J . Phys. Chem. 1994,98, 8209-8215
8209
Molecular Dynamics Simulation of the Solvation of Benzene Anion. Structural and Dynamical Aspects Kurt V. Mikkelsen'vt Department of Chemistry, H . C. 0rsted Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen 0, Denmark
Per Linse Physical Chemistry 1 , Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
Per-Olof Astrand and Gunnar Karlstrom Theoretical Chemistry, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received: May 1 1 , 1994; In Final Form: May 26, 1994"
A dilute aqueous solution of benzene anion has been investigated by means of molecular simulation. A new benzene anion-water potential based on an ab initio approach was employed. The water molecules in close contact with the carbons displayed a strong preferential ordering and a slow diffusive dynamics due to the interaction with the charge solute. In contrast, the water molecules a t the periphery of the anion and in close contact with the hydrogens showed only a weak preferential orientation. These water molecules were able to participate in the hydrogen-bonded network in a regular way. The translational motion of the benzene anion was reduced and the anisotropy of the reorientational motion increased compared to benzene in aqueous solution. I. Introduction
11. Intermolecular Potential for Benzene Anion Radical and Water
As part of an ongoing research on improving the phenomenological understanding of electron-transfer reactions in solution,3~4we present an investigation concerning the solvation of the benzene anion radical (C6H6-). In particular, we are interested in the self-exchange reaction involving benzene and the benzene anion radical in aqueous solution. Investigations concerning the solvation of benzene, the other reactant, have already been performed.$ We present a new intermolecular potential for the interactions between benzene anion radical and water. This potential is determined from ab initio calculations and is employed in molecular dynamics simulation from which both structural and dynamical information about the solvation of benzene anion are obtained. Previously, we have utilized a rather ad hoc potential for investigating the solvation of C6H6with either a localized or a delocalized charge distribution' and noticed similarities with the work by Geiger6on solvationof anionic solutes. Later in this work, we will discuss the similarities and differences between our recent results and the results in refs 1, 5, and 6. In section 11, the new intermolecular potential for C6Hs- and H2O is presentedand thepropertiesof this potential areillustrated. Section 111 covers the model system and the simulation method used, including external conditions and the classification of the solvent molecules in different groups. Section IV contains information about the structural aspects in terms of radial and angular distribution functions and about the dynamics of solvating CaHs- represented by time correlation functions, self-diffusion, and exchange rates of water molecules between the first solvation shell and the bulk. In the final section, we summarize the conclusions drawn from the results and stipulate the implications for electron transfer between solvent-separated donor-acceptor systems. t Present address: Department of Chemistry, Aarhus University, 8000 Arhus, C, Denmark. Abstract published in Advance ACS Abstracrs, July 15, 1994.
The intermolecular potential for describing the interactions between the solute, C6H6-,and the solvent, HzO, was constructed by using the NEMO approach.' In the NEMO approach, the interaction energy between the two molecules is given by
where AE,fand EdbparetheSCFinteraction energy anddispersion energy between the two molecules, respectively. If the interaction between the two molecules is treated as a perturbation of the individual HartreeFock wave functions, the SCF interaction energy may be partitioned as
where EelDoEind, and Eind are the electrostatic, induction, and repulsive interaction energies between the two molecules, respectively. The charge distribution is represented with a multicenter multipole expansion truncated at the quadrupole moment level and with the multipoles distributed to atoms and bond centers.* The electrostatic energy is then calculated as the interaction between two such multipole expansions. The total molecular polarizability is represented as a superposition of local polarizabilities situated on each atom and bond.g An estimate of the induction energy, Ein,pt, is calculated as the interaction between the local polarizabilities and the multicenter multipole expansion of the charge distributions. Since the benzene anion radical is not a closed-shell molecule, the multipole moments and polarizations of the CsHs- anion were taken as the average of the corresponding quantities of C6H6 and CgHb2-, respectively, using the optimized geometry of C6H6-.2b The repulsion energy is obtained as
which is not strictly an exchange repulsion term only, since it also includes mixing and charge-transfer terms as well as penetration
0022-3654/94/2098-8209$04.50/0 0 1994 American Chemical Society
8210
The Journal of Physicol Chemistry, Vol. 98. No. 33, 1994
4
for the benzene anion radical, where the molecular charge is distributed all over the molecule, but it might not be negligible. The potential form adopted here was chosen in order to be consistent with the previous work on the benzene molecule.' The benzene anion has a Dzh symmetry. The D6r symmetry of benzene is reduced by a slight elongation of the two carboncarbon bonds containing virtual site c (see Figure I). In order to facilitate the comparison with benzene, we will (incorrectly) refer to the axis perpendicular to the benzene anion plane as a C6 axis. The symmetry axes in the plane will (correctly) be referred to as Cz axes.
e9
0.390 e
Mikkelsen et al.
