A quantum chemical investigation of the anisole radical cation with

6811

J . Phys. Chem. 1991,95, 6811-6819 uid-phase collisions and simple energy-transfer theory, considering the approximations made in both theories and the experimental uncertainties in the relaxation data. The relaxation rates in the cryogenic liquids are consistent with the picture of V-T relaxation in the liquid as the result of repulsive, isolated binary collisions similar to the effective collisions in the higher temperature gas phase. More accurate modeling of liquid-phase vibrational re-

laxation rates for OCS and O3probably requires a careful consideration of the nonspherical nature of the intermolecular potentials.

Acknowledgment. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S.Department of Energy.

A Quantum Chemical Investlgatlon of the Anlsole Radical Cation with Incluslon of Aqueous Solvation Effects Vinzenz BacMer,* Steen Steenken, and Dietrich Schulte-Frohlinde Max- Planck-Institut far Strahlenchemie, Stiftstrasse 34-36, 0-4330 Miilheim a.d. Ruhr. Germany (Received: October 10, 1990)

Open-shell restricted SCF calculations were performed on the anisole radical cation which yielded spin densities at the various ring carbon atoms. By use of the McConnell relationship the calculated spin densities were correlated with the experimentally known ESR hyperfine coupling constants of the ring hydrogens. The correlation between theory and experiment is only fair. It can be improved by considering the effect of solvation on the spin density distribution in the anisole radical cation. This is done by using a new and simple screening method which consists of modifying the one-electron potential at those atoms effected by solvation.

1. Introduction

Radical cations are important intermediates in organic chemistry.’ A pathway for the radiation-induced damage of the biologically unique DNA molecule leading to strand breakage is believed to be driven by radical cations of nucleic acids.* Many radical cations enter into a wide range of chemistry which is related to physical properties of the reactant radical cation. Important properties are the charge and spin density distribution of radical cations which are accessible by quantum chemical calculations. Radical cations, however, are open-shell systems and they are harder to treat theoretically than closed-shell molecules. This fact implies the need for experimentally well characterized radical cations which can serve as test molecules for theoretical approaches. The spin density distribution of a radical cation is a property of special importance. Those radical cations are appropriate test molecules where the spin density at various locations of the molecule is different and well characterized experimentally. These requirements are well met by the anisole (methoxybenzene) radical cation. ONeill et al. determined five different ESR hyperfine coupling constants for the hydrogen atoms of the phenyl ring and one constant for the methyl The coupling constants of the anisole radical cation”‘ were determined in aqueous solutions. A standard quantum chemical calculation, however, provides coupling constants for the isolated molecule in the gas phase only. The anisole radical cation is a positively charged solute and a strong electrostatic interaction between the solute and the polar water molecules of the first solvation shell should occur. Consequently, gas-phase properties of the anisole radical cation could be significantly modified in aqueous solution by the surrounding water molecules. Thus, there is a need to apply a quantum chemical procedure which comprises the effect of the solvent on the solute. Consider a solution where a solute molecule is surrounded by solvent molecules. The solute molecule alone is characterized by ~

~~~~

(1) Roth, H.D. Acc. Chem. Res. 1987,20, 343. (2) Sonntrg, C. v. The Chemical Basis of Radiarion Biology; Taylor Francii: London, 1987; p 105. (3) O’Ncill, P.; Sttenken, S.;Schulte-Frohlindc. D. J . Phys. Chem. 1975. 79, 2173. (4) Stmken, S.; O’Ncill, P.;Schulte-Frohlinde. D. J. Phys. Chem. 1977, 81, 26.

0022-3654/9 1/2095-68 11S02.50/0

the Hamiltonian Hoand we can construct a single determinantal wave function @o such that the expectation value Eo

is a minimum. This requirement leads to the well-known Hartree-Fock equation^^.^ which are the basis of most ab initio methods. However, we are not primarily interested in the prop erties of the isolated solute, but how the solvent influences properties of the solute. This influence can be characterized by an operator V and a new variational calculation with the new operator Ho Vcan be carried out

+

+ v@)

E = (91Ho

(2)

In the following we give a short overview of available procedures for constructing the operator Vwhich introduces the solvent effect into a quantum chemical calculation. If Vexplicitly characterizes a number of solvent molecules, we arrive at the supermolecule approach for solvent effects? The advantage of this procedure is the accuracy with which the interaction of the solute with a number of solvent molecules can be treated. However, solvent bulk properties as characterized by the dielectric constant are not considered. Methods based on the reaction field are important for describing solvent effectsS8 The charge distribution of the solute molecule induces a dipole moment in the solvent molecules. These induced moments produce a reaction field having a feedback on the original charge distribution of the solute.8 This approach led to an effective Hartree-Fock operator for solvent effects derived by means of the variational prin~iple.~A general approach is the direct reaction field method.1° There, the solvent is simulated by a number of point polarizabilities.1° Moments are induced in the solvent by the field ( 5 ) Roothaan, C. C. J. Rev. Mod.Phys. 1951,23,69. (6) Roothaan, C. C. J. Rev. Mod.Phys. 1960,32, 179. (7) PuUmn, A. In The New World of Quantum Chemistry;Pullman, E., Parr, R., Us.; Reidel: Dordrccht, 1976. pp 149-187. (8) Wtcher, C. J. F. Theory of Elecrric Polarizarion;Elscvier: New York, 1973; Chapter IV. (9) Tapia, 0.;G d n s k y , 0.;Mol. Phys. 1975, 29, 1653. (10) Thole, E. T.; van Duijnen, P. T. Theor. Chim. Acta 1980, 55, 307. Thole, B. T.; van Duijnen, P. T. Chem. Phys. 1982, 71, 21 1.

Q 1991 American Chemical Society

Bachler et al.

6812 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991

made up by the solute charges.1° A reaction field operator is derived accounting for the influence of the induced moments on the solute.10 An iteration process could be applied to make the reaction field selfconsistent.I0 Another interesting procedure is the polarizable continuum model." Here, a cavity around a solute molecule is constructed as an ensemble of interlocking spheres. The centers of the various spheres are at the positions of the corresponding atoms of the solute. The charges of the solute molecules are assumed to induce charges on the spheres and an electrostatic interaction operator Vis constructed. By using V, new charges of the solute molecule are calculated." The whole process is continued until self-consistency is attained." A much Here, each solute atom simpler procedure is the solvaton is assumed to be surrounded by an imaginary particle, called the solvaton which has a charge of opposite sign but of the same magnitude as the atom under consideration.I2 In the virtual charge model,13the polarizing charges simulating the solvent are located on spheres surrounding the solute atoms. The effect is to modify the charges of the solute molecule^.^^ The solvaton approach12 and the virtual charge modelI3employ Born type expressions for the solvation energy. There are, however, problems about the physical meaning of these energy expressions. A careful assessment led to the conclusion that they also comprise the internal energy and entropy of the so1vent.l' An appealing way to simulate solvation is the empirical valence bond model for solvation effects;1s an operator Vis used to simulate soluttsolvent interactions which modify the energies of the ionic valence bond ~tructures.'~The energy corrections enter the diagonal matrix elements of the Hamiltonian which refer to ionic valence bond structures of the solute.'s Another appealing way to simulate solvation is to use an operator V made up of discrete point charges.I6 There, the solvent molecules surrounding the solute are simulated by fractional point charges located at the positions of the solvent mole c ~ l e s . 'The ~ presence of the solvent is manifested by new nuclear charges which enter the H F operator for the solute.I6 A similar point charge model has been implemented at a semiempirical level." The anisole radical cation represents a positively charged solute. In an aqueous solution it is surrounded by water molecules having a permanent dipole moment made up by the negative and positive charges at the oxygen and hydrogens, respectively. Thus, the soluttsolvent interactions should be dominated by the interaction of permanent charges. Indeed, about 75% of the total free energy of hydration for the sodium ion arises from classic ion-dipole interactions.I8 Therefore, an electrostatic point charge model for the solvent would be suitable for treating the solvation of radical cations. In the following sections we develop and apply a new simple electrostatic screening procedure. It permits to incorporate into a molecular orbital calculation the influence of the solvent charges on a solute. Central is the notion that the one-electron potentials of the solute electrons are modified by the permanent charges of the solvent molecules. It is illustrated how this feature can be simulated by a modified nuclear charge seen by the affected electrons.

