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Understanding Reaction Dynamics in Coordination ChemistryЧApplication of High Pressure Techniques.

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Understanding Reaction Dynamics in Coordination
Chemistry- Application of High Pressure Techniques
By Rudi van Eldik*
In order to understand the dynamics of chemical reactions in general, detailed information
on electronic, structural and kinetic properties is required. The key questions on how chemical reactions actually occur can in many cases only be answered in terms of information
obtained from kinetic studies. In conventional kinetic studies of chemical reactions in solution, the variables usually selected include concentration, acidity, solvent, and temperature.
In recent years, pressure has become a n additional selected variable in such studies. It enables the measurement of the volume of activation and the construction of reaction volume
profiles and thus assists in the elucidation of the underlying mechanism; it also completes
the comprehension of reaction kinetics by adding another kinetic parameter that the suggested reaction mechanism must account for. Furthermore, the volume of activation is the
only transition state property that can be correlated with the corresponding ground state
property in an experimentally simple manner. In this paper, the insights so gained in our
understanding of the dynamics of reactions involving coordination complexes will be presented. Such reactions are of fundamental interest to chemists since they often form the
basis of catalytic, biological, environmental and energy related processes. Any additional
information that will add to the understanding of the reaction dynamics is therefore of
exceptional importance.
pendence of the rate constant k of the reaction under investigation, viz.
1. Introduction
1.1. Fundamental Principles
AV
High pressure kineticists measure not only the usual kinetic parameters but also the pressure dependence of the
rate constants. From this data and the partial molar volumes of reactant and product species, obtainable from
density measurements, it is possible to construct a volume
profile for the reaction investigated. For a reaction of the
type
= -R
T(ah k/ap),
FA
1
FB
!L-v
\
A+BLAB
'\
the simplest conceivable mechanism that can be formulated according to the transition state theory is
A
+ B +(A---B)*
-
(1)
v,
Priv. Doz. Dr. R. van Eldik
lnstitut fur physikalische und theoretische Chemie der Universitat
Niederurseler Hang, D-6000 Frankfurt (FRG)
Angew Chem. Int. Ed. Engl 25 (1986) 673-682
I
P-
AB
for which a possible volume profile is given in Figure 1.
The magnitude and sign of the reaction volume,
- - AV= VAB- VA- VB, and of the activation volume,
AV' =
- FA
- vB,depend o n the nature of the chemical species involved and their environment. The transition
state volume (Fig. 1) does not necessarily have to be between that of the reactant and product states; it can be a
minimum during a bond formation process (see, e.g., Fig.
5). Whereas V a n d A v d a t a are obtainable from partial molar volumes (density measurements) and dilatometric results, AV' can only be determined from the pressure de-
['I
~ A B
Fig. I. Volume profile for reaction (I). V = partial molar volume, p = reaction
coordinate.
In principle AV' is not independent of pressure, i.e. the
slope of Ink versus p plots depends on pressure, and the
compressibility coefficient of activation, A/?', has been defined as
Various mathematical descriptions to account for the pressure dependence of A V' have been proposed.['-31 However, for mechanistic purposes, the value of AV' at ambient pressure alone is required for the above-mentioned
correlation with partial molar volume data measured under such conditions. In most cases, A V is almost pressure
independent u p to 100 MPa (= 1 kbar).
0 VCH Verlagsgesellschaft mbH, 0-6940 Wernherm. 1986
0570-0833/86/0808-0673 $ 02.50/0
613
In general, AV' may be thought of as the sum of two
components: a n intrinsic part (A V,tI,), which represents
the change in volume due to changes in bond lengths and
angles, and a solvational part (AV&), which represents
the change in volume due to changes in the surrounding
medium. An important part of this volume change is often
due to changes in electrostriction, i.e. the interaction that
occurs when an ion is submerged in a dielectric. It is of
course principally the AV,;f,, part that is the mechanistic
indicator in terms of changes in bond lengths and angles.
Schematic representations of these components for typical
bond formation and cleavage processes, are given in Figure 2. It follows that mechanistic assignments for processes
in which no major solvational changes occur are very
straightforward. In reactions with large polarity changes,
AV& may be much larger than AV,f,, and it can in fact
counteract and swamp the AV,tIr term; examples will be
discussed. Nevertheless, a consistent picture arises from
such studies, demonstrating the suitability of A V + for mechanistic discrimination, even in extreme cases.
A
E
Forward reaction : A
Reverse reaction : A B
A-B
-B
A
AB
+
B
AV,;,,
=
A&,
=
-
o+o=m-m
--
Forward reaction. A0 +
Reverse reaction: AB
A0
+
Overall volume effect. AV* =
AB
Be
AYs~,, =
+
AV$,
-
+
=
A&
Fig. 2. Schematic presentation to illustrate the sign and components of
AV.
1.2. Instrumentation
Initial high pressure kinetic studies of coordination
complexes in solution were conducted in a batch reactor
(autoclave) either in situ, for instance by monitoring the
reaction through optical windows and employing UV-VIS
detection,'" or by the use of a sampling technique. Advances in understanding the reaction dynamics of the coordination compounds described in this paper have resulted
from developments in recent years which enable the pressure dependence of reactions to be studied on the milli-,
micro- and nanonsecond time scales: st~pped-flow''-~Iand
T-jump
NMR spectro~copy,"~.
