First principles multielectron mixed quantum/classical simulations in the condensed phase. I. An efficient Fourier-grid method for solving the many-electron problem

Abstract

We introduce an efficient multielectron first-principles based electronic structure method, the two-electron Fourier-grid (2EFG) approach, that is particularly suited for use in mixed quantum/classical simulations of condensed-phase systems. The 2EFG method directly solves for the six-dimensional wave function of a two-electron Hamiltonian in a Fourier-grid representation such that the effects of electron correlation and exchange are treated exactly for both the ground and excited states. Due to the simplicity of a Fourier-grid representation, the 2EFG is readily parallelizable and we discuss its computational implementation in a distributed-memory parallel environment. We show our method is highly efficient, being able to find two-electron wave functions in approximately 20 s on a modern desktop computer for a calculation this is equivalent to full configuration interaction (FCI) in a basis of 17 million Slater determinants. We benchmark the accuracy of the 2EFG by applying it to two electronic structure test problems: the harmonium atom and the sodium dimer. We find that even with a modest grid basis size, our method converges to the analytically exact solutions of harmonium in both the weakly and strongly correlated electron regimes. Our method also reproduces the low-lying potential energy curves of the sodium dimer to a similar level of accuracy as a valence CI calculation, thus demonstrating its applicability to molecular systems. In the following paper [W. J. Glover, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 132, 144102 (2010)], we use the 2EFG method to explore the nature of the electronic states that comprise the charge-transfer-to-solvent absorption band of sodium anions in liquid tetrahydrofuran.