4651
J. Phys. Chem. 1986, 90, 4651-4654
Effect of Hydration on the Structure of an SN2 Transition State William L. Jorgensen* and J. Kathleen Buckner Department of Chemistry, Purdue University, West Lafayette, Indiana 47907 (Received: February 19, 1986)
Ab initio quantum mechanics and statistical perturbation theory are used to study the effect of hydration on the structure of the transition state for an SN2 reaction. Energy profiles are obtained for symmetrically stretching the C-CI bonds in the transition state for the chloride exchange reaction of CI- + CH3CI both in the gas phase and in dilute aqueous solution. Though the effects of hydration on the reaction kinetics are profound, the structure of the transition state is only slightly distorted. There is modest elongation of the C-CI bonds by ca. 0.05 A; however, the vibrational energy curve in aqueous solution is significantly more anharmonic and flatter, so a red shift is predicted for the symmetric stretch.
Introduction Solvent effects are well-known to have profound influence on the kinetics of SN2 reactions.'** For substitutions of alkyl halides by anions, better solvation of the nucleophile than the more charge-delocalized transition state can rationalize the increased activation energies with enhanced anion solvating ability. More detailed understanding of the solvent effects has been aided through recent computer simulations of the reaction of C1- + CH3Cl in water and DMF.3,4 The computations provided complete free energy profiles as a function of a reaction coordinate and characterized the changes in solvation along the reaction paths. A key finding was that the activation barrier induced by hydration results primarily from reduction in strength rather than in the number of solute-water hydrogen bonds upon proceeding to the transition state.j From the results in DMF, it also appears likely that some sN2 reactions in dipolar aprotic solvents involve an initial complexation before the rate-determining step, as in the gas phase! However, in these calculations the structure of the transition state was not allowed to vary from the geometry obtained from ab initio 6-31G* computations for the gas phase. Though the computed and experimental free energies of activation are in good accord, the fundamental question of the influence of hydration on the structure of the SN2transition state remains. Can the substantial kinetic effect really be accompanied by minor geometric distortion? Some insights are available from previous work. Shaik provides an analysis in which he points out that the transition state 1 is
TABLE I: Phase Dependence of Bond Lengths (A) and Bond Angles (deg), molecule parameter gas liquid solid r(0D)
D2O D2O CH30H C2HSOH C2HSOH C2HSOH
LDOD r(C0) r(C0) r(CC) LCCO
0.96 104.4 1.42 1.43 1.51 108
'Experimental data from ref 6 ( D 2 0 ) and ref 7 ( C H , O H , even for hydrogen-bonding molecules, the differences being comparable to the uncertainties in the measurements. However, the situation for ions is less clear in view of the stronger solvation and a shortage of structural data especially for the gas phase. A par-ticularly relevant theoretical result has been obtained by Morokuma.8 He performed ab initio calculations with the 3-21G basis set on 1 and a dihydrated form with one water molecule on each chlorine. Geometry optimization showed essentially no change in the C-CI bond lengths upon addition of the two water molecules; the bonds actually shortened from 2.395 to 2.393 A.8 Our own ab initio calculations found little change in the Mulliken populations for 1 in going to its optimal monohydrated f0rm.j The computed charges at the 6-31G* level are given below and reveal charge transfer of only 0.02e to the water molecule.
CI-
- 0 293
I
,c-CI
:A
H
262 -0740
- 0 7 3 0 - 0 293
CI-,c-
H H
1
(1) For reviews, see: Nibbering, N. M. M. In Kinetics of Ion-Molecule Reactions; Ausloos, P., Ed.; Plenum Press: New York, 1979. Albery, W. J.; Kreevoy, M. M. Adv. Phys. Org. Chem. 1978, 16, 87. (2) Olmstead, W. N.; Brauman, J. I. J . Am. Chem. SOC.1977,99,4019. (3) Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J . Am. Chem. SOC. 1984, 106, 3049; 1985, 107, 154. (4) Chandrasekhar, J.; Jorgensen, W. L. J . Am. Chem. SOC.1985, 107, 2974. ( 5 ) Shaik, S. S. Prog. Phys. Org. Chem. 1985, 15, 197. (6) Narten, A. H.; Venkatesh, C. G.; Rice, S. A. J. Chem. Phys. 1976.64, 1106. Dore, J. C. J . Phys. 1984, 45, Coll. C7, 49.