2. A Modified Potential for an Electron Moving around a Nucleus in the Presence of an Electric Charge The most simple model for a solute-solvent system is represented by an electron moving around a nucleus (solute) in the (11) Miertus, S.;Scrocco, E.; Tomasi, J. Chem. fhys. 1981, 55, 117. Miertu, S.; Tomari, J. Chem. Phys. 1982.65, 239. (12) Klopman, 0 . Chem. Phys. Lrr. 1967, I , 200. (13) Constanciel, R.; Tapia, 0. Theor. Chim. Acra 1978, 18, 75. Constancicl, R. Theor. Chfm. Acra 1980, 51, 123. (14) Blaive, B.; Mdzger, J. Nouu. 1. Chim. 1983, 7, 361. Blaive, B.; Metzger, J. Nouu. J . C h h 1983, 7, 365. (IS) Warshel, A,; Weiss, R. M. J . Am. Chem. Soc. 1980, 102, 6218. Warshel, A. J . Phys. Chem. 1982,86,2218. (16) Nall, J. 0.; Morohma, K. Chem. Phys. Lrr.1975,36,465. Noell, J. 0.;Morokuma, K. J . fhys. Chem. 1976,80, 2675. (17) Spnget-Lsrscn, J. Theor. Chim. Acra 1978, 47, 315. (18) Conway, B. E. Ionic Hydration in Chemistry and Biophysics; El(Icvier: New York, 1981; p 321.

Z A

F i e 1. Spherical coordinate system and related quantities. The point

P designates the position of an electron moving around the nucleus with

charge Z. The electron is characterized by the coordinates r,,, ,e, and 4r The electric charge q, is fixed at position i in space.

presence of an electric charge (solvent). We use this model system to develop a simple theoretical procedure for treating a solute molecule in the environment of the solvent. Consider a nucleus with a nuclear charge Z situated at the origin of a spherical coordinate system (see Figure 1). We have an electron at point P in space characterized by the three spherical coordinates, rp Op and 4p(see Figure 1). In addition, we assume that an electric charge 4, is placed at a fixed position i in space given by definite values for the coordinates r,, e,, and 4,. Our aim is to determine the electrostatic potential which the electron experiences while moving around the nucleus. The one-electron operator describing the electrostatic interactions is (3) 'P

The first part of eq 3 is the electrostatic part of the one-electron operator for a central field problem as treated in the quantum mechanical solution for the hydrogen atom.I9 The second part of eq 3 is a very simple ligand field operatorm for the interaction of the electron and the ligand charge 4,. In the following, we focus on the second part of eq 3. From the law of cosines for a plane triangle,2' it follows that (4)

where w is the angle between the lines origin-p and origin4 (see Figure 1). Abbreviating cos w as A, we can write

Now we make the assumption that the electric charge q, is far apart from the hydrogen-like atom such that r, > rp holds. The inverse square root of eq 5 can be expanded into a power series provided 51

holds. Given the fact that A can only vary between -1 and 1, a simple analysis shows that the square root of eq 5 can be expanded provided the distance ri is larger than the distance rp by a factor of at least 2.414. This condition seems to hold for most distances between a solvent molecule of a first solvation shell and the solute (19) Pauling. L.; Wilson, E. B. Introduction to Quantum Mechanics; McGraw-Hill: New York, 1932; Chapter V. (20) Schuster, P. Ligandenfeldtheorie; Verlag Chemic: Wcinheim, 1973; Chapter 2.2. (21) See for example: Spicgel, M. R. Murhemarical Handbook ofFormulas and Tables; McGraw-Hill: New York, 1968; p 19.

The Journal of Physical Chemistry, Vol. 95, No. 18, 1991 6813

The Anisole Radical Cation electron it influences. By means of the well-known binomial series, we can expand the square root in eq 5 up to the third power of rpJriand we derive

This expansion of the inverse distance of d is a well-known series: the factors of the various powers of rp!ri are the Legendre functions with argument A.22 For realistic distances between an electric charge of a solvent molecule and an electron of a solute, it seems legitimate to neglect the third-order terms in eq 7. By reintroducing the abbreviation for A, we write

1d = I ri [ 1 - L( 2 2 ri ) +

(z)

cos w

+ ?( 2 2 ri ) cos2 u ]

(8)

Thus, the inverse distance d is a function of r,, rp and cos w. Now, instead of employing eq 8 containing the explicit dependence on w, we want to derive an approximate expression where an average w dependence is used. Therefore, we write

All we have to do is to evaluate the average cos u and cos2 w. This is accomplished by using the mean value theorem of the integral calculus23and we obtain

pendence on flP and tpP is not explicitly considered. This confines the procedure to an isotropic screening of a solute atom by a solvent charge. Thus, we expect that the polarization of the solute by the solvent charges is only approximately described. This isotropic screening implies also that the screening function u is independent of the actual position of the polarizing charge qi in space. Only the distance ri is relevant. The screening function u was derived by employing the Legendre polynomial expansion for the potential which an electron experiences from one single solvent point charge. The expansion was centered around one atomic center of the solute. Generally, a solute comprises several atoms and the first solvation shell can be considered as an ensemble of a large number of point charges. The above derivation can be performed consecutively for any pair made up of a solute atom and a solvent point charge. At any solute atom Legendre expansions are centered and their number is identical with the number of solvent point charges considered. Thus, any polarizing solvent charge contributes additively to the total screening. In order to calculate the electrostatic interaction energy between two molecules, it was suggested to expand the charge distribution of the molecules by several multipole expansions where each of them is centered at an atom of the molecule.24 The total interaction energy is a sum of interactions of local multipoles.3 Our proposed screening procedure implies a similar additivity scheme. In the later applications we neglect the explicit rp dependence of u (see eq 13). Instead, we have recourse to the fact that the electron prefers a distance re which is the radius of maximum charge density. This restriction transforms the screening function u into a screening constant. If the affected electron belongs to a hydrogen atom, we obtain r

0.529167 uH

We are now in position to derive an electrostatic potential operator for an electron subject to the attraction of the nucleus and the additional charge 91. Using the approximation 10 and eq 3, we write

+

= 411

10.5291673 4

r?

