Confined helium atom low-lying 𝑆 states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

 N. Aquino^a) Jorge Garza A. Flores-Riveros and J. F. Rivas-Silva K. D. Sen

Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México, Distrito Federal, México

Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 México, Distrito Federal, México

Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla, Puebla, México

School of Chemistry, University of Hyderabad, Hyderabad 500 046, India

 

 

ABSTRACT

Calculation including the electron correlation effects is reported for the ground 1𝑆1

and lowest triplet 1𝑆3 state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance 𝑟12

, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.

 https://sci-hub.se/https://doi.org/10.1063/1.2148948