111. Model System and Simulation Methodology
F L p 1. Partialchargedistributionfor thebenzeneanion. Themoleolle is descrikd with charges situated on hydrogen atoms and on virtual charge sits. Virtual site (I is placed 0.248A from the carbon atom and along the carbon-hydrogen bond, siteb is placed 0.256 A from the carbon atom also along the carbon-hydrogen bonds, and site cis placed in the center of the carbon-carbon bond. The DL symmetry of benzene is reduced to L h by slightly different carbon-rbon bond lengths. The lengths of the bonds containing a c site are 1.461 A, whereas the other carbon-carbon bonds have lengths of 1.387A.
TABLE 1: Coefficients for the Exchange and Dispersion Part of the Intermolecular Potential between Water and Benzene Anion. atom-atom pair
B;
C,
0-c
-1539.2 -531.6 0.0 -55.7
6382.6 2352.5 2704.2 798.8
n-C
0-H H-H a Units are in kJ mol-' and angstroms. term. and C, is the cocfticicnt for the r'
B, is the Mefticicnt for the .d term.
terms. The dispersion energy is calculated from a sitbsite London-type formula utilizing the local polarizability tensors. The details of the procedure employed here are described elsewhere.10 The potential energy hypersurface described above was simplified before being adopted in the simulation. In this work, the multicenter multipole expansion is described with a partial charge distribution as shown in Figure I. The induction and dispersion energies are grouped together and represented with a term, and the repulsion energy is fitted to a r7term. The potential has the form of a linear combination of sitbsite terms
+
where i runs over all the pairs of sites. For all atom-atom terms, the coefficients Bi and C, are given in Table I. The interactions between the partial charges on water and on the benzene anion are evaluated using Coulomb's law, thereby determining the A; coefficients. The intermolecular potentials employed in the molecular dynamics simulation are based on pairwise additive potential functions derived from ab inifio calculations. The use of pairwise additive potentials is a common approximation but should be applied with care. Thcapproximation isobviously less useful for solvation studiesof small ions" where the electric field induces a dipole moment on the shell water that is substantially larger than that for the bulk water. The effect is much maller
A molecular dynamics (MD) simulation was carried out on a model systemconsistingof 1 solute, a benzeneanionradical CsH6; and 250 water molecules. All intermolecular interactions between the solute and the water molecules were evaluated explicitly, assuming pairwise additivity. The intramolecular vibrations for the solute and the water molecules were neglected, thus, all the internal degrees of freedom are frozen. The intermolecular potential between the water molecules was taken as the TIP4P potentiallzas used in the previous studiesof benzenesand benzene anion' in aqueous solution. The solute-water potential energy for different water orientations is shown in Figure 2. The potential energies as a function ofthe intermoleculardistance along the C6and a Czaxis ofbenzene anion look rather similar to our previously utilized potential for investigating the solvation of C6H6- with either a localized or delocalized charge distribution. Our previous somewhat ad hoc potentials were constructed making use of the henzene-water potential" and changing A, coefficients according to the charge distribution. The A, coefficients changed describe the chargecharge interactions between the carbon atoms in the benzene anion and the hydrogen and oxygen atoms in the water molecules. The potential energy minimum for water molecules constrained to the C6 axis with the hydrogens pointing symmetrically toward the anion is 4 1 . 1 kJ mol-1 at an intermolecular distance of 2.75 A ktwcen the centers Of mass. The global minimum occurs at 2.74A with thcdipolcof the water molecule tilted 40' away from the c6 axis and the center of mass of water diplaccd 0.04 A from the C6 axis toward an a site. The value of the global minimum for the present intermolecular potential is 48.3 kJ mol-I, which isclosed to theoneohtained using thelocalizedchargedistribution of the ad hoc potential, 48.6 kJ mol-I. The global minimum for the delocalized charge distribution was -56.4 kJ mol-'. In the plane of the anion, the potential energy surface is much more shallow than the previous one (cf. Figure 2h) and the deviation between thepresent and theadhocconstructed potentiakis larger. The MD simulation was performed with the MOLSIM package.I4 Newton's equations of motion were integrated using the velocity form of the Verlet algorithm, and the orientations of the rigid molecules were described in a quaternion representation.ls The MD simulationutilized periodic boundary conditions together with a spherical molecular cut-offdistance. In addition, the MD simulation used a neighbor list technique with automatic check of the update interval. All interactions between atoms wereevaluated from a look-up table, and aquadraticinterpolation scheme was used. The temperature and the pressure were kept constant, using 298 K and 0.103 MPa as external values, by applying a scaling procedure from Berendsen et a1.16 with time constants of 0.1 ps. Other simulation parameters are compiled in Table 2.