uc

where the function u has the form

Equation 12 shows that the impact of the solvent charges q, on a solute can be simulated in a solute calculation by using effective nuclear charges 2 in the expression for the solute one-electron operator. These effective nuclear charges are the original solute nuclear charges modified by the screening function u (seeeq 12). This simple function has been derived by characterizing the electron position only by means of the space angle w and the distance rp (see Figure 1). For a definite angle w , however, a manifold of electron coordinates 0, and tpp exists and this de(22) See ref 8, p 25, q 1.43. (23) Wygodski, M. J. Hbhcre Mathematik GrljJIJcreit;Vieweg: Braunachweig, 1977; p 451.

J

(14)

where the radius of maximum charge density here is the Bohr radius. In case the electron is a 2s or 2p electron of a carbon atom, the radius of maximum charge density is 0.65 This leads to I

I

Thus,the electron experiences not only the nuclear charge 2,but a charge modified by the last part of the numerator of eq 11. This is more concisely given by

. I

=

0.65

+

1 0.653

4 r,’J

The character of the above expressions suggests that we can simulate the impact of solvent point charges on a solute by modifying the nuclear charges of the solute. These screened nuclear charges enter into the one-electron part of the H a r t r e t Fock operator for the solute. A modified one-electron potential is also used in the surface constrained soft sphere dipole model.26 There, the solvent molecules surrounding the solute are represented by point dipoles located at the centers of adjustable spheres.26 The energy of the solute in the solvent cavity is calculated by including solutesolvent dipole interactions in the diagonal elements in the solute Hartree-Fock matrix.26 In the virtual charge technique” the oneelectron operator is also modified by additional charges.” These charges are induced by the solute charges and they depend on the dielectric constant of the medium. In the screening model suggested above, however, permanent charges of the solvent molecules are employed. Such a concept seems to be reasonable for ionic aqueous solutions for which the procedure is designed primarily. In the virtual charge model, the induced charges are located on spheres surrounding the solute atoms.I3 In the screening procedure, however, the permanent charges are assumed to be at fixed positions around the solute. Thus, a fairly detailed picture, at least (24) Claverie, P. In Localization and Deloealization in Quantum Chcm; istry; Vol. 11, Chalvet, O., Daudel, R.. Diner, S.,Malrieu, J. P., Us.Reidel: Dordrecht, 1976; Vol. 11, p 127, (section 8). (25) Fraga, S.;Karwowski, J.; Saxcna, K. M. S. Handbook of Atomic Data; Elsevier: New York, 1976; p 71, tab. 11. (26) Warshcl, A. J . Phys. Chem. 1978, 83, 1640. Warehel, A. Chrm. Phys. Lett. 1978, 55, 454. Warshel, A. J . Phys. Chem. 1979, 83, 1640.

Bachler et al.


z

10

9

t 1.4

11

12

13

Figure 3. Numbering and calculated geometry of the anisole radical

Figure 2. Mutual orientation of a water molecule and a positively charged solute atom during interaction. The water geometry and Mulliken charges are indicated. TABLE I: Screening Constants u,,, for a Positively Charged Hydrogen a d a Podtirely Charged Carbon Atom of a Solut@ rl,A

d W

1.00

-0.224 -0.106 -0,061 -0.040

1.50 2.00 2.50

.ca(C) -0.291 -0.134

-0.077 -0.050

r1,A 3.00 3.50 4.00

4H)

.,(C)

-0,028 -0,021 -0.016

-0.035 -0.026 -0.020

OThe constants uta are recorded as a function of rl the distance between the atom screened and the oxygen atom of the water molecule (see Figure 2). of the first solvation shell, is desirable for an application of the screening procedure. This concept is pursued in the later sections where the model is applied to the anisole radical cation.

3. The Screening of Hydrogen and Carbon Atoms by a Water Molecule In the previous section, the impact of a single point charge q, on an electron moving around an atomic nucleus was studied. We have seen that this influence can be simulated by a screened nuclear charge which determines the potential for the solute electron. In this section we obtain numerical values for u when screening by three point charges is effective, namely the point charges of a water molecule. Let us focus on a positively charged hydrogen atom of a solute which interacts electrostatically with a water molecule of the first solvation shell. Because negative charge is situated at the water oxygen but positive charges at the two water hydrogens, a mutual orientation is energetically favorable as shown in Figure 2. When water is calculated by using the 6-31G basis set,27the Mulliken population analysis2*gives charges at the oxygen and hydrogen atoms of 4 . 8 6 6 and 0.433, respectively. We used these values as the p i n t charges qr. The pertinent water bond distances and the bond angle are recorded in Figure 2. In order to obtain a total screening constant u, eq 14 was applied consecutively for the oxygen and the two hydrogen charges. Their distances from the origin are rl and r2, respectively (Figure 2 ) . The suggested procedure is very similar to the classic ion-diple interaction model for solvation.29 There an alkali-metal ion is placed at the origin of a coordinate system and Coulomb's law is used to calculate the electrostatic solvation energy.29 Here, we are not primarily interested in the solvation energy, but in the screening exerted by the water molecule. In the second column of Table I total screening constants u,(H) for a hydrogen atom are recorded for various hydrogen water distances rI. The negative values indicate that the nuclear charges of a screened solute hydrogen should (27) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Inirio Molecular Orbiral Theory; Wiley: New York, 1986; p 337, fig. 6.35. (28) Mulliken, R. S.J. Chem. Phys. 1955,23, 1833, 1841, 2338, 2343. (29) For a review see: Conway, B. E. Ionlc Hydrarfon In Chemlsrry and Blophyslcs; Elsevier: New York, 1981; Chapter 15,

cation. Distanchs are given in angstroms and angles in degrees.

become smaller. Moreover, we see that screening is a long-range effect. Even at a distance of 4 A there is appreciable screening. The screening for a positively charged carbon atom um(C) of a solute was calculated in the same way but by means of eq 15. The results are recorded in the third column of Table I. Since the radius of maximum charge density for the 2s and 2p electrons of a carbon atom is larger than the Bohr radius (see eqs 14 and 15), a slightly larger screening is obtained for carbon than for hydrogen (Table I). In the following sections we apply the screening procedure to the anisole radical cation being surrounded by water molecules of the first solvation shell. In particular, we illustrate how screening improves a correlation between calculated spin densities and the experimental hyperfine ESR constants measured in aqueous solution.

