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Exchange Rates of Ligands in Complex Ions.

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Exchange Rates of Ligands in Complex Ions
It is possible to study the very rapid exchange rates between molecules or ions, L, coordinated
to paramagnetic ions and the j i e e molecules or ions, L*, in the body of the solution by
measuring the line width of the N M R signal of L*.
MLn t L*
Lifetimes of’ coordinated ligands that can be nieasirred fall into the range of milliseconds
to microseconds. The lifetime, or an upper limit to the lgetime, can be measured directly,
1. Introduction
The effect of rapid chemical exchange in an equilibrium
situation on nuclear magnetic resonance spectra has
given us the rates of many types of exchange that have
not been accessible by other methods. As examples, these
types of reactions have included : exchange of hydroxylic
protons in alcohols, alcohol-water mixtures, hydrogen
peroxide solutions, and of amine protons in aqueous
amine solutions; rates of rotation about chemical bonds
as in ring inversion inIcyclohexane derivatives and rates
of rotation about the OC-N bond in amides; rates of
ligand exchange in transition metal complexes [11.
The determination of rates of exchange in paramagnetic
complexes depends upon the fact that the coordinated
species has a much shorter nuclear spin lifetime (larger
line width of the NMR signal) than the uncoordinated
species in the bulk solution.
T h e nuclear spin lifetime is short in a paramagnetic environment because t h e nucleus is subjected to strong,
fluctuating magnetic fields f r o m the unpaired electrons which
are responsible for t h e paramagnetism. These magnetic
fields act on t h e small magnetic dipole of the nucleus and
cause it to “flip over”, o r change its direction. Thus, t h e
lifetime of a given spin state (i.e. t h e orientation of t h e
magnetic dipole) is shortened.
2. Mathematical Principles
The shape of NMR signals in the absence of chemical
exchange can be predicted from the Bloch equations [ 2 ] .
Gutowsky, McCall, and Slichter [3] first published a
solution of the Bloch equations corrected to account for
the effects of chemical exchange of the nucleus between
sites that are not equivalent in nuclear magnetic resonance. Later, McConnell published a mathematically simpler approach [4]. Swifl and Connick [5]have published the
most rigorous derivation of the equations relating NMR
line shapes and lifetimes of ligands in paramagnetic environments for use where only the solvent resonance is
observed. Their derivation proceeds after the method of
McConnell in the following manner:
The first step is the addition of terms to the differential
Bloch equations to include transfer of magnetization
among three magnetically unequivalent species present in
the solution. These species are the uncoordinated
potential ligand present in the bulk solution (subscript a)
and two possible types of coordinated ligands (subscripts b and c). The original Bloch equation for the rate
of change of the magnetization of the uncoordinated species, G,, is [2]:
In this equation Ow, = (w-a,), where w is the applied
radiofrequency (customarily 40-60 Mc), and w, is the
resonance frequency for species a. Mo, is the maximum
magnetization of species a in the direction of the high
external magnetic field, y is the gyromagnetic ratio of the
proton, and H1 is the low magnetic field strength of the
applied radiofrequency. Also, Tza is the transverse relaxation time for the species a. It may be regarded theoretically as being the mean lifetime of a spin state in the
environment of a. Experimentally, Tza is related to the
line width v, at half peak height of the resonance signal
for species a only:
[ I ] A recent review article has covered the use of N M R spectroscopy in studying the kinetics of some of these reactions:
A . Loewenstein and T. M . Connor, Ber. Bunsenges. physik. Chem.
67, 280 (1963).
121 A general discussion of the Bloch equations and the effects
of chemical exchange is contained in J. A . Pople, W . G. Schneider,
and H . J . Bernsrein: High-resolution Nuclear Magnetic Resonance.
McCraw-Hill, New York 1959, Chapter 10.
131 H . S. Gutowskv, D . W . McCnII, and C. P. Slicliter, J . chcm.
Physics 21, 279 (1953).
Angew. Chern. internut. Edit.
1 Vol. 4(1965)
No. 4
The differential equation for the rate of change of G,,
corrected to account for chemical exchange is
[4] H . M . McConnell,J . chem. Physics 28, 430 (1958).
151 T. J . Swift and R. E. Connick, J. chem. Physics 37, 307 (1962).
28 1
w k r e Tab is the 1ifettm.e for chemical exchange of “a”
magnetization to b, T , ~the lifetinic for chemical exchange
of “a” magnetization to c, T~~ the lifetime forchemical exchange of “b” magnetization to a, and rca
the lifetime
for chemical exchange of “c” m.agnetization to a.
