Austin, Brian, Alán Aspuru-Guzik, Romelia Salomón-Ferrer, and William A. Lester. 2006. “Linear-Scaling Evaluation of the Local Energy in Quantum Monte Carlo.” Advances in Quantum Monte Carlo (December 31): 55–68. doi:10.1021/bk-2007-0953.ch005.
For atomic and molecular quantum Monte Carlo calculations, most of the computational effort is spent in the evaluation of the local energy. We describe a scheme for reducing the computational cost of the evaluation of the Slater determinants and correlation function for the correlated molecular orbital (CMO) ansatz. A sparse representation of the Slater determinants makes possible efficient evaluation of molecular orbitals. A modification to the scaled distance function facilitates a linear scaling implementation of the Schmidt-Moskowitz-Boys-Handy (SMBH) correlation function that preserves the efficient matrix multiplication structure of the SMBH function. For the evaluation of the local energy, these two methods lead to asymptotic linear scaling with respect to the molecule size.