q the less radiation that is lost. When
the Q is high, resonant radiation is trapped in the cavity and undergoes many reflections
which greatly increases the effective pathlength of absorption and as a result the
sensitivity of the instrument.
The mirrors are housed in a chamber measuring 46 cm in diameter by 114 cm in
length. The chamber is pumped by a Edwards mechanical rough pump backed by a
10,000 L s'1Varian diffusion pump. The chamber can be evacuated down to a pressure of
38
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39
5 x 10*7 torr. The maximum separation of the mirrors is 80 cm. The mirrors are moved
to tune to the desired frequency; the mirrors must lie an integral number of wavelengths
apart with respect to the source wavelength in order to establish resonance. When this
condition is met a standing wave results within the cavity. The current frequency range
of the spectrometer is 5-18 GHz.
The sample is introduced into the chamber by a series 9 General valve. The valve
can be mounted in two orientations, perpendicular and parallel to the cavity axis. In the
perpendicular orientation the valve is mounted on the outside of the spectrometer. This
arrangement allows for the sample to be heated, up to 200 °C. The drawback to this
orientation is that the doppler broadening of the rotational transitions is greater than when
the valve is mounted parallel to the cavity axis; linewidths are on the order of SO kHz for
the perpendicular arrangement versus 10 kHz in the parallel arrangement.
The valve is connected to a high pressure carrier gas. The sample is heated in an
aluminum tube by means of a heater cuff controlled by a thermocouple. The carrier gas
passes over the sample and is expanded into the cavity. The process of going from the
high pressure region of the valve to the low pressure region of the spectrometer results in
a supersonic expansion.23,24 In a supersonic expansion the random thermal motions of the
gas molecules are transformed into a uniform directed motion. The directional mass flow
is accompanied by a cooling of translational motion because the enthalpy needed to create
the directed flow is taken from the enthalpy of the random translations. In addition to
translational cooling, two body collisions between molecules in the early stages of the
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40
expansion cool vibrational and rotational degrees of freedom as well. These collisions
greatly aid in the simplification of the spectra by cooling out higher lying vibrational and
rotational states.
The spectrometer is controlled by a home built circuit and windows based control
program. A schematic diagram of the circuit elements is shown in Figure 8. A Hewlett
Packard 8371 IB synthesized cw generator provides the microwave radiation, 1-20 GHz.
The microwave radiation is amplified by a Miteq SMC-10 amplifier and is passed
through a splitter. The splitter sends half of the radiation to a pin diode switch and the
other half to a frequency mixer to be mixed with the molecular output signal. The
microwaves are introduced into the cavity through a 1.5 cm L-shaped antenna mounted
1.0 mm from the surface of the mirror.
When the frequency of the microwave radiation corresponds to the difference
between rotational energy states in the molecule, it is absorbed causing the molecules to
rotate. As the molecules rotate, they emit coherent polarized radiation at the frequency of
the rotational transitions. The polarized emission creates oscillations in the electric field
that are detected by the antenna. This signal is collected and sent through a low noise
amplifier. It is then routed through a second pin diode switch and frequency mixed with
the original input frequency. The result of this mixing is to reduce the molecular signal to
0-2 MHz which is then amplified and filtered. The signal is digitized at 4 MHz by a
Keithley-Metrabyte DAS-4101 data acquisition board in a personal computer.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 8: Circuit diagram for spectrometer 1. microwave source 2. splitter 3. amplifier 4. pin diode switch
5. Fabry-Perot cavity 6. directional coupler 7. amplifier 8. pin diode switch 9. frequency mixer
10. amplifier 11. amplifier 12. filter
2.2
Synthesis
Structure determination from microwave spectroscopy relies heavily on isotopic
labeling. For asymmetric tops each isotopomer provides three moments of inertia. The
least squares fitting procedure adjusts specified structural parameters in the molecule such
that the best fit to the experimental data set is attained. Clearly more isotopomers provide
more moments of inertia allowing a larger set of structural parameters to be fit. In the
Kraitchman analysis principal axis coordinates of the substituted atom are determined.
By examining a large number of isotopomers, a more complete structure can be
determined.
Isotopically labeled amino amides are not commercially available; it is necessary
to synthesize them. The synthesis involves a four step process. In general this entails
protection of the free amine as well as any reactive side chain functional groups,
activation of the carbonyl, formation of the amide, and finally removal of any protection
groups to produce the free amino amide. This reaction scheme is illustrated in Figure 9
for a general amino acid; the side chain which defines the specific amino acid has been
labeled with an R.
A number of amino acid derivitives have been synthesized for use in the present
research including; alaninamide, valinamide, cysteinamide, and N-acetylalanine
methylamide. The details of the reactions converting the starting amino acids into the
amino amides, including suitable purification methods and solvent choice, depends upon
42
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43
Figure 9: General reaction scheme for converting an amino acid into an
amino amide
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44
the specific amino acid. The intermediate and final products were characterized by
melting points as well as with various spectroscopic and chromatographic techniques
including IR spectroscopy, NMR spectroscopy and thin layer chromatography.
For illustrative purposes, the conversion of valine into valinamide will be described.
The nitrogen of the amino group is a better nucleophile than the oxygen of the
carboxylic acid and therefore must be protected before any further reactions can be
carried out.6 The protection can be accomplished by using benzylchloroformate (CBZ).25
An equimolar amount of CBZ in added in six equal potions over the course of 1 hour to
an ice cooled solution of the desired amino acid dissolved in 2 M NaOH. The reaction is
allowed to warm to room temperature and is stirred for four hours. After this period the
aqueous layer is washed with ether to remove any unreacted CBZ, acidified to pH 2, and
the product is extracted into dichloromethane. Recrystallization of N-CBZ-DL-Valine
with a 1:3 mixture of toulene:hexane typically resulted in a 90% yield.
Perhaps the most convincing evidence that the reaction was successful is the
substatial reduction in melting point. The melting point of the CBZ protected valine was
measured to be 70 °C; the melting point of unprotected valine is 295 °C. The infrared
spectrum of N-CBZ-DL-Valine is shown in Figure 10. The most convincing evidence in
the infrared spectrum is the appearance of a peak at 3320.8 cm*1. This new feature is due
to the N-H stretching motion of the newly formed amide band of the protected nitrogen.26
The activation of the carbonyl is necessary because acids do not react readily with
amines to form amides. Before the development of the DCC coupling method,27 amides
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Oat
r
o»
at
iD
«o
01
at
at
w
V)
to
•10
3800
3600 3400 3200
3000
2800 2600 2400 2200
2000
1800
1600
1400
1200
1000
W avenum ber
Figure 10: Infrared spcctmm of N-CBZ-Valine
■
p*
lh
were formed by dissolving the ethyl esters of amino acids in a concentrated NH4OH
solution.28'30 The yields for this type of reaction were typically 25%. Due to the costly
nature of the isotopically labeled materials this route does not represent a very attractive
route for the desired synthesis. The formation of the nitrophenol ester of the CBZ
protected amino acid greatly facilitates the formation of the amide bond due to the fact
that the p-nitrophenol anion is a good leaving group. Two factors6 contribute to this
effect, a large degree of resonance stabilization and inductive/field effects. Resonance
stabilization allows for the delocalization of charge around the ring. The large number of
resonance structures stabalizes the anion. Inductive and field effects result from the
interaction of charged centers within the anion. The inductive effect occurs through
bonds while the field effect occurs through space. In the case of the p-nitrophenol anion
the electronegative NOz group draws the electrons of the C-N02 bond towards itself. The
result is that the C atom directly bonded to it as well as adjacent carbons acquire a partial
positive charge. The interaction of this partial positive charge with the negative charge of
the anion results in some stabilization. The through space field effect involves the
interaction of the positive end of the bond dipole of the C-N02 bond with the negative
charge of the anion. Both these effects help to stabilize the anion making it a good
leaving group.
The formation of the activated ester is accomplished by adding equimolar
amounts of the protected amino acid, p-nitrophenol, and the coupling agent
dicyclohexylcarbodiimide (DCC). Use of the catalyst dimethylaminopyridine (DMAP)31
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47
greatly accelerates the reaction. The reaction was monitored by thin layer
chromatography and generally reached equilibrium in about two hours. The TLC plate
was spotted with the reaction mixture as well as p-nitrophenol. In a solvent system
consisting of 9 parts petroleum ether and 1 part ethyl acetate, the p-nitrophenol spot
underwent a slower migration than the activated ester of the protected amino acid.
Recrystallization of the activated esters were performed using ethanol. The seperation of
unreacted p-nitrophenol and activated ester was difficult presumbly due to similar
solubilities and as a result yields of purified product were low, typically around 50%.
An infrared spectrum of N-CBZ-DL-valine p-nitrophenyl ester is shown in
Figure II. Three new prominent features in the 1800-1300cm'1 region have appeared
that indicated the formation of the activated ester of the CBZ protected amino acid.
These features are due to the C-0 stretching motion of the newly formed ester and the
symmetric and asymmetric stretches of the N-O bonds in the nitro group.26 The melting
point of the product was 95 °C.
Once the nitophenol ester of the protected amino acid is synthesized, formation of
the amide is a relatively easy task. The addition of gaseous NH3 into the reaction flask
quickly accomplishes the desired task. The formation of NH3 is performed on a vacuum
line. The line has three U-shaped reservoirs that can be immersed in the appropriate slush
bath or liquid nitrogen. Solid NH4C1 is placed in a small amount of H20 ( typically 0.5
gram of the salt is dissolved in 1 ml of H20). The reaction flask is placed in dry ice in
order to freeze the solution. When frozen approximately (2 g) of solid NaOH is placed on
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n
S3
__________________ ___
3800 3600
3400 3200
1 1 1 1 1 1 1
* 1 1 1 1
3000 2800 2600 2400 2200
i 1 1 1 1 1 1 1 1
2000
1800
■ » *
1600
1 1
< » i
1400
> i
* i
1200
< « i
■ ■ i
1000
« i
■ ■»
800
Wavenumber
Figure 11: Infrared spectrum of N-CI3Z-Valine p-nilroplienol ester
00
49
top of the frozen mixture which is then placed onto the vacuum line. As the flask warms
the NaOH pellets drop into the water and free NH3 is generated. As the NH3 is formed it
passes through the first reservoir which is a dry ice/acetone slush bath. This bath
refreezes any H20 which may make it out of the reaction vessel while allowing the NH3
to pass. The second reservoir is cooled by liquid N2. The NH3 is liquefied and trapped in
this reservoir. Gaseous NH3 is generated by removing the liquid N2trap. The amount of
gaseous NH3 is monitored by a pressure gauge connected to the vacuum line. The NH3 is
then transferred to the reaction by immersing the reaction flask in liquid N2. An infrared
spectrum of N-CBZ-DL-Valinamide is shown in Figure 12. The appearance of two peaks
in the 3300 - 3200 cm'1region is convincing evidence that the amide has been formed.
The two peaks are typical for primary amines; they represent the symmetric and
asymmetric stretches of the N-H group.26
The final step in the formation of the amide derivatives of the amino acids is
deprotection. Deprotection is accomplished by a free radical elimination via
hydrogenation reaction. The CBZ protected amino amide is dissolved in a suitable
solvent ( MeOH, ethyl acetate) and to is added a catalytic amount of Pd/C and an excess
of cyclohexene. The mixture is refluxed for 4 hours. The catalyst is filtered off and the
solvent is evaporated producing the free amino amide.
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60
40>
C
«
1(A
C
e
3800 3600 3400 3200
3000 2800 2600
2400 2200
2000
1800
1600
1400
1200
1000
800
W avenum ber
Figure 12: Infrared spectrum of N-CBZ-Valinamide
L/l
o
CHAPTER 3
3.1 Introduction
Due to experimental difficulties, gas-phase structural information has been
obtained for only the two simplest amino acids, glycine32'39and alanine.40-41 Microwave
spectroscopy, electron diffraction, and matrix isolation infrared spectroscopy have shown
that these amino acids exist in multiple conformations. The conformations are stabilize
by different intramolecular hydrogen bonding schemes. The lowest energy amino acid
structure contains a bifurcated intramolecular hydrogen bond from the protons of the
amine group to the carbonyl oxygen. The proton of the carboxylic acid is in the preferred
syn configuration relative to the carbonyl group, x (HOCO) = 0°. A higher energy
conformation, resulting from a rotation about the C-C bond between the carbonyl and
alpha carbons, brings the amino group into the vicinity of the carboxylic acid. The syn
configuration of the acid proton is sacrificed, x (HOCO) = 180°, so that the stronger
carboxylic acid proton to amino nitrogen hydrogen bond can form. Evidence of a third
conformation of glycine comes from the matrix infrared work. In this conformation the
syn configuration of the acid proton is retained with the amino protons forming a
bifurcated intramolecular hydrogen bond with the oxygen of the carboxylic acid.
Annealing the matrix results in a disappearance of the features of this conformation.
51
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52
Figure 13: Conformations of glycine. Conformation I was found
to be the global minimum at the MP2/aug-cc-pVDZ level of theory.
Conformer II lies 2.2 kJ mol'1higher in energy while conformer III
is 6.6 kJ mol'1higher in energy
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53
As the matrix is warmed, conformer m interconverts to conformer I due to a low barrier
for rotation about the C-C bond. The three conformations of glycine are shown in
Figure 13.
The amino amides are much more amenable to investigation due to their lower
melting points. For the current research, the conformations of two amino amides have
been investigated; alaninamide and valinamide. These systems provide an excellent
opportunity to examine the roles of intramolecular hydrogen bonding and steric
repulsions on preferred conformational structure. Valinamide has a much bulkier side
chain than alaninamide, -CH(CH3)2 for valinamide, -CH3 for alaninamide. An analysis
of the structures of these two amino amides will provide useful information about the
forces that dictate conformation. In particular the precise structural determination
available from microwave spectroscopy will be able to determine slight structural
differences in bond distances, angles, and dihedral angles that may result from the steric
demands of the isopropyl group as well as any changes in the type of intramolecular
hydrogen bonding.
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3.2 Alaninamide
3.2.1 Ab initio
Gaussian 9442has been used to determine possible conformations of the amino
acid derivative alaninamide. Three minima on the potential energy surface were found.