There a r e two completely analogous equations for t h e rates
of change of Gb a n d G,.
The second step is the solution of tns differential equations for the magnetization of the hgdnd free in sslution.
Chemical equilibrium and slow passage through resonance (slow variation of the high magnetic field) are assumed so that dG,/dt, dGb/dt, and dG,/dt 0. The assumption is also made that the uncoordinated species is
present in large excess so that the total niagnetizatirn is
essentially only that of the uncoordinated species. In
such a dilute solution, the direct exchange of ligands between complexes would be rare and terms involving the
lifetimes of such exchanges are drJpped.
Finally, the complex equation for the maznetization of
the uncoordinated species is solved for the imaginary
component, which is proportional to the height of the
NMR signal. The result is further simplified by the assumption that the resonance signal is being observed
near the frequency of its maximum such that Aw, is nearly zero. The final equation for the N M R line shape is
Lorentzian in form and may be solved for the line
width at half height which is
greater than Tzb, If the paramagnetism is relatively inefficient in producing line broadening (large TZb),the
line width will depend upon three laxation produced during the time of contact. If the paramagnetic relaxation is
very efficient (small T2b),the line width will depend upon
the rate at which the paramagnetically relaxed nuclei are
released into the bulk of the solution.
The NMR signal of the released ligand will be averaged
with that of the uricomplexed and more abundant species. Measurement of the line broadening in solutions
containing paramagnetic ions will, therefore, give at least
the lower limit of the exchange rate.
It is possible to decide whether the observed line width
is controlled by relaxation (T2,) or chemical exchange
(T,,~) by temperature variation studies [6]. At a given
concentration, I/.tba will behave as a (pseudo) first order
rate constant and have a normal Arrhenius type temperature dependence. Hence, the line broadening (when dependent on T ~ will
~ increase
with increasing temperature. From the temperature variation, the value of the
activation energy, E,, can be found. A is a frequency
factor which may be dependent on concentration.
The factor IjTzb will usually have a smaII temperature
dependence, the correlation time being slightly dependent
on temperature [*I [7]. However, I/Tzb will be independent
of changin? concentrations since it is not a chemical rate
3. Examples
a) Solvent as Ligand
I n this equation, 1/T2,is the line width at half height in
the absence of paramagnetic exchange, l/Tzj is the much
larger line width of the coordinated species b and c, yja
is the lifetime for chemical exchange of the coordinated
ligand back into the solution, and Ao, is the chemical
shift of species b or c from that of a. This equation is applicable to any number of paramagcetic components i n
the solution which may be included in the summation.
The physical significance of the resultant equation is perhaps more easilb. seen from the simplified derivation by
Pcarson et a]. [6].Tnis simplified equation assumes that
only one paramagnetic environment is present in solution in small amount, and that 4 w b as well as ha
Here again 1/Tza is the line width of the signal of the uncoordinated ligand in the absence of chemical exchange,
I/T2,is the line width for the coordinated species, and
Pb/P, is the ratio of the molar concentration of thecoordinated ligand to that of the uncoordinated ligand. It is
seen that the line broadening produced by the paramagnetic species can be controlled by either the nuclear relaxatiori produced by the paramagnetism, if Tzb is
greater than Tba, or by the length of time that the ligand
spends in contact with the paramagnetism, if ‘rba is
[ 6 ] R . C. Pearson, J . Palmer, M . M. Aiidersorl. and A . L. Allred,
Z. Elektrochem., Ber. Bunsenges. physik. Chem. 64, 110 (1960).
The simplest chemical system to which the line broadening method can be applied is a solution of a paramagnetic salt in water. Swqt and Connick IS] have applied
the results of their derivation in detail to the 1 7 0 line
widths in aquesus solutions of manganous, cupric,
nickel, cobaltous, and ferrous salts to determine the rates
of solvation exchanee in M(Pi2O)6zLions as wellas AH*
and AS* of the exchange. The process involved is
M(HzO)O?- iHrO*
t HzO
Here, H20“ is a water molecule from the bulk of the s ~ I vent, M is a metal ion.