I". Sinu'1tio8 Results llsermodynamics. Table 2 shows primary results such as average temperature, pressure, volume, and potential energies fromthepresentsimulationofthcbenzcneanionradicalinaqucous solution. Thctotalsolutcwatcrpotcntialcncrgyis-368kJ mol-'.
The Journal of Physical Chemistry, Vol. 98, No. 33, I994 8211
Solvation of Benzene Anion
TABLE 2 Simulation Parameters and Thermodynamic Results. no. of solutes 1 no. of water molecules 250 no. of interaction sites 1520 cut-off distance/A 9.0 neighbor list update interval/fs 10.0 time step/fs 1.o simulation time/ps 100
-
*
.
302.5 0.1 0.1 i 0.4 1836 8
(T)/K (P)/MPa
a a 3
* **
( v) /A4
(U)/kJmol-' -10419 i 5 (Uw)/kJmol-I -10051 5 (Usw)/kJ mol-1 -368 2 4 U is the total potential energy, UW the total water-water potential energy,and USWthe total solute-water potential energy. The uncertainties given are 1 standard deviation based on a division of the total run into IO-ps segments.
O"0
1
2
3
4
5
6
7
rlA Figure3. Radial distribution functionsfor benzene anion (center of mass)oxygen (full curve) and benzene anion-hydrogen (dashed curve). \
w 3
t€H -50
t & 0
2
4
1 6
8
10
rlA Figure 2. Benzene anion-water potential energy curves along the c6 axis (a) and a C2 axis (b) of the benzene anion with the water dipole vector parallel to the axis with hydrogens pointing toward (I) or away (11) from the benzene anion for the NEMO potential (full curves), the delocalized chargedistribution (dashed curves),and the localized charge distribution (dotted curves). In a, the hydrogens point toward the a sites (NEMO potential), or one of them points toward the carbon with the localized charge (localized charge ditribution). In b, the water molecule is in the plane of the benzene anion and the oxygen approaches an a site (NEMO potential) or the carbon with the localized charge (localized charge distribution). which should be compared with - 6 2 kJ mol-1 for benzene in aqueous solutions and-373 kJ mol-' for a simulation of a prototype of a large anion in aqueous solution (spherical anion with usolutbMllvent = 5.0 A).17 The previous model simulation of benzene anions in aqueous solution gave -321 and -415 kJ mol-' for the delocalized and localized charge distribution, respectively.' Structure. In Figure 3, we present the radial distribution functions (rdfs) for the center of mass of the solute and the oxygen atom of water, gso, and the center of mass of the solute and the hydrogen atom, gSH. For the rdfs, we find very prominent peaks a t 2.15 and 1.75 A, which involve twooxygens and two hydrogens,
respectively. The oxygen peak corresponds to one water molecule located above and one below the plane of the benzene anion, and the radial difference of the peaks of gso and gSH indicates that the hydrogen atoms are firmly pointing toward the solute. The two water molecules are located closer to the solute, compared to our previous simulations of a benzene anion in aqueous solution using the ad hoc potentials (cf. Figure 3 in ref 1 and Figure 2b as well as the shift of the repulsive barrier at =2 A in Figure 2a). The second peak of gso appears at 4 A and involves six water molecules which are also above or below the plane of the solute though further away. The second peak of gSH occurs at 3.2 A and corresponds to eight hydrogen atoms of which two are associated with the two water molecules located at 2.75 A and six are the hydrogens of the second class of water molecules. The second set of peaks in gSH and gso is much more well defined as compared to the rdfs obtained in our previous work.' We clearly observe a similar behavior for the arrangement of water molecules as around small anions (spherical anion with