Lowering of the complexity of quantum chemistry methods by choice of representation

Narbe Mardirossian; James D McClain; Garnet Kin-Lic Chan

doi:10.1063/1.5007779

Lowering of the complexity of quantum chemistry methods by choice of representation

J Chem Phys. 2018 Jan 28;148(4):044106. doi: 10.1063/1.5007779.

Authors

Narbe Mardirossian¹, James D McClain¹, Garnet Kin-Lic Chan¹

Affiliation

¹ Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.

PMID: 29390857
DOI: 10.1063/1.5007779

Abstract

The complexity of the standard hierarchy of quantum chemistry methods is not invariant to the choice of representation. This work explores how the scaling of common quantum chemistry methods can be reduced using real-space, momentum-space, and time-dependent intermediate representations without introducing approximations. We find the scalings of exact Gaussian basis Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and coupled cluster theory (specifically, linearized coupled cluster doubles and the distinguishable cluster approximation with doubles) to be O(N³), O(N³), and O(N⁵), respectively, where N denotes the system size. These scalings are not asymptotic and hold over all ranges of N.