Optimization of quantum Monte Carlo wave functions using analytical energy derivatives

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Abstract
An algorithm is proposed to optimize quantum Monte Carlo (QMC) wave functions based on Newton’s method and analytical computation of the first and second derivatives of the variational energy. This direct application of the variational principle yields significantly lower 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 general theorem is presented, which substantially simplifies the analytic expressions of derivatives in the case of wave function optimization. To demonstrate the method, the ground-state energies of the first-row elements are calculated.