Variational Monte Carlo Study of the (1s² 2s) ²Se, (1s² 2p) ²Po and (1s2s2p) ⁴Po States of the Lithium Isoelectronic Sequence

Boubacar Sow^1, , Babou Diop¹, Malick Sow¹ and Omar Absatou Niass¹

¹Department of Physics, Atoms Laser Laboratory, University Cheikh Anta Diop, Dakar, Senegal

Cite this paper:
Boubacar Sow, Babou Diop, Malick Sow and Omar Absatou Niass. Variational Monte Carlo Study of the (1s² 2s) ²Se, (1s² 2p) ²Po and (1s2s2p) ⁴Po States of the Lithium Isoelectronic Sequence. International Journal of Physics. 2026; 14(4):86-92. doi: 10.12691/ijp-14-4-2

Abstract

Total energies of three-electron atomic systems along the lithium isoelectronic sequence are computed with the variational Monte Carlo (VMC) method using compact, fully correlated Slater-Jastrow trial wave functions. The calculation addresses the (1s² 2s) ²S^e ground state, the (1s² 2p) ²P^o first excited state and the metastable doubly excited (1s2s2p) ⁴P^o quartet state, and revisits, with an independent stochastic method, the states studied previously with a hypergeometric correlation factor. The trial wave functions combine a double-zeta 1s orbital, Slater-type 2s and 2p orbitals and a Padé-Jastrow correlation factor satisfying the electron-electron cusp conditions exactly; all parameters are optimised by a mixed energy-variance criterion on correlated samples. The VMC energies reproduce the full core plus correlation (FCPC) reference values to within 0.07% or better over the whole sequence, the virial ratio remains within |η - 2| ≤ 0.023 for all twenty-four states, and the 2s → 2p resonance excitation energies agree with the reference differences to about 0.1 eV or better. For the quartet state, the computed excitation energy of the lithium atom, 57.54 eV, reproduces the experimental term value 57.41 eV to 0.13 eV, and a Z-expansion fit of the sequence yields a leading coefficient 0.75022, in excellent agreement with the exact hydrogenic limit 3/4. The variational upper-bound property of the VMC energies is used to examine critically some previously published values for the ²P^o series, and the specific difficulties raised by autoionizing doublet states such as (1sns2) ²S^e, (1s2sns) ²S^e and (1s2snp) ²P^o are discussed in detail.

Keywords:
Variational Monte Carlo Correlated wave functions Lithium isoelectronic sequence Doubly excited states Jastrow factor Cusp conditions

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