Illustrations of these conformations are shown in Figure 14. The lowest energy
conformation contains an intramolecular hydrogen bond from a proton of the amide to the
nitrogen of the amine. The two higher energy structures have the intramolecular
hydrogen bonding interaction between the amino and carbonyl groups. Conformer II,
lying 6.56 kJ mol'1higher in energy, has a bifurcated intramolecular hydrogen bond of
the amino protons while conformer m, lying 15.23 kJ mol'1above the global minima, has
a single amine to carbonyl hydrogen bond. Principal axis coordinates for each of the ab
initio conformations are listed in Tables 2-4
An interesting result from the ab initio calculations is an energy ordering reversal
of the conformations of the amino amides when compared to the energies of the
corresponding amino acids. The lowest energy amino amide structure has an
intramolecular hydrogen bonding scheme most similar to the higher energy amino acid
structures; amide proton to amino nitrogen for the amino amide, hydroxyl proton to
54
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55
Figure 14: Ab initio conformations o f Alaninamide Conformer I
was found to be the lowest energy structure at the MP2/6-31G **
level; conformers II and m are 6.56 and 15.23 kJ mol'1higher
in energy than conformer I
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56
a
b
c
N1
-1.454
1.037
-0.286
H(N‘)
-1.269
1.617
-1.102
H(Nl)
-2.448
0.827
-0.317
C°
-0.701
-0.217
-0.403
H(C°)
-0.728
-0.661
-1.411
C*
-1.255
-1.239
0.590
H id )
-2.292
-1.498
0.346
H(C^)
-0.650
-2.149
0.560
H(CP)
-1.230
-0.825
1.604
C’
0.785
-0.009
-0.089
o
1.615
-0.866
-0.358
N2
1.068
1.184
0.509
H(N2)
1.989
1.297
0.903
H(N2)
0.293
1.729
0.854
Table 2: Principal axis atomic coordinates ( A ) of ab initio conformer I
of alaninamide
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57
a
b
c
N'
1.577
-0.909
-0.476
H(N‘)
1.396
-1.458
-0.364
H(N‘)
1.244
-1.506
-1.230
C
0.695
0.251
-0.395
H(C°)
0.688
0.749
-1.375
C*
1.240
1.221
0.659
HCC9)
2.268
1.498
0.408
H(C^)
0.630
-2.129
0.730
H(C*)
1.239
0.734
1.640
C
-0.741
-0.128
-0.010
o
-0.985
-1.112
0.674
NJ
-1.717
0.712
-0.484
H(NJ)
-1.466
1.619
-0.843
H(N:)
-2.634
0.617
-0.073
Table 3: Principal axis atomic coordinates ( A ) of ab initio conformer II
of alaninamide
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58
a
b
c
N'
-1.346
-1.187
-0.227
H(N‘)
-0.700
-1.960
-0.088
H(N‘)
-2.193
-1.419
0.283
C“
-0.735
-0.005
0.380
H(C°)
-0.770
-0.011
1.487
Cp
-1.457
1.249
-0.110
11(0
-2.528
1.164
0.103
H(CP)
-1.098
2.154
0.394
HCC9)
-1.343
1.356
-1.194
C’
0.763
-0.060
0.050
o
1.353
-1.127
-0.027
N2
-1.411
1.147
-0.040
H(N2)
0.895
1.970
-0.305
H(N2)
2.365
1.091
-0.365
Table 4: Principal axis atomic coordinates ( A ) of ab initio conformer m
of alaninamide
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59
amino nitrogen for the amino acid. Similarly the intramolecular hydrogen bonding
scheme of the higher energy structures of the amino amide are most similar to the lowest
energy conformation of the amino acid. This apparent energy ordering reversal is
attributed to the energy needed to overcome a cis-trans isomerization. The lowest energy
amino acid structure has the acidic proton in acis arrangement relative to the carbonyl
group. In formic acid this orientation has been shown to be 24 kcal mol'1lower in energy
than the conformation in which the proton is in the trans configuration.43 The amino
amides have a proton oriented towards the amino group and therefore do not need to
overcome this barrier to form an intramolecular hydrogen bond.
3.2.2 Experimental Data
A total of seven isotopomers of alaninamide were studied: all the heavy atoms
except for oxygen have been substituted. For the most abundant isotopomer, six a-type
and four b-type rotational transitions were measured. Due to the presence of the two l4N
quadrupolar nuclei, each rotational transition was split into many nuclear quadrupole
hyperfine components. The frequency range of these hyperfine components typically
spanned 1.5 MHz. The frequencies of the unsplit rotational transitions were obtained by
fitting the hyperfine components to the quadrupole coupling constants xM(N'), Xm>(N'),
Xa»(N2), and Xw>(N2) with N1being the amino nitrogen and N2 being the amide nitrogen.
(vob*" vcaic)rms= 6.4 kHz for the 76 hyperfine components. The frequencies of the nuclear
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F , I ’ - F", I”
101-000*
0, 1 - 1, 1
2, 2 - 2, 2
1 ,0 -0 ,0
1,0-2,2
2, 1- 1, 1
3,2 - 2, 2
1. 1 - 1, 1
1. 2- 0, 1
1.2-2,2
1 1 1- 0 0 0 '
1,0-0,0
1. 0- 2, 2
2, 1 - 1, 1
3, 2 - 2, 2
1 ,1 - 1 , 1
1,2-0,0
1. 2- 2, 2
2 2 1 -2 1 2 *
2 ,0 - 2 ,0
2, 1 - 2, 1
3. 1 - 3. 1
4. 2 - 3. 2
2, 2 - 3, 2
3.2-2,2
2, 2 - 2, 2
v*.
Av/kHz
5411.709
5411.484
5410.865
5410.865
-0.4
13.0
-0.3
-8.1
-8.1
7.3
4.9
0.0
-4.3
-4.3
7229.183
7229.370
7229.370
7229.207
7229.125
7229.037
7228.786
7228.786
2.3
3.1
3.1
-6.3
1.9
4.2
-3.0
-3.0
7904.016
7905.208
0.6
6.8
7904.911
4.0
-1.5
0.7
5.6
-4.2
-11.5
5411.853
5412.613
5412.378
5412.303
5412.303
5411.933
7903.766
7903.629
7902.770
7902.669
7902.442
J’ K; K ’„ - r K p" K0"
F’, I ’ - F", I"
2 0 2 - 111'
v*
Av/kHz
8786.700
2.7
3, 2 - 3,2
3, 2 - 2,2
8787.298
8787.042
1, 1- 0, 1
3,1-2,1
8786.880
8786.813
-0.8
6.8
3.2
2, 1 - 1. 1
2, 1 - 2, 1
1,2-1,0
1, 2 - 2 , 2
2,0-1,0
2, 0 - 2, 2
8786.384
8786.194
8786.026
8786.016
8785.888
8785.865
2 12-111'
3, 2 - 2, 2
1, 1 -0 , 1
3, 1 - 2, 1
4,2-3,2
2,0-1,2
2. 1 - 1, 1
2, 1 - 2, 1
2 , 0 - 1,0
0 , 2 - 1,0
11.0
3.2
-6.3
-13.2
3.7
-2.6
1.4
10006.346
10006.730
10006.574
10006.464
10006.102
10006.053
10005.983
10005.786
10005.469
10005.120
0.0
-6.4
3.0
1.8
-4.5
3.6
8.1
-8.4
-2.6
5.3
' The first entry is the unsplit center frequency calculated from fitting the l4N quadrupole hy perfine transitions
Table 5: Frequencies (MHz) of the assigned nuclear quadrupole hyperftne transitions of alaninamide
s
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Table 5 Continued
j* k ; k ’0- i " k / k .;
F , I ’ - F", I"
v*.
Av/kHz
10604.022
-2.2
1. 1 - 1. 1
10604.866
-3.2
2,2-1,0
10604.380
-10.0
3, 1 - 2, 1
4.9
2, 1 - 1, 1
10604.086
10603.919
4 ,2 - 3,2
10603.897
-4.1
1. 1- 0, 1
10603.758
2. 1 - 2, 1
10603.480
4.7
-0.2
1, 2- 2, 2
10603.013
-7.1
2,0-2,2
10602.882
10.5
0 , 2 - 1.0
10602.625
7.5
202-1o r
15444.456
303-202*
3, 2 - 3, 2
4, 1 - 3, 1
5. 2 - 4 , 2
15444.742
15444.503
15444.339
j ’ k ; k ’„ - J" K / K 0"
5.2
-12.0
6.8
v*.
Av/kHz
11823.672
-0.8
3,2 - 3,2
11824.420
-2.6
1, 2- 1,2
11824.131
1.2
2 , 2 - 1,0
11824.131
4.6
3,2 - 2, 2
11823.741
3, 1 - 2, 1
11823.741
-7.4
-5.2
4,2 - 3, 2
11823.522
0.0
2, 1 - 1, 1
11823.522
1.8
2, 1 - 2, 1
11823.086
7.5
11641.034
-1.2
2 , 0 - 1,0
11641.866
-6.3
2 , 2 - 1,0
11641.410
-3.0
3,1 - 2, 1
11641.087
-7.4
4,2-3,2
11640.919
8.3
2, 1 - 1, 1
11640.680
16.5
1, 1 - 1, I
11640.367
4.3
2 , 0 - 1,2
11639.853
-2.3
1,2- 1,2
11639.798
-10.2
2 12-101*
-2.9
-3.0
F’ , I ’ - F”, 1"
2 11-110*
' The first entry is the unsplit center frequency calculated from fitting the MN quadrupole hyperfine transitions
Table 5: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of alaninamide
62
l5N2-
,5N ','5N2-
alaninamide
l5Nlalaninamide
alaninamide
alaninamide
A/MHz
4931.929(1)
4878.362(4)
4857.249(4)
4803.723(2)
B/MHz
3114.6022(8)
3072.733(2)
3086.550(3)
3045.702(2)
C/MHz
2297.2573(8)
2264.864(3)
2271.780(3)
2240.033(2)
XJN1)
1.368(4)
1.288(4)
Z JN ‘)
0.606(5)
0.630(6)
XJN2)
1.618(3)
1.640(4)
X JN 2)
0.598(5)
0522(5)
10
9
N*
10
10
*Number of transitions in the fit
Table 6: Spectroscopic constants of the normal and nitrogen isotopomers of alaninamide
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63
l3C ',ISN2-
13c °, ,5n 2-
UC \ l5N2-
alaninamide
alaninamide
alaninamide
A/MHz
4856.951(3)
4857.923(3)
4775.957(2)
B/MHz
3075.483(2)
3074.041(1)
3047.9189(8)
C/MHz
2265.949(2)
2266.253(1)
2240.336(1)
XJN')
1.284(3)
1.27(2)
1.220(2)
X JN 1)
0.626(4)
0.64(2)
0.789(3)
N*
9
4
9
' Number of transitions in the fit
Table 7: Spectroscopic constants of the l3C isotopomers of alaninamide
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64
quadrupole hyperfine components and the unsplit line centers are given in Table 5. The
rotational and centrifugal distortion constants were determined by fitting the center
frequencies to the Watson S-reduction Hamiltonian and are presented in Table 6; the
uncertainty in the fit is on the order of the instrument resolution with ( v ^ -
= 2.0
kHz for the fit.
Six isotopically labeled species have also been investigated: single ISN
substitution at each of the nitrogens, double >SN substitution, and substitution at each of
the three carbon atoms; alpha, beta, and carbonyl. The 13C species were synthesized with
an 1SN nuclei on the amide to reduce the amount of hyperfine structure that had to be fit.
The frequencies of the nuclear quadrupole hyperfine components and the unsplit line
centers for the isotopically labeled species are given at the end of this section in Tables
10-15. The rotational and quadrupole coupling constants are given in Table 6 for the
nitrogen isotopomers and in Table 7 for the l3C, 1SN species.
3.2.3 Structural Information
The 21 moments of inertia were used in a nonlinear least squares fitting
procedure. Each of the three ab initio structures were used as starting points for the least
squares fit. The labeling scheme of alaninamide is shown in Figure 15. Twelve internal
coordinates describing the positions of the heavy atoms were adjusted. These parameters
are listed in Table 8. The relative orientations of the protons were fixed at their ab initio
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 15: Labeling scheme for alaninamide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
least squares
ab initio
N'—C°
1.482(6)
1.468
c°— c
1.528 (8)
1.534
c°— c"
1.520(5)
1.529
c —o
1.258(30)
1.223
C —N2
1.331(36)
1.364
N1— C°— C*
109.7 (2)
109.5
N — C“— C’
109.3 (16)
111.4
ca—c —o
119.0(26)
121.2
C —C — N2
117.2(18)
114.2
21.0
13.6
-167.4
-166.9
-100.0
-106.7
N‘—C°— C'—N2
N1—C°— C'
O
C"—C°— C'—N2
Table 8: Heavy-atom bond lengths (A ), angles ( ° ), and torsional angles ( ° )
from the least-squares fit and the ab initio model of alaninamide
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67
values: ( N ‘-H: 1.017 A; N‘-H: 1.009 A; C“-H: 1.102 A;CP- H: 1.095 A). Least
squares fitting starting with confortners II and m did not converge. The best fit structure
of conformer I reproduces the experimental moments of inertia very well with AIrms=
0.0068 amu A2
All of the heavy atoms except oxygen have been isotopically substituted in
alaninamide. Utilizing Kraitchman's equations for single isotopic substitution it is
possible to determine the coordinates of each of these substituted atoms in the principal
axis system of the normal species. This allows for an independent determination of
structure which can be compared to the corresponding values of these coordinates from
the least squares fit and ab initio structures. The Kraitchman coordinates are in the
principal axis system of the 1SN amide isotopomer because the I3C species were labeled at
this position as well.
3.2.4 Discussion
The coordinates calculated by the Kraitchman, least-squares-fit, and ab initio
methods are listed in Table 9. A comparison of the Kraitchman and least square fit
coordinates shows that the two methods are in excellent agreement. The largest
difference between the two methods occurs when the magnitude of the coordinate is small
where there is a larger contribution from vibrational averaging. The very small value of
the b coordinate of the C’ atom is heavily perturbed by vibrational averaging resulting in
an imaginary number in the Kraitchman analysis.
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68
Kraitchman
Least Squares
ab initio
N'
a
b
c
t 1.444
f 1.053
+ 0.326
1.447
-1.056
0.316
1.454
-1.037
-0.286
C“
a
b
c
t 0.712
t 0.197
t 0.405
0.720
0.234
0.392
0.701
0.217
0.403
C9
a
b
c
t 1.297
t 1.205
t 0.616
1.300
1.208
-0.620
1.255
1.239
-0.590
C'
N2
a
b
c
t 0.763
t 0.072i
t 0.108
-0.765
-0.006
0.129
-0.785
0.009
0.089
a
b
c
+ 1.109
t 1.133
f 0.535
-1.096
-1.120
-0.519
-1.068
-1.184
-0.509
Table 9: Atomic coordinates ( A) of the heavy atoms of alaninamide determined
from Kraitchman's equations, least-squares fit and the lowest energy
ab initio model
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
There are larger discrepancies between the least squares and the ab initio
coordinates. The structure determined by the least squares fit structure is an r„ structure;
an average molecular structure at the zero-point vibrational energy level. The ab inito
structure on the other hand is an restructure one which lies at the bottom of the potential
well and corresponds to an equilibrium geometry. The difference between the ab initio
and experimental structures can therefore be ascribed to the effect of vibrational
averaging. Even with the effects of vibrational averaging, the heavy atom bond lengths
and angles determined by the least squares fit fall within 3% of the values obtained by the
ab inito calculations.
The bond distances and angles determined by the least squares method changed
very little from those calculated by the ab initio methods. The largest change in the least
squares fit and ab initio structures occurs in the dihedral angles. According to the fit the
NCCN backbone is 8° less planar than that predicted for the ab initio structure. Costain’s
rule was used to estimate the vibrational contribution to the experimental uncertainties.44
The uncertainties are less than 0.01 A for the bond lengths and 3° for the bond angles.
The uncertainties in the torsional angles may be as large as 5° making the difference in
the ab initio versus least squares fit dihedral angles somewhat questionable.
