Wave‐function optimization by least‐squares fitting of the exact wave function sampled by quantum Monte Carlo

The sampling of the exact solution of the Schrödinger equation by quantum Monte Carlo methods allows one to solve the problem of the optimization of linear and nonlinear parameters of a trial wave function by minimization of the distance to the exact wave function in Hilbert space even for those systems whose exact wave function is unknown. The overlap integrals between the basis functions and the exact wave function can be easily estimated within the quantum Monte Carlo formalism. Several observables of the helium atom ground state, computed both within the orbital approximation and by an explicitly correlated basis set, evidence the overall goodness of the wave function optimized according to this criterion.