usolutbMllvcnt = 3.7 A).6 Thus, the rdfs display, as compared to our previous ones, a more structured solute-water arrangement above and below the plane of the solute, and the character of the benzene anionwater structure in this region is more along the lines of the hydration structure of small anions. For a more detailed investigation of the hydration structure of the benzene anion, water molecules have been classified into four groups according to their relative position with respect to the benzene anion. Those water molecules which are within a distance of 3.6 A from any carbon atom are regarded as belonging to group 1 (these water molecules are necessarily located above or below the plane), water molecules within 3.6 A from a hydrogen atom to group 2 (the other water molecules in the primary hydration shell), other water molecules within 7.0 A from the solute to group 3 (most water molecules in the second hydration
8212 The Journal of Physical Chemistry, Vol. 98. No. 33, 1994
TABLE 3: Classification of Water Molecules into Croups' group no. of water molecules 1 2.25 f 0.02 2 10.6 f 0.7 3 64.2 f 0.1 4 172.9 & 0.7 a Group 1 contains water molecules with the center of mass located within a distance of 3.6 A of a carbon atom in the benzene anion, group 2 water molecules with the center of mass located within a distance of 3.6 A of a hydrogen atom in the benzene anion and not belonging to group 1, group 3 water molecules with a center of mass distance to the solute smaller than 7.0 A and not belonging to group 1 or 2, and group 4 the rest of the water molecules. The uncertainties given are 1 standard deviation based on a division of the total run into IO-ps segments.
Figure 4. Angular distribution function of the angle between the benzene anion-water vector and the dipole vector of the water molecule for water molecules belonging to group 1 (full curve), group 2 (dashed curve), and group 3 (dotted curve). The horizontal solid line refers to an isotropic
distribution. 4 1 ' , ' ,
i
h
9
I
,
d
'
,
,
I
,
"
'
I
,
,
,
, ' I
3/&
/ /
/ -
~
- .._.__ - _.-. ... :..-..>..
--'=
-
*
/
--
shell), and the rest to group 4 (bulk). The exact definitions and the number of water molecules in each group are given in Table 3. Average solute-water orientations of water molecules in groups 1-3 are presented in Figures 4 and 5 by means of angular distribution functions (adfs). In Figure 4, theaverage orientation of the water dipole with respect to the solute-water interparticle vector is shown. The water molecules belonging to group 1 exhibit very strong alignment for an angle of ca. 55'. A similar tendency is seen for the water molecules in group 2, though the alignment is not as strong as for group 1. For group 2, we also notice a weak shoulder around an angle of 120'. For group 3, we still obtain a preferential orientation of the dipole vectors, but the longer solute-water distance makes the preferential orientation weak.
Mikkelsen et al.
TABLE 4 Average Number of Water Neighbors, *N, and Average Number of Hydrogen Bonds, molecule nm nnBb nnBC nnsln"b nnBlmNC water in group 1 4.19 2.32 1.30 0.55 0.31 water in group 2 4.47 3.02 1.96 0.68 0.44 water ingroup 3 4.95 3.34 2.16 0.67 0.44 water ingroup4 5.07 3.37 2.19 0.66 0.43 a Water molecules within a distance of 3.5 A are considered to be neighbors, and the subgroupof those with a pair energy lessthan a threshold value c are regarded as hydrogen bonded. The largest estimated uncertainty of and nHB is 0.03 and of nHB/nNN is 0.01. The uncertainties are 1 standard deviation based on a division of the total run into IO-ps segments. bThreshold pair energy is e = -10 kJ mol-'. Threshold pair energy is c = -16 kJ mol-'.
