VMC with ultra-compact, explicitly-correlated wave functions for the study of the Li isoelectronic sequence

Variational Monte Carlo (VMC) is one of the simplest Quantum Monte Carlo (QMC) methods, which leverages random sampling to optimize the parameters of a given wave function. VMC is therefore a powerful tool for optimizing and evaluating the properties of explicitly-correlated wave functions. Explicitly-correlated wave functions are relatively simple, and therefore compact, and can be used as trial wave functions for more advanced quantum Monte Carlo methods. In this contribution, we optimize explicitly-correlated wave functions, with only seven nonlinear parameters, using VMC to describe the lowest quartet state (1s2s2p) of the Li isoelectronic sequence with nuclear charges between 3-10. The trial wave function is motivated by the exact solution for the limit case of infinite nuclear charge multiplied by exponentials with explicit dependence on relative distances between the electrons. The variational parameters admit an interpretation of screened electric charges as seen from the electrons. After the optimization, it is found that the compact wave function correctly describes the cusp conditions in the vicinity of the nucleus and that the variational parameters can be fit by quadratic functions of the nuclear charge.