14]
and
pulsed lasers."', l6I With the increasing availability of such
instrumental techniques, the output of high pressure kinetic information has increased significantly, as can be
seen from a recent compilation of volume of activation
data for reactions of coordination compound^.^"^
and types of chemical reactions.l'. In general, such studies have been justified on the grounds that they can elucidate reaction mechanisms and resolve mechanistic discrepancies. In addition, however, pressure effects constitute
important phenomena and complete our comprehension
of chemical kinetics in that the suggested reaction mechanism must also account for these effects.l"] The examples
selected in the following sections will clearly demonstrate
both viewpoints. These include substitution, electrontransfer, and a series of miscellaneous reactions of coordination compounds. They are presented in this sequence,
since substitution reactions form the basis for many of the
other reaction types.
2.1. Substitution Reactions
Consider a substitution reaction of the type
[ML,X)
+Y
[ML,YJ
+X
(2)
in which M is the metal center, L the non-participating ligand, and X and Y the leaving and entering groups, respectively. Such reactions are generally discussed in terms
of a dissociative (D), interchange (I) or associative (A)
mechanism, depending on the degree of bonding of X and
Y in the transition state of the process. The schematic presentation in Figure 3 is a useful aid to visualizing the nature
of these mechanisms. If bond making is predominant, a
significant decrease in molar volume of the reactants is expected (negative AV'); in contrast, a significant increase
in volume will occur in a dissociatively activated process
(positive AV'). In the case of an interchange process,
bond breakage and bond formation occur simultaneously
in varying degrees and small effects are expected, viz. a
slightly negative AV' for I , and a slightly positive AV'
for Id. These trends are predicted to show up in systems
where no major solvational changes accompany the ligand
substitution process, viz., in solvent exchange reactions;
however, when charged ligands are substituted, major solvational changes are expected to influence the value of
AV'.
Reaction. [MLnX]+ Y -[MLnY]+
X
Mechanism :
( X +IMLnI* Y)*
(X---ML,---YI'
lX--MLn--Yl*,
[MLnYI+ X
0
Id
la
A
Fig. 3. Schematic presentation of the possible mechanisms of reaction (2)
2. Reaction Dynamics in Coordination Chemistry
2. I . I . Solvent Exchange Reactions
The effect of pressure on the reaction rates of coordination complexes has been studied for a variety of species
In a series of papers, Merbach and c o - ~ o r k e r s [ " ~reported A V data for solvent exchange reactions of diva-
674
+
Angew. Chem. Int. Ed. Engl. 25 (1986) 673-682
Table I . A V ' [cm' mol-'1 for solvent exchange on [[email protected] 1191.
DM F = dimethylformamide.
"20
[email protected]
[email protected]
[email protected]
H2O
H3COH
HICCN
DMF
-4.1
-5.4
-5.0
-7.0
+3.8
+0.4
t6.1
+8.9
+3.0
+7.7
6.7
+
+ 7.2
+ 11.4
+ 9.6
+ 9.1
Mechanism.
I.,
1.
I
Id
1,
L
M
Ni20
lent octahedral first-row transition-metal ions. This information is of fundamental importance in understanding the
general substitution behavior of such metal centers. The
trend in the AV' data (Table 1) was interpreted in terms of
a gradual mechanistic changeover from I, to Id in this series.
A similar trend was observed for solvent exchange o n
high spin [ML6I3 ions by the use of N M R techniques.["]
The results are summarized in Figure 4. The trends can be
rationalized according to the following complementary
ideas:["] A decrease in ionic radius (Fig. 4) will increase
the dissociative character, due to steric crowding in the
transition state. For an octahedral complex, the t2gorbitals
are nonbonding and the eg orbitals o* antibonding. From
MnZe to [email protected] t2g orbitals are gradually filled, which
makes the approach of a seventh ligand towards the face
of the octahedron less favorable electrostatically, and
could explain the tendency towards less associative behavior.
0.61
f
I
I
I
I
,0..54,
I
I
mine whether a changeover in mechanism could be observed similar to that for the solvent exchange reactions.
The first data came from a high-pressure temperaturejump study of the complexation of Mn" with 2,2'-bipyridine (bpy) and 2,2' :6',2"-terpyridine (terpy).[Z'.221
The presently available results (Table 2) clearly demonstrate that
the activation volumes for complex formation reactions
parallel those for solvent exchange, and underline the suggested changeover in mechanism along the first-row transition-metal ions.
Table 2. A Y' [cm' mol-'1 for complexation of first-row transition-metal
elements in aqueous solution.
\M
Mn2'
VZ0
NH3
pads la1
bPY
Co2'
Ni2'
+4.8i0.7 f 6 . 0 f 0 . 3
+7.2&0.2 +7.7i0.3
+4.3f1.0 t 5 . 5 f 0 . 3
- 1.2f0.2 [21]
+7.5f1.4 f5.1f0.4
-3.4f0.7 1221 t 3 . 4 i 0 . 6 t 4 . 5 f 0 . 8 t 6 . 7 f 0 . 2
f3.7i0.8 t 3 . 7 i 1 . 3 f4.5i0.4
terPY
SCN'
[email protected]
-2.lf0.8
Ref.
[lo]
[lo]
[23][b]
[23][c]
1231 [b]
[23] [c]
1241
[a] pada = 4-N,N-Dimethylaminobenzene-l
-azo-Z'-pyridine. [b] Experimental
[c] Experimental conditions such that
conditions such that [L]>[[email protected]].
[M @]%- [L].
In one case, it was possible to measure AV' for the reverse aquation process; this allowed the construction of a
volume profile (Fig. 5). The reaction volume estimated
from the activation volumes of the forward and reverse
reactions is in close agreement with that determined directly from the pressure dependence of the equilibrium
constant. The transition state is significantly denser than
both the reactant and product states, emphasizing the associative nature of the process. Prior to this work the dissociative nature of such reactions, i.e., the traditional "EigenWilkins" (or Id) mechanism, had never been seriously
questioned. The AV' data, however, strongly support an
I, substitution mechanism for the earlier members of the
first-row transition-metal elements.