Since only two environments are considered [i.L‘. solvent
(subscript H2O) and complex (subscript M)] Equation
(4) becomes :
[*I The correlation time is the average time that a molecule has
before its position or condition with respect t o the applied
magnetic field changes. It may be the time of rotation of the
molecule, the lifetime of a spin state of the unpaired electrons,
or even the chemical exchange time. I n general, whichever of
these times is the shortest will be the correlation time. The
relaxation time T2b will be inversely proportional t o the correlation time since the mechanisms for nuclear relaxation have a
greater chance to operate during longer correlation times.
[7] R . A. Bernheim, T. H . Brown, H. S . Gutowsky, and P . E.
Woessner, J. chem. Physics 30, 950 (1959).
Aiigcw. Ciiem. iitfcriint. Edit.
Vol. 4 (1965) / No. 4
Where -iab has been replaced by ;llLO, ybd by T, TZb
by TzM, and
by OW,. Four possible cases arise
for controlling factors in the line broadening :
The relaxation of nuclear spins is caused by the large
difference between the resonance frequencies in the coordinated state and in the bulk of the solution and isvery
rapid. In this case, the line broadening is controlled by
the rate of exchange [yba
Tzb in Equation ( 5 ) ] .
Only for Niz is the line broadening the same fcr both
kinds of protons. In this case the rate of exchange is
being measured. For the other metal ions the OH line
broidening is greater than the CH line broadening.
Hence, only a lower limit to the rate of exchange can t e
given using the OH data
Table 1. Rate constants I/=M = kexchange (sec 11 for the exchange of
water, methanol, and ethylene glycol coordinated to metal ions a t 25 C
Metal ion
Water [a]
3 x 10'
2 ~ / T , M T M ; l/Tl
1 / ( 7 M ) * >!l<d$,
proton fraction coordinated
3:.1 106
I 4 106
3~ 104
>2.5% 10;
1.8- lo4 [d] >3.4x 103
L O X 103 [dl
> I . ~ x105
L O X 104 (CI
2 x 10s [b]
The line brcadening is controlled by the rate of relaxation through the change of resonance Frequency, and the
chemical exchange is rapid. This intermediate case is not
covered by Equation ( 5 ) .
[a] Data from reference [S].
[b] Some evidence for a second, slower reaction.
[cj From reference [6].
Id] From reference [121.
[ej From reference [lo], temperature 21 ' C .
3. I / ( T , M ) ~ h)$,
and ~ / ( T M ~ ) ; I/T,
The relaxation is comparatively rapid and is controlled
by the lifetime of the nuclear spin state. Therefore, the
measured line width is controlled by the rate of chemical
exchange [Tab
T2b in Equation ( 5 ) ] .
4. I/T,MTM3. I / ( T 2 ~ ) and
l/T2 = P M I T ~ M
The chemical exchange is comparatively rapid, 4 c d M i s
small and the line width i s controlled by the nuclear spin
relaxation in the complex [Tzb yba in Equation (511.
Connick and Swift used the temperature dependence of
the line width to determine which factors were controlling. Their results are shown in Table 1. Pearson et al. [6]
utilized the fact that in ligands containing more than one
kind cf proton, the paramagnetic relaxation rate is inversely dependent upon the distance of the proton from
the Paramagnetic center. Therefore, if the line broadening is the same For two types ot protons, it must be controlled by the exchmge rate of the ligand.
Theoretical equations for the transverse relaxation rate,
l / T z ~have
been given by Solornoti I81 and Bloembrrgen [ 9 ] .
There are two mechanisms, a dipole-dipole interaction and
an isotropic contact interaction. The dipole-dipole interaction between an unpaired electron and a proton can
cperate over a certain distance. The contact interaction,
on the other hand, depends upon coupling of the electron
spin with the nuclear spin by the actual presence of the
electron at the proton. It therefore requires close contact
of the paramagnetic ion and the molecule containing the
protons being studied. As a result some broadening of the
N M R signal can occur due to dipole-dipole relaxation even
for a molecule which is not directly coordinated to a paramagnetic ion. However, the effect does fall off with distance
and is only significant when the molecule is in the layer right
next to the coordinated layer. This line broadening is called
"outer-sphere relaxation" and can be corrected for.
Table I gives some data for the rate of exchange of coordinated methanol 161and ethylene glycol [lo]. In these
cases signals for CH and OH protons can be observed.
[8] I , Solomon, Physical Rev. 99, 559 (1955).
[ 9 ] N . Bloembergen, J. chem. Physics 27, 572 (1957).
[lo] R . G. Pearson and R. D. Lonier, 1. Arner. chem. SOC.86,
765 (1964).
A n g r w . Cheni. internot. Edit.
