Gene

Quantum mechanics

Algorithm

Pure mathematics

Factorization

Coupled cluster

Rank (graph theory)

Eigenvalues and eigenvectors

Biochemistry

Molecule

Cholesky decomposition

Tensor (intrinsic definition)

Physics

Amplitude

Mathematics

Quartic function

Transcription factor

Computational chemistry

Combinatorics

Repressor

Chemistry

Operator (biology)

The Journal of Chemical Physics

We develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes