LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules

A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.