A Linear-Scaling Divide-and-Conquer Quantum Chemical Method for Open-Shell Systems and Excited States

The acceleration of ab initio electronic structure calculations has been one of the most important themes in the field of quantum chemistry since the mid-1980s when a series of single-reference theories starting from the Hartree-Fock (HF) method were already mature. The standard single-reference quantum chemical calculations consist of three time-consuming steps, namely, the Fock-matrix construction, its diagonalization to obtain the molecular orbitals (MOs) and/or one-electron density matrix, and the post-HF correlation calculation that does not appear in the HF and Kohn-Sham (KS) density functional theory (DFT) calculations. This chapter reviews the linear-scaling quantum chemical calculation for the extension to open-shell and excited-state theories based on the divide-and-conquer (DC) method. Finally, it describes the efficiencies of the DC-UHF and UMP2 methods in measuring the central processing unit (CPU) time. The performance of the present DC-CIS, DC-TDDFT, and DC-SACCI methods is numerically assessed by comparing the results with those of conventional CIS, TDDFT, and SACCI calculations.