Optimization of Quantum Monte Carlo Wave Functions Using Analytical Energy Derivatives

Abstract

An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on New ton's method and analytical computation of the first and second derivatives of the variati onal energy. This direct application of the variational principle yields significantly low er energy than variance minimization methods when applied to the same trial wave function. Quadratic convergence to the local minimum of the variational parameters is achieved. A g eneral theorem is presented, which substantially simplifies the analytic expressions of de rivatives in the case of wave function optimization. To demonstrate the method, the ground state energies of the first-row elements are calculated.