Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled...

The representation and storage of two-electron integral tensors are vital in large-scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this work, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of the atomic basis set, N_b, ranging from ∼100 up to ∼2,000, the observed numerical scaling of our implementation shows [Formula: see text] versus [Formula: see text] cost of performing single CD on the two-electron integral tensor in most of the other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic orbital (AO) two-electron integral tensor from [Formula: see text] to [Formula: see text] with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled cluster formalism employing single and double excitations (CCSD) on several benchmark systems including the C₆₀ molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^-4 to 10^-3 to give acceptable compromise between efficiency and accuracy.