The reference energy E ref in the above equation is used to stabilize the diffusion system in its ground state and thus is the estimator of the zero-point energy. We employed the unbiased, unconstrained implementation of DMC, in which the DMC calculation starts from an initial guess of the ground-state wave function, represented by a population of N (0) equally weighted Gaussian random walkers. These walkers then diffuse randomly in imaginary time according to a Gaussian distribution. The population is controlled by a birth-death processes, described elsewhere. To maintain the number of random walkers at about the initial value N (0), E ref is adjusted at the end of each time step according to