Nonadiabatic variational calculations on dipositronium using explicitly correlated Gaussian basis functions

Abstract

Nonadiabatic variational calculations are described for dipositronium (${\mathit{e}}^{+}$,${\mathit{e}}^{+}$,${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,${\mathit{e}}^{\mathrm{\ensuremath{-}}}$) using explicitly correlated Gaussian basis functions with angular momentum zero. An improved rigorous upper bound for the ${\mathit{A}}_{1}$ ground-state energy for dipositronium is achieved (-0.515 976 7 a.u.) leading to a corresponding bound for the binding energy, \ensuremath{\Delta}${\mathrm{\ensuremath{\varepsilon}}}_{0}$>0.435 eV, which is greater than previous estimates by 0.024 eV. This improved energy is obtained by exploiting the full permutational symmetry of the Hamiltonian including charge-reversal symmetry which was ignored in recent calculations. The first excited ${\mathit{A}}_{1}$ state, and the lowest ${\mathit{B}}_{1}$ and ${\mathit{A}}_{2}$ states of dipositronium are found to be unbound while the ${\mathit{B}}_{2}$ and E states appear to be metastable. For comparison, by the same method, the $^{2}$S ground-state energy of the lithium atom is found to be -7.476 716 1 a.u., which lies 0.001 343 a.u. above the accepted true energy. Expectation values for individual terms of the Hamiltonian along with moments of interparticle distances 〈${\mathit{r}}^{\ifmmode\pm\else\textpm\fi{}1}$〉, 〈${\mathit{r}}^{\ifmmode\pm\else\textpm\fi{}2}$〉, and 〈\ensuremath{\delta}(${\mathit{r}}_{\mathit{i}\mathit{j}}$)〉 are also reported.