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We develop a formalism and present an algorithm for optimization of the trialwave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods.We take advantage of a basic property of the walker configuration distributiongenerated in a DMC calculation, to (i) project-out a multi-determinantexpansion of the fixed-node ground-state wave function and (ii) to define acost function that relates the fixed-node ground-state and the non-interactingtrial wave functions. We show that (a) locally smoothing out the kink of thefixed-node ground-state wave function at the node generates a new trialwave-function with better nodal structure and (b) we argue that the noise inthe fixed-node wave-function resulting from finite sampling plays a beneficialrole, allowing the nodes to adjust towards the ones of the exact many-bodyground state in a simulated annealing-like process. We propose a method toimprove both single determinant and multi-determinant expansions of the trialwave-function. We test the method in a model system where benchmarkconfiguration interaction calculations can be performed. Comparing the DMCcalculations with the exact solutions, we find that the trial wave-function issystematically improved. The overlap of the optimized trial wave function andthe exact ground state converges to 100% even starting from wave-functionsorthogonal to the exact ground state. In the optimization process we find anoptimal non-interacting nodal potential of density-functional-like form whoseexistence was predicted earlier[Phys.Rev. B {\bf 77}, 245110 (2008)]. We obtainthe exact Kohn-Sham effective potential from the DMC data.

Self-healing diffusion quantum Monte Carlo algorithms: methods for direct reduction of the fermion sign error in electronic structure calculations