Optimization of quantum Monte Carlo wave functions by energy minimization
- Julien Toulouse (Université Pierre et Marie Curie, Laboratoire de Chimie Théorique, Paris, France)
Abstract
I will present a simple, robust and highly efficient method for optimizing the parameters of many-body wave functions by energy minimization in quantum Monte Carlo calculations. Using a strong zero-variance principle, the optimal parameters are determined by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its derivatives [1-2]. We apply this method to obtain accurate multideterminant Jastrow-Slater wave functions for atomic and molecular systems, where the Jastrow parameters, the configuration state function coefficients, the orbital coefficients and the basis function exponents are simultaneously optimized. This allows one to reach near chemical accuracy on the dissociation energies of the first-row diatomic homonuclear molecules [3]. If time permits, I will also illustrate the use of these optimized wave functions, together with the construction of improved statistical estimators, to compute observables such as dipole moments and pair densities [4].
[1] J. Toulouse and C. J. Umrigar, J. Chem. Phys. 126, 084102 (2007).
[2] C. J. Umrigar, J. Toulouse, C. Filippi, S. Sorella, and R. G. Hennig, Phys. Rev. Lett. 98, 110201 (2007).
[3] J. Toulouse, C. J. Umrigar, J. Chem. Phys. 128, 174101 (2008).
[4] J. Toulouse, R. Assaraf, C. J. Umrigar, J. Chem. Phys. 126, 244112 (2007).
