Large-scale excited-state calculation using dynamical polarizability evaluated by divide-and-conquer based coupled cluster linear response method

Abstract

This study attempted to propose an efficient scheme at the coupled cluster linear response (CCLR) level to perform large-scale excited-state calculations of not only local excitations but also nonlocal ones such as charge transfers and transitions between delocalized orbitals. Although standard applications of fragmentation techniques to the excited-state calculations brought about the limitations that could only deal with local excitations, this study solved the problem by evaluating the excited states as the poles of dynamical polarizability. Because such an approach previously succeeded at the time-dependent density functional theory level [H. Nakai and T. Yoshikawa, J. Chem. Phys. 146, 124123 (2017)], this study was considered as an extension to the CCLR level. To evaluate the dynamical polarizability at the CCLR level, we revisited three equivalent formulas, namely, coupled-perturbed self-consistent field (CPSCF), random phase approximation (RPA), and Green’s function (GF). We further extended these formulas to the linear-scaling methods based on the divide-and-conquer (DC) technique. We implemented the CCLR with singles and doubles (CCSDLR) program for the six schemes, i.e., the standard and DC-type CPSCF, RPA, and GF. Illustrative applications of the present methods demonstrated the accuracy and efficiency. Although the standard three treatments could exactly reproduced the conventional frequency-domain CCSDLR results, their computational costs were commonly higher than that of the conventional ones due to large amount of computations for individual frequencies of the external electric field. The DC-type treatments, which approximately reproduced the conventional results, could achieve quasilinear scaling computational costs. Among them, DC-GF was found to exhibit the best performance.