On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

Abstract

The exchange dispersion energy for the interaction of two helium atoms is expressed as a sum of multipole components. In contrast to the analogous expansion for the dispersion energy the derived series converges very slowly and the rate of convergence does not improve with an increasing interatomic distance. Numerical calculations show that at the van der Waals minimum the first term of the series, referred to as dipole-dipole exchange energy, represents merely 17 per cent of the exchange dispersion energy. Moreover, even the inclusion of dipole-quadrupole and quadrupole-quadrupole terms can account for only half of the total exchange dispersion interaction. The above difficulty can be avoided by expanding the dispersion pair function in terms of ionic type or explicitly correlated functions. INTRODUCTIONA common practice in the theory of long-range intermolecular forces is to represent various contributions to the interaction energy by means of the so-called multipole expansions [1]. The interaction energies of the first and second order then acquire a simple physical interpretation as the result of the interaction of various permanent, induced or instantaneous multipoles [2]. A similar, though less transparent interpretation, can also be given to the third [3] and higher-order energies [4]. At large intermolecular distances the multipole expansions converge very fast and their application is very effective in practice. At smaller distances where the overlap between interacting systems cannot be neglected, e.g. at the van der Waals minimum region, the multipole expansions can still be made to converge, provided that the charge-overlap effects are properly taken into account [5,6]. In this region, however, the application of the usual RayleighSchr6dinger perturbation theory is no longer legitimate and a suitable symmetryadapted perturbation theory must be employed to allow for the exchange effects [7]. Among the theories proposed the Murrell-Shaw [8] and Musher-Amos [9] approach is distinguished for the simplicity and clear physical sense of the loworder contributions to the energy. When applied through the second order, this theory provides two new contributions: the first-order exchange energy, implicit in the Heitler-London treatment of short-range intermolecular forces [10] and the exchange polarization energy first derived by Murrell et al. [11]. The latter energy can be interpreted as arising from the antisymmetrization of the corrections to the wave function which are due to the induction and dispersion

Intermolecular exchange-induction energies without overlap expansion

“…In the framework of SAPT, the so-called single-exchange or S 2 -approximation was introduced early on [8][9][10][11]. It includes only terms up to the second order of the intermonomer overlap.…”

Gaussian geminals in explicitly correlated coupled cluster theory including single and double excitations

“…In this context it was exploited in early applications of Gaussian geminals. [39][40][41][42][43][44] Basis sets used in these applications were very small, however, since the functional used to optimize the nonlinear parameters contained numerous four-electron integrals resulting from the strong orthogonality requirement. In mid-1980s, the cost of the nonlinear optimizations was significantly reduced by the introduction of a new type of functional, referred to as the weak orthogonality ͑WO͒ functional, [45][46][47] containing, at most, three-electron integrals.…”

Theory and application of explicitly correlated Gaussians

“…In SAPT, the interaction energy is expanded in a double perturbation series with respect to the intermonomer (intermolecular) interaction operator and to the intramonomer correlation operators. The dominant (for nonpolar systems) attractive component, the second-order dispersion energy, can be obtained by minimization of an appropriate Hylleraas-type functional (Chalasinski et al, 1977;Szalewicz and Jeziorski, 1979;Rybak et al, 1987) with a two-electron dispersion pair function. The main repulsive component, the first-order energy, can be obtained from the accurate wave functions of the monomers.…”