Charge-density susceptibilities

The charge-density susceptibility is a linear response function it is nonlocal because a perturbing potential applied at any point r affects the charge density throughoutthe molecule. Quantum mechanically,x(r, r co) is specified by (2)... 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

The total electronic potential energy of a molecule depends on the averaged electronic charge density and the nonlocal charge-density susceptibility. The molecule is assumed to be in equilibrium with a radiation bath at temperature T, so that the probability distribution over electronic states is determined by the partition function at T. The electronic potential energy is given exactly by... 

Linder B, Lee KF, Malinowski P, Tanner AC (1980) On the relation between charge-density susceptibility, scattering functions, and Van der Waals forces. Chem Phys 52 353-361... 

Malinowski P, Tanner AC, Lee KF, Linder B (1981) Van der Waals forces, scattering functions and charge density susceptibility. II. Application to the He-He interaction potential. Chem Phys 62 423-438... 

We saw earlier that a very simple form of the dispersion energy is obtained from frequency-dependent polarizabilities at the so-called uncoupled Hartree-Fock level. The sum over states appearing in second order RS perturbation theory is simply a sum over (occupied and virtual) orbitals. A first improvement of this simple model is obtained by including apparent correlation [140], i.e. by using frequency-dependent polarizabilities obtained from the TDCHF method [36,141]. This method was initially proposed in the context of the multipole expansion, but could be generalized [142-146] to charge density susceptibility functions (or polarization propagators), which avoids the use... 

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