On the numerical integration of two-particle functions for pair entropies of diatomic molecules

In order to compute two-electron informational entropies of atoms or molecules, highly-accurate numerical integration methods are needed. In this contribution, we describe the details of a numerical algorithm specific for diatomic molecules, originally designed to numerically integrate 3D functions. The algorithm is adapted to integrate functions of two particles, i.e., to integrate functions in domains of the form Ω × Ω, where Ω ∈ R3 . The diatomic integration scheme is a cubature rule that combines Gauss-Legendre quadratures for the radial and angular parts, and the domain Ω is split into two semi-spheres, each with its own local center of coordinates. In addition, we compare the performance of the diatomic integration scheme vs. a Monte Carlo integrator, both for the 3D and 6D cases.