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

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 $\mathcal{O}(N^3)$, $\mathcal{O}(N^3)$, and $\mathcal{O}(N^5)$ respectively, where $N$ denotes system size. These scalings are not asymptotic and hold over all ranges of $N$.

References in corpus (3)

• Gaussian and plane-wave mixed density fitting for periodic systems
• Low rank factorization of the Coulomb integrals for periodic coupled cluster theory
• Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

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