0022-3654/86/2090-4651$01.50/0
1.OO-1.01 109.5 1.42 f 0.03 1.43 1S O 109
*
C2HSOH).
H *O
relatively tight with modest distortion of the C-CI bond lengths from equilibrium values for alkyl chloride^.^ Ab initio 6-31G* results predict a lengthening from 1.785 A for methyl chloride to 2.383 A for 1.) The apparent strong bonding for XCH3Xtransition states was also supported by thermodynamic arguments. This led to the conclusion that the "TS will be quite implastic and its tightness or looseness will not be strongly affected by the solvent".5 The lack of condensed-phase effects on bond lengths and bond angles for neutral molecules can be readily supported by experimental data as in Table I. As noted previously for water,6 the phase dependence of bond lengths and angles is slight
0.96-0.98 104 2 1.44 1.44 1.54 112
1'
I
+0.2(14 -0754
A
H +O
+0502
Cl----H
\
-0 932
0
+O 409
H
287
I
Thus, the available results indicate that addition of one or two water molecules has little effect on the structure and charge distribution for the sN2 transition state, 1. However, what is really desired to provide a more definitive answer to the problem is to obtain the free energy of 1 as a function of C-Cl bond length in aqueous solution. This has now been achieved through a novel combination of ab inito quantum mechanics and statistical perturbation theory. The methodology and results are summarized below.
Methodology There are two parts to the computations. First, the energy change for symmetrically stretching the C-CI bonds in 1 needs to be determined for the gas phase. This was accomplished by using ab initio molecular orbital calculations with the 6-3 lG* basis (7) Tauer, K. J.; Lipscomb, W. N. Acta Crystallogr. 1952, 5 , 606. Jonsson, P.-G. Acta Crystallogr. 1976, B32, 232. Narten, A. H . ; Habenschuss, A. J. Chem. Phys. 1984, 80, 3387. Lees, R. M.; Baker, J. G. Ibid. 1968,48, 5299. Culot, J. P. Presented at the Fourth Austin Symposium on Gas Phase Molecular Structure, 1972. Paper T8. (8) Morokuma, K. J . Am. Chem. SOC.1982, 104, 3732.
0 1986 American Chemical Society
4652 The Journal of Physical Chemistry, Vol. 90, No. 19, 1986
set. The same basis set was shown to be appropriate for our earlier determination of the minimum energy reaction path in the gas phase.3 The basis set is of the split valence type with d-orbitals on carbon and ~ h l o r i n e . These ~ calculations were performed on a Harris 800 computer at Purdue with the Gaussian 80 program.I0 The second step is to compute the relative free energy of hydration for the transition state as a function of C-Cl bond length. Molecular dynamics or Monte Carlo statistical mechanics might be appropriate, though sufficient precision cannot be achieved by performing independent fluid simulations at fixed values of the C-Cl bond lengths. However, two more sophisticated procedures featuring umbrella sampling or statistical perturbation theory are viable. These alternatives have been discussed recently in the context of computing the relative free energies of hydration for two solutes, ethane and methanol, using the perturbation approach." In umbrella sampling, a probability distribution g(r) is calculated by sampling over values of r and is related to the free energy change by w(r) = -kT In g(r).I2 Use of a biasing function allows sampling of a wider range of r than would otherwise be possible. Proper averages can be obtained subsequently by correcting for the influence of the biasing function. A series of simulations can also be run for overlapping ranges of r and the results spliced together to give the full g(r).I3 This procedure has been used to obtain the free energy profiles for the SN2reaction and an addition reaction in ~ o l u t i o n . ~ ~ ~ ~ ' ~ The perturbation approach follows from eq 1 which expresses G1- Go = -kT In (exp[-/3(Hl - H O ) ]),,
(1)
the free energy difference between systems 0 and 1 by an average of a function of their enthalpy difference. The average is for sampling based on system 0, so system 1 is treated as a perturbation. Clearly, if the systems are too different, convergence of eq 1 will be slow. However, multiple simulations may be used to connect 0 and 1 through intermediate points via a coupling parameter X (eq 2). Features e of the systems are then inter-
converted as X goes from 0 to 1. As shown previously for the ethane-methanol mutation, this procedure can yield free energy differences with excellent precision." The method also gave good results in a recent calculation of the relative free energies of hydration of CI- and Br- and of their binding to the ionophore SC-24.I5 The perturbation approach was chosen for the present calculation. Umbrella sampling would have been perfectly reasonable, though the selection of biasing functions can be problematic since it involves trial and error. The perturbation method provides better control in this sense; however, the free energy change is obtained at discrete points rather than as a smooth function of the mutation variable.
