Physical Review B 79 195117 (2009)
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground state probability density. We argue in favor of the conjecture that removing the kink of the fixed-node ground-state wave-function at the node improves the resulting wave-function nodal structure. If this conjecture is valid, then the noise in the fixed-noded wave function would play a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. Based on these conjectures, we propose a method to improve both single determinant and multi-determinant expressions of the trial wave-function. We test the method in a model system where a near analytical solution can be found. Comparing the DMC calculations with the exact solutions, we find that the trial wave-function is systematically improved. The overlap of the optimized trial wave-function and the exact ground state converges to 100% even starting from wave-functions orthogonal to the exact ground state. Tests of the method are extended to a model system with a full Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.
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