Spherical tensor theory of long‐range interactions between two molecules

Abstract

The Rayleigh-Schrodinger perturbation treatment can be applied in the quantum mechanical study of long-range interactions between molecules, when we can assume that the molecular charge distributions do not overlap. In these cases the multipole expansion is a good approximation of real interaction potential and can be treated as a perturbation. In this paper we obtain closed expressions for the anisotropic long-range interaction energy between two molecules in all orders of the perturbation, using spherical tensor formalism. Then we show how spherical multipoles and polarizabilities of the isolated molecules can be inserted into general formulas for interaction energy.

Tensorial analysis of the long-range interaction between metastable alkaline-earth-metal atoms

“…In particular, we show that the electric quadrupolequadrupole operator transforms like a spherical tensor of rank four, and we decompose the electric dipole-dipole dispersion operator into tensors of rank zero, two, and four. Similar tensorial ideas have been applied, for instance, to the anisotropic interactions between molecules [26,27,28] and these were crucial to formally demonstrate the surprising existence of a vector interaction-a tensorial coupling of rank one-between a high-angular momentum Rydberg electron and an anisotropic ionic core [29,30]. General introductions to the techniques of spherical tensor algebra may be found in Refs.…”

Towards Classification and Analytical Description of Molecular Interactions Including Quantum-Mechanical Many-Body Effects

“…A more recent rederivation of Wormer's formulas can be found in [80,132]. Piecuch [138,139] has generalized all the above results showing that an extensive use of spherical tensor formalism and Racah-Wigner algebra leads to closed expressions for the interaction energy between two molecules in all orders of the perturbation. Similarly as in the case of the first-and second-order formulas, these expressions are related to irreducible tensors localized on interacting molecules and the orientational dependence that appears in them is pushed to its limits.…”

“…The derivation of the analogous formulas for the remaining interaction energy contributions discussed in this article are similar and can be found elsewhere (see e.g. [64,[84][85][86]124,134,138,139]). …”

“…At the end of this section it should be only added that all the contributions to the intermolecular energy discussed in this survey can be treated in the same way as we have described above [84,85,124,138]. This remark particularly concerns the use of Racah-Wigner algebra in the graphical representation (for the details, see [84,138]).…”

Angular Momentum Diagrams

“…This requires a recoupling of the multipoles arising in the multipole expansion [57]. This recoupling was applied by Piecuch [58][59][60][61][62] to systems consisting of N closed-shell monomers through third-order of intermolecular perturbation. The graphical technique proved indispensable to handle the very complicated angular momentum algebra arising in this work.…”