Details on the Monte Carlo Simulations A set of three Monte Carlo simulations was carried out to cover a range of C-C1 bond lengths for 1 between 2.1 and 2.7 A. The system setup was the same as before3 and consisted of 250 water molecules plus the solute in a tetragonal box (ca. 17 X 17 X 26 A) with periodic boundary conditions. The N P T ensemble was used at 25 O C and 1 atm along with Metropolis and preferential (9) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 203. Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1983, 77, 3054. (IO) Binkley, J. S.;Whiteside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S.;Kahn, L. R.; Pople, J. A. QCPE 1981, 13, 406. The Harris 800 version was kindly provided by Dr. John Yates. (11) Jorgensen, W. L.; Ravimohan, C. J . Chem. Phys. 1985, 83, 3050. ( I 2) Valleau, J. P.;Tome, G. M. In Statistical Mechanics, Part A; Berne, B. J., Ed.; Plenum Press: New York, 1977; p 169. (13) Patey, G. N.; Valleau, J. P. J. Chem. Phys. 1975, 63, 2334. (14) Madura, J. D.; Jorgensen, W. L. J . Am. Chem. SOC.1986,108,2511. (15) Lybrand, T. P.; Ghosh, I.; McCammon, J. A. J. Am. Chem. SOC. 1985, 107,1793.
Jorgensen and Buckner sampling. The water-water interactions were described by the TIP4P modelI6 while the potential functions for the water-transition state interactions were derived from ab initio 6-31G* calculations on monohydrated complexes of 1.) The latter were obtained for a C-C1 bond length of 2.383 A, the optimal value for the gas phase. For the present calculations, the variation of the potential functions for the water-transition state interactions must be known as a function of C-Cl bond length. In view of the form of the potential functions (eq 3),3 this reduces to eson m on n
emn
= C I
C (q,q,e2/rtj + A d j / r f : - CiCj/rt) 1
(3)
tablishing the variation of the charges and Lennard-Jones parameters for the C1, C, and H atoms in l. The Lennard-Jones parameters are slowly variant over the entire SN2reaction path.3 Consequently, in view of the relatively small perturbation of interest here, the Lennard-Jones parameters for 1 were kept fixed for all values of r(CC1). Specifically, the A' and values are for CI (2.6 X IO', 1500), C (8.7 X lo5, 500), and H (650, 32) in units of kcal-A1*/moland kcal.A6/mol, respectively. The key item is the alteration in the charges. 6-31G* calculations were executed for 1 varying r(CC1) in 0.1 A increments between 2.1 and 2.8 A. Optimization of the remaining variable, r(CH), was carried out at each point in D3,, symmetry; the C H bond length is nearly constant at 1.06 A. The Mulliken populations change essentially linearly over this range between values of -0.66 and -0.82 for C1, -0.43 and -0.17 for C, and +0.25 and +0.27 for H. These variations are significant and suggest more exothermic solvation with increasing r(CC1) due to the increasing charge on the chlorines and the greater separation between the centers of plus and minus charge. As illustrated above, the Mulliken charges are -0.75, -0.29, and +0.26 for CI, C, and H at r(CC1) = 2.383 A. These are similar to the values (-0.77, -0.24, +0.26) used in the potential functions derived from the ab initio calculations on monohydrated l.3Thus, it seemed reasonable to use the latter values as an anchor at r(CC1) = 2.383 8, and obtain slopes for the charge variations from the Mulliken populations. This yields eq 4-6 to express the variation in charges for 1 as a qcl = -0.7056 - 0.2276(rccl - 2.1)
+ 0.3622(rccl - 2.1) q H = 0.2512 + O.O312(rccl - 2.1)
qc = -0.3425
(4) (5) (6)
function of r(CC1). An issue at this point is whether the addition of water would significantly affect the charge distributions for 1. The results for the monohydrated complex discussed in the Introduction suggest this effect is comparatively minor. The polarization of the first-shell water molecules appears to be of greater concern. It is not accommodated by the TIP4P potential function which maintains fixed charges. The lack of such polarization effects is probably the chief source of potential error in the present study. This is a general problem in fluid simulations where the use of two-body potential functions is predominant. A more subtle point concerns the charge variations in eq 4-6. Though the shifts are in accord with expectations for aqueous solution, the actual variations are undoubtedly affected by the present use of a single-determinant wave function. Having defined the potential functions, we carried out the three perturbation calculations with double-wide sampling' centered at r(CC1) = 2.2, 2.4, and 2.6 A. Perturbations of 10.1 A around the center were made so, for example, the calculation at 2.4 A considered change to solutes with r(CC1) = 2.3 and 2.5 A. In this way, the range from 2.1 to 2.7 A was spanned in 0.1-A increments. The starting configuration for 2.4 A was taken from the earlier Monte Carlo simulation at 2.383 A.3 The calculations readily equilibrated in ca. 2 X lo5 configurations. Subsequent averaging entailed an additional 2 X IO6 configurations for each (16) Jorgensen, W. L.;Chandrasekhar, J.; Madura, J. D.; Impey, R.W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926.
