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, 4^ème 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 N_e of determinants, to N³ in the large N_e regime. The overall scaling to optimize the energy is O(N₃) + O(N_e) 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.