Adiabatic polarizable model

When the Drude particles are treated adiabatically, a SCF method must be used to solve for the displacements of the Drude particle, d, similarly to the dipoles Jtj in the induced dipole model. The implementation of the SCF condition corresponding to the Born-Oppenheimer approximation is straightforward and the real forces acting on the nuclei must be determined after the Drude particles have attained the energy minimum for a particular nuclear configuration. In the case of N polarizable atoms with positions r, the relaxed Drude particle positions r + d5CF are found by solving... 

Kevan (1974) and Tachiya (1972) point out that CKJ use an SCF approximation to calculate the medium polarization energy, but in everything else they use the adiabatic approximation. This somewhat inconsistent procedure, which may be called the modified adiabatic approximation, gives results similar to those obtained by FFK. Varying the dipole moment and the polarizability in the semicontinuum models varies the result qualitatively in the same direction. It increases the electron-solvent attraction in the first shell and also increases the dipole-dipole repulsion. Both hv and I increase with the dipole moment, but not proportionately. 

While the agreement of the measured and calculated Ba+ quadrupole polarizabilities is not very good, compared to an analysis based on adiabatic core polarization the agreement in Table 17.3 is superb. The adiabatic core polarization model leads to ad = 146flo and aq = —5800. The ground state of Ba+ cannot have a negative quadrupole polarizability. Taken together, the Ca and Ba experiments show clearly that the nonadiabatic effects in core polarization in the alkaline earth atoms are important and may be calculated with some accuracy. 

When the electron is partially delocalized, one should switch to the adiabatic representation in which the upper and lower CT surface are split by an energy gap depending on P. If this energy gap is expanded in P with truncation after the second-order term, we come to the model of a donor-acceptor complex whose dipolar polarizabilities are different in the ground and excited states. The solute-solvent interaction energy then attains the energy of solute polarization that is quadratic in P... 

Fig. 7.4 Adiabatic (left panel) and diabatic (right panel) static polarizabilities along the Qioa normal coordinate. The Oqq, ccjj, af2 and 0/ 2 components are shown in blade, blue, red and magenta, respectively. The cirdes represent the ab initio computed adiabatic static polarizability and the diabatic static polarizabriity obtained from application of the transformation S(Q). The full lines represent the static polarizabilities obtained from our model...

Thanks to the simple mathematical expressions assumed in our model for the dia-batic potential energy and polarizability matrices (Eqs. (7.4) and (7.16) respectively), the position and energies of the minima of the upper dressed adiabatic potential energy surface and Cl seam are given by simple analytic expressions [33]. Specifically, in our case the position of the minimum of the upper adiabatic surface is identical to that of the diabatic V2iQ) and simply reads... 

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