Second-order Møller-Plesset perturbation energy obtained from divide-and-conquer Hartree-Fock density matrix

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg(2+)-sensitive dye

A density-fragment interaction (DFI) approach for large-scale calculations is proposed. The DFI scheme describes electron density interaction between many quantum-mechanical (QM) fragments, which overcomes errors in electrostatic interactions with the fixed point-charge description in the conventional quantum-mechanical/molecular-mechanical (QM/MM) method. A self-consistent method, which is a mean-field treatment of the QM fragment interactions, was adopted to include equally the electron density interactions between the QM fragments. As a result, this method enables the evaluation of the polarization effects of the solvent and the protein surroundings. This method was combined with not only density functional theory (DFT) but also time-dependent DFT. In order to evaluate the solvent polarization effects in the DFI-QM/MM method, we have applied it to the excited states of the magnesium-sensitive dye, KMG-20. The DFI-QM/MM method succeeds in including solvent polarization effects and predicting accurately the spectral shift caused by Mg(2+) binding.

Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method

A new scheme for obtaining the approximate correlation energy in the divide-and-conquer (DC) method of Yang [Phys. Rev. Lett. 66, 1438 (1991)] is presented. In this method, the correlation energy of the total system is evaluated by summing up subsystem contributions, which are calculated from subsystem orbitals based on a scheme for partitioning the correlation energy. We applied this method to the second-order Moller-Plesset perturbation theory (MP2), which we call DC-MP2. Numerical assessment revealed that this scheme provides a reliable correlation energy with significantly less computational cost than the conventional MP2 calculation.

Implementation of divide-and-conquer method including Hartree-Fock exchange interaction

The divide-and-conquer (DC) method, which is one of the linear-scaling methods avoiding explicit diagonalization of the Fock matrix, has been applied mainly to pure density functional theory (DFT) or semiempirical molecular orbital calculations so far. The present study applies the DC method to such calculations including the Hartree-Fock (HF) exchange terms as the HF and hybrid HF/DFT. Reliability of the DC-HF and DC-hybrid HF/DFT is found to be strongly dependent on the cut-off radius, which defines the localization region in the DC formalism. This dependence on the cut-off radius is assessed from various points of view: that is, total energy, energy components, local energies, and density of states. Additionally, to accelerate the self-consistent field convergence in DC calculations, a new convergence technique is proposed.