Distance dependence polarizability effects

Let us now examine the effect of a surface upon the various contributions to the free-energy f(z). Let x be the distance to the surface and F(z,x) the local free-eneigy density. We suppose that the same decomposition can be made for F(z,x) as was made for f(z) in (45). Of all the terms in that decomposition, only EpQ (z,x) does not return to its bulk value pQ (z) within a few molecular planes of the surfaces. Consider a point charge q at the center of a spherical cavity in a polarizable medium a distance x from the surface. The energy of polarization of the medium by q,EpQ (x) has the distance dependence... 

Maroulis117 has applied the finite field method to a study of HC1. In a systematic analysis with large basis sets, MBPT and CC techniques, the dipole, quadrupole, octupole and hexadecapole moments have been calculated at the experimental internuclear distance. The polarizability and several orders of hyperpolarizability have been calculated and the mean a and -values for the 18-electron systems HC1, HOOH, HOF, A, F2, H2S are compared. Fernandez et a/.118 have calculated the frequency dependent a, / and tensors for HC1 and HBr using the Multiple Configuration Self Consistent Field method (MCSCF), including the effect of molecular vibration. The results show good agreement with available experimental and theoretical data. 

The dispersion interaction between an atom and a metal surface was first calculated by Lennard-Jones in 1932, who considered the metal as a perfect conductor for static and time-dependent fields, using a point dipole for the molecule [44], Although these results overestimate the dispersion energy, the correct l/d3 dependence was recovered (d is the metal-molecule distance). Later studies [45 17] extended the work of Lennard-Jones to dielectrics with a frequency-dependent dielectric constant [48] (real metals may be approximated in this way) and took into account electromagnetic retardation effects. Limiting ourselves to small molecule-metal distances, the dispersion interaction of a molecule characterized by a frequency-dependent isotropic polarizability a embedded in a dielectric medium with permittivity esol (note that no cavity is built around the molecule) reads ... 

This is summed over all probe (p)-target (t) atom pairs and is a function of the distance, rj, between the atoms in the pair, which have van der Waals radii, Rj, and R,. A = 0.5C(Rj, + R,) and C is given by the Slater-Kirkwood formula [18] and is dependent on atomic polarizability and the number of effective electrons per atom. 

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