In comparison to our previous work,l we find a stronger preferential orientation of the water molecules. The next set of adfs in Figure 5 shows the average orientation of the OH bond with respect to the solute-water interparticle vector. The same trends as before are observed; the water molecules belonging to group 1 are very strongly aligned with the OH bond pointing toward the solute, as previously inferred. The peak at 107' is due to the other hydrogen atom, belonging to the OH-bonding water, which is not pointing toward the solute. The preferential orientation in group 2 is weaker, but still marked, whereas the preferential alignment for the water molecules belonging to group 3 is even smaller but still present. The preferential orientation of the water molecules in groups 1 and 2 together (number-weighted average) resembles that of negatively charged solutes, albeit waker. However, if we restrict the comparison to water molecules in group 1 only, the preferential ordering is considerably larger (cf. Figure 7 of ref 6 and Figure 4 and 5 ) , mainly due to the smaller solute-solvent separation. The water structure per se is examined by considering the number of water neighbors and hydrogen bonds as well as by adfs. In Table 4, we present the number of water neighbors (nm) and hydrogen bonds (nHB) for the water molecules belonging to the four different groups. We have used two energy criteria for defining intermolecular hydrogen bonds, namely, -10 and -16 kJ mol-'. The ratio between the number of hydrogen bonds and the number of water neighbors for the different groups of water molecules gives a notion of how well the hydrogen-bond network is retained in the aqueous solution. Typically, this ratio increases for hydrophobic hydrated water molecules,sJ8J9 whereas it decreases for ionic hydrated water molecules.20 This ratio is similar for the water molecules belonging to groups 2-4, while the ratio is much lower for the water molecules belonging to group 1. Thus, the (about two) water molecules in group 1, one on each side, are clearly ruptured from the hydrogen-bonding network, whereas those on the side of the benzene anion do not display any significant change. The hydration of a benzene molecule display an increase in n H B / n N N for both regions as compared with bulk.5 Thus, the influence of the change on the anion is the alternation of the hydration from hydrophobic to hydrophilic in group 1 and the neutralization of the hydrophobic character in group 2. The adfs for the interparticle water O H ...0 hydrogen-bond vector are shown in Figure 6. We observe a very similar behavior for the water molecules belonging to groups 2-4, whereas the water molecules belonging to group 1 exhibit a smaller probability of angles close to 180'. Thus, also a geometrical definition of hydrogen bonds shows that the strong electrostatic interaction between the solute and the water molecules in group 1 reduces the possibility of favorable linear hydrogen bonds. Dynamics. The exchange of water molecules initially belonging to different groups is investigated using reduced propagators. Let the propagator P(I',tlI',O)denote the probability that a water molecule belongs to the group I' at time t, if it belong_ed to the same group at time zero. The reduced propagator P for the
The Journal of Physical Chemistry, Vol. 98, No. 33, 1994 8213
Solvation of Benzene Anion
6 A
1, i
I,:
molecule
I
Dda
DVtCP
,
9g 4[
8
TABLE 5: T r ~ ~ ~ ~ l aSelf-Diffusion tio~l Coefficient, O/W9 m2s-l, for Benzene Anion and Water Molecules in the Different Groups
1
I \
.. .. . . ' ' ' ' -,- . .....____ -0.8 -0.6 -0.4 -0.2 0 cos yono Figure 6. Angular distribution function of the angle between the waterwater interparticleoxygen-oxygenvector and the OH-bond vector of one of the water molecules for water molecules belonging to group 1 (full curve), 2 (dashed curve), and 3 (dotted curve). The horizontal solid line refers to an isotropic distribution.
0 -1
'
'
'
I
'
'
'
exchange process is defined as
P(r,tlr,o)= where p(I',OlI',O) = 1 and P(r,=(I',O)= 0. The exchange time is defined as the time integral of the reduced propagator according to
We have calculated the exchange times using eq 6 for the interval 0-10 ps and used an exponential continuation for t > 10 ps with the time constants for the exponential continuation obtained from the behavior of the reduced propagators in the 5-10-ps interval. For water molecules belonging to groups 1, 2, and 3, we obtain theexchange times 10 f 1,4.6 f 0.5,and 4.0 & 0.4ps, respectively. The larger exchange time for the water molecules belonging to group 1 is again associated with the larger attraction between the molecules and the anion. The translational motion is analyzed in terms of the meansquare displacement (msd) and the velocity correlation function (vtcf). The translational diffusion coefficient can be calculated either from the long-time limit of the msd according to
D = 1imt-.= ([r(t) - r(O)I2)/6t
(7)
or from the integral of the vtcf
D = (1/3)
s," ( v ( O ) ~ ( t ) ) dt
where (...) is an ensemble average and r(t) and v(t) are the timedependent position and velocity vectors, respectively. Since the correlation time of the vtcf is at least an order of magnitude smaller than T ~it ~is possible , to obtain D for water molecules in the different groups using the linear behavior of the msd up to t == T ~ Table ~ . 5 shows that the translational self-diffusion of the benzene anion is reduced by a factor 2.5 compared to bulk water (water in group 4). The self-diffusion of water molecules close to the benzene anion is also reduced but by 25-50%. In the study of the hydration of a benzene molecule, it was found that the self-diffusion of the benzene molecule was about two-thirds of the bulk water and the water self-diffusion in the hydration shell was reduced by only ==lo%.We also note that the self-diffusion of the bulk water in the present study, 4.7 X 10-9 m2 s-1, is higher than that obtained in the simulation of the benzene molecule, 3.4 X 10-9 m2 s-1.5 (The incomplete sampling of the phase space is probably the reason for this difference. A new simulation with
. \ . \
>o.>i .
