Nonadiabatic variational calculations on dipositronium using explicitly correlated Gaussian basis functions

Nonadiabatic variational calculations are described for dipositronium (${\mathit{e}}^{+}$,${\mathit{e}}^{+}$,${\mathit{e}}^{\mathrm{-}}$,${\mathit{e}}^{\mathrm{-}}$) 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, Δ${\mathrm{\varepsilon }}_0$>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 〈${\mathit{r}}^{\pm 1}$〉, 〈${\mathit{r}}^{\pm 2}$〉, and 〈δ(${\mathit{r}}_{\mathit{i}\mathit{j}}$)〉 are also reported.