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4653
Structure of sN2 Transition State
TABLE II: Energetic Results for the SN2Transition State as a
2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80
15.37 5.67 0.99 0.00 1.58 4.91 9.39 14.62
\
2.19 f 0.11 1.62 f 0.10 0.79 f 0.07 0.00 -1.16 f 0.09 -2.56 f 0.16 -4.62 f 0.19
15
17.56 f 0.11 7.29 f 0.10 1.78 f 0.07 0.00 0.42 f 0.09 2.35 & 0.16 4.17 f 0.19
i5
C-CL
12
B
'Energies in kcal/mol. bAE is from ab initio 6-31G* calculations. Total E for R(CC1) = 2.40 A is -958.61340 au. cRelative free energy of hydration from the Monte Carlo simulations. ENERGY VS.
ENERGY VS. C-CL BONO LENGTH
18
Function of C-Cl Bond Length"
2 5 r
9
'
6
z w
3
BOND LENGTH
8 0
2.10
z
CH3C\L',' A
-30
-20
710
.O .10 .20 R - RIEQI. RNGSTROMS
I
/
.30
.qO
i
.SO
Figure 1. Dependence of the gas-phase energy on C-C1 bond length for the S Ntransition ~ state and methyl chloride. Results from ab initio 6-31G* calculations. Equilibrium C-C1 bond lengths are 2.383 A for the
transition state and 1.785 8, for methyl chloride. of the three runs. The free energy differences were well converged within 1 X lo6 configurations. Spherical cutoffs were used to truncate the intermolecular interactions beyond 8 8, based on the 0-0 and C1-0 distance^.^ The Monte Carlo calculations were run on a Microvax I1 computer in our laboratory. Roughly 3 X lo5 configurations could be processed in 24 h.
Results and Discussion The energetic results from the ab initio calculations are summarized in Table I1 and Figure 1. The energy change for symmetricall stretching the C-CI bonds in 1 is given over the range 2.1-2.8 relative to 2.4 A. It should be noted that the global minimum for 1 at 2.383 8, is only 0.04kcal/mol lower in energy than for 2.40 8,. It was also verified that Djhsymmetry is still preferred at 2.8A as opposed to distortion to C , . For comparison, the energy change for stretching the C-CI bond in methyl chloride is also shown in Figure 1. 6-3lG*calculations were again used with complete geometry optimization in C,, symmetry. The minimum occurs at r(CC1) = 1.785 8,. The stretching motions for both molecules are significantly anharmonic with extension easier than compression. 1 is more deformable than methyl chloride; however, a stretching of 0.2 A still requires 5 kcal/mol, and 15 kcal/mol is needed for 0.4A. The solvation energy would have to vary rapidly to overcome this resistance. Parabolas were least-squares fit to the curves in Figure 1. Though the anharmonicity makes the fits poor, harmonic force constants of 1.70 and 3.44 mdyn are obtained for 1 and methyl chloride. These may be translated into frequencies of 684 and 746 cm-', respectively." Experimentally derived values for the force constant and frequency of the C-C1 stretch in methyl chloride are 3.50 mdyn A-' and 733 cm-'.18
K
( 1 7) Cotton, F. A. Chemical Applications of Group Theory; Wiley: New
York, 1979.
