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-Induced Shift of the Lowest Singlet π → π* Charge-Transfer Excited State of p-Nitroaniline in Water: An Application of the TDDFT/EFP1 Method

The combined time-dependent density functional theory effective fragment potential method (TDDFT/EFP1) is applied to a study of the solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline (pNA) from the gas to the condensed phase in water. Molecular dynamics simulations of pNA with 150 EFP1 water molecules are used to model the condensed-phase and generate a simulated spectrum of the lowest singlet charge-transfer excitation. The TDDFT/EFP1 method successfully reproduces the experimental condensed-phase π → π* vertical excitation energy and solvent-induced red shift of pNA in water. The largest contribution to the red shift comes from Coulomb interactions, betweenpNA and water, and solute relaxation. The solvent shift contributions reflect the increase in zwitterionic character of pNA upon solvation

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

A Paradigm for Blue- or Red-Shifted Absorption of Small Molecules Depending on the Site of π-Extension

Benzannulation of aromatic molecules is often used to red-shift absorption and emission bands of organic and inorganic, molecular, and polymeric materials; however, in some cases, either red or blue shifts are observed, depending on the site of benzannulation. A series of five platinum(II) complexes of the form (N∧N∧N)PtCl are reported here that illustrate this phenomenon, where N∧N∧N represents the tridentate monoanionic ligands 2,5-bis(2-pyridylimino)3,4-diethylpyrrolate (1), 1,3-bis(2-pyridylimino)isoindolate (2), 1,3-bis(2-pyridylimino)benz(f)isoindolate (3), 1,3-bis(2-pyridylimino)benz(e)isoindolate (4), and 1,3-bis(1-isoquinolylimino) isoindolate (5). For this series of molecules, either a blue shift (2 and3) or a red shift (4 and 5) in absorption and emission maxima, relative to their respective nonbenzannulated compounds, was observed that depends on the site of benzannulation. Experimental data and first principles calculations suggest that a similar HOMO energy level and a destabilized or stabilized LUMO with benzannulation is responsible for the observed trends. A rationale for LUMO stabilization/destabilization is presented using simple molecular orbital theory. This explanation is expanded to describe other molecules with this unusual behavior