AIHFLTF: Integrals in Laguerre function bases for electronic structure calculations in atoms

Abstract

A program for calculating atomic integrals over Laguerre-type basis functions is provided. The Λ functions are used. They can generate complete orthonormal systems for bound states of atoms. The orthogonality property makes it possible to use large-scale basis sets without loss of accuracy. We have previously published the results of our nonrelativistic Hartree-Fock calculations for He–Og. Total energies were obtained to 30 significant figures for the atoms in the first to third periods. The integrals for this computation were calculated according to the analytical formulation given by Freund and Hill using a multiple-precision arithmetic package. This program for calculating integrals has been rewritten using Gauss-Laguerre quadrature. This version is twice as fast as the previous one while maintaining precision. Since quadruple precision arithmetic implemented in Fortran is used in this version, the program can be further accelerated by OpenMP parallelization. This version has been released. Program summaryProgram Title: AIHFLTFCPC Library link to program files:https://doi.org/10.17632/t4nxzbyssc.1Licensing provisions: MITProgramming language: Fortran 95Nature of problem: The basis set expansion method is widely used in studies of the electronic structure of atoms using the Hartree-Fock method or the post-HF method. The Λ functions which are able to generate complete orthonormal systems for bound states of atoms are used in the present paper. Because of orthogonality, the number of expansion terms can be increased without problems arising from linear dependence, enabling accurate electronic structure calculations. However, evaluation of 2-electron repulsion integrals demands much CPU-time. It is therefore vital in studies of the electronic structure of atoms to calculate 2-electron integrals efficiently.Solution method: Numerical integration based on Gauss-Laguerre quadrature is used to evaluate efficiently 2-electron repulsion integrals over the Λ functions. For this purpose, quadruple precision arithmetic is used, implemented in the Fortran programming language. Accuracy to 30 significant figures is confirmed for the integrals generated, even when the principal quantum number n is up to 200. The most time-consuming step in generating the integral is multiply-add arithmetic in which the values of the integrands at abscissae (zeros of a Laguerre polynomial) are multiplied by the weights. This step can be parallelized by OpenMP.