2.20
2x1
2.40
2.50
2.60
2.70
2.80
R[ C-CL I v RNGSTROMS Figure 2. Comparison of the energy in the gas phase and free energy in aqueous solution for symmetrically stretching the C-CI bonds in the SN2 transition state.
The key results from the Monte Carlo simulations are recorded in Table I1 and Figure 2. The free energies of hydration relative to r(CC1) = 2.40 8, are listed in the third column of the table. As expected, solvation is more favorable with increasing C-CI bond length. The difference of -4.6 kcal/mol in going from 2.4 to 2.88,is substantial, but it is not enough to offset the rapid rise in the intramolecular energy of 1 upon bond stretching. Combining the gas-phase energy with the relative free energies of hydration yields the dashed curve in Figure 2. This represents our best estimate of the free energy profile for symmetrically stretching the sN2 transition state in aqueous solution. Hydration appears to shift the minimum in the curve out by ca. 0.05 A. The principal effects are to make stretching easier and to increase the anharmonicity. There is a flattening of the vibrational potential curve near the minimum. Parabolic fitting predicts a red shift of ca. 100 cm-' for the symmetric stretch in going from the gas phase to aqueous solution. Overall, it is clear that hydration has little effect on the structure of the SN2 transition state as anticipated on the basis of the prior indirect e v i d e n ~ e This . ~ ~ is ~ ~the ~ case in spite of the ca. lOI5rate enhancement for the reaction upon transfer from the gas phase to aqueous solution.* The origin of the kinetic effects has been discussed at length p r e v i o u ~ l y . ~ - ~ * ~ Some more technical points should be noted. The uncertainties reported in Table I1 for the free energy changes were obtained from separate averages over blocks of 1 X lo5 configurations. They are flu and are cumulative from r(CC1) = 2.408,. The uncertainties are small, which is a principal strength of the perturbation method." The free energy differences of only 1-2 kcal/mol between increments in r(CC1) are smaller than necessary with this methodology. Differences of 4-6 kT in one step do not appear to be problematic, though further study is desirable."J5 It may also be noted that the total intermolecular energy from the Monte Carlo simulation with r(CC1) = 2.40A, -2552 f 4 kcal/mol, agrees fortuitously well with the previous result at 2.383 A, -2555 f 3 k ~ a l / m o l . However, ~ the results from the simulations at 2.2 and 2.6 8, are both -2562 4 kcal/mol. The uncertainties are large enough that conclusions of relevance in the present context can clearly not be drawn from the total energies. They are dominated by the water-water interactions with only a ca. 5% contribution from the solute-solvent interactions. The perturbation method focuses instead on the latter term since H1- Ho in eq 1 is just the difference in the solutesolvent energies for the two systems. In the present simulations average solutesolvent energies of -100, -109, and -1 1 1 were obtained with uncertainties of fl-2 kcal/mol at r(CC1) = 2.2,2.4,and 2.6 A.
*
(18) Jones, E. W.; Popplewell, R. J. L.; Thompson, H. W. Spectrochim. Acta 1965, 22, 669. Bron, J. Can .I Chem. . 1974, 52, 3078.
J . Phys. Chem. 1986, 90, 4654-4663
4654
CL-Cl RRDIRL DISTRIBUTION FUNCTIONS
1 .E-
mixture of the two effects, the reduced solute-solvent ordering at 2.2 8, is apparent in Figure 3. The C1-0 radial distribution functions obtained from the three simulations are illustrated and reveal a reduced height for the first peak when r(CC1) = 2.2 8,. Also, integration of the first peaks to the minima at 3.75 8,shows an increase in the number of nearest water molecules from 4.2 to 4.7 to 5.0 per chlorine in going from r(CC1) = 2.2 to 2.4 to 2.6 8,. The greater hydration follows from the increased charge on the chlorines and the greater separation of plus and minus charge that occur upon stretching the transition state.
l .&
Conclusion A combined approach featuring a b initio quantum mechanics
3 .O
2.E-
2.0.
and statistical perturbation theory has been used to study the influence of hydration on the structure of an SN2transition state. Hydration causes slight lengthening of the C-Cl bonds in 1, though probably less than 0.1 8,. However, the symmetric vibration is made substantially more anharmonic. The vibrational energy surface is also flatter which implies a significant red shift for the symmetric stretch upon hydration. The methodology used here appears promising for many applications including determination of reaction surfaces in solution and of relative binding constants for donor-acceptor complexes. Through this and other developments, it is now possible to perform computer simulations to expand the detailed understanding of organic reactivity in solution.