Vol. 4 (1965) / No. 4
Thc csordinated ligand can also give an N M R spectrum
which can be seen i n special cases. For example ethylenediamine coordinated t o nickel(I1) or cobait(1l) shows an
NH2 peak about 200 p.p.m. on the high-field side and a CH2
peak about 100 p.p.m. on the low-field side with respect to
water [I I]. At 60 Mc for the resonance frequency these
, of the order of 103 to 104 cps. Similar shifts
shifts, ~ C O Mare
can be found for coordinated OH protons.
Loz and Meiboom [I21 have observed the resonance lines
for the methyl and hydroxy groups of bound methanol
separate from those of bulk solvent methanol in solutions
containing Ni(C104)~and C O ( C I O ~ Below
) ~ ~ -40 "C the exchange was sufficiently slow, so that the line width observed
was completely caused by the coordinated ligand. Above
-40 O C additional line broadening occurred due to chemical
exchange. The rate of exchange could be calculated from the
line width in the usual way.
When coordination of a paramagnetic ion to nitrogen occurs,
for the protons on the nitrogen atom are
the values of T ~ M
very small, about 10-5 to 10-7 seconds [lo]. Coordination t o
oxygen produces values of TZMwhich are much greater for
bound protons, about 10-3 to 10-4 seconds 16,121. This
difference is due to the greater polarizability of nitrogen
compared to oxygen. Thus, a higher unpaired spin density
due to the isotropic contact interaction will be found o n
nitrogen. By polarization this spin density will be transmitted
to the proton bound to nitrogen and produce relaxation [I 31.
Since, moreover, TM is greater for nitrogen ligands than for
oxygen ligands, this means that rates of exchange will be
commonly measured for nitrogen-containing ligands, but not
so often for oxygen ligands.
b) Solvent and Ligand Different
The results of Table 1 refer to cases i n which the solvent
is also the coordinated ligand. It is also possible to study
the exchange of ligands, L, present in smaller amounts
in a solvent such as water.
M L n + L'
i- L
(111 R . S. Miker and L. P r a f t , Discuss. Faraday SOC.34, 88
( I 962).
[I21 Z . Luz and S. Meiboorn, J. chern. Physics 40, 1058 (1964).
[I31 R . E. Benson, D . R . Enton, A . 0. JoJey, and W . D. Pl?iilips,
J. Amer. chem. SOC.83, 3714 (1961).
The N M R spectrum for free L will show the usual line
broadening due to exchange. If the protons of L are
being observed, as IS usually the case, then it must be remembered that N H and O H protons of free L will very
rapidly average with the solvent. Thus, if L is glycine
(glyc = NH2CH2CO0 I), the N M R spectrum in water
will show a CH2 peak and a H20/NH2 averaged peak.
The glycine must be about 1 molar for easy observation,
but a large portion of this can be in the form of LHO, or
” , NH3@will also exchange rapidly with the solvent.
The experiments are done at a constant value of P,
(or Pb). This means a constant concentration of metal
ion and a constant amount of [L] + [LH”]. The line
broadening, Av, is plotted as a function of [L], the concentration of free ligand, which is varied by changing the
pH. Four kinds of results can be found as shown in
Figure 1.
C L l 4
For case I, there is no dependence of Av on [L]. Such
results were found for some nickel complexes, where the
rate of exchange is so slow that only a small broadening
due to “outer-sphere relaxation” [6] was observed.
Case I1 has ligand dependence and a nonzero intercept.
Thus, there is a line broadening process which is independent of the concentration of free ligand, L, and one
which is directly proportional to the concentration of L.
This suggests that there is a kinetically first-order exchange mechanism (independent of [L]) and a secondorder exchange mechanism with a rate directly dependent
on [L]. A positive temperaturecoefficient and near equality of the OH and CHline broadenings would be needed to
confirm that exchange rates are controlling. Rate constants kl and k2 would govern the first order and second
order processes, respectively. The dashed line is for the
case where T 2 M remains small compared to T~ at all
concentrations of L used. Eventually, of course, T~ must
become smaller than TzM with increasing [L] because
of the relation
+ k, [Ll
Hence, at large [L], the curve must flatten out and reach
a constant slope. It is possible, in principle, to obtain kl,
k2, and T2M in such cases.
The third case, IIT, involves dependence on [L] and a
zero intercept. This indicates that only a second order
Accordingly, a plot of the reciprocal of the line broadening, A v , against the reciprocal of the concentration, [L],
gives a straight line from which TZband k2 can be found.
