J. Phys. Chem. 1980, 84, 2641-2645 (21) S. Yamauchi and D. W. Pratt, Chem. Phys. Lett., 82, 615 (1979). (22) J. A. Mucha and D. W. Pratt, J. Chem. Phys., 88, 5399 (1977). (23) G. P. M. vain der Velden, Thesis, Nijmegen, 1980. (24) D. W. Pratt, “Excited States”, Vol. IV, Academic Press, New York, In press. (25) D. Owens, hd. A. ECSayed, and S.Zlegler, J. Chem. Phys., 52,4315 (1970). (26) E. T. Harrigan and N. Hirota, Mol. Phys., 31, 663, 681 (1976). (27) J. Woning, Gi. P. M. van der Velden, and W. S.Veeman, Chem. Phys., in press. (28) L. Davis, B. T . Feld, C.W. Zabel, and J. R. Zacharias, Phys. Rev., 27, 1076 (1949). (29) M. J. Buckley and C. B. Harris, Chem. Phys. Lett., 5, 205 (1970). (30) D. S. Tlnti, (3. Kothandaraman, and C.B. Harris, J. Chem. Phys., 59, 191 (19173).
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(31) V. I. Gerko, N. P. Kovalenko, V. A. Smirnov, H. V. Alfimov, H. I. Bardamova, and I. L. Kotiyaresskii, Opt. Specrrosc. (Engl. Trans/.), 41, 128 (1976). (32) J. M. Morris and D. F. Wllllams, Chem. Phys. Left., 25, 312 (1974). (33) N. J. Turro, “Modem Molecular Photochemistry”, Benjamin Cummings, New York, 1978, p 342. (34) C. MiJouleand J. M. Leclercq, J. Chem. Phys., 70, 2560 (1979). (35) C.R. Jones, A. H. Maki, and D. R. Kearns, J. Chem. Phys., 59, 873 (1973). (36) R. M. Hochstrasser and J. W. Michaluk, J. Mol. Specfrosc., 42, 197 (1972). (37) N. Hirota, M. Baba, Y. Hirata, and S.Nagaoka, J. Phys. Chem., 83, 3350 (1979). (38) H. Hayashi and S. Nagakura, Mol. Phys., 24, 801 (1972). (39) S.Niizuma and N. Hirota, J. Phys. Chem., 83, 706 (1979).
Correlations Based on the Polarization Model of the Solvent Influence Examined by ab Inltlo Calculations Antonino Sabatlno, Glanfranco La Manna, and Leonello Paolonl” Gruppo Chlmica Teorica Istitututo di Chlmica Fisice Universiti, 90 123 Palerrno, Ita/y (Received: January 14, 1980)
The correlation of reaction rates and of free energies of solvation with the solvent acceptor number (AN) or donor number (DN) is shown to be parallel with the correlation based on the lowest unoccupied (LUMO) or the highest occupied molecular orbital (HOMO) eigenvalues of the solvent molecule. Our results show under what conditions the mutually induced electronic polarization between solute and solvent molecules is the main factor in determining the solvation effects. We also point out the dependence of solvation on the LUMO or HOMO energy levels of the solvent molecule and the specific role of hydrogen bonding in the anion solvation. The correspondencebetween each correlation based on AN or DN with that respectively based on the LUMO or HOMO eigenvalues is also stressed by the fact that both succeed or fail in the same cases.
Introduction Attempts to predict the influence of the solvent in determining the value of quantities of chemical interest such as reaction rates and equilibrium constants have been rationalized in recent years by the systematic work of Gutmann and his co-workers.’ The solvent molecules are considered as electron acceptor and/or electron donor, and the measure of these potentialities is expressed by certain quantities defined’ as the acceptor number (AN) and the donor number (DN). The basic model of this approach is represented by Gutmannl with the interaction scheme donor
- AB
acceptor
which induces a 6- electron polarization on the A side of the substrate AB and a 6+ polarization on its B side. The main merit of this approach is, according to Gutmann,’ that “it is simply concerned with the changes in bond properties within a molecule that are induced by other molecules or ions”. The same substance, antimony pentachloride, has been taken as the standard for defining the AN and DN parameters. This latter is identified as the negative value of AH for the interaction of the electron pair donor solvent with SbC15in a very dilute solution of 1,2dichloroethane, this being the reference solvent. The AN is defined by taking as AN = 100 the normalized NMR chemical shift of 31Pin the adduct of SbC15 with triethylphosphine oxide dissolved in 1,Zdichloroethane. The shift, extrapolated to infinite dilution, is referred to hexane, which gets therefore AN = 0. This approach, fairly consistent with the model, reduces to a minimum the influence of the bulk properties of the solvent and aims to use certain empirical observations as 0022-3654/80/2084-264 1$01.OO/O
a guide to further experiments. However, it does not specify the nature of the solvent-solute interaction beyond the simple polarization scheme, and the evaluation of the solvent influence is reduced to distinguish between electron donor or acceptor or their combined effects. Moreover this distinction needs to be based either on an assumed model of the chemical process or on a certain representation of the measured physical property. Information related to the electronic structure of the interacting solvent molecules is outside of the philosophy of the approach itself, and therefore it is not possible to extract them from the observed empirical correlations. This paper reports an attempt to remove these shortcomings of the empirical approach by using the ground-state wave function and energy eigenvalues of the solvent molecule.
