Zero-variance zero-bias quantum Monte Carlo estimators for the electron density at a nucleus

We derive new quantum Monte Carlo (QMC) estimators for the electronic density at the position of a point nucleus using the zero-variance and zero-bias principles. The resulting estimators are highly efficient, and are significantly simpler to implement and use than alternative methods, as they contain no adjustable parameters. In addition, they can be used in both variational and diffusion QMC calculations. Our best estimator is used to calculate the most accurate available estimates of the total electron density at the nucleus for the first-row atoms Li-Ne, the Ar atom, and the diatomic molecules B2, N2, and F2