Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework: Applications to positronic molecular systems

In the application of the nuclear-electronic orbital (NEO) method to positronic systems, all electrons and the positron are treated quantum mechanically on the same level. Explicit electron-positron correlation can be included using Gaussian-type geminal functions within the variational self-consistent-field procedure. In this paper, we apply the recently developed reduced explicitly correlated Hartree-Fock (RXCHF) approach to positronic molecular systems. In the application of RXCHF to positronic systems, only a single electronic orbital is explicitly correlated to the positronic orbital. We apply NEO-RXCHF to three systems: positron-lithium, lithium positride, and positron-lithium hydride. For all three of these systems, the RXCHF approach provides accurate two-photon annihilation rates, average contact densities, electronic and positronic single-particle densities, and electron-positron contact densities. Moreover, the RXCHF approach is significantly more accurate than the original XCHF approach, in which all electronic orbitals are explicitly correlated to the positronic orbital in the same manner, because the RXCHF wavefunction is optimized to produce a highly accurate description of the short-ranged electron-positron interaction that dictates the annihilation rates and other local properties. Furthermore, RXCHF methods that neglect or approximate the electronic exchange interactions between the geminal-coupled electronic orbital and the regular electronic orbitals lead to virtually identical annihilation rates and densities as the fully antisymmetric RXCHF method but offer substantial advantages in computational tractability. Thus, NEO-RXCHF is a promising, computationally practical approach for studying larger positron-containing systems.