The R–7 Dispersion Interaction in the General Effective Fragment Potential Method

The R–7 term (E7) in the dispersion expansion is developed in the framework of the general effective fragment potential (EFP2) method, formulated with the dynamic anisotropic Cartesian polarizability tensors over the imaginary frequency range. The E7 formulation is presented in terms of both the total molecular polarizability and the localized molecular orbital (LMO) contributions. An origin transformation from the center of mass to the LMO centroids is incorporated for the computation of the LMO dipole–quadrupole polarizability. The two forms considered for the damping function for the R–7 dispersion interaction, the overlap-based and Tang–Toennies damping functions, are extensions of the existing damping functions for theR–6 term in the dispersion expansion. The R–7 dispersion interaction is highly orientation dependent: it can be either attractive or repulsive, and its magnitude can change substantially as the relative orientation of two interacting molecules changes. Although the R–7 dispersion energy rotationally averages to zero, it may be significant for systems in which rotational averaging does not occur, such as rotationally rigid molecular systems as in molecular solids or constrained surface reactions

Solvent Effects on Optical Properties of Molecules: A Combined Time-Dependent Density Functional Theory/Effective Fragment Potential Approach

A quantum mechanics/molecular mechanics (QM/MM) type of scheme is employed to calculate the solvent-induced shifts of molecular electronic excitations. The effective fragment potential (EFP) method was used for the classical potential. Since EFP has a density dependent functional form, in contrast with most other MM potentials, time-dependent density functional theory (TDDFT) has been modified to combine TDDFT with EFP. This new method is then used to perform a hybrid QM/MM molecular dynamics simulation to generate a simulated spectrum of the n→π∗ vertical excitation energy of acetone in vacuum and with 100 water molecules. The calculated watersolvent effect on the vertical excitation energy exhibits a blueshift of the n→π∗ vertical excitation energy in acetone (Δω1=0.211 eV), which is in good agreement with the experimental blueshift

Analytic Gradient for Density Functional Theory Based on the Fragment Molecular Orbital Method

The equations for the response terms for the fragment molecular orbital (FMO) method interfaced with the density functional theory (DFT) gradient are derived and implemented. Compared to the previous FMO–DFT gradient, which lacks response terms, the FMO–DFT analytic gradient has improved accuracy for a variety of functionals, when compared to numerical gradients. The FMO–DFT gradient agrees with the fully ab initio DFT gradient in which no fragmentation is performed, while reducing the nonlinear scaling associated with standard DFT. Solving for the response terms requires the solution of the coupled perturbed Kohn–Sham (CPKS) equations, where the CPKS equations are solved through a decoupled Z-vector procedure called the self-consistent Z-vector method. FMO–DFT is a nonvariational method and the FMO–DFT gradient is unique compared to standard DFT gradients in that the FMO–DFT gradient requires terms from both DFT and time-dependent density functional theory (TDDFT) theories