Theory of Dispersion Energy and Solvent Effects on Molecular Spectra

Abstract

The theory of dispersion energy has been shown to directly give an explicit expression for the solvent shifts in the spectra of non-polar solute molecules.Solvent effects on the spectra of molecules arise from various interactions between the solute and solvent molecules 2 . Dispersion effects are primarily responsible for the influence of non-polar solvents on the spectra of non-polar solutes and can in the simplest form be regarded as arising from London dipole interactions. Such effects on spectra are generally discussed in the literature 2 in terms of Onsager's reaction field. In this paper we analyze solvent effects on spectra from the viewpoint of the dispersion energy 3 of the solute molecule in the solvent medium and show that in this way an explicit relation for solvent-induced spectral shifts similar to that obtained from perturbation theory can be derived. The MethodThe dispersion energy of a molecule arises from the change in the energy of the electromagnetic field due to the presence of the molecule. If we consider a fluctuating dipole moment p (co) on the molecule located at R, the electric field due to that can be written as e(r,co)=4nG(r,R;oj)p(oj)where 4aG(r, R; co) is the diadic Green's function giving the electric field at V with a unit dipole source at R. The dipole moment of the molecule can be considered as being due to the same field at R, i. e., p(co) =a(<o) s(R) = 4 .i a(co) G(R, R; w)p(oj) .* Two whom all correspondence should be addressed.The electrostatic diadic Green's function G(r, r'; co) will diverge if but the finite size of the molecule at R removes this divergence by folding the Green's function with a form factor function representing the distribution of polarization over the size of the molecules 3 . In that case, Eq. (2) is replaced by p(oj)=4jiG(R,R;co)p(co)where G n (r, r'; co) = / G(r, r"; co) a n {r" -r'; co) dV (4) a,, (r) being the polarizability density of the molecule, assumed to be in the n-th quantum state.The frequencies for which solutions of Eq. (3) will exist will give the perturbed frequencies of the electromagnetic field. They are roots of the (3x3) determinant D n (w) = |I-4aG n (R,R;eo)| = 0.The change in the zero-point energy of the electromagnetic field due to the presence of the molecule, which is the dispersion energy of the molecule, is given by E n * = --r j dco In 11 -4 n G n (R,R ; co)'where the contour for co-integration encloses the positive real axis.In the formulation proposed here, the solvent comes into the picture through G. We shall restrict ourselves here to the non-retarded form of G, since retardation effects are unimportant in this problem. Unauthenticated Download Date | 5/13/18 6:15 AM

Notizen: Dispersion Energy Contribution to Solute-Solvent Interaction

“…Assuming the solvent to be a dielectric continuum and employing equation (18) of our earlier paper [3], we can write the expression for the free energy change as,…”

“…This sort of approach, however, ignores three-body and other many-body dispersion forces in the system. A more rigorous approach is possible through the use of the dispersion self-energy concept [2] employed in the analysis of solvent effects on molecular spectra [3]. The details are described in our earlier paper [3] and will not be repeated here.…”