\
c, axis -'
-0.5 0
0.2
0.6
0.4
0.8
1
I ps Figure 7. Velocity time correlation function along the c6 axis and along a Cz axis of the benzene anion. t
c, axis
0.8 \ \
0.41
.... c,axis
.'.
2
3
i i
0.2 0.0
0
1
4
5
t Ips
Figure 8. Angular time correlation function for the c6 axis and for a C2
axis of the benzene anion. different initial conditions gave 3.8 X le9m2 s-I for bulk water in the present system.) The vtcfs for the benzene anion along the CSand C2 axes are presented in Figure 7. The initial decay of the vtcf along the Ca axis is faster than the one along the CZaxis. The negative part of the vtcf along the CZaxis that appears between 0.2 and 0.6 ps illustrates a cage effect. The comparison with the vtcf for benzene in a dilute aqueous solution shows a somewhat stronger cage for the benzene anion than that for the benzene molecule. The rotational motion is described by angular time correlation functions (atcfs) and angular velocity time correlation functions (avtcfs) of the molecular principal axes. In Figure 8, we present atcfs for the solute, and a much slower reorientation of the C, axis than of a C2 axis is observed. The reorientations are much slower than for benzene in aqueous solution. From the avtcfs in Figure 9, we observe how the spinning of the benzene anion around its molecular axis is affected by the surrounding water molecules. The rotation around the Cz axis is strongly hindered as illustrated by the oscillating behavior of the avtcf for the Cz axis. The observed cage effect is much stronger than that for benzene in aqueous solution.5
8214 The Journal of Physical Chemistry, Vol. 98, No. 33, 1994
Mikkelsen et al.
TABLE 7: Reorientational Correlation Times, r/ps, for the Principal Axes of the Water Molecules in the Different Groups. molecule water in group 1 water in group 2 water in group 3 water in group 4
0.6 0.8 1 t Ips Figure 9. Angular velocity time correlation function for the c6 axis and for a C2 axis of the benzene anion. 0
0.2
0.4
TABLE 6 Rotational Diffusion Coefficient, 8/ps, for Benzene Anion e1a 61b gll a 611 b 0.011 f 0,001
0.004 f 0.001
0.26 f 0.03
0.23 f 0.04
a Calculated from the angular time correlation function using the firstorder Legendre polynomials and a least-squares exponential fit for the interval 1-10 ps. Calculated from the integral of the angular velocity time correlation function using the time interval 0-1 ps.
Assuming diffusive rotational motion, the rotational diffusion coefficients are obtained from the long-time behavior of the atcfs or from the integral of avtcfs. For a symmetric top, the diffusion coefficients for the rotation perpendicular and parallel to the molecular plane is given by fitting the atcfs to exp[-281t] and exp[-(@ Oll)t], neglecting very fast librational modes. From the avtcf, the rotational diffusion coefficients are given as
+
0' = JOm
72
T J
TP
3.6 2.9 2.7 2.6
7.8 4.4 3.6 3.4
5.8 3.1 3.7 3.4
a Calculated from the least-squares exponential fits of the angular time correlation functions for the time interval 1-5 ps. The largest ' a vector parallel to the estimated uncertainty is 10%.b ~ denotes intramolecular vector between the two hydrogen atoms. c y' denotes a vector perpendicular to the plane of the water molecule. z'denotes a vector parallel to the dipole vector of the water molecule.
to the van der Waals attraction, a weak electrostatic interaction (the quadrupole-quadrupole interaction is the leading one); in case ii, the solute-solvent electrostatic interaction is stronger (quadrupole-dipole interaction), whereas in the last case, the rotational motion of the charged solute is strongly impeded by nearby solvent molecules attracted by the strong electrostatic interaction (charge-dipole). Finally, the reorientation of water molecules in the different groups will be considered. A comparison of the reorientation correlation times for the three principal axes of water (Table 7) with those for water molecules in an aqueous solution of benzene (Table 5 of ref 5) shows somewhat larger correlation times (slower dynamics) in the present work. In particular, water molecules in group 1have substantially larger reorientation correlation times compared to the water molecules in the three other groups. This comes as no surprise given the properties of the intermolecular potential between water and benzene anion and the static results from the MD simulation.