The plot for case IV shows a maximum. This is due to a
change in theconcentration of species contributingdifferently to the line broadening. Some copper(I1) systems
show this behavior. For example, Cu2+/NH3 gave such
a result because Cu(NH3)52+ formed at high concentration of NH3 is inefficient at line broadening.
Table 2 shows some data obtained for metal ionlligand
systems in aqueous solution. The results can be confirmed by information from other sources in several instances. For example, data on the rate of dissociation of
Ni(en)$+ (kl = 3 sec-1) and of Ni(gly)3- (kl = 10 sec-1)
[14] show that the rates are too small to be measured by
NMR line broadening methods. They can be measured
by flow methods however 1141. Thus, the rate of acid
catalysed dissociation was found to be some 20-30
times faster than ligand exchange since only one end of
the chelate needs to be free for acid dissociation, but both
ends must be free for ligand exchange.
It will be noted that rates of exchange in Table 2 calculated from the averaged OH/NH signals are usually
Fig. 1. Experimental results for plots of line broadening A.J vs. concentration of free ligand [LJ.
~ / T M=
exchange reaction is occurring, kl in Equation (10)
being zero. Curvature will occur when [L] becomes large
enough so that TzM is greater than T ~ Equation
with kl - 0, Equation (2), and Equation ( 5 ) can be combined to give
Table 2. Rate limits for the ligand exchange in complexes at 27 ’C.
en = ethylenediamine, gly = glycine, sarc = N-methylglycine (sarcosine), dmg = N,N-dimethylglycine.
Ea = 7 kcal/mole
Ea = 7 kcal/mole
Ea = 10.5 kcal/mole
Ea = 10.5 kcalimole
Ea = 6 kcal/mole
Ea = 6 kcal/mole
Ea = 10 kcal/mole
Ea = 10 kcai/mole
Ea = 9.5 kcal/mole
Ea = 9.5 kcal/mole
kOH = 6 x 1 0 5 M-1 sec-1
kCH, = 60 sec-1
1 x 102 M-1 sec-1 La]
kOH = 6 . 7 ~102 sec-1
3 . 3 ~103 M-1 sec-1
~ sec-1 2 . 1 lo3
~ M-1 sec-1
kCH2 = 4 . 2 102
Ea = 7 kcaljmole
Ea = 13 kcal/mole
Ea = 13 kcal/mole
kCH2 = 1 . 3 ~1 0 4 M-1 sec-1
4.7x 102 M-1 sec-1
kCH2 = 70 sec-I
103 sec-1
7 . 3 ~lo3 M-1 sec-1
kCIlz = 3 . 2 ~
Ea = 9.5 kcaljmole
Ea = 17 kcaljmole
[a] Rate constant at 54 ”C.
[14] R. G. Wilkins and A. K . Shamsuddin-Ahmed, J. chem. SOC.
(London) 1959, 3700; 1960, 2901; P. €//is and R. G.Wi/kins,
ibid. 1959, 299.
Angew. Chem. intcmat. Edit. / Vol. 4(1965)
1 No. 4
somewhat larger than those from the C H signals. This is
expected because release of the N H end of the chelate
will lead to an acid-base proton exchange which will
broaden the OH peak only. The extreme case is Co(en)32
where the OH peak gives a k l of 3.3 x 103 sec-1 and the
CH peak shows kl == 0. If kl is entirely due to one end
only beirig released and if Wilkins' factor [14] of 30 is
valid, then the contribution of a first-order process for
the complete dissociation of the group en would be too
small to be measured from the C H signal.
The difference between the rate constants derived from
the OH and CH signals is small for glycine and sarcosine. I n these cases it is probably the carboxylate end
which is released first. This does not lead to proton exchange and hence kl and k2 calculated from the C H and
OH signals should be the same. Copper gives the largest
difference in k2 values between the two signals for glycine. This may be due to an additional exchange of a glycine ion coordinated through the amine group only to
one of the axial positions above and below the plane of
Cu(g1y)z [15]. It is known [ 5 ] that groups held in the axial position are very labile. Hence, T~~ in Equation ( 5 ) is
very small compared to Tzb Since the coordinated NH2
group is closer to the copper ion than the CH2 group, its
signal would be broadened more.
Copper, manganese, and iron(t1) have two water molecules still coordinated in most of the complexes studied.
