Software implementation and performance study of the rank-reduced relativistic coupled-cluster method
Rumiantsev A. S.1,2, Oleynichenko A. V.1,3, Zaitsevskii A.V.1
1Konstantinov Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute, Gatchina, Russia
2St. Petersburg State University, St. Petersburg, Russia
3Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
Email: rumyantsev_as@pnpi.nrcki.ru
A relativistic version of the rank-reduced coupled-cluster method accounting for double excitations (RR-RCCD) has been developed and implemented as a software package. The method is designed for accurate electronic structure calculations of systems containing heavy elements in their ground states possessing single-reference character. High computational efficiency is achieved through the simultaneous application of the Tucker approximation for the cluster amplitude tensor and the partial Cholesky decomposition for the tensor of two-electron integrals. The scalability of the developed method has been studied numerically for a series of linear molecules (AuCN)n, n=1-5. It has been shown that for a fixed threshold for discarding singular values identical for all studied systems, the effective rank of the cluster amplitude tensor grows approximately linearly with the number of atoms in the system. This makes possible a reduction of the computational complexity of the relativistic coupled-cluster RCCD algorithm from O(N^6) to O(N^5) (N stands for the number of one-electron spinors). Keywords: Relativistic coupled-cluster method, tensor decompositions, Tucker decomposition, partial Cholesky decomposition, effective core potentials, gold(I) cyanide.
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