Ground state of Li and Be${}^{+}$ using explicitly correlated functions

Abstract

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and Be${}^{+}$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground state energies $-7.47806032391010(32)$, $-14.32476317679043(22)$ of Li and Be${}^{+}$ correspondingly, are the most accurate to date. When small basis set is considered, explicitly correlated exponential functions are much more effective. With only 128 functions we obtained about $10^{-9}$ relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.

15 pages

References in corpus (8)

• Nonrelativistic ionization energy for the helium ground state
• Ground state wave function and energy of the lithium atom
• Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be${}^{+}$
• Fine and hyperfine splitting of the 2P state in Li and Be${}^{+}$
• Recursion relations for Hylleraas three-electron integral
• Two-center two-electron integrals with exponential functions
• Analytic Evaluation of Four-Particle Integrals with Complex Parameters
• Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions

Cited by in corpus (10)

• Explicitly correlated wave function for a boron atom
• Hylleraas-configuration-interaction analysis of the low-lying states in the three-electron Li atom and Be+ ion
• Helium- and Lithium-like ionic sequences: Critical charges
• D1 and D2 lines in ${}^{6,7}$Li including QED effects
• Applications of four-body exponentially correlated functions
• Ground state hyperfine splitting in the Be${}^{+}$ ion
• Atomic excitations during the nuclear ß- decay in light atoms
• How Large are Nonadiabatic Effects in Atomic and Diatomic Systems?
• Coupled-cluster calculations of properties of Boron atom as a monovalent system
• On the ß- decay in the Li-8 and Li-9 atoms