The structural parameters of alaninamide determined by the least squares fit and
Kraitchman analysis were compared to corresponding parameters in formamide45 and
conformer II of glycine32; systems that contain similar functional group and similar
intramolecular hydrogen bonding schemes. The N1- C“ and C’- C° bonds are 1.459 and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
70
1.545 A in glycine and the C’- O and C’- N2 are 1.219A and 1.352 A in formamide. The
values obtained for alaninamide are consistent with these values.
The experimental is stabilized by an intramolecular hydrogen bond from the
amide to the amine. The 2.678 A N-N distance in the fit structure is similar to the O-N
separation in the analogous glycine46 and alanine47conformations calculated at the MP2
level of theory (2.614 and 2.591 A respectively). The distance between the proton and
nitrogen involved in the intramolecular hydrogen bond and the H...N-H angle were
calculated using the best fit structure of alaninamide; the relative proton positions rely on
ab initio values. The H....N distance of 2.235 A and N... H-N angle of 104.9° are
consistent with previously reported values for systems containing these types of
intramolecular hydrogen bonds.
Despite extensive searching no evidence of other conformations of alaninamide
were found. There are a number of factors that may contribute to this observation. The
dipole moments of other conformers may be small leading to low spectral intensity. A
higher energy conformation of glycine was detected initially; ab initio calculations
predicted a lower energy conformation that was found at a later date. It is also possible
that the cooling of the supersonic expansion removes population from higher energy
conformations. A third possibility is that the amide to amine hydrogen bond is so strong
that it eliminates other intramolecular hydrogen bonding arrangements.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V K'pK’0- r K/’K"
Av/kHz
TKVK'.-J"K,"K."
1,1 -1,1
2,1 -1,1
0,1 -1.1
v,*,
5337.598
5338.003
5337.512
5336.788
7.3
-5.2
-4.3
9.5
202-101'
1.1 -1.1
2, 1 -1.1
0,1 -1.1
7143.214
7143.348
7143.191
7142.947
-5.6
3.3
2.9
-6.2
2,1 -2,1
2,1 -1,1
3, 1-2,1
1.1 -0,1
1,1 -1,1
8653.290
8653.821
8653.668
8653.174
8653.044
8652.650
-4.1
-1.9
1.7
2.8
0.0
-2.6
2,1 -2,1
2,1 -1.1
3,1 -2,1
1, 1-0, 1
1,1 - 1, 1
9867.299
9867.856
9867.716
9867.174
9867.017
9866.631
3.7
-9.7
6.8
3.1
-2.8
2.6
3,1 -2,1
4,1 -3,1
15233.423
15233.533
15233.365
6.1
-4.3
4.3
F,T - F", 1"
101- 000'
1 1 1- 0 0 0 '
202-101'
212- 1 1 1'
303- 202*
F', r ••F", I"
v*
Av/kHz
2, 1-2, 1
1,1 -0,1
2,1 -1,1
3.1 -2,1
1.1 -1,1
10458.920
10459.510
10459.230
10459.019
10458.869
10457.992
-2.5
1.0
-3.1
1.9
11.7
-11.4
1,1 - 1, 1
2, 1- 1, 1
3.1 -2,1
1.1 -0, 1
11483.033
11483.698
11483.441
11482.968
11482.085
0.8
-6.0
-2.0
5.7
2.2
2,1 -2,1
2,1 -1,1
3, 1 -2, 1
1,1 -1,1
11672.925
11673.545
11673.062
11672.859
11671.964
0.7
-2.3
6.6
6.4
-10.7
3, 1-2, 1
2,1 -1,1
4,1 -3,1
14679.859
14679.987
14679.870
14679.784
-5.7
-0.3
6.3
-6.0
2 11 - 1 1O'
2 12-101'
3 13-212*
‘ The first entry is the unsplit center frequency calculated from fitting the ,4N quadrupole hyperfine transitions
Table 10: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of ISN-alaninamide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J’ K’p K '„- J" K,," K„"
f
, r - F", i"
10 I -000'
Av/kHz
i, i - i , i
2, 1 - 1, 1
0, 1 - 1, 1
-0.7
-0.4
1.1
1, l - M
2, 1 - 1, 1
0, 1 - 1, 1
7129.024
7129.182
7128.996
7128.706
0.2
0.3
3.2
-3.5
2,
2,
3,
1,
1- 2, 1
1 - 1, 1
1- 2, 1
1- 1, 1
8723.056
8723.503
8723.312
8722.966
8722.492
7.0
-4.7
-6.9
-1.6
13.3
2,
2,
3,
1,
1,
1- 2,
1 - 1,
1- 2,
1 -0 ,
1 - 1,
9901.872
9902.381
9902.202
9901.764
9901.700
9901.238
7756.409
7757.219
7756.640
7755.598
6.4
-1.6
8.3
-2.3
-7.2
2.9
5.2
8.4
1.7
-10.1
15274.924
15275.050
15274.909
15274.862
-14.7
12.8
-6.5
-4.3
202-1 I 1
2 I 2-11 I
1
1
1
1
1
22 1-2 1 2 '
1, 1- 1, 1
3,1 - 3 , 1
2, 1- 2, 1
^ 1 a |
3, 1 * 2, 1
i it
2, 1 - 1, I
A t1 • 3,
1 1I
4,
J' K'p K'0- J" K /' K„"
F', I' - F", I"
v*.
Y.l
5358.327
5358.648
5358.262
5357.684
1 1 1- 0 0 0 '
303-202*
VU___
2 0 2 - 1 0 1*
Av/kHz
0.2
2, 1 - 2, 1
1, 1- 0, 1
2, 1 - 1, 1
10493.748
10494.244
10493.966
10493.838
3, 1- 2, 1
1, 1- 1, 1
10493.692
10493.008
11.7
-5.7
-8.0
-0.2
-2.2
11531.396
-8.7
1, 1- 1, 1
11532.034
1.2
2, 1 - 1, 1
3, 1- 2, 1
1,1-0,1
11531.724
11531.339
11530.594
5.9
-6.2
-0.9
11672.558
-5.9
2, 1- 2, 1
11673.098
1 , 1- 0, 1
11672.716
3, 1- 2, 1
11672.483
11671.769
-3.6
-6.5
-2.3
12.4
14728.260
-14.7
3, 1- 2, 1
14728.364
12.8
2, 1 - 1, 1
4, 1- 3, 1
14728.278
-6.5
-4.3
2 11-110'
2 12-101'
1, 1- 1, 1
3 1 3 - 2 12*
14728.196
' The first entry is the unsplit center frequency calculated from fitting the UN quadrupole hyperfine transitions
Table 11: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of lsN2-alaninamide
■'j
to
J’ K’pK'0- r K/K."
Av/kHz
10 1-000
5285.732
2.2
1 1 1-000
7043.750
-0.2
221-212
7691.071
2.8
202-111
8593.715
3.0
2 12-111
9765.778
5.7
202-101
10351.730
-2.4
2 11-110
11377.106
-4.2
2 12-101
11523.789
-3.7
3 13-212
14525.848
6.5
303-202
15068.077
-6.1
Table 12: Frequencies (MHz) of the assigned transitions of l5N', ,5N2- alaninamide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J1K’pK'0- r K /’ K„"
f
, r - F", I"
1 0 1 - 0 0 O'
5341.363
5340.785
f
, r - F” , i ”
10463.506
-7.4
10463.987
-0.6
2, 1 - 1, 1
10463.606
3.5
3, 1- 2, 1
10463.450
-1.0
1, 1 - 1 , 1
10462.766
-1.9
11492.367
1.1
2.8
2.0
3.1
0.0
-3.1
8682.045
0.4
2,1 - 2, 1
2,1 - 1, 1
8682.503
8682.305
9.2
-0.9
1.1 - 0, 1
8681.938
1.1 - 1. 1
8681.466
-3.1
-5.2
9873.305
9873.812
2, 1 - 1, 1
2,1 - 2, 1
6.0
-2.0
2,1 - 1, 1
3,1 - 2, 1
9873.716
9873.205
-9.0
5.0
1, 1 - 1 , 1
1,1 - 1, 1
9872.677
6.0
3,1 - 2, 1
4,1 -3 , 1
15235.599
15235.708
15235.544
3.0
-2.6
2.6
202-101'
212-111*
303-202*
---------------------. . . .
___-. ...
- —
........... .......
_
....
2 11-110*
1, 1 - 1 , 1
2, 1 - 1, 1
3, 1- 2, 1
2, 1- 2, 1
11493.004
11492.695
11492.317
11492.114
0.7
-0.9
1, 1 - 0 , 1
11491.559
-9.7
11654.766
11654.697
11653.975
-1.7
-10.8
0.3
3.2
7.3
14687.275
-2.6
14687.381
14687.284
0.3
-1.0
14687.217
0.7
2 12-101*
2, 1- 2, 1
.
. . . .
11655.297
11654.923
3,1-2,1
313-212*
3, 1- 2, 1
2, 1 - 1, 1
4, 1
* - 3,
•'I •1
....
.
.
.. . . .
.................. _
.
Av/kHz
2, 1- 2, 1
7122.896
1.1 - 1, 1
2,1 - 1, 1
0,1 - 1, 1
v*.
2 0 2 - 1 0 1*
7123.056
7122.865
7122.580
1 1 1- 0 0 0 '
-------------------------
0.1
-2.6
1.5
1.1
5341.426
5341.744
i , i • 1, 1
2, 1 - 1, 1
0,1 - 1, 1
J’ K ^ K ’. - r K,," K„"
Av/kHz
Vot»
.
_ _ _
_____________
.__
_____
.
7.1
____ _____ _
_
‘ The first entry is the unsplit center frequency calculated from fitting the l4N quadrupole hyperfine transitions
Table 13: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of >SNZ,I>C' -alaninamide
75
j 'K v i c . - r K p " k ."
F , r - F”, r
v*
5340.289
10 1 - 0 0 0 *
Av/kHz
9.1
-4.9
7114.170
0.0
7114.329
7114.141
7113.849
-0.5
2.8
-2.3
14686.572
0.1
3, I - 2, 1
14686.672
OO
•
0.0
-42
5340.602
5340.234
5339.648
4, 1 -3 , 1
14686.520
5.8
15232.844
-0.1
3, 1- 2, 1
15232.952
-4.5
4, 1- 3, 1
15232.791
4.5
1,1 *1, 1
2,1 - 1, 1
0,1 - 1, 1
111-000*
1,1 - 1, 1
2, I - 1, 1
0,1 - 1, 1
313-212*
*The firstentiy is the unspiit center frequency calculated from fitting the ,4N quadrupole hyperfine transitions
Table 14: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions
of ISN\ l3C° -alaninamide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F, r - F", I"
10 1-000*
1. 1 - 1, 1
2, 1 - 1. 1
0,1 - 1, 1
1 1 1-000*
1.1 - 1, 1
2,1 - 1. 1
0,1 - 1, 1
v*
Av/kHz
3288.230
0.1
3288.332
-2.7
3288.193
5287.638
4.3
-1.6
7016.291
2.7
7016.489
7016.251
7015.895
1.3
-0.1
1.2
8624.860
1.1
8625.315
8625.073
•0.8
-6.2
8624.784
3.1
1. 1 - 1. 1
8624.251
3.9
2,1 - 2, 1
9768.902
9769.438
1.8
-5.1
2,1 - 1. 1
3,1 - 2, 1
1, 1 -0 , 1
1,1 - 1. 1
9769.200
9768.800
9768.800
9768.205
-6.5
2.5
6.3
2.8
3,1 - 2, 1
4,1 - 3, 1
15064.051
15064.177
15063.989
1.7
-0.6
0.6
202-101*
2,1 - 2, 1
2,1 - 1, 1
3,1 - 2, 1
2 12-111'
303-202*
J' K'p K'„ * J" K / K . "
P, I*. F", |»
v*
Av/kHz
2, 1- 2, 1
10352.894
10353.378
-3.2
6.7
2, 1 -1 , 1
10352.997
8.3
3, 1- 2, 1
10352.841
1, 1 - 1 , 1
10352.170
4.7
-3.1
11384.065
-0.2
1,1-1,1
2, 1 - 1, 1
3,1-2, 1
2,1-2, 1
11384.765
11384.373
11384.023
11383.766
3.5
2.6
-0.9
1, 1- 0, 1
11383.251
-6.3
11496.936
-1.7
2, 1- 2, 1
11497.495
-4.3
I, 1 - 0 , 1
11497.048
4.0
3,1-2, 1
11496.857
3.3
11496.126
-3.0
14528.539
-1.2
3, 1- 2 , 1
14528.645
0.4
2, 1 - 1, 1
14528.552
-2.1
4, 1 - 3 , 1
14528.481
1.7
202-101 *
211-110*
2 12-101*
1,1-1,1
3 1 3 - 2 12*
1.2
‘ The first entry is the unsplit center frequency calculated from fitting the l4N quadrupole hyperfine transitions
Table 15: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of l5N2,l3Cp-alaninamide
ON
3 J Valin amide
3.3.1 Ab initio
Geometry optimizations42 were performed at the UMP2 level of theory with a
6-31G** basis set. Six minima for valinamide were found on the potential energy
surface. The conformational minima belonged to one of two intramolecular hydrogen
schemes; amide-to-amine or bifurcated amine-to-carbonyl oxygen. The schemes are
illustrated in Figure 16. Within each scheme there are three possible orientations of the
isopropyl side chain. The orientations is described by t (Hb Cb Ca H*), the dihedral angle
between the protons on the alpha and beta carbons. The ab initio calculations determined
that t can take the values o f 300°, 180°, and 60°. These illustrations are best viewed as
Newman projections down the Cb - C* bond. Figure 17 illustrates the three
conformations within the amide-to-amine hydrogen bonding scheme. They are labeled as
AAI - AAHI. Figure 18 gives the analogous conformations in the bifurcated amine-tocarbonyl scheme labels as BAI - BAIR The calculations indicate that there are several
low energy conformations; four of which lie within 4 kJ mol*'. Within each
intramolecular hydrogen bonding scheme the orientation of the isopropyl side chain has a
significant effect on the stability of the conformers. The energy difference between the
conformers spans 3.7 kJ mol'1 in the amide to amine scheme and 5.7 kJ mol'1 in the
77
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
78
a)
b)
Figure 16: The two intramolecular hydrogen bonding schemes of valinamide
a) amide-to-amine
b) bifurcated amine-to-carbonyl
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
79
H,C
Hp
AAI
h 2n '
CH,
AE = 0 kJ/mol
H“
H,N2
CH
AE = 0.8 kJ/mol
AAII
H,Ni
AAIII
CH,
Hp
AE = 3.7 kJ/mol
I
H,N'
CH,
Ha
Figure 17: Newman projections of the isopropyl group orientation in the ab initio
conformations of valinamide in the amide-to-amine intramolecular
hydrogen bonding scheme. Relative energies were calculated at the
UMP2/6-31+G* * level of theory
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
°x
h 3c
’NH=
, X
hs
BAI
'
H2N’
AE = 3.4 kJ/mol
\
CH,
H°
2NH,
CH,
AE = 5.3 kJ/mol
BAII
H,N
CH,
H°
2nh,
H,C
CH,
baid
1
\
AE = 9.1 kJ/mol
H“
H2N
Hp
Figure 18: Newman projections of the isopropyl group orientation in the ab initio
conformations of valinamide in the bifurcated amine-carbonyl
intramolecular hydrogen bonding scheme. Relative energies were
calculated at the UMP2/6-31+G* * level of theory
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
bifurcated amine to carbonyl scheme. Because the intramolecular hydrogen bonding is
unchanged within a given scheme, this energy difference is attributed to the steric
demands of different orientations of the isopropyl side chain. In addition the preferred
orientation of the isopropyl group depends upon the intramolecular hydrogen bonding
scheme. For the amide to amine hydrogen bonding scheme the relative energy ordering
of the conformations is 60° <300° < 180° while in the bifurcated amine to carbonyl
oxygen the energy ordering is 60° < 180° < 300°.
