Calculation of the positron annihilation rate in PsH with the positronic extension of the explicitly correlated nuclear-electronic orbital method.

The nuclear-electronic orbital explicitly correlated Hartree-Fock (NEO-XCHF) method is modified and extended to study electron-positron quantum systems. The NEO-XCHF method is more computationally efficient than the explicitly correlated methods previously applied to positron systems because only the electron-positron dynamical correlation is treated explicitly in NEO-XCHF. As a result, the form of the wave function is much simpler with fewer parameters, and the variational optimization of the molecular orbital parameters is performed through an iterative scheme rather than a stochastic optimization. The NEO-XCHF approach is used to calculate the positron annihilation rate for positronium hydride (PsH). The resulting annihilation rate for PsH is within 20% of the most accurate values available and is calculated at a fraction of the computational cost. These results suggest that qualitatively accurate positron annihilation rates can be calculated treating only electron-positron correlation explicitly, leading to significant computational savings by neglecting electron-electron dynamical correlation. Thus, the NEO-XCHF approach could potentially enable the calculation of qualitatively accurate positron annihilation rates for larger positron systems.