4. Applied Metbod and Geometry for tbe Anisole Radical Cation All calculations were performed on a VAX-station 3200 and we applied the TURBOMOLE system of programsMas developed by Prof. Ahlrichs and his group. The characteristic feature of its SCF part is that a continuous transition between the conventional and the direct SCF approach can be made. In a conventional calculation for the anisole radical cation all two-electron integrals would be calculated once and stored on a large amount of disk space. The large integral file would then be processed in any SCF cycle. In the direct SCF approach the large disk space requirements would be avoided because in any SCF cycle the two-electron integrals are recalculated. This procedure, however, iS bound to a large amount of CPU time. We used the "RBOMOLE program to blend the two approaches for making a compromise between the required disk space and the CPU time needed. The anisole radical cation was treated by employing the restricted open-shell HartreeFock procedure.6 For the carbon and oxygen atoms, a basis set of (8s4p/4s2p) quality" was used. We employed a (4s/2s) basis32for the hydrogen atoms. A complete geometry optimization was performed by using the analytical gradient and the Hessian update components of the TURBOMOLE program systemg0 At the applied minimal geometry, the norm of the gradient vector was 0.54 X The calculated internal coordinates for the minimal geometry of the anisole radical cation are recorded in Figure 3. An average value of 1.36 A is obtained for the C3-C4and the C6-C7bonds. All other ring C-C bonds have the larger value of about 1.42 A. In addition, the C& bond length turned out to be 1.30 A which is a rather small value. The derived bond length alternation in (30) Hiser, M.; Ahlrichs, R. J. Compur. Chem. 1989, IO, 104. Ahlrichs, R.; Bar, M.; HILser, M.; Horn, H.; Kblmel, C. Chem. Phys. h r r . 1989, 162, 165. (31)

Huzinap, S.Approximate Atomic Wave Functiom, Department of Chemistry Technical Report, University of Alberta, Edmonton, Alberta, Canada 197I (32) Dunning, T. H.; Hay, P. J. Gaussian Basis Seta for Molecular Calculations. In Merhods of Elecrronic Srrucrure Theory;Schaefer, 111. H. F., Ed.; Plenum: New York, 1977; Tab. A.2. I


The Anisole Radical Cation 0.201

0.200

1’I

0.182

.--f

-0.570

0.211

0.204

0.111

F’igure 4. Charge distribution of the anisole radical cation as indicated

by the Mulliken population analysis. The positive charge is located at the hydrogens and at the carbon atom C1only.

the phenyl ring (Figure 3) and the short CI-08 bond (Figure 3) supports the notion of O’Neill et al. that the anisole radical cation is properly described by a chinoid form.3 One feature of such a chinoid form is a partial double bond character of the C1-08 bond. The calculated short bond distance of 1.3 A indicates that the K orbitals of the atoms CI and O8overlap significantly and a rotation about the C1-08 bond should be partially inhibited. This notion is also supported by the fact that not three but five different ring hydrogen hyperfine coupling constants were observed in the ESR spectrum.” Recently, the geometry of the neutral anisole has been calculated by using an extended basis set with polarization functions.33 By comparing our derived geometry for the radical cation with the geometry for the neutral closed-shell molecule3’ we are led to the conclusion that bond length alternation is important only in the radical cation. It is interesting to compare the calculated geometry with the experimental geometry of pdimethoxybenzene.” This molecule has a C, geometry, but the phenyl ring is highly distorted: all ring bond lengths have the value of 1.36 A, except the CI-C7and C , X 5 bonds which are elongated to 1.44 A. Thus, our calculation for the anisole radical cation yields a bond length alternation similar to the one observed in p-dimethoxybenzene. 5. Tbe Anisole Radical Cation as a Solute The anisole radical cation is a positively charged solute and in an aqueous solution the surrounding water molecules should orient their negatively charged oxygen atoms toward the radical cation. The electrostatic interaction might locate a few water molecules in a first solvation shell. For alkali-metal ions the existence of a first solvation shell in the gas phase is experimentally established. By using high-pressure mass spectrometry it can be shown that up to five water molecules are bound to the c a t i ~ n . ’ ~ The standard enthalpies of the successive hydration steps could be det~rmined.’~Recently, the reaction mechanism of the Meyer-Schuster reaction has been investigated the~retically.’~ In order to elucidate the role of the solvent water, the protonated acetylenic alcohol was considered to be surrounded by a large number of water molecules and a Monte Carlo simulation of the aqueous solution was performed. The simulation shows that a statistically significant spedific arrangement of water molecules around the protonated alcohol exists.% The water molecules orient their oxygen atoms toward the hydrogen atoms of the protonated acetylenic alcohoLM Therefore, we suppose that a first solvation shell may also exist for the anisole radical cation. Acctss to the structure of the first solvation shell should come from the knowledge of the charge distribution of the anisole radical (33) Spcllmeyer, D. C.; Oroptenhuis, P.D. J.; Miller, M. D.; Kuyper, L. F.; Kollman, P. A. J . Phys. Chem., 1990, 94, 4483. (34) Tablesfor Interatomlc‘Distancesand Coflgurat1on.v In Molecules and Ions; The Chemical Societb: London, 1958; M 217. (35) See ref 18, Chapter 5. (36)Tapia, 0.;Leuch, J. M.;Cardenas, R.;Andred, J. J. Am. Chem. Soe. 1989, 11 I, 829.

Figure 5. Proposed spatial arrangement of water molecults of the first solvation shell around the solute molecule. The negatively charged water oxygens point toward the positively charged atoms of the solute.

cation. In figure 4 the net charges of the various atoms are recorded. These numbers were derived by employing the gross charges of the Mulliken population analysis.m A charge of 4 . 0 4 7 is situated at the O-CH3 group, whereas a charge of 1.047 is located at the phenyl ring. In the neutral closed-shell anisole the corresponding values are 4 . 2 3 5 for the M H 3 group and 0.235 for the phenyl ring. Thus, the O-CH3 group is less negatively charged in the radical cation than in the parent molecule. This finding illustrates the strong electron-accepting power of the positively charged phenyl ring in the radical cation. Interestingly, all hydrogens and the carbon atom C1 of the radical cation are positively charged; all other carbon and oxygen atoms are negatively charged (Figure 4). Thus, the positive charge of the anisole radical cation is distributed on the periphery of the molecule, namely at the hydrogen atoms. Such a situation is favorable for aqueous solvation. The negatively charged oxygen atoms of the water molecules have easy acceSs to the positively charged solute hydrogen atoms and a binding interaction occurs. Guided by the charge distribution of Figure 4, we arrive at the simple qualitative model for the first solvation shell given in Figure 5. Since the solute hydrogen atoms carry almost the same positive charge (see Figure 4) we assume that the distance RHO(Figure 5) is the same for all eight water molecules. A large positive charge of 0.367 is calculated for atom C1 (Figure 4). Therefore, water molecules are assumed to be attached to the CI atom. Their distance to the solute is Rco (Figure 5). Recently, the polarizable continuum model was modified for treating biomolecules.” The essential part of the extension is the assumption that the polarizable continuum can be represented by an appropriate set of point charges.” They are arranged in a geometry having the same point group as the solute.” We have adopted this geometry criteria and applied the C, symmetry of the anisole radical cation also for its solvation shell. A consequence is that atom CI and the methyl group are solvated from above and below of the molecular plane (Figure 5). 6. Selection of the Intermolecular Distances between the Anisole Radical Cation and the Water Molecules of the First Solvation Shell In Figure 5 an approximate form of the first solvation shell for the anisole radical cation in aqueous solution is suggested and we are left with the problem of how to set the two distances RHOand Rco (Figure 5 ) . An interesting X-ray structure determination of the a-oxalic acid dihydrate has been performed.38 In the elementary cell, every oxalic acid molecule is surrounded by four water molecules. The positively charged hydrogen atoms of the carboxylic groups face the water molecules in a fashion as suggested in Figure 5. The distance R H 0 is found to be 1.537 A at (37) Frecer, V.; Majckova, M.; Miertus, S. THeOCHEM 1989, 183, 403. (38) Wang, Y.; Tsai, C. J.; Liu, W. L.; Calvert, L. D. Acra Crystallogr.