Presumably these molecules are labile and could cause
O H line broadening. However, a consideration of the
high rates of exchange of such water moIecules and the
low rates of relaxation of protons bonded to oxygen [ 161
suggests that the contribution of such a process to the
overall line broadening would be small. Manganese(I1)
would possibly he an exception, since it gives higher
rates of relaxation, and part of the difference between
the OH and C H signals for this ion in Table 2 could be
due to water exchange. Otherwise, it should be noted
that the approximate activation energies listed in Table 2
are the same for both OH and C H signals. This suggests
that the same process is rate determining for both.
In all cases the order of exchange reactivity found,
Mn(lI)> Fe(II)>Co(II) >Ni(ll)eCu(Il), agrees with previous observations for the same series [17]. An explanation
has been given in terms of crystal field theory, in which the
important factor is the different loss of crystal field stabilization energy in going from the ground state to the
transition state for each metal ion. To use such a theory, it is
necessary t o assume a mechanism and a structure for the
transition state as well as for the ground state.
they may be considered essentially as planar. It has been
found that octahedral coniplexes react by mechanisms
which are, or strongly resemble, SN1or dissociation niechanisms [17]. Planar complexes, however. have always
been found to react by SN2or displacement mechanisms
i n their substitution reactions [17, 181.
It is significant that in Table 2 copper always reacts by a
totally second-order process, where exchange rates are
being measured. This suggests an SN2 mechanism for
copper(1I) complexes in agreement with their structures.
By analogy with complexes of platinuni(l1) and palladiuni(I1) [IS], the first step in the reaction would be the
facile replacement of an axial water molecule by the substituting ligand. This would be followed, probably, by
rearrangement to a trigonal bipyramid structure, expulsion of one end of the coordinated ligand, and return
to a planar structure ( I ) containing two unidentate
ligands. (In the formulae N -0 is a glycinate anion.) At
this point exchange has been assured since the ligand
originally in solution has taken up a position identical
with that of the ligand originally present in the coniplex.
The rate of exchange would be equal to the rate of formation of ( I ) , i. e. it would be second order, depending
on the concentrations of the complex and of the free
ligand. A corresponding first-order reaction in which
water is the nucleophilic reagent would be too slow to be
detectable because planar complexes are very sensitive
to the reactivity of the nucleophile [ 181.
Octahedral complexes with three bidentate ligands are
not as easily accessible for an incoming ligand molecule.
Instead, by a mechanism which may be described as a
dissociation assisted by water (see below), one end of a
bound chelate is replaced by a water niolecule in a readily reversible process. After releasing one end of the chelate, the intermediate (3) could reclose the chelate, could
The data are in agreement with a number of possible
mechanisms. They are best considered in combination
with available information on substitution reactions of
other complex ions. It is safe to assume that the complexes of Mn(II), Fe(II), Co(II), and Ni(I1) are octahedral, or slightly distorted octahedral, structures. Cu(I1)
Complexes have such a serious tetragonal distortion that
1151 The third en group of Cu(en)32+ is attached as a unidentate
ligand: J . Bjerrum, Acta chern. scand. 2, 297 (1948).
[I61 L. 0. Morgan and A . W. Nolle, J. chern. Physics 31, 365
[I71 F. Bas010 and R. G. Pearsori: Mechanisms of Inorganic
Reactions. Wiley, New York 1958; R . G. Pearson, J. chern.
Educat. 38, 164 (1961); R . G. Wi/kins, Quart. Rev. (chern. Soc.
London) 16, 316 (1962).
Angew. Chem. internat. Edit. 1 Vol. 4(1965)
[ I S ] F. Basolo and R . G. Pearson in F. A. Cotton: Progress in
Inorganic Chemistry. Interscience, New York 1962, Vol. 4.
react by the same dissociation mechanism to release both
ends of the chelate, or could have the coordinated water
replaced by an external ligand molecule. Either of the
last two events would lead to exchange. The rate of exchange would be given by
are known for platinum(I1) complexes [18j. For octahedral cobalt(11) and nickel(lI) complexes the opposite
order is found: dimethylglycine > sarcosine > glycine.
This is readily explained as steric acceleration of the dissociation mechanism and has been observed for other
octahedral systems, too [17]. Wilkins [21] has found the
same order for the rate of dissociation of N-methylethylenediamine complexes of nickel(I1).