V. Conclusion (w'(O)w'(t))
dt
(9)
and similarly for 811.21 Table 6 shows the two rotational diffusion coefficients for the benzene anion in aqueous solution, again treating the benzene anion as a symmetric top. We observe that the rotational diffusion coefficients for benzene anion in aqueous solution are smaller by more than a factor of 2 compared to those for benzene in aqueous solution ( 8 1 = 0.06 and 811 = 0.6 ps).5 The ratioOIl/P givesan idea of theanisotropy of therotational motion, this ratio being much larger for benzene anion (=40)than for benzene (IO) in aqueous solution. The vtcf, atcf, and avtcf show that the short-time vibrational and librational motions of the benzene anion have a higher frequency and the accompanied diffusion coefficients indicate a slower long-time diffusive motion compared to benzene in aqueous solution. The origin of this difference is the strong electrostatic attraction of a few water molecules on either side of the plane of the benzene anion causing a higher hydrogen density above and below the plane. These hydrogens create a narrow and steep potential well for the tumbling motion of the benzene anion. The reduction of the spinning motion is less and is likely due to the variation of the electrostatic potential above and below the plane due to the reduced symmetry (as compared with benzene) of the position of the charges (cf. Figure 1). At this stage, it is also interesting to compare the above with the motion of benzene in pure benzene.21 Considering the three cases, (i) pure benzene, (ii) benzene in aqueous solution, and (iii) benzene anion in aqueous solution, we find an increased cage effect both in the vtcf and avtcf as well as a slower decay of the atcf in the sequence i to iii. Moreover, the rotational anisotropy, expressed as ell/@, increases from 2.5 to 10 to -40. Although the geometry of the solute is almost the same in the three cases, the nature of the solute-solvent and solvent-solvent interaction strongly influences the dynamics. In case i, there is, in addition
The structural analysis shows that the overall hydration of the benzene anion is clearly influenced by the negative charge, and we find differences in comparison to our previous simulations utilizing ad hoc intermolecular potentials for the interactions between the benzene anion and the water molecules. It is rather clear when comparing with the results of Geigeld that the hydration resembles that of small anions but is more complex due to the nonspherical shape. At the periphery of the benzene anion, the influence of the net charge is reduced in such a way that the capability of the water molecules to participate the hydrogenbonding network is no longer reduced. The fact that the water molecules located above or below the plane of the benzene anion and close to it have a very different behavior compared to the ones in the other groups illustrates the need for introducing explicit water molecules around and between the reacting electron donor-acceptor compounds when calculating the rates/probabilities of electron transfer, but it also implies that a description of the polarization effects with explicit polarizabilities may be important.
Acknowledgment. This research was supported by Statens Naturvidenskabelige ForskningsrHd, Denmark, and the Swedish Natural Science Research Council (NFR). A grant from Kungliga Fysiografiska Sallskapet, Lund, is gratefully acknowledged. References and Notes ( 1 ) Linse, P.; Mikkelsen, K. V. J . Phys. Chem. 1991, 95, 4843. (2) (a) Mikkelsen, K. V.; Dalgaard, E.; Swanstrem, P. J . Phys. Chem. 1987,91, 3081. (b) Mikkelsen, K. V.; Ratner, M. A. Int. J. Quantum Chem. Symp. 1987, 21, 341. (c) Mikkelsen, K. V.; Ratner, M. A. Ibid. 1988, 22, 707. (d) Mikkelsen, K. V.; Ratner, M. A. J. Phys. Chem. 1989, 93, 1759. (e) Mikkelsen, K. V.; Ratner, M. A. J . Chem. Phys. 1989, 90, 4237. (3) (a) Ulstrup, J. Charge Transfer Processes in Condensed Media; Springer Verlag: Berlin, 1979. (b) Newton, M. D.; Sutin, N. Annu. Reu.
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