Elongation method with cutoff technique for linear SCF scaling

Abstract

ABSTRACT:The elongation method uses the concept of locality and works in a regionally localized molecular orbital basis set. In this method the system is partitioned into several frozen fragments and an active one. If the coupling between a given frozen fragment and the active space is small enough, one can develop a cutoff scheme for effectively discarding the former in all further calculations. At the Hartree-Fock level many two-electron integrals are thereby eliminated, leading to a reduction in selfconsistent field computation time. In test calculations on four polyglycine conformers, with an appropriate default threshold for coupling, the cutoff error is very small and/ or comparable to that of a normal elongation calculation. On the other hand, the computation time for 20 residues is a factor of 5 less than that of a normal Hartree-Fock treatment and scales linearly (or even sublinearly) with the number of residues.

Elongation cutoff technique at Kohn–Sham level of theory

“…The cutoff variant of ELG [20,21] takes the full advantage of LMOs. In the limit of perfect localization, LMOs assigned to frozen fragment (C A i) have no tails in active fragment and vice versa, LMOs assigned to active fragment (C S i ) have no tails in the frozen one.…”

“…The ELG method works within localized molecular orbital (LMO) reference frame. The cutoff elongation (ELG/C) method [20] takes into account the sparsity of KS or HF matrix in LMO representation. This allowed diminishing the size of all matrices used in the SCF process.…”

Elongation cutoff technique armed with quantum fast multipole method for linear scaling

“…The idea of ELG/C technique [30][31][32][33] is very simple. In the limit of perfect localization, the frozen MOs have no tails in the active part and vice versa, the active MOs have no tails in the frozen region:…”

“…Therefore, a threshold value reflecting coupling between frozen and active fragments is introduced: 31 If the coupling, d n , is below the threshold, then the frozen part A k is disregarded in the next (n 1 1) propagation step.…”

“…The elongation (ELG) method has been developed to efficiently calculate the electronic structures of large aperiodic systems with high accuracy. [18][19][20][21][22][23] Its cutoff variant [30][31][32][33] takes into account sparse matrix algebra in a very efficient way. In contrast to majority fragmentation methods, the ELG (ELG/C) method does not simplify the picture of interaction and exactly the same number of ERI is computed as for supermolecule.…”