Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

TL;DR

This paper demonstrates that semi-exponential radial basis functions significantly improve the accuracy of variational calculations for three-electron atomic systems, achieving energies close to the exact ground state.

Contribution

The study introduces the use of semi-exponential basis functions to enhance variational wave functions for three-electron atoms, surpassing previous accuracy levels.

Findings

Achieved ground state energy of -7.47805413551 a.u. for ${}^{inite}$Li atom.

Improved energy results are very close to the exact ground state energy.

Semi-exponential basis functions outperform original basis sets in accuracy.

Abstract

The semi-exponential basis set of radial functions (A.M. Frolov, Physics Letters A {\bf 374}, 2361 (2010)) is used for variational computations of bound states in three-electron atomic systems. It appears that semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than it was originally anticipated. In particular, the 40-term Larson's wave function improved with the use of semi-exponential radial basis functions now produces the total energy \linebreak -7.47805413551 $a.u.$ for the ground $1^2S-$state in the ${}^{\infty}$Li atom (only one spin function $\chi_1 = \alpha \beta \alpha - \beta \alpha \alpha$ was used in these calculations). This variational energy is very close to the exact ground state energy of the ${}^{\infty}$Li atom and it substantially lower than the total energy obtained with the original Larson's 40-term wave function (-7.477944869 $a.u.$).