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.

The numerical accuracy of linear scaling semiempirical methods LocalSCF and MOZYME is analyzed in comparison to conventional matrix diagonalization with respect to a variety of molecular properties including conformational energy, dipole moment, atomic charges, and bond orders. Major semiempirical MNDO, AM1, PM3, and PM5 Hamiltonians were considered in the study. As the numerical tests demonstrate, both LocalSCF and MOZYME reasonably reproduce matrix diagonalization results with the deviations being below the accuracy of semiempirical methods. However, the economical LocalSCF memory consumption and faster calculations are more beneficial for the quantum-mechanical modeling of large biological systems. The computational performance of the LocalSCF method is tested on the conformational energy calculation of a series of molecular dynamics snapshots of insulin in a large box of water.

Rovibrational states of a diatomic molecule placed into a spherical cavity with impenetrable walls are studied within the adiabatic approximation. The finite-difference results for the nuclear Schrö dinger equation are presented for cavities of the radius 3-10 atomic units for LiF and LiCl molecules as samples. The intensities of rovibrational transitions are evaluated within a rough dipole-like approximation. Perturbation theory gives a clue for qualitative understanding of some features of the spectrum, such as practically constant ⌬G(1/2) values for confined molecules in various cavities and essential enlargement of the distance between R-and P-band branches in rovibrational spectrum for small cavities.

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