3.3.2 Experimental
Twenty three transitions were measured for the most abundant isotopomer of
valinamide. Nuclear quadrupole hyperfine structure was assigned for eleven o f these
transitions; 4 a-types, 6 6-types, and 1 c-type. The frequencies of the unsplit rotational
transitions were obtained by fitting the hyperfine components to the quadrupole coupling
constants for the amino and amide nitrogens. The frequencies of the nuclear quadrupole
hyperfine components and the unsplit line centers are given in Table 16.
Two isotopically labeled species have also been investigated; single >SN labels at
the amide and amino nitrogens. Nuclear quadrupole hyperfine structure was assigned for
thirteen transitions of the ISN labeled amine, Table 18, and fifteen transitions of the >SN
labeled amide, Table 19. Spectroscopic constants obtained for all three isotopomers are
listed in Table 17.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J' K'pK'„ - J" K,," K„"
p, r - F", i"
Vob.
Av/kHz
3, 1 - 3 , 2
4, 1 - 4 , 2
4, 1- 3, 1
3,1-2, 1
2, 1 - 2 , 2
1,2-1,2
4,2-4,2
3,2-3,!
8090.387
8091.894
8091.093
8090.529
8090.149
8089.934
8089.469
8089.301
8089.152
4.5
-2.5
-0.9
3,2-3,!
4,2-4,2
4,2-3,2
5,2-4,2
3,2-2,2
4,1-3, 1
3, 1 - 3 , 2
7832.881
7834.092
7833.961
7833.104
7832.898
7832.801
7832.594
7831.490
2.7
5.4
1.1
-1.0
-3.8
1.2
-5.5
2, 1 - 1 , 2
3,0-2, 1
4,2-3, 1
5,2-4,2
3 ,0 - 2,0
4,2-4, 2
3, 1 - 2 , 2
4, 1 - 3 , 2
2,2-1,1
8263.131
8264.122
8264.003
8263.639
8263.280
8263.198
8263.077
8262.493
8262.274
8262.126
303-202*
3 1 3 - 2 12*
32 1-220*
-1.9
-1.0
-3.9
-0.8
2.6
K'p K'0- J" K /'K ."
P, | ' . F", I"
3 13-202*
0.8
-0.8
-8.2
-1.0
2.5
Av/kHz
9180.490
1, 2 - 1 , 1
4,2-4,2
4,2 - 3, 1
3, 1 - 2 , 2
2, 1 - 1 , 2
4, 1 - 3 , 2
2,2-1,1
9181.509
9181.392
9180.829
9180.630
5 , 2 - 4, 2
9180.630
9180.502
9180.393
9180.342
3,2-2,!
3, 1 - 2 , 0
3,0-2,!
4, 1 - 4 , 2
3, 1- 3, 1
3, 1- 2, 1
4, 1- 3, 1
9180.241
9179.866
9179.651
9179.475
9179.225
9179.080
9178.920
4 13-3 12*
12.4
-4.6
-1.8
0.6
v*
-2.3
-8.2
•8.1
-12.3
-6.2
14.3
19.9
-1.6
-0.8
-7.0
-7.4
-0.5
-4.7
1.7
7.6
11295.124
3,2-3,2
4,0-4,2
5,1-4,!
11296.181
11296.130
11295.228
-9.3
3.2
-5.9
5,2-4,!
4,2-4, 1
5,2-5,2
3,1-3, 1
11294.467
11294.373
11294.284
11294.241
-2.9
3.8
11.3
-0.2
The first entry is the unsplit center frequency calculated from fitting the l4N quadrupole hyperfine transitions
Table 16: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of valinamide
00
N>
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 16 continued
J’K’pK'0- r K,”K0"
F , I’ - F , I"
404-313*
4, 1- 4, 1
4,0-3, 1
4, 1 - 3 , 0
2,2-1,2
6,2-5,2
4 ,0 - 3 ,0
5, 1 - 4 , 2
4,1-3,2
5,2-4,!
4,0-3,2
3, 1- 3, 1
5,2-5,2
4,2-4,2
Av/kHz
13810.320
13808.944
13809.006
13809.123
13809.381
13810.116
13810.198
13811.802
5,1 - 5,1
4, 1- 4, 1
6 ,2 - 6,2
3,2-3,1
5,2-5,2
12425.722
12427.159
12424.895
12424.654
12424.381
12424.202
TKVK'.-rK^K."
F, r - F", I"
4 14-303*
9604.724
9606.109
9605.328
9605.191
9604.949
9604.830
9604.743
9604.663
9604.623
9604.580
9604.151
9604.055
9603.712
9603.250
5, 1- 5, 1
3 ,2 - 3,2
6,1-6,2
4,2-4,2
3,2-2,2
4,2-3,1
5,2-5,2
5 15 -4 0 4 *
5 0 5 - 4 14*
v*.
0.8
0.6
-4.1
-4.0
-0.3
11.4
-
1.8
11.4
-6.7
2.8
221-110*
0.1
-
6.6
-3.8
6.9
-4.9
3.5
-7.8
-0.5
2.9
-
-
0.1
10.8
-
0.1
6.7
-
1.0
5.2
220-110*
V*.
Av/kHz
4, 1- 4, 1
2,2 - 2,2
5, 1 - 5 , 2
3,2-3,2
4, 1 - 3 , 0
2,2-1,2
3,2-2, 1
5,1-4,2
3, 1 - 2 , 2
5,2-4, 1
4,2-4,2
11511.317
11510.019
11510.073
11510.171
11510.538
11510.799
11511.018
11511.182
11511.241
11511.545
11511.646
11512.799
10.8
-2.4
-2.7
-7.7
-3.1
0.5
2.1
-4.7
1.5
1.6
4.1
2,2 - 2,2
1, 1- 0, 1
3,2-3,2
3,2-2,!
3, 1 - 2 , 2
4,2-3,2
3,1-3,2
2,2-1,2
2, 1- 2, 1
2,0-1,2
1, 2- 2, 1
10310.261
10311.697
10311.572
10311.113
10310.641
10310.363
10310.102
10309.612
10309.491
10308.909
10308.718
10308.663
2.5
1.4
1.5
2.6
7.1
3.5
0.6
-1.7
-14.3
-7.6
4.5
2,2 - 2,2
2, 1 - 1, 1
4,2-3,2
2, 1- 2, 1
1, 2- 2, 1
0 , 2 - 1,2
10332.198
10333.641
10332.608
10332.063
10330.852
10330.540
10330.341
-6.3
6.0
9.8
2.0
-6.1
-5.4
*The first entry is the unsplit center frequency calculated from fitting the '*N quadrupole hyperfine transitions
Table 16: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of alaninamide
00
u>
84
valinamide
ISN‘- valinamide
A (MHz)
3018.09(5)
2963.661(2)
3012.18(2)
B (MHz)
1472.97(3)
1472.9360(8)
1451.024(6)
C (MHz)
1252.48(3)
1242.921(1)
1236.070(8)
Aj (kHz)
0.14(2)
0.15(2)
AJ1C(kHz)
0.4(2)
0.3(2)
i5N2-
valinamide
XJCN')
1.626
1.631
X JN ')
1.170
1.169
XJN2)
-3.284
-3.318
Xbb(N2)
1.407
1.442
23
15
N*
13
*Number of transitions measured
Table 17: Spectroscopic constants of the isotopomers of valinamide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J'K'pK'.,- J" K,," K„"
F , I ' - F", I"
303-202'
3,1 -3 , 1
3, 1 -2 , 1
2,1 - 1, 1
4,1 - 3, 1
2,1 -2 , 1
3 1 3 - 2 12*
3,1
2,1
4,1
2,1
- 2, 1
- 1, 1
- 3, 1
- 2, 1
V*.
Av/kHz
8050.905
8051.613
8051.005
8050.923
8050.849
8049.971
-1.7
3.4
-0.9
-1.7
0.8
7787.892
7788.010
7787.944
7787.819
7786.528
-4.0
9.6
1.0
-6.5
2,1 - 2, 1
3,1 - 2, 1
4,1 - 3, 1
8244.201
8244.808
8244.512
8244.121
9073.212
-0.1
-2.1
2.2
3,1 - 3, 1
3,1 - 2, 1
4,1 - 3, 1
2, 1 -2 , 1
9074.172
9073.559
9073.074
9072.075
1.6
1.7
-0.5
-2.8
4,1 - 3, 1
5,1 - 4, 1
11268.884
11268.962
11268.861
-0.6
0.6
32 1 - 2 2 0 *
3 13-202*
4 1 3 - 3 12*
220-110*
r K'r K'„ - J" W
4 0 4 - 3 13*
1, 1 -0 , 1
10158.723
10158.508
10157.896
10157.598
-11.5
0.3
1.5
9.6
F, I' - F", I"
3,1 - 2, 1
5,1 -4 , 1
4,1 - 3, 1
5 15-404*
Vot,
9610.204
9610.375
9610.227
9610.066
Av/kHz
3.6
-1.4
-2.2
4,1 - 3, 1
6,1 - 5, 1
5,1 - 4, 1
13660.884
13662.069
13661.138
13660.776
13659.572
12405.488
12405.590
12405.504
12405.398
- 4, 1
- 3, 1
- 4, 1
- 3, 1
11381.022
11382.102
11381.346
11380.888
11379.808
-0.8
7.2
-1.2
-5.1
13431.031
13431.862
13431.288
13430.164
0.6
2.8
-3.4
5,1
5,1
6,1
4,1
- 5, 1
- 4, 1
- 5, 1
- 4, 1
505-414*
4 14-303*
4,1
4,1
5,1
3,1
32 1 -2 12*
2,1 - 1, 1
4, 1 -3 , 1
3,1 - 2, 1
221-110*
1,1
2,1
3,1
2,1
10158.511
2,1 - 1, 1
3,1 - 2, 1
2,1 - 2, 1
'
- 1, 1
- 1, 1
- 2, 1
- 2, 1
3 12-202*
2,1 - 1, 1
4,1 - 3, 1
3. 1 -2 , 1
10133.889
10134.993
10134.177
10133.870
10133.342
10451.648
10452.262
10451.840
10451.001
-5.7
-1.0
4.7
1.9
-1.1
-0.3
1.4
-5.3
-2.0
4.3
3.0
4.9
0,5
-5.4
*The first entry is the unsplit center frequency calculated from fitting the '*N quadrupole hyperfine transitions
Table 18: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of l5N' -valinamide
v*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
j - ic/ k ."
P, I’ - F", I"
303-202'
Av/kH
7979.703
2, 1- 2, 1
4, 1- 3, 1
3, 1- 2, 1
2, 1 - 1, 1
7981.204
7979.739
7979.700
7979.540
2.6
-4.2
0.1
1.4
2,1-2, I
4, 1- 3, 1
3, 1- 2, 1
3, 1- 3, 1
7726.466
7727.477
7726.559
7726.258
7725.653
0.5
1.4
0.0
-2.0
2, 1- 1, 1
4, 1- 3, 1
3, I - 2, 1
8142.825
8143.652
8143.063
8141.998
-l.l
1.6
-0.6
9093.371
9093.524
9093.356
9093.087
9094.746
9092.453
-1.4
-3.1
5.9
2.1
-3.5
3 13-2 12'
32 1 - 2 2 0 *
3 13 - 2 0 2 *
V*.
3, 1- 2, 1
4, 1- 3, 1
2,1-1,1
2, 1- 2, 1
3, 1 - 3, 1
4 1 3 - 3 12*
K /’ K."
P.P-FM"
Av/kHz
9438.260
404-313*
3,1 - 3, 1
5,1 - 4, 1
4,1 - 3, 1
4, 1-4 , 1
9439.540
9438.342
9438.092
9437.197
4.2
2.7
-7.2
0.4
13661.857
5 15-404*
4,1
5,1
4,1
5,1
- 4, 1
- 4, 1
- 3, 1
- 5, 1
13663.223
13661.898
13661.789
13660.754
-7.2
6.6
-4.7
5.3
- 4, 1
- 5, 1
- 3, 1
- 4, 1
- 5, 1
12226.680
12228.006
12226.740
12226.688
12226.590
12225.565
2.9
12.1
-10.9
-8.2
4.1
505-414*
4,1
6,1
4,1
5,1
5,1
11394.188
4 14-303*
11132.863
v*.
3, 1- 3, 1
11133.898
0.6
11132.909
-1.6
3,1 - 3, 1
5,1 - 4, 1
11395.567
5, 1 - 4, 1
11394.184
1.0
1.8
-2.2
4, I - 3, 1
11132.773
•6.0
3,1 - 2, 1
11394.063
-0.7
4, 1- 4, 1
11132.028
7.0
4,1 -3 , 1
11394.262
*The first entry is the unsplit center frequency calculated from fitting the '*N quadrupole hyperfine transitions
Table 19: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of l5N‘ -valinamide
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 19 continued
J' K',, K'„ - 1" K,," K„"
F,l'-F",l"
220- 110*
V*.
Av/kHz
10293.308
2 , 1 - 2,1
2, 1 - 1, 1
1,1-0,1
3, I - 2, 1
1, 1 - 1 , 1
221- 110*
tf MSI If* - f* MS *1M
S II
J
u
F, 1* - F", I"
3.8
10294.667
10383.139
10382.102
10293.417
10293.163
10292.006
2.4
4, 1 - 3, 1
10381.805
4.7
10381.466
-5.8
10381.048
5.8
-1.2
-1.6
2, 1 - 1, 1
3, 1- 3, 1
13491.862
3 2 1 -2 12*
2, 1- 2, 1
10273.527
-5.8
2, I - I, I
10272.976
5.9
I, 1-0, 1
10272.718
0.1
3, 1- 2, 1
10272.469
1, 1 - 1, 1
10271.308
2.7
-2.9
3,1-2, 1
4, 1- 3 , 1
2, 1 -1 , 1
4 1 4 - 3 13*
7365.250
2, I - 1, 1
4.5
-9.2
-3.4
2, 1- 2, 1
3, 1- 2, 1
10272.609
2 1 1 - 1 0 1*
Av/kHz
10381.848
3 12-202*
10294.237
v*.