I
Fig. 4. First row octahedral transition metal ions (high and low spin) solvent
exchange mechanisms (radii quoted in A ; @;=mechanisms A, I,; @=mechanisms D, Id) taken from ref. [19].
2.1.2. Complex Formation Reactions
A logical question is whether complex formation reactions exhibit the same trend as discussed above for solvent
exchange reactions. If this is indeed the case it will be of
direct importance to all reactions involving such substitution processes at these metal centers. At the time the above
mentioned solvent exchange work was reported,['91 only a
few pressure dependence studies of fast complex forrnation reactions of these metal ions had been described, and
the available data for complex formation with Nil' and
CO " [*~]
seemed to be in good agreement with the solvent
exchange data (Table 1). It was crucial to measure A V c
for complex formation of Mn" or V", in order to deterAnyen,. Chrm. I n t . Ed. Engl. 25 (1986) 673-682
.. .- . .. . .-
AV
I
1.
i
....
IMn(H,0I,l2"
terpy
l2 '
t
.. . . - .
. . . . .- .
[iterPy;.
H,O'
,; Mn(H,015
[Mnlterpy)(H20),12e
3H20
Fig. 5 . Typical example of a volume profile for a complex formation reaction
of Mn".
675
2.1.3. Ligand Substitution Reactions of Square-Planar
Complexes
Such reactions are of general importance in the catalytic
and cytostatic behavior of square-planar complexes. In
general, substitution reactions of complexes of Pd" and
Pt" follow an associative mechanism via a five-coordinate
transition state. This is true for the solvolysis reaction ( k , ) ,
the subsequent rapid anation reaction (replacement of a
H 2 0 Iigand by another ligand), and the direct substitution
(k2)(see Fig. 6). The general question has been raised by
these complexes at 25 "C [Reaction (3)] nicely demonstrate
that steric hindrance alone cannot induce a changeover in
mechanism'251even though the solvolysis rate constant decreases by u p to five orders of magnitude. This reflects a
gradual increase in AH', but no trend is visible in AS'
and AV'.
[Pd(L)CI]"
L = R'R'N-
[ML3X]+ Y
Rate l a w :
kobs = kl
Mechanism
:
[ML3X]
+
+
k2 [ Y I
-
L'
kl
[Pd(L)H20lz
@
C H 2- C H 2- N(R3)-CH2
+ C1"
(3)
- C H 2- NR4R5
The average volume of activation ( - 12+2 cm3 mol-')
is close to the maximum value expected for the associative
entrance of a water molecule. This value, which is expected mainly to represent the intrinsic component, is significantly more negative than those (between -3 and - 4
cm3 mol - I) reported[261recently for similar solvolysis reactions involving NH3 and pyridine as leaving ligands, and
than those
for the solvent exchange on
[Pd(H20),]'@ and [F't(H20),]20 (-2.2 and -4.6 cm3
mol I, respectively). These tendencies in fact indicate that
the values in Table 3 must arise partly from solvational
changes probably involving dipole interactions with the
charged leaving group. Such solvational contributions also
show u p in the data reported in Table 4 for the anation
reaction (4), where partial charge neutralization during the
associative reaction will result in a more positive AV' value.16.29.301
Furthermore, the volumes of activation become
more negative with increasing size of the entering ligand,
demonstrating the effect of the overlap of the van der
Waals radii during the bond formation process.
[ML3Y]+ X
Reaction:
+ HzO
[ML3L']+ X
-
Fig. 6. A typical square planar substitution reaction; these reactions are
usually associative (L'=solvent).
many investigators whether sterically hindered squareplanar complexes could undergo substitution via a dissociative reaction mode. By increasing steric hindrance
around the metal center, it may be possible to hinder the
direct attack of the entering ligand or solvent molecule.
Such a changeover in mechanism should clearly be seen in
AV' data. We have gradually increased the steric hindrance on a series of Pd" complexes by introducing methyl
and ethyl groups on the diethylenetriamine(dien) ligand.