Theoretical Basis The simplest basis for a quantum-mechanical approach to the weak charge-transfer forces which control the donor-acceptor (D,A) interactions between solvent and solute molecules is offered by the theory developed by Mulliken.2 In his resonance-structure description the configuration taken by the two interacting molecules corresponds to the maximum value of u = ( b / a ) ,the ratio between the dative and the no-bond structure functions on which is built the ground-state wave function of the complex. This occurs when the overlapping orbitals of D and A are so chosen that ‘‘4Dis the most easily ionized MO of D and 4 A is the acceptor orbital of largest electron affinity.” In the MO description Mulliken2 adopts the LCMO approximation where 4DA is a simple linear combination of 4 D and $A, assuming that only the electron pair in 4DA contributes appreciably to the bonding interaction. 0 1980 American Chemical Society
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The Journal of Physical Chemistty, Vol. 84, No, 20, 1980
Accordingly,2a solvent molecule acts as a better donor the lower its ionization potential, and as a better acceptor the larger its electron affinity. In Koopmans’ approximation this is tantamount to adopting the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) eigenvalues of the solvent molecule as the quantum-mechanical correlation parameters to replace DN or AN, respectively. Moreover, according to the Mulliken charge-transfer theory,2 “electrostatic attractions should also contribute [to the formation energy of the complex] if D and/or A are ions or have dipole or quadrupole moments.” Since this is the case with several of the solute species considered by Gutmann,l we have also determined whether a correlation could be found with the net charges of the appropriate interacting atoms. One of the aims of our work was to show that the use of quantum chemistry, even in the simple form of singlemolecule ab initio calculation, is an improvement with respect to empirical parameters. The plots which constitute the main body of our results, compared to the plots based on DN or AN, show that the correlation patterns are similar and that successes and failures are the same. However, in discussing the various examples we have differentiated the net charge and the LUMO as a measure of the solvent influence and pointed out the role of hydrogen bonding in the anion solvation and in the reaction rate, showing the advantage of the quantum-chemical approach even at the simple level of the charge-transfer correlation. The calculations have been done in the SCFMO ab initio approximation, using the STO-3G minimal basis set,5on the available geometries of the following solvent molecules: water: methanol (MeOH),7ethanol (EtOH)? acetonitrile (An),9acetone (Ac),l0formamide (FA),ll dimethylformamide (DMF),12dimethyl sulfoxide (MezS0).I3The net charges on the atoms have been evaluated from the Mulliken population analysis.
Results and Discussion The experimental data we have examined fall into three groups: reaction rate constants, free energies of solvation, and standard free energies of transfer of ions from a reference solvent (acetonitrile). The first two groups are taken from the quoted paper by Gutmann,l with the original data from the references there given, and the third group is from a more recent work by Mayer.14 Reaction Rate Constants. (1)The rate coefficient for the substitution reaction of one solvent (S) molecule for the trifluoroacetate (TFA) anion (NiS5TFA)+ (NiS#+ + TFA-
-
increases with the solvent DN. The set of these data gives a linear plot with the HOMO energy of the solvent molecules (Figure la). When the plotting is done against the net negative charge of the polar atom (Figure lb) An, MeOH and MepSOfall on the same line. Dimethylformamide however makes an exception because the calculated negative charge on either the N or 0 atom corresponds to a lower rate constant. For a possible explanation of this failure, one can assume that each negative atom has an independent access to the coordination sphere of the cation and therefore each one is effective in increasing the reaction rate. If this is correct the log k values separately obtained from the linear plot by q ( 0 ) and q(N) should be added and give the rate coefficient “predicted” by the established correlation. The result is very close to the observed value, and therefore the assumption made seems correct.
Sabatino et al. a
b
,1 loaK -
loaK
9 DMSO
Figure 1. Rate constants for the substitution reaction of a solvent molecule in the coordination sphere of nickel trifluoroacetate plotted (a) vs. the HOMO eigenvalues (correlation Coefficient r = 0.994; its value for the DN plot is r = 0.998) and (b) vs. the net charge (r = 0.999, without the DMF values). The square point of DMF in plot (b) Is obtained by adding the log kvalues calculated from the straight line for predicting the rate from the net charge on the DMF oxygen and nitrogen atoms, q(0) = -0.270, q(N) = -0.307, log k = (1.17 1.48) = 2.65 (Observed, 2.435).
+
-3
i
HIO.
Flgure 2. Rate constants of the iodine isotopic exchange reaction of iodomethane in various solvents, plotted vs. the LUMO eigenvalues of solvent molecule ( r = 0.955; the AN plot has r = 0,999).
(2) The second-order rate constants of the isotropic exchange reaction of iodomethane with labeled iodide anions decrease with the increase of AN. This has been interpreted as due to the increase of the I- solvation energy, a circumstance which makes the attacking species of the process less easily available for the transition state complex H
H
H
This mechanism suggests a correlation of log k with the LUMO energy, the virtual orbital eigenvalue of the solvent molecule taken as a measure of its electron affinity. The plot in Figure 2 shows this expectation approximately fulfilled. The comparison of this LUMO correlation with that involving the anion solvation energy to be discussed later (see Figure 5) suggests the existence of a direct correlation between AGo(I-) and log h. This result, which seems to
The Journal of Physical Chemistry, Vol. 84, No. 20, 1980 2643
Polarization Model of the Solvent Influence
3;
t
/
P
Ac
MeoHi/
19
-11
i
/6 -4
-3
18
-
17
-
/
/
/
/
MeoH
-2
-1
0
1
log k
Flgure 3. Rate c~onstantsas in Figure 2 plotted vs. the solvation free energies of I- in each solvent ( r = 0.996).
have remained unnoticed so far, is shown in Figure 3. (3) Another example examined by Gutmann' of the solvent influence on bimolecular nucleophilic substitutions is the reaction of n-butyl bromide with azide anions C,IHgBr-t- N
