The parameter derivative of the expectation value of the energy, $partial E/partial p$, is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. In some cases, a naive Monte Carlo estimate of this derivative suffers from an infinite variance which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naive estimator which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of $partial E/partial p$ for a multi-Slater-Jastrow trial wave function on the LiH molecule. This regularized estimator is a simple and efficient estimator of $partial E/partial p$ for VMC optimization techniques.
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