Applying the steady-state treatment to (3) and assuming the concentrations of (4) and (5) to be very small,
gives for the rate of exchange
The water-assisted dissociations, i. e. the steps with rate
constants k, and k,, are visualized as requiring a criiical
extension of the metal-ligand bond and the partial coordination of a water molecule before the bond is completely broken. This follows from the improbability for
energetic reasons of a five-coordinated intermediate with
a square pyramid structure [22]. Rearrangement to a
trigonal bipyramid structure might occur instead in certain cases, for example, where there is no crystal field
stabilization energy or where x-boiiding is importai!t.
If a water molecule is required, then the transition state
will be seven-coordinated, with five groups in the original octahedral positions and two groups, water and the
leaving group, adjacent to each other and somewhat further away [23].
If kd[L] is small compared to (kb + kc), then the observed rate constant for exchange will be the sum of a
first-order term and a second-order term, in agreement
with the experimental results.
This mechanism can be tested because, first of all, it
should be true that k, is 20-30 times as large as k,, as
mentioned above for Ni(en)32+ and Ni(gly); Secondly.
let us assume that (kb + k,) is large compared to kd[L].
The denominator of Equation (13) is then simply a constant since kd[L] can be ignored. This means the
equation is of the same form as Equation (lo),
found experimentally. We can now identify kl
as k,k,/(k, -t k,) or k,k,/kb, since kb
k,. In
the same way kz becomes k,kd/kb. An examination of
Table 2 shows that in no case does k2[L] become as much
as ten times kl for the highest [L] used. This means that
(kb ik,) will indeed be large compared to kd[L], as
assumed. Some leveling of the rate with increasing [L]
may occur but would ordinarily be obscured by the normal curvature of plots of line broadening vs. [L] due to
relaxation control superseding exchange control. A similar mechanism can be written for octahedral chelates
containing two bidentate ligands and, in addition, a
second-order path in which the reverse process ( 5 ) +(3)
occurs can be visualized.
The results for glycol exchange given in Table 1 call for
some special comment. First of all, the rates of exchange
of this chelate ligand are about the same as those for the
unidentate methanol. This is understandable in terms of
the mechanism of a solvent-assisted dissociation. The
intermediate (6) guarantees exchange after only one end
There is no absolute reason why a mechanism involving a n
s N 2 attack on the metal by the incoming ligand should not
account for the second-order rateconstants for exchange in
the octahedral systems. The chief evidence against such a
process is the general failure to detect nucleophilic displacement reactions with octahedral complexes of transition
metals [19]. It is significant that it is the “special mechanism
for chelate compounds” [17] which causes second-order
kinetics without a true bimolecular reaction. In the dissociation of any chelate ligand (bidentate or polydentate), it is
necessary that one point of attachment be broken at a time.
Almost invariably a water molecule will replace the released
part of the ligand. Since other ligands can replace water, it is
now possible for the rates of Iigand substitution or exchange
to depend on the concentration of the new ligand. When
unidentate ligands such as NH3 or CNS- are exchanging,
only first-order exchange is observed 1201.
The rate sequence glycine > sarcosine > dimethylglycine observed for copper(I1) complexes is expected for
an SN2 mechanism and may be attributed to steric hindrance to the approach of the nucleophile. Similar cases
1191 R . G. Pearson, D. N . Edgington, and F. Basolo, J. Amer.
chem. SOC.84, 3233 (1962).
[ZO] J. P. Hunt, H . W. Dodgen, and F. Klanberg, Inorg. Chem. 2,
478 (1 963).
O\I ,o-0
oc:, \o-0
of the chelate has dissociated. A five-coordinated intermediate, {7), would lead to a greatly reduced exchange
rate for glycol compared to methanol because of rapid
reclosing of the chelate ring.
4. Other Methods
Another NMK line broadening nicthod not using paramagnetic metal ions has been developed chiefly by
Hertz [24]. Here, advantage is taken of the fact that a
halide ion coordinated to any metal ion has a high rate
of magnetic relaxation, due to coupling of the nuclear
quadrupole moment of the halide ion with the asyniI211 R . G. Wilkins, J. chem. SOC.(London) 1962, 4475.
[221 See reference [17], pp. 98 -101 and p. 165.
[ 2 3 ] R. Dyke and W. C. E. Higginson, J. chem. SOC.(,London)
1963,2788; S. A. Johnson, F. Basolo, and R . G. Pearson, J. Amer.
chem. SOC.85, 1741 (1963).
[241 H . G. H e r t z , 2. Elektrochem., Ber. Bunsenges. physik.