1985, B l l , 131.


300 K.38 This experimental solvation pattern supports the idea that the simple electrostatic view which led to the qualitative picture for the solvation shell (Figure 5) might be reasonable. The small value of 1.537 A for the distance RHOseems to indicate the presence of a hydrogen bond.39 We feel, however, that in an aqueous solution the distance RH0 should be larger. The van der Waals atomic radii for oxygen and hydrogen are 1.40 and 1.2 A, respectively."' Thus, the contact distance is 2.60 A. By using the Monte Carlo technique, a statistically significant solvation pattern around the protonated acetylenic alcohol has been generatedSMThe majority of RHOdistances is found in the range from 2.8 to 3.1 A.36 In a preceding paper" the authors pointed out that improved intermolecular potentials might lead to smaller distances. Consequently, we selected a value of 2.5 A for RHO. This distance is slightly shorter than the contact distance of 2.6 A which is compatible with the presence of a positive charge. The half-thickness of a phenyl group is 1.7 A."' Thus, the contact distance between the carbon atom C, and a water oxygen is 3.10 A. We adopted this value for the distance Rco.

7. Experimental Hyperfine Coupling Constants and Theoretical Case-Phase Spin Densities The spin density distribution in a radical cation is directly related to the experimental ESR hyperfine coupling constants. If only the dominant Fermi contact term is considered, a direct proportionality between the spin densities and the hyperfine coupling constants exists.42 It is important for a theoretical treatment to use a calculational procedure which produces an electronic wave function which is an eigenfunction to the total spin operator S2. The restricted open-shell Hartree-Fock procedure6 applied here yields such a wave function. In the framework of this method, the spin density distribution is the density distribution of the singly occupied molecular orbital (SOMO). In the anisole radical cation, the SOMO is a r orbital and the hydrogen atoms of the phenyl ring are located in the nodal plane of the SOMO. Thus, spin densities at the ring hydrogens are absent when the open-shell SCF method is applied. The spin densities at the ring hydrogens arise solely from electronic correlation effects. For small molecules these correlation effects have been carefully calculated by using configuration interaction techniques which are driven by multireference configurations (MRDCI) and a good agreement with experiment was obtained?' Here, we use the well-known McConnell equation which treats these correlation effects in an empirical fashion." The essence of this equation is that the spin density at a ring hydrogen is direct1 proportional to the spin density at the attached ring carbon a t o m 4 A linear relationship, without intercept, should hold between the calculated spin densities and the observed coupling constants. Because we used a split valence basis set, namely (8s4p/4s2p), any 7~ atomic orbital p of a ring carbon atom comprises an inner and outer part. The outer part extends significantly into the spatial region of the attached hydrogen atom and we use this part in the application of the McConnell relationship. For the McConnell spin densi pa at a ring carbon atom A, the following formula was a p q e d

Here, C,,t, is the linear coefficient in the SOMO referring to the outer part of the r atomic orbital p. The r-orbital p belongs to the ring carbon atom A. (39) Schuster, P. In The Hydrogen Bond I . Theory;Schwtcr, P., Zundel, G., Sandorfy, C., Us.; North-Holland: Amsterdam, 1976. (40) Pauling, L. Dle Narur der Chemlschen Blndung, Verlag Chemic: Weinheim, 1962; tab. 7-20. (41) Tapia, 0.;Lluch, J. M. J . Chem. Phys. 1985,83, 3970. (42) Pople, J. A.; Beveridge, L). L. Approximate Molecular Orblral Theory; McGraw-Hill: New York, 1970; p 128, eq (4.8). (43) Engels, B.; Peyerimhoff, S. D.; Davidson, E. R. Mol. Phys. 1987,62, 109. Engels, B.; Peyerimhoff, S.D. Mol. Phys. 1989,67, 583. (44) McConnell, H. M. J. J . Chem. Phys. 1956,24764. For a detailed d-ion aee: Athaton, M. M.Electron Spin Resonance; Wiley: New York, 1973; Chapters 3.4 and 3.5.

Bachler et al. 10.0

"

I 5.0

XA H 1 l

11.001 16.521 IO 16

1 0

\a

I/

10.211.X A

I i i lI

H13

X A H 9

5.0

10.0

P Figure 6. Correlation between the experimental ESR coupling constants of the ring hydrogen atoms and the theoretical spin densities at the corresponding ring carbon atoms. Full circles represent the unscreened gase-phase situation. For the crosses a screening of Z, = 0.96 and Zc, = 5.9 was applied. The triangles are obtained when any affected electron feels a screened nuclear charge induced by the total number of point charges of the solvation shell.

In Figure 6 full circles represent the correlation between the experimental ring hydrogen coupling constants'*' and the theoretical spin densities at the corresponding ring carbon atoms. The spin densities, in units of lo-*, are recorded along the abscissa; along the ordinate the coupling constants in gauss are given. Because all full circles ought to be located on one line we see that only a fair correlation is achieved. O"eil1 et al. measured five different ring coupling con~tants.~.'They were, however, unable to assign coupling constants to the individual ortho and meta ring positi0ns.'9~ The fair correlation in Elgure 6 suggests that the larger ortho coupling constant refers to the ortho hydrogen being trans-located to methyl group (Figure 6). In contrast, the largest meta coupling constant should belong to the meta hydrogen which is cis oriented to the methyl group (Figure 6). In order to have a quantitative measure of the agreement between theory and experiment, a linear regression analysis was performed. If a correlation line of the form y = A Bx is fitted

+

y = 0.9226

+ 0.9217~

(17)

is obtained and a correlation coefficient of r = 0.9495 is derived. As required by the McConnell relationship, the line of correlation should pass the origin of the coordinate system. The intercept of A = 0.9226 (see eq 17) indicates that the McConnell relationship holds roughly for the anisole radical cation.

8. Application of the Screening Model 8.1. Implementation of the Screening Model for the Anisole Radical Cation. On the basis of charge distribution of the anisole radical cation we proposed in section 5 a qualitative picture as to how the water molecules of the first solvation shell should be oriented around the solute in aqueous solution. In section 6 we specified this water arrangement more in detail by assigning values respectively. For those distances of 2.5 and 3.1 A to RHOand b, a further reasonable assumption seems to be that only electrons on the periphery of the solute are strongly influenced by the solvation shell. Thus, only electrons at the periphery should experience screened nuclear charges. The modified nuclear charges enter solely the nuclear attraction integrals in the matrix representation of the oneelectron operator V. By using for carbon and oxygen the (8s4p/4s2p) and for hydrogen the (4s/2s) basis set we are in a position to implement this concept of peripheral screening. The integral program was slightly modified such that for the hydrogen atoms those diagonal elements of the Vmatrix are calculated with a screened nuclear charge which refer to the Gaussian with the smallest exponent (a = 0.123). In addition, diagonal V matrix elements are computed with a modified nuclear


The Anisole Radical Cation TABLE II: Results of the Linear Regression Analysis of the Correlation betweeo Experiwatal Hydrogen Coupling Constants rad Tbeoretid spia DclrritiesO

ZH

zc,

1.00 0.96 0.90 1.04

6.00 5.90 5.84 6.01

A 0.9226 0.5414 0.3848 0.9894

B

r

0.9217 0.9004 0.8906 0.9293

0.9495 0.9715 0.9789 0.9467

OA line of the type. y = A + Bx was fitted. When screened values for ZHand Z,, are applied, the correlation coefficient r increases and the intercept A decreases. The unrealistic situation (last row) leads to a worsc correlation as compared to the unscreened treatment (first row).