The data in Table 3 for the solvolysis/anation reaction of
*
+
[Pd(L)H,O]'@ X
L = R'R'N - C H 2 - C H 2 -
+
[Pd(L)X]@ H 2 0
N(R3)-CH2 -CH2- NR4R5
(4)
Table 3. Kinetic parameters for the reaction (3) at 25 "C 1251
R'
H
Me
Et
Me
Et
Me
Et
Et
Et
R'
R'
H
H
H
H
Me
Et
Me
Et
Me
Et
Et
Et
H
R"
RS
H
H
H
H
Me
Et
Me
Et
Me
H
Me
Et
Me
H
H
Me
Et
Et
Et
Me
Et
Et
Et
1s - 'I
AH*
[kJ mol - '1
43.8 f 0 . 5
25.0 +4.2
10.0 +0.1
0.99 f0.02
0.77f0.01
(2.76 0.04). l o - '
12.1 *0.4).10-3
(6.8 f O . l ) (6.7 k0.1).1 0 - ~
43f3
38t4
41f5
49% 1
51f1
50+ I
69f2
66+7
59f3
k,
+
A S'
[J K - ' mol-'1
- 69f12
- 87f15
- 86+18
~
79f 3
- 76f 3
- 88f 3
~
67f 8
- 84t25
-106f
9
AV'
icm' mol-'l
- 10.0f0.6
- 9.220.6
- 10.8i 1.0
- 13.4f 1.9
- 14.5+ 1.2
- 10.9 f0.3
- 14.9 f0.2
- 14.3f0.6
- 12.8f0.8
Table 4 Kinetic parameters for the reaction (4) at 25 "C [6, 29, 301
R'
R2
R'
R'
RS
Me
Me
H
Me
Me
Et
Me
Et
Me
Et
Me
H
Me
H
Me
X
CI
Br
I
CI
CI
Br
I
N3
Et
Et
676
Et
Et
H
Et
Et
Et
Et
Et
CI
CI
[M-'S-']
AH'
[kJ mol '1
1908+SO
3126+ 120
808 1 890
1558i 7
6 2 9 f 19
1087f 20
4162f 140
6678 f440
4.1950.06
2.27 0.01
4022
395 1
34f2
44k3
44+2
40+2
3355
31f2
56f2
70f2
k,,,,,,,,
+
+
~
AS'
[J K - ' rnol-'1
-49f6
-47f5
-5556
- 3 6 2 10
-4258
-54f7
- 6 3 f I7
-66f9
-45f5
- I f 5
AV'
[cm' mol-'1
- 7.220.2
- 7.650.3
- 9.3f0.8
- 2750.2
- 4.9f0.4
- 7.3 +0.4
- 9.95 1.2
- 11.7 f 1.2
- 3.050.02
- 7.7f0.5
Angew. Chem. Inr. Ed. Engl. 25 (lY86) 673-682
2.1.4. Liyand Substitution Reactions of
Octahedral Complexes
A number of reactions involving the substitution of ligands other than solvent molecules will be presented in
this section. Such reactions occur mainly in non-coordinating solvents. For instance, the exchange of phosphane in
the four-coordinated species [Co(PPh3),BrZ] in CDCI3 exhibits a AV' value of -12.1f0.3 cm3 mol-', which
clearly underlines the associative nature of the substitution
process.["' Conversely, A V' for the substitution of acetate
in Ni(OAc)2 by 2-hydroxynaphthalene-l-azo-2'-pyridinein
acetic acid as solvent is
15.5f2.6 om3 mol-', demonstrating the dissociative nature of that process.[321In the
latter case, charge formation is involved so that AV,$r
must be even more positive than the reported number. A
of substitution reactions of the type
recent
+
[ ~ r s - M o ( C O ) ~ ( p y ) ~N]N
-+
-[Mo(CO),(NnN)]f
2py
n
where N N is bpy, 1,lO-phenanthroline (phen) or N,N'-diphenyl-2,3-butanediimine (dab), resulted in A V values of
+3.6 to +4.5 cm3 mol-I. These results are consistent with
the rate-limiting step being the dissociation of pyridine:
Many organometallic kineticists have run into problems
with the interpretation of A S f data in terms of the suggested reaction mechanisms. (The general fact that A S f
data are not very reliable for mechanistic assignments will
be treated in the final section of this paper.) Positive volumes of activation have been found for systems in which
other kinetic evidence, such as a negative AS', points to
an associative mechanism. Substitution of [Cr(CO),(bte)]
by P(OEt), in 1,2-dichloroethane (bte = bis(terf-butylthi0)is a typical
ethylene (2,2,7,7-tetramethyl-3,6-dithiaoctane))
example of such a case. The volume of activation of 14.0
t 0.6 cm' mol-. ' clearly supports the dissociative nature of
the process and emphasizes the value of this kinetic parameter. A similar value of + 14.7f0.7 cm3 mol-' was
found for the corresponding 3,6-dithiooctane complex.[341
In a recent study[351a A Vf value of + 20.6 f 0.4 cm3 mol - '
was found for the rate-determining loss of C O in the reaction
+
[Mn(CO):CI]
+ dab
-
[Mn(CO),(Cl)(dab)]
+2CO
This is indeed a very exciting result and motivates further
study.
2.1.5. Base-Catalyzed Hydrobsis Reactions
Volumes of activation and volume profiles reveal significant mechanistic detail not only in the case of relatively
simple chemical systems such as those discussed in the
Angew. Chem. Ini. Ed. Engl. 25 (1986) 673-682
previous sections, but also for significantly more complicated processes. One of these concerns base-catalyzed hydrolysis reactions in which various complex species participate. In the case of Co"'-ammine complexes, base catalysis increases the rate of aquation from the hour to the millisecond time scale: Such reactions are generally accepted to
proceed according to a S,lCB mechanism which can be
summarized as follows:
[CO(NH~)~X]'~-+
"'@
OH"
+
[CO(NH,),(NH~)X]'~-"'~ H,O
+
[Co(NH3),(NH2)Xf2-")@~ [ C O ( N H ~ ) ~ NX""
H ~ ] ~ ~
+
[ C O ( N H ~ ) ~ N H ~ ]HZO
~ @ 5[ C O ( N H , ) ~ O H ] ' ~
Net reaction:
[CO(NH,)~X]'~-")@
+ OHQ
-
[Co(NH,),OH]'@
+ X"*
In this mechanism, formation of the conjugate base species
is followed by rate-determining dissociation of X"' to produce the five-coordinate [Co(NH3),[email protected] species, which
rapidly reacts with the solvent to produce the hydrolysis
product. The volume profile expected for this reaction
scheme is given in Figure 7.
PFig. 7. Volume profile for the base hydrolysis of [ C O ( N H ~ ) ~ X ] ' ' - accord'"~
ing to a SNICB mechanism.
