Basis sets and Coulomb resolutions in rotational coordinates

Abstract

Using generalised Laplacian symmetry operators, we construct basis sets or Coulomb resolutions in several separable coordinate systems, including two R-separable systems. This expands the possible geometries in which basis set construction is feasible, a problem which is relevant to both galactic dynamics and computational chemistry. In particular we derive three basis sets (two in prolate spheroidal and one in cylindrical coordinates) which are expressible in closed-form using a single Jacobi polynomial. We also show how any spherical polar or prolate spheroidal basis set may be transformed into a bispherical or toroidal basis set.

Author-accepted manuscript; see J. Phys. A for final published version

References in corpus (4)

• New biorthogonal potential--density basis functions
• Efficient Algorithm for Two-Center Coulomb and Exchange Integrals of Electronic Prolate Spheroidal Orbitals
• A general basis set algorithm for galactic haloes and discs
• Two-integral distribution functions for axisymmetric stellar systems with separable densities