Initial Guesses for Multicomponent Mean-Field Methods: Assessment and New Developments

Abstract

The convergence of self-consistent field equations in mean-field nuclear-electronic orbital methods strongly depends on the choice of initial guesses for quantum nuclei. Although several such guesses have been proposed in the literature, a systematic comparison of their performance as well as attempts of constructing novel approximations based on model tasks of quantum mechanics were not reported to date. In this work, we address both issues by introducing novel nuclear initial guesses derived from the analytical solutions of the three-dimensional quantum harmonic oscillator and benchmarking them against existing approaches. We demonstrate that the isotropic variant of our guess outperforms existing approximations in nuclear-electronic orbital density functional theory calculations employing a simultaneous self-consistent field convergence protocol. Although our guess requires the computation of partial Hessians, we demonstrate that these can be evaluated with low-cost methods without affecting the accuracy of resulting protonic density matrices. Our results demonstrate that the proposed guess is robust and efficient and could provide a route to improved convergence in mean-field nuclear-electronic orbital computations.