Overlap integral Polarizability

After separation, the polarizability in Equation (9.22) is the sum of four terms (i) the A-term, also known as the Condon approximation, is a result of the pure electronic transition moment and vibrational overlap integrals (ii) the B-term results from vibronic coupling of the resonant excited state with other excited states (iii) the C-term has to do with the vibronic coupling of the ground state with one or more excited states and (iv) the D-term results from vibronic coupling of the resonant excited state to other excited states coupling in both the electronic transition moments. 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

The surface changes in the polarizability, a, can be due to electromagnetic interactions, or to chemical effects. By electromagnetic interactions is meant interactions given by macroscopic Maxwell equations, or their microscopic modification, when the adsorbed molecules and the substrate retain their own chemical identity and integrity. Chemical interactions involve some overlap of the molecular orbitals and those of the substrate. 

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