Hylleraas-Configuration Interaction calculations on the 1 ^1S ground state of helium atom

TL;DR

This paper presents highly accurate Hylleraas-Configuration Interaction calculations for the helium atom's ground state, introducing new techniques for configuration construction and a novel method for evaluating two-electron integrals.

Contribution

It introduces a new method for evaluating two-electron kinetic energy integrals within Hy-CI calculations and compares its accuracy and efficiency with existing methods.

Findings

Achieved approximately 10 picohartree accuracy in non-relativistic energy calculations.

Demonstrated the effectiveness of the new integral evaluation method.

Compared computational times and accuracy with CI and Hy methods.

Abstract

Hylleraas-Configuration Interaction (Hy-CI) calculations on the ground $1^1$S state of helium atom are presented using s-, p-, d-, and f-Slater orbitals of both real and complex form. Techniques of construction of adapted configurations, optimization of the orbital exponents and structure of the wave function expansion are explored. A new method to evaluate the two-electron kinetic energy integrals occurring in the Hy-CI method has been tested here and compared with other methods. The non-relativistic Hy-CI values are approximately 10 picohartree accurate, about 2.2 x 10$^{-6}$ cm$^{-1}$. The Hy-CI calculations are compared with Configuration Interaction (CI) and Hylleraas (Hy) calculations employing the same orbital basis set, same computer code and same computer machines. The computational required times are reported.