Abstract
The manipulation of the rank-four tensor of double excitation amplitudes represents a challenge to the efficient implementation of many electronic structure methods. We present a proof of concept for the approximation of doubles amplitudes in the tensor hypercontraction (THC) representation. In particular, we show how THC can be used to both reduce the scaling with respect to molecular size of coupled cluster singles and doubles (CCSD) (and related methods) by two orders [from O(N(6)) to O(N(4))] and remove the memory bottleneck associated with storage of the doubles amplitudes. The accuracy of correlated methods as integral and amplitude approximations are introduced is examined. For a set of 20 small molecules, single and double-excitation configuration interaction (CISD), quadratic CISD (QCISD), and CCSD correlation energies could be reproduced with millihartree accuracy after the introduction of these approximations. Our approach exploits otherwise hidden factorizable tensor structure in both the electron repulsion integrals and the wavefunction coefficients and should be applicable with suitable modifications to many methods in electronic structure theory.
Highlights
Rank reduction has become increasingly popular in electronic structure theory as a means of reducing the computational cost associated with many methods
We have performed computations at the configuration interaction singles and doubles (CISD)/cc-pVDZ, quadratic CISD (QCISD)/cc-pVDZ, and coupled cluster singles and doubles (CCSD)/cc-pVDZ levels of theory on a set of 20 small molecules; the results are summarized in Table I and details can be found in the supplementary material
These computations use LS-tensor hypercontraction (THC) electron repulsion integrals (ERIs) or both least-squares THC representation (LS-THC) ERIs and LS-THC doubles amplitudes (T2); the reference values are obtained from density fitting (DF)-CISD, DF-QCISD, and DF-CCSD calculations
Summary
Rank reduction has become increasingly popular in electronic structure theory as a means of reducing the computational cost associated with many methods. The density fitting (DF) and related Cholesky decomposition (CD) approximations to the electron repulsion integrals (ERIs) are widely employed Despite their successes, DF and CD provide improved efficiency primarily through prefactor reduction rather than reducing the overall scaling of a method, there are a few notable exceptions where scaling reduction can be achieved.. We propose to apply the recently developed least-squares THC representation (LS-THC) to the doubles amplitudes as well as the ERIs in CCSD This will provide a scaling reduction of two orders with respect to system size and will remove the memory and disk I/O bottlenecks often associated with the method
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