charge which refer to the p-type Gaussian of atom C, having the smallest exponent (a= 0.155). For all other integrals unscreened nuclear charges are employed. The importance of modifying the description of outer electrons for simulating the solvent influence in a solute calculation has been pointed out by Clark.4s This author calculated the acetonitrile radical anion surrounded by helium atoms to simulate helium matrix effects on the radical anion.45 For the radical anion a Rydberg-augmented basis set was a~plied.4~ The cavity effect turned out to be a contraction of the singly occupied molecular orbital of the radical anion toward a valence-like orbital. The conclusion is that a valence electron basis set, without Rydberg functions, might be appropriate to simulate the environmental effect on a radical anion in a cavity.45 In our scheme we do not change the basis set for the outer electrons but modify the oneelectron potential seen by these electrons. 8.2. Experimental Hyperfine Coupling Constants and Theoretical Spin Densities Derived by the Screening Modd. In section 7 we employed the McConnell relationship&and a fair correlation between the experimental ring hydrogen coupling constants and theoretical gas phase spin densities was obtained. This correlation is represented in Figure 6 by the full circles. Now we apply the screening model to derive spin densities which should correspond more closely to the spin densities in aqueous solution. In Figure 6 the crosses represent the correlation derived by the screening model. For the hydrogens, ZH = 0.96, and for the carbon atom C,, Zc, = 5.9, was applied. A linear regression analysis was performed and a line of the form y = A Bx fitted. The results are recorded in the second row of Table 11; the unscreened treatment is repeated in the first row. A comparison indicates that the intercept A becomes smaller when screening is introduced (Table 11). In addition, the correlation coefficient r increases to 0.972. The open triangles in Figure 6 represent the correlation when full screening is applied. Full screening means an electron at the periphery of the solute experiences the screening from all water p i n t charges of the solvation shell. Such a calculation is suggested because screening is of long-range character (see eq 13). The full screening leads to Zc, = 5.84 and different hydrogen screenings where the average value is ZH = 0.90. The outcome of the linear regression analysis is recorded in the third row of Table 11. A further increase of the correlation coefficient r up to 0.979 and a smaller intercept A are obtained. This finding shows the McConnell relationship gives a better agreement between experiment and theoretical spin densities when screening is employed. The improvement was achieved by assuming that the water molecules of the first solvation shell orient their oxygen atoms toward the positively charged atoms of the anisole radical cation. This simple concept led to a nuclear charge decrease seen by the affected solute electrons. An unrealistic assumption would be an increase of the nuclear charges of the positively charged solute atoms. Such an increase would imply the surrounding water molecules orient their positively charged hydrogen atoms toward the positively charged atoms of the anisole radical cation. Thus, we expect less agreement with experiment when such an unrealistic screening is applied. The results of the linear regression analysis

+

(45) Clark, T. Faraday Discuss. 1984, 78, 203.

for such a screening are represented in the last row of Table 11. Indeed, the intercept A turned out to be larger and the correlation coefficient r is slightly smaller as compared to the unscreened treatment (Table 11). If we accept the validity of the McConnell equation,‘4 the correct qualitative response of the screening procedure to a probable and improbable solvation pattern supports the expectation that the simple screening procedure and the model for the first solvation shell are reasonable. 8.3. The Dependence of the Hydrogen Hyperfine Coupling Constants on the Size and Properties of the First Solvation Shell. The application of a simple screening procedure for solvent effects led to an improved agreement between experimental hyperfine coupling constants and theoretical spin densities. This improvement was obtained when for the solutesolvent distances RH0 and Rco (Figure 5 ) , distances of 2.5 and 3.1 A were assumed. An expansion of the solvent cavity would result in an increase of those distances and a consequence would be less screening. An expansion of the solvent cavity could arise from a temperature increase in the ESR experiment. The temperature-induced cavity expansion, however, is only one effect influencing the coupling constants. By raising the temperature, vibrations of the molecular skeleton become excited and this effect on the coupling constants is well documented.46 However, we focus here on the cavity expansion effect on the coupling constants. ONeill et al. measured the coupling constants at a temperature of 5 0C.3*4The dependence of the spin densities on screening (Figure 6) leads to the prediction that at higher temperatures the expanded cavity tends to decrease the para and ortho ring hydrogen coupling constants. The two meta hydrogens, however, should be almost unaffected. From Figure 6 it also follows that only a small effect should be expected. A small temperature dependence of the hydrogen hyperfine coupling constants has been observed for the N,N’-dihydro- 1,4pyrazine radical cation and its derivatives measured in N,N-dimethylf~rmamide.~’ A small but experimentally significant lowering of the hydrogen coupling constants is detected when the temperature is increased from -30 to 25 OC. As pointed out,” such a lowering might arise from a vibrational mechanism in which the C-H out-of-plane bending motions are excited by the temperature increase. The finding, however, is also compatible with an expansion of the solvent cavity. From Figure 6 it is apparent that less screening should lead to smaller hydrogen hyperfine coupling constants. Such a diminished screening could result when the anisole radical cation is solvated by a solvent having a smaller polarity than water. Thus, we predict that in such a solvent, smaller hydrogen hyperfine coupling constants should be observed. The basis of the above predictions are assumed changes of the electrostatic field surrounding the solute. Spanget-Larsen used representative point charges in INDO calculations to simulate the influence of the solvent on the spin densities at the various atoms of the monoprotonated 1,4-ben~osemiquinone.~*This author discussed their dependence on the temperature and the polarity of the solvent in terms of strength changes of the electrostatic field?* We adopted the same basis for our predictions. 8.4. The Anisole Radical Cation in the Solvent Cavity. So far the influence of the first solvation shell on the solvated anisole radical cation was simulated by means of a simple screening procedure. This method can be considered as a way for an a p proximate treatment of the anisole radical cation in the electrostatic field of the surrounding water molecules. In order to test the coherence of the model, it is of interest to know how properties of the anisole radical cation are changed by the field made up by the surrounding solvent molecules. If the first solvation shell of Figure 5 is applied and the values of 2.5 A and 3.1 A are used for RH0 and &, respectively, the screening method yields a total energy for the anisole radical cation which is 6.3 kcal/mol higher than the energy of the isolated molecule. A destabilization of the solute is reasonable because screening leads to a lowering of the (46) Sullivan, P. D. Menger-Egbert. M. Adu. Magn. Reson. 1977, 9, 1. (47) Das, M. R.; Fraenkel, G. K. J . Chem. Phys. 1965,42, 792. (48) Spanget-Larsen, J. Chem. Phys. Lerr. 1976, 44, 543.

Bachler et al.


(4.0912)

(0.1329)

0.1 163

(00967) 0.1165 (0.0904)

(0.1287)

\

01176

(00869)

0.6351

/

(uJ(IzD’

0 1263 (009841

Figure 7. Charge distribution in the anisole radical cation when smening is applied. The charges are the atomic charges as defined in the occupation number and by the application of modified atomic orbitals (MAO).“ The values in parentheses are the charges for the isolated radical cation.