3, 1- 2, 1
7365.713
7365.191
-6.4
3.4
2 , 1 - 2, 1
7364.727
3.0
13492.335
13491.730
13491.386
-0.5
3.7
-3.2
10280.521
3, 1- 3, 1
10281.738
5, 1- 4, 1
10280.570
-3.1
-1.8
3, 1 - 2, 1
10280.527
4.4
4, 1 - 3, 1
4, 1- 4, 1
10280.441
10279.531
4.0
-3.4
*The first entry is the unsplit center frequency calculated from fitting the >4N quadrupole hyperfine transitions
Table 19: Frequencies (MHz) of the assigned nuclear quadrupole hyperfine transitions of l5N' -valinamide
00
"J
3.3.2 Structure and Discussion
An comparison o f the experimental moments of inertia with those obtained from
the ab initio models indicates that three of the model structures reproduce the
experimental structure equally well. These are AAI, BAI, and BAll with DI^, values of
14.50 kJ mol'1, 17.92 kJ mol'1, and 16.03 kJ mol'1respectively. These conformations all
lie within approximately 5 kJ mol'1o f the global minimum. The lowest energy of these
three conformations, AAI, belongs to the amide-to-amine intramolecular hydrogen
bonding scheme and has the isopropyl group oriented such that the dihedral angle
between the alpha and beta protons is 59.98°. The two higher energy conformations, BAI
and BAH, have bifurcated amine-to-carbonyl intramolecular hydrogen bonds and have
the isopropyl group oriented with dihedral angles o f66.87° and 176.76° respectively.
Kraitchman’s equations of single isotopic substitution were used to calculate the
coordinates of the amide and amino nitrogens of valinamide. The value o f these
coordinates are listed in Table 20 along with the values for the three ab initio structures.
A comparison of the coordinates from the Kraitchman analysis and the ab initio structures
indicates that there is better agreement with AAI, the lowest energy amide-to-amine
conformation. Although the a-coordinate of both the amide and amino nitrogens for all
three ab initio conformers agree with those calculated with the Kraitchman method, there
are significant deviations of the b- and c- coordinates of the higher energy structures.
88
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Kraitchman
Least-squares fit
AAI
BAI
BAII
-0.2242
N' (amine)
a
t
0.1333
-0.075
-0.21242
-0.3664
b
t
1.7643
1.775
1.7298
1.5564
1.9155
c
t
(0)
-0.215
-0.2225
-0.7913
-0.2648
a
t
2.2680
-2.271
2.0217
1.9067
1.9391
b
t
0.5069
0.458
0.6000
-1.3126
-0.8700
c
t
0.2884
-0.295
0.6258
-0.3637
-0.8427
N2(amide)
0: Atomic coordinates ( A ) of the nitrogens in valinamide determined by the Kraitchman analysis,
least-squares fit, and ab initio calculations
<5
90
The lowest energy amide-to-amine conformer was used as a starting
structure for a least-squares fit. Four parameters that described the orientation o f the
backbone of valinamide were fit. The parameters are listed in Table 21 along with their
values from the ab initio starting structure. The coordinates from the least-squares fit are
listed in Table 20. A comparison of the coordinates from the least-squares fit and
Kraitchman analysis indicates that they are in general agreement. The differences in these
coordinates is attributed to the isopropyl side chain. At the present time no isotopic data
is available for this portion of the molecule. The orientation of the isopropyl side chain is
expected to have a large effect on the orientation of the principal axes and as a result the
values of the least-squares fit coordinates. The general agreement of the least-squares fit
and Kraitchman structures indicates that the intramolecular hydrogen bonding scheme has
been correctly identified as amide-to-amine. Also it would appear from the data that the
isopropyl side chain is generally oriented in the lowest energy ab initio configuration for
this amide-to-amine intramolecular hydrogen bonding scheme, 60°. What remains
unclear is its exact orientation. It is expected that further isotopic substitution of the
atoms o f this group will allow for the precise determination of the orientation of the
isopropyl group.
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91
N' C“ C'
N'
c°
c
C*
c°
N'
cp c°
N'
N2
H2
Fit
ab initio AAI
110.9(6)
114.5
-8.90(6)
9.3
-154.41(3)
-165.0
120.5(2)
111.3
Table 21: Parameters used in the least-squares fit and their values
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CHAPTER 4
Alaninamide - H20
4.1.1 Introduction
The examination of the 1:1 van der Waals complex of alaninamide-H20 has a
number o f interesting aspects. The simple amino acids, like the larger biomolecules they
comprise, have a variety of sites which can participate in hydrogen bonds; the protons of
the amide and amine groups can act as hydrogen bond donors while the nitrogen and
oxygen atoms can act as hydrogen bond acceptors. The examination o f the structure of
the 1:1 van der Waals complex of the amino amides with water will determine the
preferential site for water complexation. This site may represent the first site occupied
during the process of solvation. A further feature of the amino amides is that they possess
conformational flexibility; ab initio calculations indicate that they can exist in a number
o f low energy conformations. The structural study of the alaninamide monomer51 found
only one of these conformations with substantial spectral intensity, one with an amide to
amine intramolecular hydrogen bond. It is unclear if upon complexation the preferred
conformation of the alaninamide monomer will be retained. Furthermore, this study will
examine the effect of the intermolecular hydrogen bonds from HzO on the intramolecular
hydrogen bonding known to exist in the alaninamide monomer.
92
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4.1.2 Ab initio
Geometry optimizations42 of the 1:1 van der Waals complex of alaninamide-H20
at the UMP2/6-31G** level of theory were performed using the two lowest energy ab
initio conformations o f the alaninamide monomer. Within each monomer two different
intermolecular hydrogen bonding arrangements were considered: a “terminally bound”
structure and a “bridging” structure. The optimized structures of these complexes are
illustrated in Figure 19. In the terminally bound structure the water molecule binds to
alaninamide without disrupting the preexisting intramolecular hydrogen bonding network.
The water molecule essentially hangs off the amide linkage; donating a proton to the
carbonyl oxygen and accepting the proton of the amide not involved in the intramolecular
hydrogen bond. In the bridging structures the water molecule inserts itself into and
disrupts the intramolecular hydrogen bonding network; interrupting the amine-tocarbonyl hydrogen bond in one and the amide-to-amine hydrogen bond of the other. The
terminally bound arrangement of both alaninamide monomer conformations represent the
two lowest energy structures. The lowest energy complex involves the experimentally
determined monomer conformation with a terminally bound water molecule; the
terminally bound complex of the other monomer conformation lies 7.3 kJ mol'1higher in
energy. The bridging structures o f both monomers lie 15 kJ mol'1higher in energy.
93
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94
\
T1
B1
V
T2
B2
Figure 19: Ab initio conformations of the alaninamide-H^O van der Waals complex
The subscripts 1 and 2 indicte the intramolecular hydrogen bonding scheme;
1: amide-to-amine; 2: bifurcated amine-to-carbonyl The T and B stand
for terminally bound and bridging structures respectively
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4.1.3 Experimental
Nine a-type transitions were measured for the most abundant isotopomer o f the
alaninamide-water van der Waals complex. Despite extensive searching no b- or c-type
transitions were found. Unlike in the alaninamide monomer,51 the nuclear quadrupole
hyperfine structure was unresolvable possibly due to the higher J transitions measured for
the complex or a rotation o f the principal axes upon complexation. The unsplit line
centers of the rotational transitions were estimated to be at the center of the resulting
cluster of lines and are given in Table 22. The estimated uncertainties of the reported
frequencies are approximately 100 kHz.
Rotational transitions have been measured for three 1SN isotopomers: the two
singly substituted species as well as the double ISN species. Although the substitution o f
an ISN nuclei into the molecule reduces the amount of hyperfine components it was still
not possible to assign the hyperfine structure for the single ISN isotopomers. The
estimated frequencies of the unsplit line centers o f the transitions due to the l5N
isotopomers are given at the end of the chapter in Tables 26-28. Rotational constants
were obtained by fitting the transitions to a rigid rotor Hamiltonian. Due to the
uncertainties in the unsplit line centers, the uncertainties in the fit are on the order o f 30
kHz for the normal and single 15N isotopomers. Centrifugal distortion constants were not
95
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96
transition
obs. freq(MHz)
obs - calc. (MHz)
3 -2AI2
-,IJ
6905.783
0.019
3 3-2*02
J0
7128.373
0.017
3,2 ■2„
7387.103
0.014
-3„
9201.700
0.019
4<m" 3 (j)
9479.711
-0.026
4,3- 3 I2
9842.967
0.042
5„-4h
11492.746
-0.032
5oS " 404
11810.766
0.021
5u - 4 , 3
12292.775
-0.047
Table 22: Approximate center frequencies of the rotational transitions of
the normal isotopomer of alaninamide-H20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
97
determined for these species because their values would be much less than the
experimental uncertainties. The transition frequencies o f the double l5N isotopomer are
well determined due to the lack of nuclear quadrupole hyperfine structure which allowed
for the determination o f A, B, C and Dj. Spectroscopic constants for all four isotopomers
are given in Table 23.
4.1.4 Structure
For the least squares fitting procedure of the structure, the geometry of the
alaninamide and water monomers were assumed to be unchanged. This is usually a valid
assumption; there are few cases of a change in conformation upon gas phase dimer
formation. With this assumption there remain six parameters that fully describe the
relative orientation of two monomer units. These include their center of mass separation,
Rcm , as well as various tilt angles denoted by 6 and %which describe the angular
orientation of the monomer units. These parameters are shown in Figure 20. The center
of mass separation and the alaninamide tilt angle 0, were fit to the 12 moments of inertia.
The remaining parameters ( 02,
%2
and 4*) were found to be insensitive to the
moments of inertia of the l5N isotopomers and were fixed at their ab initio values.
The initial fits used the geometry of the ab initio structure. In this structure the
water proton and oxygen atoms involved in the intermolecular hydrogen bonding network
lie in the plane defined by the amide group of alaninamide. The free water proton lies
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
,5N'-
,5Nj-
liNl , i5N2-
alaninamide - H20
alaninamide - H20
A (MHz)
4789.5(16)
4736.5(19)
4729.4(15)
4680.3(2)
B (MHz)
1271.870(4)
1258.028(5)
1270.643(4)
1256.791(1)
C (MHz)
1111.391(4)
1098.049(5)
1107.937(4)
1094.693(1)
alaninamide - HzO
Dj (kHz)
N*
Av™, (kHz)
alaninamide - H20
0.22(2)
9
28.5
9
9
34.5
26.3
9
5.2
*Number of transitions in the fit
Table 23: Spectroscopic constants of Alaninamide - H20
SO
00
Figure 20: Fitting parameteres of the alaninamide-HjO van der Waals complex
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
Initial
LSF
Planar
LSF
ab intio
R ( A)
3.968(2)
3.972(1)
3.936
e,(°)
33(2)°
40.2°
40.2°
AI^ ( amu A2)
0.628
0.094
H2..... Ow( A)
2.395(70)
2.042(6)
2.061
Hb..... 0 ( A )
1.750(37)
1.931(4)
1.914
Table 24: Values o f the fitting parameters and intermolecular hydrogen bonding
distances for the least squares fit and ab initio structures
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101
approximately 80° out of this plane trans to the methyl group attached to the alpha carbon.
The fit using this starting structure is labeled as "Initial LSF" in Table 24. Although the
fit changed the center of mass separation only slightly, from 3.936 A to 3.968(2) A,
6, changed substantially from the ab initio value of 40.2° to 33(2)° moving the water
molecule closer to the carbonyl group. This can be seen in the calculated hydrogen bond
distances shown in Table 24. The water oxygen-to-amide proton distance, Ow- H2, has
increased by 0.334 A while the carbonyl oxygen-to-water proton distance, O - Hb, has
decreased by 0,164 A with respect to the ab initio values.
A second fit was performed using a structure in which the free water proton was
constrained to lie in the plane containing the amide linkage and the rest o f the water
molecule. This fit is labeled as "Planar LSF” in Table 24. This fit converged nicely
without such drastic changes in the position of the water. The calculated hydrogen bond
distances for this fit are in better agreement with those predicted by the ab initio
structure.
Principal axis coordinates were determined for the nitrogen atoms in the
alaninamide-water complex using Kraitchman's equations for single isotopic substitution.
The value of these coordinates along with those determined by the two least-squares-fit
attempts and the ab initio calculations are shown in Table 25. A comparison of the
coordinates from the Kraitchman analysis and the two least-squares-fit attempts show that
they are in somewhat poor agreement. In particular the largest deviations occur for the
initial least squares fit structure based on the ab initio orientation of the free proton. This
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102
Kraitchman
LSF
Planar
LSF
ab initio
N*
a
t
2.096(7)
2.162(1)
2.038(1)
2.069
b
i
1.095(13)
-1.013(1)
-1.151(1)
-1.121
c
t
0.12(12)
0.221(8)
0.243(6)
0.194
a
t
0.481(26)
-0.410(4)
-0.545(3)
-0.538
b
i
1.095(11)
-1.180(1)
-1.039(1)
-1.074
c
i
0.399(33)
-0.437(3)
-0.385(4)
-0.334
N2
Table 25: Atomic coordinates (A) of the nitrogen atoms from the Kraitchman
analysis, least squares fitting, planar least squares fitting and the
initial ab initio structure
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103
structure may be unreliable because it attempts to compensate for vibrational averaging
by moving the water closer to the carbonyl oxygen by reducing the tilt angle 0,.
A comparison of the nitrogen coordinates in Table 25 indicates that the "planar"
least-squares-fit agrees better with the Kraitchman and ab initio methods than the "initial"
least-squares-fit. The somewhat large differences between the coordinates calculated by
the Kraitchman and "planar" least-squares-fit methods is attributed to vibrational
averaging. As indicated in Chapter 1 Section 5, the Kraitchman substitution coordinates
are less affected by vibrational averaging because they are calculated as differences in
moments of inertia.
4.1.5
Discussion
The hydrogen bonding distances in alaninamide-H20 were compared with those
obtained for the microwave structure of the formamide-H20 complex.32 Although the
formamide monomer contains no intramolecular hydrogen bonds, the formamide-H20
complex forms a intennolecular hydrogen bonding arrangement similar to the
alaninamide-H2Q complex. The intennolecular hydrogen bond distances determined for
the alaninamide-H20 complex agree well with those determined for formamide-H20. In
alaninamide-H20 the amide proton-to-water-oxygen distance was determined to be
1.931(4) A while the carbonyl oxygen-to-water proton distance is 2.042(6) A. The
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104
corresponding parameters in fbnnamide-H20 are 2.006(3) A and 2.020(2) A.
In many cases the water subunit involved in complexes has been shown to
undergo large amplitude motions. Examples of this includes the dimethylamine-HjO33
complex in the which the free proton undergoes a wagging motion and the complete
internal rotation in and trimethylamine-HjS54 and trimethylamine-H20 55 A complete
internal rotation produces a doubling of the rotational transitions due to the ortho and para
spin states of the protons which must combine with the tunneling and rotational
wavefunctions to produce and overall antisymmetric wavefunction.56
For the alaninamide-HzO complex both these types o f motions are possible.
Although no evidence of the complete internal rotation was found in the rotational
spectrum it is expected that the free proton is undergoing a wagging motion. Single point
energies were calculated for both the wagging motion and the internal rotation at the
UMP2-6-31G** level of theory. Plots of these calculations are shown in Figures 21 and
22. The potential energy surface of the flapping motion was calculated by fixing the
structure of the alaninamide monomer and the orientation o f the Ow- H1 bond at the
minimum energy configuration while the out of plane angle of the free water proton was
varied. The resulting potential energy surface of the flapping motion indicates that there
is a low barrier about the planar configuration and that the potential surface for this
motion is rather flat. There are two minima on the surface; the global minimum occurs
when the free proton lies -80° out o f the plane on the opposite side o f the methyl group,
the higher energy well lies 90 cm'1 above the global minimum and has the free proton
oriented 50° out of the plane on the same side of the methyl group. A shallow barrier of
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105
240 cm'1 separates these minima.
