Elongation method with cutoff technique for linear SCF scaling

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 self-consistent 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.