-7 I . s 1
2
3
5
r)
6
7
R
Figure 3. C1-0 radial distribution functions obtained from the three Monte Carlo simulations. Distances in angstroms.
The difference of 2 kcal/mol between 2.4 and 2.6 8,can account for nearly all of the 2.6 kcal/mol difference in the free energy of hydration (Table 11). However, the 11 kcal/mol difference between 2.2 and 2.6 8, is much greater than the 4.2 kcal/mol change in AAG. This suggests that either the solutesolvent energy at 2.2 8, is not fully converged or there is significantly greater solvent ordering at 2.4 and 2.6 8,. Though the truth may be a
Acknowledgment. Gratitude is expressed to the National Science Foundation for support of this work. The study was stimulated by discussions following the Symposium on Nucleophilicity organized by Professors S. P. McManus and J. M. Harris at the 1985 ACS Annual Meeting in Chicago.
Computer Simulations of Photochemical Water Cleavage Systems. 1. A Kinetic Model for the Production of Hydrogen on a Colloidal Catalyst Richard E. Sassoon,* Pierre M. Lenoir, and John J. Kozak Radiation Laboratory and Department of Chemistry, University of Notre Dame, Notre Dame, Indiana 46556 (Received: March 24, 1986) A mechanism is proposed for the colloidal-catalyst-mediated reduction of water to hydrogen by a reduced electron acceptor. Adsorption of several of the reactants is invoked, and electrons, hydrogen atoms, hydride ions, and molecular hydrogen, all adsorbed on the colloids, are suggested as probable intermediates. Adsorption of H+ and OH- ions onto the catalyst surface at appropriate pHs is also postulated and electrostatic factors are introduced to account for the total electrical charge carried by the colloid. Computer simulations were performed for the change in concentration with time of the reduced methylviologen cation radical, MV+, in the presence of a colloidal platinum catalyst over the pH range 1-1 1, the range investigated in earlier pulse radiolysis studies. Values of the rate constants for the individual steps in the reduction process, obtained by optimizing the fits of the computer-simulated decays and growths with those obtained experimentally,are given. The changes occurring with time in the chemical system in the pH range 1-1 1 are described in detail. The effects on the computer-simulated plots of varying several of the parameters of the system such as the initial concentration of MV+, the concentration of methylviologen, MV2+,and the concentration of platinum are also described and in most cases good agreement is obtained with experiment. In particular, deviations from a first-order dependence of the rate of decay of MV+ on colloid concentration were found in our computer simulations similar to those found experimentally, and are attributed to changes in the coverage of the colloidal particles by adsorbed species as the concentration of catalyst is varied. Possible future refinements to our proposed model are also discussed briefly.
Introduction Photochemical systems leading to the cleavage of water into its component elements have been investigated extensively in recent years particularly because of their special relevance to solar energy con~ersion.'-~In many systems electron-transfer products are formed following absorption of light in reactions of the type shown (1) Fendler, J. H. J . Phys. Chem. 1985, 89, 2730.
(2) GrBtzel, M. Acc. Chem. Res. 1981, 14, 376. (3) Kiwi, J.; Kalyanasundaram. K.; Gratzel, M. Visible Light Induced Cleavage of Water into Hydrogen and Oxygen in Colloidal Microheterogeneous Systems; Springer-Verlag: Heidelberg, West Germany, 198 1 Struct. Bonding (Berlin) 1982, 49, 31
0022-3654/86/2090-4654$01.50/0
in eq a where A represents an electron acceptor species and D
A
+D
+ k-a
A-
+ D+
(a)
an electron donor species. Since the reactions of the redox products with water are either two- or four-electron processes, much effort has been directed toward finding colloidal catalysts which may act as charge storage pools to mediate the production of hydrogen or ~ x y g e n . ~ , ~ Until now several computer simulations have been carried out on photochemical water cleavage systems in which it was attempted to give additional insights into both the mechanisms of 0 1986 American Chemical Society