The barrier hindering the internal rotation o f the water molecule was calculated to
be 4500 cm 1. This large barrier is sufficient to prevent the internal rotation of the water
molecule and as a result the tunneling doublets characteristic of this motion were not
found in the microwave spectrum.
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106
1500
E
V
1000
0J
c
UJ
CJ
>
]5
500
0)
cc
-120
-60
0
60
O ut-cf-Plane Angle / d e g re e s
Figure 21: Potential energy surface of the flapping motion of the free water proton
of the alaninamide-H;0 complex calculated at the UMP2/6-3IG** level
of theory
r
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107
6000
E
>
o
5c
UJ
~
_C3
4000
2000
CJ
c
0
0
60
120
180
240
300
360
Internal Rotation Angle / d eg rees
Figure 22: Potential energy surface o f the internal rotation of the water molecule
about its C; axis in the alaninamide-H.O complex calculated at the
UMP2/6-31G** level of theory
r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
obs. freq (MHz)
obs - calc. (MHz)
3J !3 -2^12
6825.000
0.054
3J03-2*02
7046.700
-0.003
J3 12-2^11
7304.722
-0.048
4 14-3J I3
9093.895
-0.002
^04 " ^03
9370.785
0.031
4,3 “ 3|2
9733.184
0.051
5,5 " 4,«
11357.971
-0.039
s
1
transition
11674.345
-0.008
5,4-4,3
12155.507
-0.019
Table 26: Approximate center frequencies of the rotational transitions of
ISN‘- alaninamide-H20
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109
transition
obs. freq(MHz)
obs - calc. (MHz)
3 3-2^12
J1
6888.250
0.009
3 3-2^02
J0
7113.410
0.029
3,2 ” 2||
7376.250
0.012
4,-3,3
9178.058
-0.004
4(14 - 3Q3
9458.730
0.026
4,3 - 3,2
9828.200
0.037
5,5-4,4
11462.849
-0.018
5oS * 404
11782.820
-0.007
5,4 - 4,3
12273.820
-0.052
Table 27: Approximate center frequencies of the rotational transitions of
ISN2- alaninamide-HjO
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110
obs - calc. (MHz)
J3 I3 -2*12
6807.830
0.002
3 3-2*02
J0
7031.995
0.007
3|2 ■2„
7294.000
0.001
4«-3B
9070.798
-0.001
S
obs. freq(MHz)
1
transition
9350.068
-0.002
4,3 -3 b
9718.448
-0.011
5„-4w
11328.720
-0.002
^05 “ 4(|4
11646.873
-0.001
~4,3
12136.663
0.007
^14
Table 28: Approximate center frequencies o f the rotational transitions of
ISN‘, ,5N2- alaninamide-H20
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CHAPTER 5
5.1 3-Hydroxytetrahydrofuran
5.1.2 Introduction
Ring systems offer attractive systems for structural analysis because of their
conformational flexibility. The flexibility arises because o f ring strain; the ring strain
being due to eclipsing methylene groups in the planar form. In order to alleviate this ring
strain, five membered rings will adopt a conformation that contains a pucker. The
location and magnitude o f the pucker is heavily influenced by the nature o f the ring atoms
as well as any substituents attached to them.8
3-hydroxytetrahydrofuran has been chosen for study due to its use as a simple
theoretical model for the furanose ring within nucleotides. Figure 23 shows the furanose
ring within a nucleotide and in 3-hydroxytetrahydrofuran. The nucleotides are important
because they are the constituents of the right-handed double helices of DNA and RNA.S7
These helices are grouped into two major categories, the A-family and the B-family.
These categories are described in terms of the number of nucleotide units per turn of the
helix. In the A-family, the helix is more loosely wound having 11 or 12 nucleotide units
for each complete turn o f the helix.58 The B-family of helices are more tightly wound;
111
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112
O — CH
B ase
4’
H
H
1’
4’
o
H
OH
H
— P
(A)
(B)
Figure 23: Furanose ring (A) within a nucleotide and (B) in 3-hydroxytetrahydrofuran
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
113
there are 8 to 10 nucleotide units per turn.*8
The A- and B- family of helices have furanose rings with different ring puckering
conformations. The A-family associates with a C3endo conformation ( as well as closely
related twist structures). This conformation positions the phosphorous linkages attached
to adjacent ring carbons relatively close; the phosphorous-phosphorous separation is 5.9
A, and as a result each turn can accommodate more nucleotide units. The B-family.
associates with a C2 endo structure. This conformation has a larger phosphorous
separation, 7.0 A, and is more tightly wound because there are fewer nucleotide units per
turn.
The unsubstituted tetrahydrofuran ring has been investigated by numerous
techniques. The crystal structure has been determined by x-ray crystallography39and
neutron diffraction experiments.60 It has been show to exist as a twist conformation with
the C2 and C3 carbon atoms on opposite sides of the plane defined by C„ C4, and O.
Gas phase electron diffraction experiments61,62 were unable to determine a unique
ring conformation. This result was interpreted as being due to a low barrier to
pseudorotation. Later microwave experiments63 confirmed this hypothesis. Nine separate
rotational spectra were measured at dry ice temperatures arising from different
vibrational- pseudorotational states. The spectra displayed large vibration-rotation
interactions. It was found that the two lowest energy pseudorotational states are separated
by 0.65 cm'1and that all eight excited states fall within 200 cm*1o f the ground state. The
barrier around the pseudorotation pathway is low with the largest barrier being 57 c m 1.64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
114
A detailed structural analysis o f 3-hydroxytetrahydrofuran will provide much
useful information. It has been assumed to be a simple theoretical model for the furanose
ring in nucleotides.65-67 The determination of the ring puckering conformation of 3hydroxytetrahydrofuran will provide experimental justification of this assumption.
Furthermore it will be interesting to see what effect the added hydroxyl group will have
on the barrier to pseudorotation.
5.1.2 Ab initio
Previous theoretical work6869on 3-hydroxytetrahydrofuran has found
conformations differing by as much as 14 kJ mol'1 in energy. These include a C2endo
conformation as well as a twist structure with C2exo and C3endo. Recent ab intio
calculations69 have shown that the lowest energy conformation has a C4endo pucker. In
this conformation, the hydroxyl proton is oriented towards the ring oxygen and is
proposed to form a weak intramolecular hydrogen bond.
We performed additional ab initio calculations on 3-hydroxytetrahydrofuran.
Geometry optimizations were performed at the MP2/6-31G** level starting at both a
planar structure as well as various ring puckering conformations. The ab initio structures
are shown in Figure 24. The lowest energy structure has a C4endo pucker. This
orientation positions the proton of the alcohol 2.351 A away from the ring oxygen. This
distance is typical of intramolecular hydrogen bonds and it is therefore proposed that this
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115
AE = 0 kJ mol'1
a) C4-endo
AE = 0.8 kJ mol'1
b) Cj-endo
Figure 24: Ab initio conformers of 3-hydroxytetrahydrofuran calculated at the
UMP2/6-31G** level o f theory
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
116
conformation is stabilized by a weak intramolecular hydrogen bond. A second
conformation was found lying 0.8 U mol'1higher in energy than the C4endo
conformation. The pucker for this conformation is located at the C2 position with the
alcohol proton oriented away from the ring oxygen.
5 .0
Results
A total of six isotopomers were examined for the ring system 3-hydroxytetra­
hydrofuran. Spectroscopic constants for all six isotopomers are given in Table 29.
Thirty one rotational transitions have been measured for the most abundant isotopomer of
3-hydroxytetrahydrofuran. The frequencies for these transitions are given in Table 30.
All three selection rules are allowed and several Q branch series were observed.
Sixteen transitions were measured for deuterated 3-hydroxytetrahydrofuran. The
hyperfine splitting due to the quadrupolar deuterium nuclei was not resolvable; the
linewidths of the transitions were on the order o f 200 kHz. Transition frequencies were
estimated at the centers of the broadened transitions and are given Table 31.
Rotational transitions were measured in natural abundance for each of the I3C
isotopomers. Transitions frequencies for each o f the 13C isotopomers are given in Table
32.
Fewer transitions were measured for these species because the spectra were much
weaker and required longer averaging times. As a result it was not possible to include the
distortion constants in the fit. The rotational constants of the l3C isotopomers were
determined using the distortion constants determined for the normal isotopomer.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Normal
Deuterated
”C(r)
”C(2')
nC(3*)
i3C(4')
A (MHz)
5581.8230(7)
5469.091(3)
5557.170(2)
5477.2482(5)
5564.669(1)
B (MHz)
3638.8316(7)
3558.671(3)
3587.125(3)
3636.1096(5)
3613.616(1)
3629.398(3)
C (MHz)
2924.7410(7)
2900.492(3)
2886.976(1)
2897.5916(3)
2912.8167(7)
2905.303(1)
A, (kHz)
2.38(5)
1.8(4)
2.38‘
2.38'
2.38*
2.38*
Ant (kHz)
-9.58(5)
-8.8(2)
-9.58*
-9.58'
-9.58*
-9.58*
A, (kHz)
13.93(6)
13.1(3)
13.93*
13.93*
13.93*
8, (kHz)
-0.028(6)
-0.028"
-0.028"
-0.028*
8* (kHz)
0.47
0.47"
0.47*
0.47*
0.47*
6
5
7
6
2.5
0.4
2.0
N"
31
AvTO (kHz)
2.5
16
‘Fixedtothecorresponding value ofthe most abundant isotopomer
5490.853(2)
'’Number ofcenter frequencies included inthe fit
Table 29: Spectroscopic constants of 3-hydroxytetrahydrofuran isotopic species
13.93*
-0.028*
2.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
K ’, K ’0
J" V
K o"
v*.
A v /k H z
J' K 'p K'„
j"
V
k
;
Vob,
A v /k H z
3u
3.3
5092.988
-1.2
333
30J
9967.743
1.0
3*.
3|2
5642.113
1.9
4,,
433
10099.617
-0.6
4«
4,3
5776.816
-1.2
5„
5.,
10293.382
0.1
2 21
2„
5828.943
3.4
2 o3
1,0
10306.610
1.9
2m
2„
5992.312
-2.2
3,3
2 2,
10555.508
-0.2
lo,
0.0
6563.562
-1.1
32,
32,
10825.163
1.8
4„
4„
7402.945
-4.1
3,0
32,
10849.270
-1.6
2 21
2,3
7971.203
-4.7
203
1„
11020.695
-2.1
2 2,
2 ,2
8134.579
-3.4
3 30
322
11616.633
3.1
In
Ooo
8506.562
1.4
4,3
4 23
11988.604
-2.3
3.
3,3
9135.187
4.3
2,3
12413.016
-1.9
l,o
oM
9220.648
-1.5
2 o3
lo ,
12963.697
2.5
2 2,
2.3
9363.525
-3.5
2„
1,0
13841.197
-0.1
3 2,
3„
9902.547
6.0
2,3
lo ,
14356.016
0.7
4„
433
9936.172
-1.7
423
4m
10701.852
1.8
Table 30: Frequencies ( MHz) of the assigned transitions of 3-hydroxytetrahydrofuran
119
J 'K ’p K'„
J" v
v
Vo*
Av/kHz
3„
3.2
5519.942
-0.8
4a
4.,
5587.693
0.9
2*.
2,.
5731.220
-2.9
2„
5874.023
0.3
lo .
Ooo
6459.156
0.1
2u
2.2
7705.754
-5.1
2*,
2.2
7848.570
11.1
1„
Ooo
8369.590
9.3
3n
3.3
8774.525
-0.9
1.0
o«,
9027.750
-9.4
3„
32.
10603.998
0.0
2m
1..
10865.048
4.3
4.2
423
11626.945
9.4
4„
423
11762.445
-10.1
2 .2
1..
12260.128
3.2
2<*
lo .
12775.461
-7.5
Table 31: Frequencies of the assigned transitions of d-3-hydroxytetrahydrofiiran
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J'K'pK',
J"K p"K 0"
l3C(l')
,3C(2')
,JC(3')
l3C(4')
lo ,
Ooo
6474.093
6553.691
6526.419
6534.695
1„
Ooo
8444.145
8374.836
8477.483
8396.155
1,0
Ooo
9144.288
9113.353
9178.281
9120.245
20J
1,0
10122.083
10243.579
10310.303
2,j
1„
12248.013
12328.848
12352.027
12345.266
2(12
lo ,
12792.284
12885.987
12895.434
12895.855
2,:
lo ,
14303.088
Table 32: Frequencies of the assigned transitions of the nC isotopic species of 3-hydroxytetrahydrofuran
121
Many of the transitions for the different l3C isotopomers lie within 1 MHZ of one
another, therefore assignment of the transitions to the correct isotopomer proved difficult
The initial assignments were based on predictions made from ab initio calculations. The
rotational constants for two sets of l3C isotopomers are very similar; l3C2 and 13C4 as well
as l3C, and 13C}. Alternative assignments were considered by exchanging the rotational
constants for these species and refitting the structure. When the rotational constants for
the *3C2 and l3C4 were exchanged the fits deteriorated and bond lengths became
unreasonable, for example the C4- O bond length increased form the ab initio value of
1.426 A to the fit value of 1.609 A. Exchange of the rotational constants for the 13C, and
13C3failed to converge.
5.1.4
Structure
The two lowest energy ab intio structures, C4endo and C2endo, reproduce the 15
experimental moments of inertia equally w ell; A I^ =2.96 amu A2. Both structures
were used as starting points in the least squares fitting procedure. The ring puckering
conformation was fit by adjusting the bond distances, angles and dihedral angles of the
ring atoms. The positions o f the ring protons are expected to be insensitive to the fitting
process due to their small relative mass and the lack of isotopic data for these protons. As
a result their positions were fixed at the ab inito values. The orientation o f the hydroxyl
group was fit by adjusting the OC3C2C, dihedral angle. The other parameters describing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122
the hydroxyl group orientation, the C3-0 bond distance and the H-C3-0 angle.
were not well determined in the fit and were therefore set at their ab inito values: 1.418 A
and 104° respectively.
The fit from the lowest energy C4-endo ab initio structure converged after
changing the structure only slightly. The fitted bond lengths are within 0.02 A of the
corresponding bond lengths in the ab initio structure, the fitted bond angles agreed to
within 2° and the torsional angles to within 4°. The value of A l^ for this fit was 0.0070
amu • A2. The values of these fit parameters and their ab initio values are shown in Table
33.
The fit beginning from the C2endo ab initio structure did not converge.
Interestingly, the fitting procedure adjusted the ring conformation from the starting C2
endo to a C4endo structure. The dihedral angles o f the protons of the ring carbons depend
upon the location of the pucker. For the C4endo structure the values range from 117.5°
for H-C2C ,0 to 169.5° for H-C4C3C2. The reason this fit did not converge is that when
the pucker was changed from the C2 endo to the C4endo conformation, the proton
positions were located far from equilibrium due to their dihedral angles being fixed at the
C2endo values.