attractive nuclear-electron potential at the atoms affected by solvation. Such a lowering tends to move the electrons away from their nuclei and the energy should increase. This destabilization energy is only a portion of the total solvation energy. It is the energy which arises when the electrons of the solute readjust in the permanent electrostatic field of the solvent molecules. An estimate of the solvation energy, however, would be obtained by adding the electrostatic interaction energy between solute and solvent molecules and the changes in the solventsolvent interaction energy. Here we perform only an approximate treatment of the solvation cluster and we are unable to assess the solvent-solvent contribution. As in the classic electrostatic dipole interaction models for the solvation energy,29we can calculate the Coulombic solute-solvent interaction by assuming that all solute atomic charges interact with all atomic charges of the cluster solvent molecules. Unfortunately, atomic charges in molecules are not uniquely defined in a molecular orbital calculation. The straightforward application of the Mulliken population analysis is not recommended because those atomic charges are known to be strongly basis set dependent. Ahlrichs et al.49 extended a population analysis method which is based on a projection operator technique and the concept of occupation numbers.s0 The essence of the extended analysis is the application of modified atomic orbitals (MAO).49 The M A 0 are obtained from the original atomic orbitals by a transformation which retains their atomic character but minimizes the amount of unassigned charge.” The defined atomic charges turned out to be significantly less basis set depe~~dent.’~ The M A 0 atomic charges for the anisole radical cation, as obtained after employing the screening procedure, are recorded in Figure 7. Thus, the solute charge distribution is the distribution influenced by the permanent charges of the surrounding solvent molecules. The unscreened atomic charges are also recorded (Figure 7). We see these unscreened charges are smaller than the Mulliken charges (Figure 4). Comparing the unscreened and the screened atomic charges (Figure 7), we realize that almost all polar C-H bonds of the phenyl ring become even more polar by the influence of the water molecules of the solvent cluster. Using the screened atomic charges and for the water oxygen and hydrogen atoms -0.350 and 0.175, respectively, we obtained a Coulombic interaction energy of -30.5 kcal/mol. In order to assess the validity of that number we employed Born’s quation” to get an estimate for the solvation energy. The adopted geometry of the anisole radical cation fits into a spherical cavity with a radius of 3.463 A. However, it is reasonable to assume the surrounding continuum approaches the solute only up to the van der Waals atomic spheres of the hydrogen atoms at the periphery of the solute. Consequently, the above cavity radius (49) Heinzmann. R.; Ahlrichs, R. Theor. Chlm. Acto 1976.42, 33. Ehrhardt, C.; Ahlrichs, R. Thror. Chim. Actu 1985, 68, 231. (50) Davidson, E. R . J . Chrm. Phys. 1%7,46,3320. Roby, K. R. Mol. Phys. 1974, 27, 8 1. (51) Born, M. Z . Phys. 1920, I , 45.

should be enlarged by 1.2 A and we arrive at a cavity radius of 4.663 A. Using the Born equations’ we obtain a value of -35.2 kcal/mol for the solvation energy. This value is close to the electrostatic interaction energy of -30.5 kcal/mol. However, this agreement might be fortuitous. The Born equation is based on the continuum approach whereas a detailed model for the solute and the first solvation shell is needed for calculating the electrostatic interaction energy. Our results may be compared with the gase phase solvation energy of the rerr-butyl carbocation. By using high-pressure mass spectrometry it was shown that up to four water molecules cluster around the carboation?* The heats of formation for the consecutive solvation steps have been determineds2and a total value of -42.9 kcal/mol is obtained. We do not claim that our simple electrostatic procedure is capable of generating accurate values for the solvation energy. Our value of -30.5 kcal/mol, however, is in the cottect order of magnitude. This finding supports the expectation that the screening method and the selection of the nuclear arrangement for the fmt solvation shell are reasonable. 83. TaeEaergyoftbeUapriredEkctroaintbeSdventCavity. The closed-shell SCF calculation for the neutral anisole gives an energy of -8.656 eV for the orbital Sa” which is the highest occupied molecular orbital (HOMO). If we assume the validity of Koopmans’s theorem,s3 this value should equal the negative value of the experimental gase-phase ionization potential. Our theoretical value is close to the experimental ionization potential of I = 8.21 eV measured by photoelectron spectroscopy.u Due to t i e methoxy group, the doubly degenerate 5 orbitals of benzene are split and two low-energy bands of equal intensity are observed in the photoelectron spectrum of anisole.% The energies of both bands are well r e p r o d u d by the orbital energies Sa” and 4a”. Thus, the ionization from the extended r electron system seems to be well described. The restricted open-shell calculation for the anisole radical cation places the energy of the singly occupied molecular orbital (SOMO) at -14.64 eV. If we apply the screening procedure as above, the energy of the SOMO is only marginally lowered by 0.003 eV. Solvation effects on the energy of the solute frontier electrons are important in photoionization experiments conducted in the liquid phaseass The first step is the ejection of an electron from the solute into the first solvation shell surrounding the solute.ss Afterwards, the ionized solute and the emitted electron are solvated.55 A determining factor for the first step is the energy needed to remove an electron from the solute. This energy requirement should be influenced by the impact of the first solvation shell. The above-suggested screening method may be useful in evaluating those energies hardly accessible by experiment. 9. Summary and Conclusion

In this paper a simple screening procedure is proposed for the inclusion of solvent effects into a quantum chemical calculation. It is shown that the impact of a solvent on the solute can be simulated by using screened nuclear charges for solute atoms. The procedure was illustrated by treating the anisole radical cation in aqueous solution. An improved agreement between experimental ring hydrogen hyperfine coupling constants and theoretical spin densities was achieved when screening was applied. The improvement, however, turned out to be only small. This finding supports the notion that a calculation which comprises electron correlation explicitly should be applied to obtain spin densities at the ring hydrogen atoms directly. An advantage of the proposed screening procedure is that all solvent molecules contribute additively to the screening of the solute. This fact leads to the option that a large number of solvent (52) Hiraoka, K.; Kekrle, P. J . Am. Chrm. Soc. 1977,99,360. For an illustrative discusaion ace: Vogel, P. Carbocution Chemistry; Elsevier: New York, 1985; pp 215-216. (53) Koopmans, T. Physicu 1933, I , 104. See also ref 5. (54) Turner, D. W.; Baker, C.; Baker, A. D.; Brundle, C. R. Mdcculur Photoelectron Spectroscopy; Wiley: New York, 1970; p 298, fig. 11.16. (55) Lcsclaux, R.; Jourrsot-Dubien, J. In Orgunic Molmtlur Phorophysics: Birks, J. B., Ed.;Wiley: New York, 1973.

J . Phys. Chem. 1991,95,6819-6822 molecules could be considered in the calculation. As a further advantage, the procedure permits the electrons of the solute to readjust in the field of the electric charges of the solvent molecules. This adjustment is a consequence of the fact that the solventdependent nuclear charges lead in the solute SCF calculation to electron density redistribution. A disadvantage of the simple screening procedure is that the polarization of the solvent molecules by the solute is not included. Such a polarization, however, is the basis of the reaction field techniques9J0and the basic concept of the polarized continuum model" for solvent effects. This deficiency should limit the proposed screening method to charged solutes and polar solvents where electrostatic interactions of

6819

permanent charges are important. In further applications a more detailed picture of the solute environment could be obtained by means of Monte Carlo or molecular dynamics techniques which employ reliable classical force fields. Subsequently, quantum chemical methods, supplemented by screening, could be used to treat the influence of the solvent molecules on the electronic properties of the solute.

