Improving the scaling of Quantum Monte Carlo methods, with multi-determinant expansions: illustration on the structural optimization of polyenes
Roland Assaraf
Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Paris, France.
Mercredi 14 Février 2018, 11h00
bibliothèque LCT, tour 12 - 13, 4ème étage
We present an improved formalism for quantum Monte Carlo calculations of energy derivatives and properties (e.g. the interatomic forces), with a multideterminant Jastrow-Slater function. As a function of the number of electrons N, the numerical scaling to optimize all the parameters including the structure is reduced by a factor N, for a small number Ne of determinants, to N3 in the large Ne regime. The overall scaling to optimize the energy is O(N3) + O(Ne) for a fixed number of walkers. This scaling is demonstrated on linear polyenes up to C60H62 and the efficiency of the method is illustrated with the structural optimization of butadiene and octatetraene with Jastrow-Slater wave functions comprising as many as 200000 determinants and 60000 parameters.