Three‐dimensional numerical integration for electronic structure calculations

TLDR

The paper presents two three‑dimensional numerical schemes for evaluating molecular integrands, including matrix elements of one‑electron operators in the Fock operator and expectation values of one‑electron operators for molecular properties. The methods partition space to apply product‑Gaussian integration rules in each region and use point‑group symmetry to reduce the number of integration points. Convergence is achieved to 8–10 digits with a modest number of points, and the methods are demonstrated on overlap, nuclear potential, and electric field gradient integrals.

Abstract

Abstract Two three‐dimensional numerical schemes are presented for molecular integrands such as matrix alements of one‐electron operators occuring in the Fock operator and expectation values of one‐electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product‐Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.