Solvational effects are expected to significantly influence the values of AV& (consisting of AV(K) and
AV'(k), since kob,=kKIOHQ] for these reactions) and
AVO (the overall volume change), since significant charge
formation will be present when X"' is a charged leaving
group. This was indeed found to be the case,1361and typical
AV&, values are (X"'): 40.2f0.5 (MezSO); 31.0f0.8
(NO:); 33.6f 1.0 (Ie); 3 2 . 5 f 1.4 (Br'); 3 3 . 0 f 1.4 (CI');
26.4f 1.0 (F'); and 22.250.7 (SO:') cm3 mol-' at 25°C.
The decrease in AVZp in this series is ascribed to the
change in charge formation. A similar trend is seen in
These data not only underline the validity of the
suggested reaction mechanism, but reveal other interesting
information. For instance, it is now possible for the first time
to estimate the partial molar volume of the five-coordinate intermediate, on the assumption that the rate-determining step has a late (product-like) transition state in the
case of a limiting dissociative mechanism. This volume
should be independent of the nature of X"'. It turns out
that the volume of the five-coordinate intermediate has an
average value of 71 f 4 cm3 mol-', which is remarkably
677
close to the value of 68 cm3 mol-' for the six-coordinate
[CO(NH,)~OH]'@ species. Furthermore, the quantity
AV&-Av, should also be independent of the nature of
X n Q since it only involves the reaction of water with
[Co(NH3),NH2]'@ to produce [CO(NH~)~OH]'@.
It was
found[361that this volume difference is indeed constant and
has an average value of 20 f 2 cm3 mol - I . This essentially
equals the molar volume of water (viz. 18 cm3 mol-I),
which demonstrates that the water molecule is completely
"absorbed" by the live-coordinate species during the final
step of the reaction. In addition, this is also in line with the
similarity found between the partial molar volumes of
[Co(NH3),[email protected] [ C O ( N H ~ ) ~ O H ]Recent
[email protected]
has demonstrated that similar trends exist for larger fivecoordinate species, in which substituents were introduced
on the ammine ligands.
and indeed, the data in Me,SO as solvent were found to be
+10.3+0.4 (X=F), t 3 . 8 k 0 . 7 (X=Cl), 0.0f0.4 ( X = B r )
and + 6 . 5 f 0 . 2 cm3 mol-' ( X = N3).[39.401
In later work,
Stranks["] studied the effect of pressure on some typical
outer-sphere electron-transfer reactions, and indeed found
quite large negative values for AV". He developed a theoretical treatment based on the theories of Marcus and Hush
and demonstrated that A V " can be calculated by considering contributions from coulombic interaction, solvent
rearrangement, internal metal-ligand rearrangement, and a
Debye-Huckel component. His success is seen in the examples [C~(en),]"/[Co(en),][email protected] (en = ethylenediamine), for
which AV' is - 19.8f 1.5 (exp.), and - 18.4 (theor.) cm3
mol-I, and Fe(H20)[email protected]/Fe(H20)[email protected],for which AV' is
- 12.2f 1.5 (exp.) and - 14.4 (theor.) cm3 mol - I .
In contrast, the
AV' values for inner-sphere electron
transfer between [Fe(H20)SOH]2 and [Fe(H20)6][email protected]
(-0.4f0.4 cm3 mol-I), and between [Cr(H20)50H]20and
[Cr(H,O),]'@ (+4.2+ 1.1 cm3 mol-I) are significantly
more positive than the values predicted for an outer-sphere
electron-transfer process, viz. - 11.4 and - 11.6 cm3
mol - I, respectively. This difference was ascribed to the
dissociative release of a solvent molecule during the formation of the hydroxy-bridged inner-sphere intermediate.
This trend is also in line with the data quoted above for the
reduction of [ C O ( N H ~ ) ~ X ]with
~ @ [Fe(H20)6]'@ and
[Fe(Me2S0)6][email protected][38-401
However, Wherland [421 recently pointed out that Stranks'
theoretical treatment contained an error in the sign of the
Debye-Huckel component, and that the close correlation
between predicted and experimentally observed volumes
of activation is only apparent. We[431recently studied the
outer-sphere electron-transfer reaction between [Co(terp~)~]'@
and [ C ~ ( b p y ) ~ ](terpy
~ @ = 2,2' :6',2"-terpyridine;
bpy = 2,2'-bipyridine) in various solvents and found a A V'
value of - 9.4& 0.9 cm3 mol - I for the reaction in water.
This is in good agreement with the value of -7.3 cm3
mol- ' theoretically predicted on the basis of Wherlund's
@
2.2. Electron-Transfer Reactions
Mechanistic studies on electron transfer reactions of
coordination complexes have been a popular research area
for kineticists over the past decade, and the progress made
and general importance of this work were recently emphasized by the award of a Nobel prize to Henry Taube. And
yet, the mechanistic assignment in terms of inner- and outer-sphere mechanisms [Eq. (a)] has not been unambiguous.
These mechanisms only differ with respect to the nature of
the precursor intermediate species, Ox//Red, in the overall reaction scheme; it can be either an ion-pair o r an encounter species in the case of the outer-sphere process, o r
a bridge intermediate in the case of an inner-sphere process. The electron-transfer [Eq. (b)] is then followed by dissociation of the successor complex [Eq. (c)]. In many systems, reaction (b) is rate-determining and in the presence
of excess reducing agent, kobs= kETKIRed]/(l K[Red]).
+
Ox + Red
Ox//Red
Ox // Red
*
Ox"// Rede
(a)
Ox" // Red0
(b)
+Ox' + Rede
(c)
The interpretation of the kinetic parameters is usually
complicated by the fact that K is rather small, such that
kobr=kETK[Red] and the observed second-order rate constant (ICETIC) is a composite quantity. However, the occurrence of bond formation and/or bond breakage in the inner-sphere mechanism should be clearly reflected in the
volume of activation of the process as compared to that for
outer-sphere reactions.