Acknowledgment. Stimulating discussions with Dr.K.Hildenbrand are gratefully appreciated. We thank Prof. E. Ziegler for providing a generous amount of CPU time for performing the calculations.

EPR Study of Gallium Atoms In Benzene' J. A. Howard,* H. A. Joly,Zt B. Mile,$and R. Sutcliffe3~~ Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario. Canada Kl A OR9 (Received: November 26, 1990; In Final Form: April 16, 1991)

An EPR study of a Ga atom matrix isolated in benzene at 77 K has revealed the presence of a paramagnetic species with the magnetic parameters a,(69) = 256 MHz, a,(69) = 270 MHz, a ,(69) = 284 MHz, a,(71) = 325 MHz, a,(71) = 343 MHz, ~ ~ ( 7=1 361 ) MHz, g, = 1.9970, g, = 1.9750, and gw = 1.4350. These parameters are consistent with a trapped atom or a weak Ga-benzene complex that has had the degeneracy of the Ga p orbitals lifted by interaction with the benzene matrix. This contrasts with A1 in benzene which gives a mononuclear monoligand complex, Al[C6H6],with quite strong bonding between the metal atom and the ligand.

Introduction

The reactions of ground-state Ga atoms (4s24p', 2P1/2)mimic many of the reactions of the other well-studied group 13 metal atom, All under matrix isolation conditions. Thus, electron paramagnetic resonance (EPR) spectroscopic studies in inert hydrocarbon and rare gas matrices have revealed that both metal atoms give the dicarbonyl, M(C0)2, with CO," the monoligand T complex, M[C2H4],with ethyIene,*I3 the 2-substituted allyl, CH2C(M)CH2, with allene,I4 and the 1-substituted allyl, MCH2CHCHCH2,with buta-1,3diene.I5J6 Ga atoms, however, do not appear to undergo a 1,4-cheleotropic addition to buta1,3diene to give gallacyclopentene,'6 a reaction that readily occurs with AI to give aluminacyclopentene. In the absence of reactant the triatomic clusters, M3, are formed in inert hydrocarbons at 77 KI1'J* while the atoms are detected in rare gases.19 Reaction of AI atoms with benzene has been studied in rare g a m m and in benzene and inert hydrocarbon matrices?' and the monoligand complex, AI[C&], is formed under all conditions. There is, however, some disagreement over the exact structure of this complex. Thus, in rare gas matrices it has been suggested that AI forms a dative 7r complex with just one double bond of the benzene ringImi.e., an q2 complex, whereas in hydrocarbons AI undergoes a chelcotropic 1,4-addition to give 1,4-dihydro1,rl-aluminabenzene that is rigid at low temperatures but is fluxional at higher temperatures.2' In the present paper we discuss the results of a matrix isolation EPR study of the reaction of Ga atoms with benzene in hydrocarbon matrices that demonstrates that Ga, in this case, behaves differently from AI. ExperimentrlSection

The rotating cryostat, instruments, and computational methods used to record, calibrate, and analyze EPR spectra have been Present address: Department of Chemistry, Laurentian University, Sudbury, ON, Canada. $Presentaddreas: School of Chemistry and Applied Chemistry, University of Wales, College of Cardiff, P.O.Box 912, Cardiff, U.K. CFI 3TB. 'Preacnt address: Wood Bio-innovations Department, Forintek Canada Corp., 800 Montreal Road, Ottawa, ON, Canada.

0022-3654/91/2095-6819$02.50/0

described previously.*a Gallium was evaporated from a tungsten basket (No. 12070, Ernest F. Fullam, Inc., Schenectady, NY) suspended from the molybdenum electrodes of the furnace. Isotopically pure 69Ga(99.46 atom W )was prepared by electrolysis of 69Ga203(Oak Ridge National Laboratory, TN). Adamantane (Aldrich), benzene (Anachemia), perdeuterioadamantane, and perdeuteriobenzene (MSD Canada Ltd.) were used as received (1) Issued as NRCC No. 32913. (2) NRCC Research Associate 1987-1990. (3) NRCC Research Associate 1979-1984. f4) Kasai. P. H.: Jones. P. M.J. Am. Chem. Soc. 1984.106.8018-8020. (Sj Chenier, J. H. B.; Hampson, C. A.; Howard, J. A,; Mile,'B.; Sutcliffe, R. J . Phys. Chcm. 1986,90, 1524-1528. (6) Kasai, P. H.; Jones, P. M. J . Phys. Chem. 1985, 89, 2019-2021, (71 Howard. J. A,; Sutcliffe. R.; Hampson. C. A,; Mile, B. J. Phvs. Chcm. 1%; 90.4268-4273. ( 8 ) Chenier, J. H. B.; Hampson, C. A,; Howard, J. A.; Mile, B. J . Chem. Soc., Chcm. Commun. 1986,730-732. (9) Kasai, P. H.; M c W D., Jr. J. Am. Chem.Soc. 1975,97,5609-5611. (10) Kasai, P. H. J. Am. Chcm. Soc. 1982,104, 1165-1172. ( 1 1 ) Chenier. J. H. B.; Howard. J. A.: Mile. B. J . Am. Chcm. Soc. 1987. (12) Howard, J. A.; Mile, B.; Tse, J. S.; Morris, H. J . Chcm. Soc., Forodoy Trans. 1 1987,83, 3701-3707. (13) Jones, P. M.; Kasai, P. H. J . Phys. Chcm. 1988,92, 1060. (14) Mile, B.; Howard, J. A.; Tse, J. S. Organomcrallics 1988. 7, 1278-1282. (IS) Chenier, J. H. B.; Howard, J. A.; Tse, J. S.; Mile, B. J . Am. Chem. Soc. 1985, 107,7290-7294. (16) Howard, J. A,; Joly, H. A.; Mile, B. Unpublished results. (17) Howard, J. A,; Sutcliffe, R.; Tse, J. S.;Dahmane, H.; Mile, B. J. Phys. Chrm. 1985,89,3595-3598. (18) Howard, .I. A.; Mile, B. Acc. Chem. Res. 1987, 20, 173-179. (19) Ammeter, J. H.; Schlosnagle, D. C. J . Chcm. Phys. 1973, 59, 4784-4a20. (20) Kasai, P. H.; McLeod, D., Jr. J . Am. Chrm. Soc. 1979, 101, 5860-5862. (21) Howard, J. A,; Joly, H. A.; Mile, B. J . Am. Chcm. Soc. 1989, 111, 8094-8098, (22) Buck, A. J.; Mile, B.; Howard, J. A. J . Am. Chcm. Soc. 1983,105, 3381-3387. (23) Chenier, J. H. B.; Hampson, C. A,; Howard, J. A.; Mile, B. J . Phys. Chem. 1989, 93, 114-117. (24) Belford, R.L.; Nilges, M. J. Resented at the EPR Symposium, Zlst Rocky Mountain Conference, Denver, CO, Aug 1979.

Published 1991 by the American Chemical Society

A quantum chemical investigation of the anisole radical cation with

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