Chem. 64, 53 (1960); 65, 36 (1961).
Angew. Cliern. inferntit. Edit. 1 Vol. 4(1965)
No. 4
metric electric field produced at the halide nucleus by the
metal ion. Rates of reactions such as
+ Br- +
+ H,O
can be evaluated.
Finally, it is of interest to mention that rates of rapid
exchange reactions can also be measured by using the
line broadefiing in EPR or ESR spectra [25]. Since the
time scale of EPR is some 103 times larger than that of
NMR (the frequency used is of the order 1010 cps rather
than lo7 cps) only very rapid reactions can be studied.
Half-lives of 10-6- 10-9 seconds are most convenient.
It has been possible to study rates of outer-sphere complex formation between paramagnetic cations and a para[?5] R . G. Pearson and T. Buch, J. chern. Physics 36, 1277 (1962).
magnetic anion, the nitrosyldisulfonate ion. Such outersphere reactions are very rapid, being diffusion controlled [26]. It is also possible to study rates of innersphere complex conversions by selecting a cation the complexes of which are very labile, for example Mn(II), and
going to high temperatures where the rates become sufficiently rapid [271.
We are indebted to Prof. A. L. Allrzd for much help in the
theory and practice of nuclear magnetic resonance spectroscopy.
Received: July24th, 1964. Supplemented: October 19th, 1964[A440/2041E]
German version: Angew. Chem. 77, 361 (1965)
1261 M . Eigen and K.Tamm, 2. Elektrochem., Ber. Bunsenges.
physik. Chern. 66, 93, 107 (1962).
[27] R . G. Hayes and R . J . Myers, J. chem. Physics 40,877 (1964).
Formation and Reactivity of Phosphonium Salts in the Vitamin A Series
Pubhhed on the occasion of the 100th nnnivcvmry of the establishment of Badische Anilin& Soda-Fabrik AG., on April 6th, 1965.
For syntheses in the carotenoid j e l d using the Wittig reaction, particularly on the technical
scale, it was necessary to ccrry out extensive studies on the preparation and properties of
the intermediates. Here the part of this work is discussed which dealt with quaternary
phosphoniunz compounds of triniethylcyclohexene derivatives.
1. Formation of Phosphonium Salts
The well-known reaction of tertiary phosphines with
organic halides to form quaternary phosphonium compounds [l] is unsatisfactory in the vitamin A series, since
here the halogen compounds are extremely unstable.
However, this difficulty has been overcome by a new
method for the preparation of quaternary phosphonium
salts [2].
When alcohols are treated simultaneously with tertiary
phosphines and acids, they give high yields of quaternary phosphonium salts [3]:
+ PR; + HX
+ [R-PR;]@ XO
+ HzO
Suitable starting materials include primary and secondary alcohols; substituted ally1 alcohols react particularly smoothly.
[ I ] G. M . Kosolapof Organophosphorus Compounds. Wiley,
New York 1950.
L21 H . Pommer, Angew. Chem. 72, 811, 911 (1960).
131 German Patent 1046046 (June 29th, 1956), BASF; inventors:
W. Sarnecki and H . Pommer; Chem. Zbl. 1959, 13003.
Angew. Chem. internat. Edit. 1 Vo1. 4 (1965)
1 No. 4
Thus, p-ionol (I) reacts with triphenylphosphine [*] and
an acid HX to give the @-ionyltriphenylphosphonium
salt (2) ; similarly (3-ionylidene-ethanol (3) gives the Pionylidene-ethyltriphenylphosphoniurn salt (6).
We assume an ionic mechanism for the formation of the
quaternary phosphonium salt from alcohol, phosphine,
and acid. Under the action of the proton, the alcohol
R-OH forms the carbonium ion Re, which then alkylates the tertiary phosphine to yield the quaternary salt.
In support of this mechanism, replacement of p-ionylidene-ethanol (3) by its isomer 9-vinyl-P-ion01 (4) leads
to the s a m e P-ionylidene-ethyltriphenylphosphonium
salt (6) [4].
[ * ] The tertiary phosphine used here and throughout this work
is triphenylphosphine, the preferred reagent for the Wittig
olefination. The components (C&&P and HX'can be replaced
by the quaternary phosphoniurn salt [(C,jH&PH]@XQ.
[4] German Patent 1060386 (Sept. 3rd, 1957), BASF; inventors:
W . Sarnecki and H . Pommer; Chem. Zbl. 1960, 13171.
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