Casimir-Polder formula

The dispersion nonadditivity Eib arises from the coupling of intermonomer pah-correlations in subsystems XY and YZ via the intermolecular interaction operator Vzx. This contribution can be expressed as a generalized Casimir-Polder formula,... 

An alternative, yet equivalent, expression for the dipole dispersion constant is the Casimir-Polder formula (Casimir and Polder, 1948) ... 

We shall henceforth refer to (58) and (59) as of generalizations of the London formula [55] and the Casimir-Polder formula [56], respectively. The latter, in fact, refer to Cg dispersion coefficients for atoms expressed in terms of static (London) or dynamic (Casimir-Polder) polarizabilities, whereas (58) and (59) describe, in a completely general way, non-expanded dispersion between atoms or molecules. (59) expresses the coupling of two electrostatic interactions (l/ri2 and l/r ) involving four space points in the two molecules, with a strength factor which depends on how readily density fluctuations propagate between r and on A, r 2 and F2 on B (Fig. 4). 

This equation is known as the Casimir-Polder formula. The polarizability at imaginary frequencies, a(-io) iw), can be obtained for instance using Eq. 11.111 with an imaginary value of or. The n > 6 coefficients depend on similar higher-order multipole polarizabilities of one or both atoms. The same approach can be applied for atom-molecule and molecule-molecule interactions considering individual tensor components of the required polarizabilities. It can also be used for three-body interactions, and to describe the dispersion contributions to the pair polarizability function (Fowler et al. 1994). 

A related manuscript has been devoted to the coupled Kohn-Sham dispersion energies in SAPT(DFT) [134]. The method utihzes a generalized Casimir-Polder formula and frequency-dependent density susceptibilities of monomers obtained from time-dependent DFT. Numerical calculations were performed for the same systems as in [133]. It has been shown that for a wide range of intermonomer separations, including the van der Waals and the short-range repulsion regions, the method provides dispersion energies with... 

At larger distances, the leading term obviously dominates and one recovers the formula derived originally by Casimir and Polder [55]. The force of interactions between atoms ean be obtained directly from the above formulas by a simple differentiation in respect to r. 

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