Implementation of the diagonalization‐free algorithm in the self‐consistent field procedure within the four‐component relativistic scheme

Abstract

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Šimunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization.

High-Frequency 1H NMR Chemical Shifts of SnII and PbII Hydrides Induced by Relativistic Effects: Quest for PbII Hydrides

“…This level of theory is noted as 4c-PBE in this work. A novel, more efficient diagonalization-free algorithm was employed in the self-consistent field procedure within the four-component relativistic scheme, 50 effectively reducing the time required for the SCF procedure by approximately one-third in the case of parallel runs (>48 cores). The 1 H NMR chemical shifts are referenced relative to TMS.…”

ReSpect: Relativistic spectroscopy DFT program package

“…Various attempts have been reported in the literature to reduce the computational burden associated with the solution of the 4c eigenvalue problem, such as the diagonalization-free approach implemented in ReSpect. 79 In the case of the two-component X2C Hamiltonian, the eigenvalue equation is only 2n × 2n in size, and hence, its solution poses a lesser computational challenge than the full 4c treatment. Additional computational complexity arises in 4c SCF in the evaluation of the overlap and Fock operators in the RKB basis.…”

“…• resolution-of-the-identity integral acceleration for the Coulomb term (RI-J), 42 • PCM solvent model, 45,46 • diagonalization-free SCF approach, 79 • initial guess based either on a superposition of atomic densities or on a restart from approximate 1c/2c Hamiltonians, and • hybrid MPI/OpenMP parallelization.…”

Full Parallel Implementation of an All-Electron Four-Component Dirac–Kohn–Sham Program

“…Figure 5 shows therefore that the only limitation to the overall SCF speedup is due to the matrix diagonalization step. Diagonalization free approaches, in this respect, such as the Thouless expansion-based one 57 that has recently been extended to the four-component formalism, 58 present themselves as a promising alternative.…”