Configuration Interaction and Fixed Node Diffusion Monte Carlo

E. Giner
Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Ferrara, Ferrara, Italie.
Lundi 12 Janvier 2015, 11^h00
bibliothèque LCT, tour 12 - 13, 4e étage

In this talk I will present some of my PhD works [1] that mainly concern the use of selected configuration interaction (CI) for fixed node diffusion Monte Carlo (FN-DMC).
FN-DMC is a powerful stochastic method to solve the Schrödinger equation in real space that suffers mainly from one approximation: the fixed node approximation. The latter is introduced implicitly through the nodes (zeroes) of the trial wave function given in input of a FN-DMC calculation. Improving the nodes is still a hot topic in the field of FN-DMC, and the state of the art method consists in the optimization of an explicitly correlated wave function [2] within a stochastic framework.
Alternatively, I have proposed the use of compact selected CI wave functions that lead to improved nodal structures [3-5]. To select the Slater determinants in an efficient way, we use a perturbative criterion as in the CIPSI algorithm [6]. The CIPSI like algorithm allows one to get a quantitative approximation of the Full CI (FCI) wave function and energy, as I will show in various applications [7]. With such near FCI trial wave function, I will show that the energy differences are of comparable quality with FCI using at least cc-pVTZ basis set. I will then conclude and expose some of the current development and ideas I am involved in.

[1] E. Giner, Coupling Configuration Interaction and Quantum Monte Carlo Methods: The Best of Both Worlds. Thesis, Université de Toulouse, October 2014.
[2] C. J. Umrigar, J. Toulouse, C. Filippi, S. Sorella, and R. G. Hennig, Phys. Rev. Lett. 98, 110201 (2007).
[3] E. Giner, A. Scemama, and M. Caffarel, Can. J. Chem. 91, 879 (2013).
[4] E. Giner, A. Scemama, and M. Caffarel, Fixed-Node Diffusion Monte Carlo Potential Energy Curve of the Fluorine Molecule F₂ Using Selected Configuration Interaction Trial Wavefunctions. ArXiv e-prints, August 2014.
[5] A. Scemama, T. Applencourt, E. Giner, and M. Caffarel, J. Chem. Phys. 141, 244110 (2014).
[6] B. Huron, P. Rancurel, and J. P. Malrieu, J. Chem. Phys. 58, 5745 (1973).
[7] M. Caffarel, E. Giner, A. Scemama, and A. Ramírez-Solís, J. Chem. Theory Comput. 10, 5286 (2014).