GPU acceleration of rank-reduced coupled-cluster singles and doubles.

Abstract

We have developed a graphical processing unit (GPU) accelerated implementation of our recently introduced rank-reduced coupled-cluster singles and doubles (RR-CCSD) method. RR-CCSDintroduces a low-rank approximation of the doubles amplitudes. This is combined with a low-rank approximation of the electron repulsion integrals via Cholesky decomposition. The result of these two low-rank approximations is the replacement of the usual fourth-order CCSDtensors with products of second- and third-order tensors. In our implementation, only a single fourth-order tensor must be constructed as an intermediate during the solution of the amplitude equations. Owing in large part to the compression of the doubles amplitudes, the GPU-accelerated implementation shows excellent parallel efficiency (95% on eight GPUs). Our implementation can solve the RR-CCSDequations for up to 400 electrons and 1550 basis functions-roughly 50% larger than the largest canonical CCSDcomputations that have been performed on any hardware. In addition to increased scalability, the RR-CCSDcomputations are faster than the corresponding CCSDcomputations for all but the smallest molecules. We test the accuracy of RR-CCSDfor a variety of chemical systems including up to 1000 basis functions and determine that accuracy to better than 0.1% error in the correlation energy can be achieved with roughly 95% compression of the ov space for the largest systems considered. We also demonstrate that conformational energies can be predicted to be within 0.1kcal mol-1 with efficient compression applied to the wavefunction. Finally, we find that low-rank approximations of the CCSDdoubles amplitudes used in the similarity transformation of the Hamiltonian prior to a conventional equation-of-motion CCSDcomputation will not introduce significant errors (on the order of a few hundredths of an electronvolt) into the resulting excitation energies.