Principal axis coordinates were calculated using Kraitchmans equations o f single
isotopic substitution for each of the ring carbons. The values of these coordinates are
listed in Table 34. Also listed in Table 34 are the values of these coordinates obtained
from the best least squares fit and ab initio structures. The values of the coordinates from
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
123
Least squares
ab initio
1.434(20)
1.434
C .-Q
1.566(30)
1.550
Cr -Cr
1.526(31)
1.541
Cr-C,
1.521(23)
1.527
c,-o
1.438(65)
1.426
Cr -0(H)
O -H
1.418*
0.965*
1.418
0.965
H-C-H
109.0*
avg = 109.0
o -c,.-cr
106.1(11)
106.5
C..-C7-C,.
103.1(5)
102.7
C r - C T- C r
101.9(28)
100.5
Cy-Ct - 0
102.9(28)
102.2
C^-O-C,.
105.5(26)
104.7
H-Cr -0(H)
106.9*
106.9
C j. -0 - H
104.5*
104.5
28.6(20)
30.3
- U (6)
-1.1
v,
=
0
u1
avg. = 1.096
u1
o
t
w
u
II
1.100*
>°
C- H
O-C,.
-C..-C 3.-C,.
Vj =
C,.-Cr -C r-C,
-24.4(10)
-25.9
=
Cr - C r - C , - o
42.6(20)
45.2
Cr - C , - O - C , .
-44.9(20)
-47.7
H -Q -O -C,
152.6*
152.6
H- Cr - C , .- 0
117.5*
117.5
94.8(20)
91.1
H - C, - Q. - Cr
161.6*
161.6
H - Cr - O - H
169.2*
169.2
v,
v* =
0(H) - Cr - Cr - C,.
Table 33: Bond lengths ( A ), angles ( degrees), and torsional angles ( degrees ) o f the C , - endo
conformation o f 3-hydroxytetrahydrofuran from the least-squares fit and ab intio
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
124
CP
Cr
CT
c.
Kraitchman
least squares
ab initio
a
S
1.390
-1.391
-1.376
b
:
0.587
-0.590
-0.565
c
s
0.273
02 8 5
0.304
a
:
0.052i
-0.122
-0.151
b
s
1277
-1277
-1289
c
*
0.336
-0.325
-0.311
a
-
0.838
0.847
0.853
b
-
0.094
-0.113
-0.139
c
*
0.524
-0.510
-0.521
a
t
0.091
-0.103
-0.102
b
i
1.070
1.071
1.044
c
i
0.606
-0.611
-0.653
Table 34: Atomic coordinates ( A ) o f the ring carbons o f 3-hydroxytetrahydrofuran from
the Kraitchman analysis, best-fit structure, and ab initio structure
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
125
the three methods are in good agreement although the imaginary value for the a
coordinate of the C2 atom suggests that vibrational averaging may be significant.
5.1.5 Discussion
The best fit structure agrees well with that predicted by ab initio calculations.
This structure contains a pucker at the C4 position. This orientation allows for the
formation of a weak intramolecular hydrogen bond between the proton o f the alcohol and
the oxygen of the ring. This weak intramolecular hydrogen bond is thought to stabilize
the conformation.
No evidence of pseudorotation was found in the microwave spectrum of
3-hydroxytetrahydrofuran. In tetrahydrofuran63, nine separate rotational spectra arising
from different vibrational-pseudorotational states were observed. The addition of a
hydroxyl as a ring substituent in 3-hydroxytetrahydrofuran seems to have raised the
barriers to pseudorotation relative to the unsubstituted tetrahydrofuran. This effect may
be due to the formation of the intramolecular hydrogen bond between the hydroxyl proton
and the ring oxygen. This bond may be strong enough to prevent the ring from leaving
the C4endo pucker
The experimental structure of 3-hydroxytetrahydrofuran, C4endo, is not
representative of the ring puckering conformation of the furanose ring in nucloetides.
The structures of 178 nucleotide derivatives have been determined using X-ray
crystallography.70 All of the these structures exist in one of two ring puckering
conformations; C2endo or C3endo. The difference is not surprising. The ring puckering
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126
conformation o f five-membered rings is very sensitive to the nature of the ring
substituents. The nucleotides have phosphate linkages and nucleotide bases attached to
the furanose ring. 3-hydroxytetrahydrofuran may be too simple a system to model these
structures.
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5.2
3-Hydroxytetrahyd rofuran- HzO
5.2.1 Introduction
The 3-hydroxytetrahydrofiiran monomer was found to be in a C4endo envelope
ring puckering conformation.71 This conformation places the hydrogen of the alcohol in
an orientation which allows it to form a weak intramolecular hydrogen bond with the
oxygen of the ring. The 1:1 van der Waals complex o f 3-hydroxytetrahydrofuran-H20 is
interesting for a number o f reasons. The first of these is the determination of the
preferred binding site. The fiiran monomer has two sites that can interact with H20 , the
alcohol group and the ring oxygen. The microwave study of the 1:1 complex will
determine which of these sites the water molecule prefers. A second motivation for the
study of this complex is to examine the interplay of intermolecular and intramolecular
hydrogen bonds. It is unknown whether the water molecule will disrupt the
intramolecular hydrogen bond present in the 3-hydroxytetrahydrofiiran monomer or if it
will remain intact. A final motivation for this study involves the possible change in ring
puckering conformation of the 3-hydroxytetrahydrofiiran monomer upon complexation.
The ring puckering conformations o f five membered rings has been shown to be heavily
dependent upon the nature o f the ring atoms as well as any substituents attached to them.8
It may also be influenced by intermolecular interactions.
127
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5.2.2 Ab initio
Ab initio calculations were performed on the 3-hydroxytetrahydrofuran-H20 van
der Waals complex using Gaussian 9442 at the MP2/6-31G** level. Starting structures
were based on the previously determined C4endo experimental structure of the 3hydroxytetrahydrofuran monomer.71 For each optimized structure, the geometry o f the 3hydroxytetrahydrofiiran monomer has been retained despite a complete geometry
optimization. Three minima were found for the 3-hydroxytetrahydrofiiran-H20 complex;
two structures containing single hydrogen bonds from H20 and one with a double
hydrogen bonded arrangement. These structures are shown in Figure 25. Conformer I,
the lowest energy structure, has a double hydrogen bonded arrangement in which the 3hydroxytetrahydrofuran acts as both an hydrogen bond donor, donating its hydroxyl
proton to the water oxygen and as a hydrogen bond acceptor, accepting a proton from the
water at the ring oxygen. Two higher energy complexes containing single hydrogen
bonds were also found, one with the water interacting with the hydroxyl oxygen the other
with the ring oxygen; conformers II and m of Figure 25.
128
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129
AE - OkJmol1
AE -
II
m
12.6 kJ mol'1
AE = 15.3 kJ mol'
i
Figure 25: Ab initio conformations o f S-hydroxytetrahydrofuran-H^O
Optimization and single point energies calculated with UMP2/6-31G**
level o f theory
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5.2.3
Results
A total of 25 a b - , and c-type transitions for the most abundant isotopomer and
21 a-, b-, and c- type transitions for the l80 water containing isotopomer o f the 3hydroxytetrahydrofuran-H20 complex have been measured. The center frequencies o f the
transitions o f the normal isotopomer are given in Table 35 and in Table 36 for the l80
species.
The complex contains three labile protons; the hydrogens of the water molecule
and the alcohol proton o f the monomer, resulting in 7 possible permutations for
deuterium substitution. A minimum o f 13 transitions have been measured for each of
these 7 isotopomers. The center frequencies for each o f the deuterium isotopomers are
given at the end of the chapter in Tables 41-47. The largest uncertainty for the line
centers occur for the fully deuterated species; Dn is on the order o f 100 kHz due to the
presence o f three quadrupolar nuclei. Assignment o f the resulting spectra was made
difficult by the fact that there was typically more than one isotopomer present in the beam
at any given time and that the makeup of the distribution shifted throughout the day. The
easiest deuterium containing complexes to form and assign involved the deuterated
3-hydroxytetrahydrofuran monomer with either D2O or H20 . The singly deuterated
complex forms when d-3-hydroxytetrahydrofuran is expanded with HzO; an excess of
130
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J' K'p K'„
J" V K."
v*.
Av/kHz
2o:
Ml
7675.075
2.2
2„
Ml
7836.445
1.6
8080.809
8242.177
8880.216
0.2
-2.5
0.7
-2.0
-1.0
2.
2,2
2„
*10
2,i
*01
2„
*10
9807.846
10097.426
2m
MO
10374.955
2.0
*11
*u
10619.328
10896.849
4.3
*01
11302.595
-0.7
9.3
2„
11565.500
3.6
2„
210
2,o
30,
*01
*01
£'pK'0
J" K /' K„"
v*.
Av/kHz
3,3
2„
11609.590
-0.5
30J
3„
3„
2.,
11726.866
-1.0
2m
2o,
2„
11770.957
14973.270
14842.620
-4.2
15300.134
4m
3,3
3,3
15310.012
1.7
-3.3
3„
2„
4m
4m
30J
15320.238
15344.226
-4.0
-0.4
15354.108
3J0
4,3
3o3
2,o
3„
-1.5
-1.3
4,3
3„
16897.155
3„
4m
15847.189
16484700
Table 35: Frequencies of the assigned transitions of 3-hydroxytetrahydrofuran-H20
-2.3
-6.3
12.2
-3.7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J'K 'PK'0 J" Kp" K0"
v*.
Av/kHz
K K'o
J" Kp" K0"
2<a
*11
7260.786
-3.1
3,3
2,2
2,2
2m
Ml
*01
7509.230
-0.5
2,2
2n
*01
*01
7774.906
8023.355
2.9
10.5
30,
31,
312
202
2o2
2„
*10
-2.3
8.5
3,2
4„
20J
2ji
9459.617
10009.102
2„
*11
10700.939
-2.9
3«
2,2
11064.141
-6.7
3,o
3*
3j,
2J0
2,2
2,2
15716.375
14960.492
15842.849
-8.7
0.6
4.3
4,«
3„
4W
4m
Vob.
11150.335
11312.591
11398.777
12519.845
14204.559
3,3
3,1
14698.316
2„
30,
14406.570
14784.508
14809.052
30,
14722.853
Av/kHz
-4.3
1.9
-3.7
2.0
-0.3
-0.8
-0.7
0.1
-0.4
6.6
Table 36: Frequencies of the assigned transitions of 3-hydroxytetrahydrofuran-H2"0
u»
ts)
133
DzO in the expansion ensures formation of the fully deuterated species. The spectral
intensity of these isotopomers served as a gauge for estimating the level o f deuterium
substitution within the expansion. The assignment of the spectrum o f the folly deuterated
species was aided by the extent o f deuterium substitution; these transitions had the largest
frequency shift relative to the normal species due to the largest mass change as well as the
broadest linewidth due to the quadruopole coupling of the three deuterium nuclei.
Assignment of the partially deuterated isotopomers relied on predictions based on ab
initio structures as well as the expected makeup o f the expansion. Further verification of
the correct assignment provided by a Kraitchman analysis with each o f the isotopes
serving the parent will be discussed later. Rotational and distortion constants were
determined by a least squares fit o f the transition frequencies to a Watson A-reduction
Hamiltonian. Spectroscopic constants for all nine isotopomers are given in Table 37.
Many weakly bound water complexes undergo a tunneling motion which
exchanges equivalent protons. A C2 rotation about an axis through the oxygen of the
water molecule can be shown to accomplish such an exchange o f free and hydrogen
bonded protons. Despite an extensive search, no transitions were found that could be
assigned to such a tunneling state.
Stark shifts were measured for five M=0 lobes of the 3-hydroxytetrahydrofuran HzO complex. These shifts were then fit to the a-, b-, and c- components of the dipole
moment using second-order coefficients calculated from the rotational constants. The
best fit values were ma = 1.2(3), nib = 1.8(2), mc = 0.7(4) and mlot = 2.2(2). The observed
and calculated Stark shifts are listed in Table 38 and are in good agreement.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
species*
A (MHz)
B (MHz)
C (MHz)
A, (kHz)
A* (kHz)
AK(kHz)
5, (kHz)
Nb
furan-HjO
2756.284(1)
2350.548(1)
1828.6480(8)
1.80(5)
1.3(3)
-0.8(3)
-0.45(3)
25
d-furan-HjO
2735.399(12)
2338.551(3)
1813.108(2)
1.4(2)
4.(2)
-3.5(9)
-0.39(6)
15
fiiran-DOH
2741.762(4)
2323.996(2)
1807.006(1)
1.99(8)
-0.9(6)
1.1(5)
-0.54(3)
16
d-furan-DOH
2718.476(10)
2314.314(3)
1791.942(2)
13(2)
4.(1)
-1.9(8)
-0.34(6)
15
fiiran-HOD
2750.190(6)
2248.586(2)
1765.692(1)
1.69(10)
2.3(7)
-4.(1)
-0.52(6)
16
d-fiiran-HOD
2726.768(6)
2240.165(2)
1751.6612(9)
1.41(7)
2.5(7)
-1.1(4)
-0.37(2)
13
furan-DjO
2737.879(12)
2223.883(2)
1746.146(2)
1.06(10)
1.(1)
0.0*
0.0*
14
d-fiiran-DjO
2712.782(11)
2217.050(3)
1732.524(3)
1.1(1)
3.4(8)
0.0'
0.0*
20
furan-H,"0
2750.509(1)
2236.397(2)
1757.6257(8)
1.92(5)
0.0‘
0.0*
-0.55(3)
21
*d indicates substitution o f the alcohol proton HmlDOH indicates substitution o f the hydrogen-bonded proton, Hfc, and HOD indicates substitution ofH,
bNumberofcenterfrequencies included in the fit
‘Held constant in the fit
Table 37: Spectroscopic constants for the isotopic species o f 3-hydroxytetrahydrofuran-HjO
135
Transition
|M|
Av / e2
(MHz cm2/ kV2)
observed
A v/e2
(MHz cm2/ kV2)
calculated*
313-2 12
0
-2.22(3)
-2.27
221- 1110
0
19.96(7)
19.93
^2■02- 1*01
0
9.98(4)
9.94
3 3-2“12
J0
0
-2.40(3)
-2.49
2“12- *101
0
11.88(4)
11.94
'Calculated using p.. = 1.2 D, p„ = 1.8 D, and p c = 0.7 D and the rotational constants in Table 37
Table 38: Comparison o f the observed and calculated stark effects for 3-hydroxytetrahydrofuran-H20
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5.2.4
Structure
A comparison of the experimentally determined moments of inertia with those
calculated by the models indicates that the two single hydrogen bonded structures are in
poor agreement, D I^ = 165.7 amu A2 for conformer II and D I^ = 191.9 amu A2 for
conformer HI, and will not be considered further. Conformer I, the lowest energy ab
initio structure with a double hydrogen bonded arrangement, reproduces the moments of
inertia the best within the three models; D I^ = 9.3 amu A2. This structure represents a
good starting point to perform a least squares fit.
Attempts to least squares fit the structure o f the complex to the experimental
moments o f inertia were unsuccessful. The initial attempts sought to fit the six
parameters described in Chapter 4 section 4 and illustrated in Figure 26 to the 27
moments o f inertia. These attempts failed to converge. More restrictive fits were
considered which included fitting a smaller set o f isotopomers ( n-HOH, n-Hl8OH, dDOD), a smaller subset of the fitting parameters, or only fitting to the b- and c- moments
o f inertia. These attempts also failed to converge or gave unreasonable values for bond
distances or angles.
Fits were also considered that abandoned the assumption that the geometry of the
3-hydroxytetrahydrofuran monomer is unchanged upon complexation. Because of its
136
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137
Figure 26: Fitting parameters in 3-hydroxytetrahydrofuran-H20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
138
suspected involvement in the hydrogen bonding network the orientation of the hydroxyl
group o f 3-hydroxytetrahydrofuran was included in the fit This fit attempt converged by
moving the hydroxyl group away from the ring. This seemed reasonable; the hydroxyl
group may have to reorient if the complexed water molecule is to be inserted into the
intramolecular hydrogen bonding network. A closer examination o f the structure
revealed implausible bond distances. For the fit structure the C-O and O-H bond lengths
o f the alcohol group were 1.516 A and 0.714 A respectively. Typical bond lengths for
this functional group are 1.425 A and 0.945 A.72 There was also a poor match o f the
coordinates of these atoms between the least-squares fit and Kraitchman analysis.
The ring puckering conformation o f five membered rings have been shown to
depend heavily on the nature o f the ring atoms and the substituents bonded to the ring.
The conformation is likely dependent upon intermolecular interactions as well. Fits were
attempted in which the pucker o f the ring was allowed to change. These fit converged by
adjusting the ring pucker from a C4endo to a C3endo conformation. A closer
examination revealed that this fit produced implausible values for bond distances and
angles, O-H: 0.826 A , C4C30 : 122°, and a poor match to the Kraitchman coordinates.
Typical values of the CCO angle are 107.8° for ethanol73and 110.7° in furan.74
Kraitchman coordinates in the principal axis system o f the normal isotopomer
were calculated for each of the labile protons, Hb, Hf, and H„, and the water oxygen Ow.
These coordinates are presented in Table 39 along with those determined from the lowest
energy ab initio structure, conformer I.
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139
Kraitchman
ab initio
Hm
Hb
a
t
0.997
-1.096
b
1.175
1.114
c
t
t
0.264
-0.214
a
?
1.529
-1.671
b
t
t
0.990
-0.792
0.248
0.269
3.0911
-3.038
0.562
-0.137
c
t
t
t
0.408
0.401
a
t
2.342
-2.347
b
t
t
0.430
-0.315
0.233
-0.239
c
Hf
a
b
. ow
c
Table 39: Principal-axis-system coordinates (A) o f isotopically labeled atoms
from Kraitchman and ab initio calculations
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140
The extensive data set for deuterated isotopomers allows for six independent
determinations of the Kraitchman coordinates of the hydroxyl and water protons.
This is accomplished by using each o f the deuterium isotopomers as the parent
isotopomer in the Kratichman calculation. The results o f these calculations are given in
Table 40. The values of the coordinates for each o f the labile protons is consistent
throughout the principal axis systems o f the different deuterium isotopomers. Small
variations occur due to a rotation o f the principal axes upon isotopic substitution. The
agreement o f the proton coordinates calculated with the different parent isotopomers
verifies that the deuterated spectra were assigned to the correct isotopomer.
A comparison of the atomic coordinates o f the protons determined by the
Kraitchman analysis and the ab initio calculations listed in Table 39 show that there are
large discrepancies between the two methods. In particularly poor agreement are the
b-coordinates of the free and bound protons.
5.2.5 Discussion
The poor agreement between the structures calculated by the Kraitchman and ab
initio methods along with the inability to least-squares fit the large isotopic data set
indicates that vibrational averaging may be significant in the 3-hydroxtetrahydrofuranHzO complex. Structural determinations o f many water complexes have been
complicated by large-amplitude vibrations. This effect was seen for the alaninamideH20 75and dimethylamine-f^O33 complexes. The 3-hydroxtetrahydrofuran-H20 complex
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141
Parent
H.
H,
H,
furan-HOD
<f-furan-HOD
furan-D:0
furan-H.O
a =±0.867
a = ±1549
a =±3.086
fc =±1.243
* = ±0.901
*= ± 0 .4 3 9
c = ±0.260
c = ±0.243
c = ±0.366
<f-furan>DOH
furan-HjO
furan-DjO
a =±0.897
a = ±1.558
a = ±3.103
fc =±1.246
. * = ±0.913
* = ±0.367
c = ±0.267
c = ±0.236
c = ±0.408
furan-H:0
rf-furan-DOH
rf-furan-HOD
a = ±1.031
a = ±1.461
a = ±3.037
fc = ±1.127
*= ± 1 .0 8 0
* = ±0.752
c = ±0.253
c = ±0.251
c = ±0.407
rf-furan-D.O
furan-KOD
furan-DOK
a = ±0.781
a = ±1.563
a = ±3.0S7
b = ±1.252
* = ±0.844
fc = ±0.290
c = ±0.262
c = ±0.238
c= ±0.363
furan-HOD
<f-furan-D;0
</-furan-H;0
a = ±0.893
a = ±1.499
a = ±3.051
* = ±1.209
* = ±0.973
* = ±0.575
c = ±0.250
c = ±0.250
c = ±0.364
furan-DOH
J-furan-H.O
J-furan-D;0
a = ±0.931
a = ±1.498
a = ±3.065
b =±1.204
* = ±1.000
* = ±0.544
c = ±0.256
c = ±0.239
c = ±0.404
furan-DOH
rf-(uran-H.O
furan-D.O
4-furan-HOD
d-furan-COH
Table 40: Kraitchman coordinates (A) of the hydroxyl and water hydrogens
in the principal axis system of additional isotopic species
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142
contains an intramolecular hydrogen bonding scheme similar to alaninamide-H20 ; a
double hydrogen bond with the water acting as both a proton donor and acceptor. As a
result it is expected that the free proton o f the water will be undergoing a large amplitude
wagging motion as it does in the alaninamide-H2Q case. Single point energy calculations
(MP2/6-31G**) were performed to determine the barrier to the wagging motion by
varying t, the Hf- Ow - Hb- Or dihedral angle. The potential energy along this coordinate
is shown in Figure 27. A very shallow minimum was found at t = 141° corresponding to
a configuration in which one o f the lone pairs of the water oxygen is directed towards the
hydroxyl hydrogen and the free proton o f the water is oriented towards the pucker. The
shallowness of the potential energy surface lends support to the belief that the
the non-hydrogen bonded proton o f the water molecule in 3-hydroxtetrahydro furan-H20
undergoes a large amplitude wagging motion.
Single point energy calculations were also performed to estimate the barrier
hindering the internal rotation o f the water molecule about its C2 axis. This motion would
produce a doubling of the rotational spectrum. No such doubling was observed. The
potential energy surface o f this motion is shown in Figure 28. The minimum energy
orientation corresponds to an internal rotation angle of 0°. The barrier hindering this
motion was calculated to be quite high, 4900 cm'1, supporting the lack o f observable
tunneling doublets.
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143
Relative Energy / cm ''
3000
2500
2000
1500
1000
500
0
•240
-180
-120
-60
60
Figure 27: Potential energy surface of the flapping motion of the free water proton
of the 3-hydroxytetrahydrofuran-H:0 complex calculated at the
UMP2/6-31G** level of theory
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Relative
E n e rg y /c m '1
144
4000-
2000 -
-200
-ICO
0
100
200
Interns! R o tstio n A ngle / d e a r e e s
Figure 28: Potential energy surface of the internal rotation of the water molecule
in the 3-hydroxytetrahydrofuran-H,0 complex calculated at the
UMP2/6-31G** level of theory
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145
Because o f vibrational averaging, the ab initio calculations provide the best
insight into the structure o f the 3-hydroxtetrahydrofuran-H20 complex. The weak
intramolecular hydrogen bond reported for the 3-hydroxtetrahydrofuran monomer
(2.351 A in the ab initio structures; 2.461 A in the least-squares tit structure) is replaced
by two stronger intermolecular hydrogen bonds between the monomer and water. The
hydroxyl-to-water hydrogen bond length is 1.899 A, the water-to-furanose hydrogen bond
is 1.850 A, and the hydrogen bond angles are 168° and 151°, respectively, in the lowest
energy ab initio structure.
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146
J’ K 'p K '0
J" K„" K„"
2,2
Vob.
Av/kHz
7 7 7 7 .8 1 8
-9.5
2o2
lo,
8 0 1 9 .7 8 3
-12.9
2,2
lo,
8 1 7 4 .6 8 0
7.0
2„
lo,
8 8 2 8 .7 0 2
13.0
30J
2,2
1 1 4 7 7 .4 1 8
-0.7
3„
2,2
1 1 5 1 8 .7 9 5
-2.2
30j
202
11632 .3 0 1
5.3
3,2
202
1 1 6 7 3 .6 7 9
4.7
4m
3,3
1 5 1 7 7 .8 6 5
-7.2
4,4
3 1,
1 5 1 8 6 .9 4 2
-2.0
404
3o,
1 5 2 1 9 .2 5 3
2.2
3,2
2,2
1 5 2 2 1 .5 7 1
-5.9
4,4
3o,
1 5 2 2 8 .3 2 0
1.5
3,0
220
1 5 7 3 0 .4 3 4
1.5
4„
3,2
1 6 7 7 2 .6 3 4
1.5
Table 41: Frequencies o f the assigned transitions of
d-3-hydroxytetrahydrofuran -H20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
147
J' K'pK'„
J" K," K0"
V*.
Av/kHz
2«
1„
7744.962
-8.5
2„
1.,
7992.398
6.1
2,2
lo,
8162.741
1.2
2 ii
1,0
8778.920
4.6
30,
2,2
11428.304
0.6
3u
2,2
11476.253
-3.5
3c
202
11598.653
1.7
3,3
2«
11646.605
0.6
4m
3,3
15123.984
-2.4
4U
3,3
15135.052
-6.8
4m
30J
15171.938
-1.5
322
2,2
15197.057
-2.0
4m
30J
15183.023
1.5
3j0
220
15748.783
1.0
4,3
3,2
16723.367
0.2
22,
1,0
10032.231
-2.0
Table 42: Frequencies of the assigned transitions o f
3-hydroxytetrahydrofuran -DOH
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J ’ K 'P K ’0
J " K / ’ K D"
v*.
A v/kH z
2n
lo,
7 9 3 4 .0 1 0
- 6 .5
2,2
lo,
8 0 9 4 .2 4 0
- 1 0 .6
2„
1,0
8 7 3 4 .8 0 2
-1 1 .1
3 0J
2,2
1 1 346.024
3 .0
3,2
2,2
11389.648
11.8
3„j
202
11506.258
2 .8
3,3
202
11549.875
4 .6
4m
3,3
15006.723
-3 .9
4,4
3,3
1 5016.465
1.3
404
3 0J
1 5 0 5 0 .3 4 4
1.9
322
2,2
1 5098.073
0 .8
4,4
3„
15060.073
- 5 .9
3*
220
15621.821
-0 .3
4,3
3,2
1 6603.008
-0 .4
2„
lo,
9 6 6 1 .3 4 8
8 .3
Table 43: Frequencies o f the assigned transitions o f
d-3-hydroxytetrahydrofuran -DOH
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
149
J'K 'p K'0 J" V K o ”
2,2
v,*.
Av/kHz
7545.618
1.5
2n
lo,
7809.316
2.9
2B
lo,
8047.227
5.0
2„
1,0
8511.371
1.1
3m
2,2
11121.309
-9.1
3,
2,2
11201.927
4.8
3<h
202
11359.227
0.0
3,3
2«
11439.822
-9.0
4m
3,3
14766.671
1.2
4„
3,3
14789.075
4.8
4m
303
14847.270
-3.9
2„
lo,
9495.865
0.3
4m
303
14869.676
1.7
3,2
2„
12580.203
4.1
3,2
202
14266.747
-3.4
32,
2„
14450.063
-0.3
Table 44: Frequencies o f the assigned transitions of
3-hydroxytetrahydrofuran -HOD
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
150
J' K 'p K'„
Av/kHz
r v K ."
2o2
lo,
7756.391
4.3
2|2
lo,
7 9 8 1 .7 0 4
-2 .2
3„3
2,2
11048.126
-2 .9
3 |J
2,2
11122.205
0.8
3m
202
11273.445
-3 .4
3,3
2q2
11347.527
3.3
3,3
1 4 6 5 9 .4 5 7
0 .0
3,3
1 4 6 7 9 .4 3 0
1.6
4m
3,0
14733.535
2.7
4m
303
14 7 5 3 .5 0 0
-3 .7
330
220
1 5 5 9 7 .7 5 9
0.1
3b
2,2
1 4 9 0 0 .5 4 6
-0.3
4,3
3,2
1 6 2 6 1 .6 7 7
0 .2
Table 45 : Frequencies o f the assigned transitions of
d-3 -hydroxytetrahydrofiiran -HOD
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
151
r K’„ K'0 J" V K - "
2„
Vo*
Av/kHz
7462.300
19.0
2«
lo ,
7727.645
9.0
2»
lo ,
7976.275
0.6
2,i
lo ,
9409.498
12.1
3(d
2,3
10993.902
-15.2
3,3
2,3
11080.284
0.9
3ra
203
11242.540
-15.6
3,3
203
14128.949
-6.0
3,3
2k
11328.913
-8.6
3„
2„
14331.705
-1.9
4«
3,3
14605.215
0.1
4„
3,3
14629.834
5.1
4«
303
14691.582
1.2
4,4
3(0
14716.203
8.1
Table 46: Frequencies o f the assigned transitions of
3-hydroxytetrahydrofuran -D20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J’K'pK'0 J" Kp" K0"
v*.
Av/kHz
J' K'pK'0
J" K,," K0"
-*13
2,3
11 0 0 4 .0 2 0
-2 .4
03
2 0J
11158.979
-2 2 .8
13
12
21
203
203
1 1 2 3 7 .0 8 9
-2 7 .7
1 4 0 7 2 .3 2 0
-2.3
2„
1 4 8 4 2 .6 2 0
15.3
04
1 4 5 0 2 .6 1 7
8.1
'14
3,3
3,3
14524.091
12.5
04
30J
1 4 5 8 0.735
11.2
14
3 0}
1 4 6 0 2 .2 0 2
8.7
333
1 5 6 1 6 .0 5 3
15.3
2n
1„
7 1 8 1 .5 0 0
19.4
2U
In
7 4 1 4 .6 0 0
25.2
2o j
lo,
7677.191
-14.2
2„
lo,
7 9 1 0 .3 3 2
-32.5
2,i
1,0
8 3 8 3 .6 4 0
13.3
30J
2,3
1 0 9 2 5 .8 9 8
-9 .6
3,3
2„
12385 .6 0 6
-2 6 .6
2,3
14789.222
-15.1
3J0
2 J0
15506 .1 4 4
-15.2
3„
2„
1 4 2 4 7 .1 4 5
-28.8
3a
4 2J
Vco.
Av/kHz
Table 47: Frequencies of the assigned transitions of d-3-hydroxytetrahydrofuran-D30
L /l
N>
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