Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories forthe calculation of frequency-dependent molecular response properties and excitation energies ispresented, based on a nonredundant exponential parametrization of the one-electron density matrixin the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solvediteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory.Important features of the subspace method are the use of paired trial vectors to preserve thealgebraic structure of the response equations, a nondiagonal preconditioner for rapid convergence,and the generation of good initial guesses for robust solution. As a result, the performance of theiterative method is the same as in canonical molecular-orbital theory, with five to ten iterationsneeded for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, thecalculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once ineach iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated incalculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptidescontaining up to 1400 atoms.