Halpern et a1.[381studied the pressure dependence of
some typical inner-sphere electron-transfer reactions of the
type
[Co(NH,),X]'@
[ C O ( N H , ) ~ X I '+
~ [Fe(CN)6]4Q
([Co(NH3),[email protected][Fe(cN),]"')
i ktT
Coz'
+ 5 NH3 + X + [Fe(CN),]3Q
X = H 2 0 , MezSO, pyridine
The pressure dependence of kET results in large positive
volumes of activation, viz.,
26.5 f 2.4 (X = HZO),
f 2 9 . 8 k 1 . 4 (X=py), and + 3 4 . 4 f l . l cm3 mol-'
(X = Me,SO). Partial molar volume considerations
showed[451that these volume increases are due to the large
volume increase in going from the precursor to the successor ion-pairs, e.g. 65 cm3 mol-' when [Fe(CN)6]4Q is oxid~ , [ C O ( N H ~ ) ~ X is
][email protected]
reduced to
ized to [ F c ? ( C N ) ~ ] ~and
+
+ [Fe(H,0)6]20
+
CoZO 5 NH3
+ [Fe(H20)sX]ze + HzO
They reported A V " values of + 1 1 (X=F), + 8 (X=Cl,
Br) and t 1 4 cm3 mol-' (X=N,). These values are expected to involve significant contributions from AVS$Y
678
The pressure dependence of a series of outer-sphere
electron-transfer reactions in which significant ion-pair
formation occurs, was also i n v e ~ t i g a t e d . ~In
~ ~this
. ~ ~case,
'
K and kETcan be determined separately.
Angew. Chem. Inl. Ed. Engl. 25 (1986) 673-682
derstandable since such reactions, viz. M -0NOM-NO2, M-OSO,+M-SO,,
and M-SCN-M-NCS,
are expected to proceed via a transition state in which both
coordination sites of the ligand are weakly bonded to the
metal center. However, base-catalyzed isomerization reactions of [ C O ( N H ~ ) ~ O N O ] ~and
@ cis- and trans[ C O ( ~ ~ ) , ( O N O )exhibit
~ ] @ large positive volumes of activat i ~ n , ~ ' ~ indicating
,'~]
that a S,lCB mechanism is operative
in these cases (see Section 2.1.5).
Processes that involve addition or elimination reactions
2.3. Miscellaneous Thermal Reactions
are expected mainly to exhibit intrinsic volumes of activation. For instance, CO, uptake by complexes of the type
High pressure kinetic measurements have also assisted
[M(NH3)50H][email protected](M=Co'", Rh"', Ir"') to produce the corin the understanding of racemization and geometrical and
responding carbonato complexes, is characterized by negalinkage isomerization reactions of coordination comtive volumes of
Similarly, the reactions of
pounds. Various mechanisms have been proposed for the
[Ir(cod)(phen)]@and [Ir(cod)(phen)I] (cod = cycloocta- 1,5racemization of octahedral complexes, and these are prediene, phen = 1,lO-phenanthroline) with oxygen to prosented schematically in Figure 8. Although it is in many
duce [Ir(cod)(phen)02]@exhibit volumes of activation of
cases not possible to distinguish between all of these mech- 3 1.1 f 1.7 and - 44.4 f 1.6 cm3 mol I , re~pectively.'~~]
anisms, some racemization reactions exhibit very distinct
The more negative value for the reaction of the
pressure effects. For instance, A V + for the racemization of
[Ir(cod)(phen)I] species is due to charge formation with the
[Fe(phen),]'@ (phen = 1,lO-phenanthroline) is
15.6f0.3
release of iodide. Large negative volumes of activation of
cm3 mol - compared to a value of - 12.3 & 0.3 cm3 mol - I
this sort demonstrate the significance of bond formation in
reported for the racemization of [Cr(C,0,)2(phen)]Q.1461
such addition reactions, and also demonstrate the signifiThe former result indicates a dissociative mechanism, and
cant catalytic effect pressure would have in such processes.
the latter a n intramolecular one-ended ring-opening of the
On the other hand, decarboxylation reactions of comoxalate ligand. The large negative A V f originates mainly
plexes of the type [M(NH3)s0C02H][email protected]
all exhibit positive
from the increase in electrostriction during ring-opening of
volumes of activation, in agreement with the release and
the oxalate chelate. A similar conclusion was drawn from
elimination of C02.['21A typical volume profile for such C 0 2
the AV' value of - 16.6k0.5 cm3 mol-' r e p ~ r t e d ' ~ 'for
]
uptake and elimination [Reaction (5)] is given in Figure 9,
the geometrical isomerization of t r ~ n s - [ C r ( C ~ O , ) ~ ( H ~ 0 ) ~and
] ~ .the corresponding transition state for C 0 2 uptake is
On the other hand, a AV' value of 14.3k0.2 cm3 mol-'
illustrated schematically in Figure 10. These results are in
for the trans to cis isomerization of [C0(en),(H,0)~][email protected]
good agreement with the volume profile reported'541for the
clearly supports the dissociative release of a water molehydrolysis of C 0 2 and the dehydration of carbonic acid.
cule to produce a five-coordinate intermediate.i481A similar result was recently
for the tram to cis isom[ C O ( N H ~ ) ~ O+
HC
] ~0 ~2 i
[CO(NH,)~OCO~H]*~
(5)
erization of [CO(~~),(CH~COO)(H,O)][email protected],
in which the dissociation of the aqua ligand is believed to proceed accordBased on the results reported for organic ~ y s t e r n s , " ~ ~ " ~
ing to an Id mechanism since AV' is between +5.6 and
homolytic and heterolytic decomposition reactions of
7.9 cm' mol - I.
coordination complexes are expected to exhibit characterLinkage isomerization reactions are usually concerted
intramolecular processes, and in general exhibit small
pressure effects and volumes of activation.[','71This is un-
[Co(NH,),X]*@. This means that on a volume basis the
transition state for the electron-transfer step is approximately halfway between the two ion-pairs, and that the
metal centers have a geometry halfway between the oxidation states involved. This simplified picture indicates how
the molecular dimensions adjust prior to the actual electron-transfer step, which must obey the Franck-Condon restriction.
