Performance of Lambda functions in atomic Hartree-Fock calculations

Abstract

Hartree-Fock calculations are performed with quadruple-precision arithmetic for 117 single atoms, from He to Og (Z = 118), using Lambda functions. Lambda functions are typical Laguerre-type basis functions, and are suitable for constructing complete orthonormal system for bound states. Through computation, the performance of Lambda functions are investigated. The number of expansion terms for s-type, p-, d- and f-type symmetries are respectively 150, 149, 148, and 147. The numbers of significant figures of the total energies obtained for Group 18 atoms (He, Ne, Ar, Kr, Xe, Rn, Og) are respectively 30, 30, 30, 23, 20, 17, and 15. For Group 1 atoms (Li, Na, K, Rb, Cs, and Fr), the numbers of significant figures are respectively 30, 28, 22, 17, 14, and 13. High precision results, to 30 digits, can be obtained for atoms from the first to the third period (except Na, Al, Si). For atoms with greater atomic number, however, accuracy was degraded. A much larger expansion is necessary to ensure accuracy when the cusp condition is relevant. Values of the energy, virial ratios, orbital energies, and expectation values of $r^n$ (n = 2, 1, −1, −2) are given in the Supplementary Material.

GRAPHICAL ABSTRACT

Keywords:

• Hartree-Fock limit
• Laguerre-type basis function
• complete orthonormal system
• significant figures
• quadruple-precision

Acknowledgements

The authors thank Professor Jacek Karwowski for the opportunity to contribute to this special issue of Molecular Physics commemorating Professor Lutosław Wolniewicz. The authors also thank Professor Emeritus Hiroshi Tatewaki of Nagoya City University for critical reading of the manuscript. The main computation was performed on a cluster of Intel Xeon-based computers at Chukyo University's Institute for Advanced Studies in Artificial Intelligence (IASAI).

Disclosure statement

No potential conflict of interest was reported by the author(s).