+
+
+
1
intermolecular dissociation
intramolecular ring-opening
6o
intramolecular twisting
tig. X. Schcmnlic representation ol' different racemization mechanisms of
octahedral species.
Angew. Chem.
hi.
E d . Engl. 25 (1986) 673-682
t
[ColNH3),0H,13e
t
I
PFig. 9. Volume profile for the reaction (5).
679
Fig. 10 Suggested transition state during C 0 2 uptake and decarboxylation
[Reaction (S)]
istic pressure dependencies. Such reactions were investigated for two organochromium(ii1) complexes of the type
[Cr(H20)5R]20,where R = C(CH3)20H and CH(CH3)2.[581
The heterolytic decomposition path exhibited volumes of
activation of 0.3 f0.2 and - 0.2 f0.2 cm3 mol - I , respectively. These small effects point to a transition state (I in
Figure 11) which involves no net development of charge or
major net changes in bond lengths. On the contrary, the
volumes of activation for the homolysis reaction to produce [Cr(H2O),IZ0 and R o are
15.1 f 1.6 and + 2 6 + 2
cm3 mol - ' for the 2-hydroxyprop-2-yl and 2-propyl complexes, respectively. These large positive effects are ascribed to massive desolvation, i.e. breakup of the solvent
cage, as the organic radicals separate from [email protected] the
transition state (I1 in Figure 1
Such mechanistic detail
could not be obtained with conventional kinetic techniques.
+
Earlier studies by Ford et al. (see literature cited in ref. 1161)
indicate that the lowest energy excited state is a ligand
field triplet state from which the primary photoreaction
(kp), nonradiative (k,) and radiative deactivation ( k , )
occur. Since k , < ( k , + k , ) it can be shown that @ =
k , / ( k , + k , ) = k , I, from which it follows that the quantum
yield @ and the lifetime of the lowest excited state I must
both be measured to yield k , at any pressure. A typical example of the pressure dependence of @ is given in Figure
12, which clearly shows different dependencies for the two
photosolvolysis reactions.
+
I
0
100
1000
1500
2000
2500
plbar u
[Cr I H ~ O ) C , R ] ~ ~
Fig. 12. Pressure dependence of the reaction (d). X=CI, L = H 2 0 .
homolysis
I1
Fig. 1 I . Heterolytic and homolytic reactions of organochromium(ii1) complexes.
2.4. Photochemical reactions
The examples discussed in the preceeding sections have
demonstrated how insight into reaction dynamics can be
obtained from the pressure dependence of a rate constant.
In photochemical reactions of coordination compounds
we are dealing with the chemistry of excited state species.
Since so little is known about the molecular dynamics of
such reactions, the pressure dependence of the photochemical reaction step may help reveal the intimate nature
of this process. The interpretation of such data can be expected to be more difficult than for ground state thermal
p r o c e ~ s e s . I ~Nevertheless,
~]
the results obtained so far for
the photosolvolysis reactions of a series of rhodium(r1r)ammine complexes are very reasonable and deserve to be
mentioned in this paper.
The photosolvolysis reactions investigated all proceed
according to the overall scheme:['6.60-621
[Rh(N H3)5X]'3- ")"
[Rh(NH&LI3"
+ X"'
3. Concluding Remarks
+
L
L F = ligand field excitation
680
(4
trans-[Rh(NH,),(L)X]')
Pulsed laser techniques were employed to measure the
pressure dependence of I- 1/'6.621 and the corresponding
volumes of activation are summarized in Table 5 .
Throughout the series of complexes the solvolysis of NH3
is accompanied by a positive AV:
value, which underlines the dissociative nature of the ligand substitution
process. The negative AV: values reported for the solvolysis of X"' are attributed to electrostriction due to charge
formation during the dissociative release of X"'. This is
also in line with the more positive values found for the solvolysis of chloride in t r a n ~ - [ R h ( N H ~ ) ~ C lfor
~]@
which
,
significantly less electrostriction is expected to occur. These
data also enable the calculation of AV:,
the volume of
activation for the non-radiative deactivation process, and
throw more light on the nature of this step.['6.621It follows
that such studies can provide insight into the dynamics of
the excited state processes.[591The method can equally well
be applied to study charge transfer photochemical processes, as illustrated by a series of s t ~ d i e s ' ~ recently
~ - ~ ~ l performed in our laboratories. The construction of volume
profiles, however, is complicated by the lack of data on the
partial molar volume of ligand field and charge transfer
excited species.[591
- "m
+ NH,
We have described in the preceeding sections how the
application of high pressure techniques can contribute to
the understanding of thermal and photochemical reaction
dynamics in coordination chemistry.[661Such data can help
Angew. Chem. Int. Ed. Engl. 25 (1986) 673-682
Table 5. Volumes of activation from photochemical and photophysical measurements on the photosolvolysis reactions of rhodium( 1 1 1 )ammine complexes at 2 5 ° C
FMA = formamide.
Solvent
Complex
Photosolvolysis product
HZO
[Rh(NH3)sCII2"
D20
[ Rh(N D,)5C1]2Q
H >O
[RhfNH,),Brj'"
D20
IRh(ND,),BrI2"
H20
H20
H20
H 2O
HZO
FMA
trans-[Rh( NH,),CI,]"
trans-[Rh( NH3)[email protected]
[Rh( NH 3)oI'
[ Rh( NH $)[email protected]
IRh(NH3)sS04IQ
[Rh(NH,)sC1]2Q
DMF
MeZSO
[Rh(N H,)5C1]2Q
[Rh(NH,),CI]"
[R~(NH~)sHBI~~
/r~ns-[Rh(NH,)~(H~0)Cl]~~
IRh(ND3)5D2013"
[runs-[Rh(N D&( D20)Cl]20
[Rh(NH3)sH2OI3"
trans-[Rh( NH,)4(H20)Br12Q
[ Rh( ND,)51>20]3"
trans-[Rh( N D&( D20)[email protected]
trans-[Rh( N H3)4(H2O)[email protected]
trans-[Rh( N H3)4(H20)Br]*@
[Rh(NH3)5H20]3"
/runs-[ Rh( NH,),( H20)l]'"
[R~(NH~)sHIOI'@
[Rh(NH3),[email protected]
/runs-[Rh(NH3)d FMA)Cll2"
truns-[Rh(NH,),( DMF)Cl]*@
[Rh(NH3)sMe2SO130
rr~ns-[Rh(NH,)~(
Me2SO)C1]2Q
"
solve mechanistic questions by providing direct information on the size (volume) of transition state species. The
interpretation of AV' data offers a pictorial presentation
of the chemical process on a volume basis that usually supports the mechanistic interpretation in an intuitive way.
The occurrence of large solvational contributions may
complicate the interpretation of AV', and additional
measurements in other solvents o r for differently charged
species are then helpful.
Some investigators have called attention to the apparent
correlation between A V c and AS' data,".67-691 although
there is no thermodynamic function that links these parameters directly. It would be misleading to use such a
generalized correlation since there are numerous exceptions. In many of these A V f and AS have opposite signs
and it is therefore wrong to generalize this "correlation". It
is important to note that A S c is usually subject to large
error limits since it is determined by extrapolating the experimental data to 1/T-O. In contrast, AV' can usually
be determined with good accuracy since it results from the
slope of the Ink versus p plot, similar to AH'.
Our present activities in this area are focussed on the
thermal and photochemical dynamics of organometallic
species, a research area in which many mechanistic uncertainties still persist. The advantage of such systems is the
low oxidation states of the metal centers such that minor
solvational contributions are expected to influence AV' in
most cases. The method described in this paper should
also enable one to distinguish between the various reaction
modes of metal clusters in solution.
Finally, these results find practical application in various areas. A better understanding of the intimate mechanism of a chemical reaction assists the design of modified
systems with special behavior, for instance for use in catalytic cycles. Such information can also be applied directly
in synthetic work where the application of pressure may
favor a particular reaction product (see for instance Figure
12) or reduce the reaction time required; especially in or-
'
Angew. Chrm. lnr. Ed. Engl. 25 (1986) 673-682
A V'
5.2t0.4
+12.7f1.2
- 4.2 f0.8
9.5f1.6
- 10.3 i 1.2
+ 4.6t0.6
- 9 . 4 f 1.5
+ 3.4t0.5
+ 2.5f0.5
+ 3.450.7
+ 3.7f0.5
0.3f0.1
- 2.7f0.4
- 4.6k0.7
+ 4.2k0.9
6.3f0.9
- 7 . 8 f 1.8
+ 4.450.9
-
+
AV$-?
A v , + [a1
A V ? Ibl
( - 3.4) Icl
- 8 . 6 f 1.6
9.3 f 1.9
- 7 . 7 f 1.6
6.0 i2.2
- 6 . 8 i 1.6
+ % I f 1.2
- 5.3 f 1.8
+7.5fl.I
2.8 f0.6
+ 2.9k 0.7
C3.950.5
1.4f0.9
-3.920.6
- 4 . 9 c 1.1
+3.9+ 1.3
+ 7 . 6 i 1.1
- 8.9 f2.7
+3.3? 1.8
(-2.6) [cl
-3.5f1.1
( + 3.5) [cl
+4.1 5 0 . 6
+
[dl
[dl
[dl
[dl
[dl
- 0.3 f0.4
+
+ 1.3f0.2
-1il
+
+
+
+
Ref.
- 2.6 f 1.0
( + 2.5) [CI
+ 2.5 t 1.2
=o
=o
[c]
[c]
= o [c]
s o [c]
= o [c]
+0.2i0.5
+ 0.7 f0.3
-If1
ganic chemistry there are numerous examples of the application of high pressure to assist the synthesis of particular
species or isomers. In addition, such techniques are being
applied to biochemical and environmental processes, in
order to contribute to the understanding of the underlying
mechanisms.
The author gratefully acknowledges~nancialsupport from
the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie and the Scientific Affairs Division of NA TO.
He sincerely appreciates the very fine collaboration with
graduate students, post-doctoral fellows and visiting scientists during recent years; their names appear on the papers
cited from this laboratory. This paper is dedicated to Prof.
Dr. Hartwig Kelm in recognition of his pioneering work in
this area, and for his continued interest and support over the
last six years during which he served as President of the University.
Received: November 18, 1985;
revised: January 27, 1986 [A 585 IEI
German version: Angew. Chem. 98 (1986) 671
[I]
[2]
[3]
[4]
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Angew. Chem. Inr. Ed. Engl. 25 (1986) 673-682
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