Federico Zahariev

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.

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-->pi(*) vertical excitation energy of acetone in vacuum and with 100 water molecules. The calculated water solvent effect on the vertical excitation energy exhibits a blueshift of the n-->pi(*) vertical excitation energy in acetone (Delta omega(1)=0.211 eV), which is in good agreement with the experimental blueshift.

Nonlinear Response Time-Dependent Density Functional Theory Combined with the Effective Fragment Potential Method

This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

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 and 3) 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.

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, between pNA and water, and solute relaxation. The solvent shift contributions reflect the increase in zwitterionic character of pNA upon solvation.

Dynamics Simulations with Spin-Flip Time-Dependent Density Functional Theory: Photoisomerization and Photocyclization Mechanisms of cis-Stilbene in ππ* States

On-the-fly dynamics simulations were carried out using spin-flip time dependent density functional theory (SF-TDDFT) to examine the photoisomerization and photocyclization mechanisms of cis-stilbene following excitation to the ππ* state. A state tracking method was devised to follow the target state among nearly degenerate electronic states during the dynamics simulations. The steepest descent path from the Franck-Condon structure of cis-stilbene in the ππ* state is shown to reach the S1-minimum of 4,4-dihydrophenanthrene (DHP) via a cis-stilbene-like structure (referred to as (S1)cis-min) on a very flat region of the S1-potential energy surface. From the dynamics simulations, the branching ratio of the photoisomerization is calculated as trans:DHP = 35:13, in very good agreement with the experimental data, trans:DHP = 35:10. The discrepancy between the steepest descent pathway and the significant trans-stilbene presence in the branching ratio observed experimentally and herein computationally is clarified from an analysis of geometrical features along the reaction pathway, as well as the low barrier of 0.1 eV for the pathway from (S1)cis-min to the twisted pyramidal structure on the S1-potential energy surface. It is concluded that ππ*-excited cis-stilbene propagates primarily toward the twisted structural region due to dynamic effects, with partial branching to the DHP structural region via the flat-surface region around (S1)cis-min.

Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: Application to excited-state molecular dynamics simulations

Excited-state quantum mechanics/molecular mechanics molecular dynamics simulations are performed, to examine the solvent effects on the fluorescence spectra of aqueous formaldehyde. For that purpose, the analytical energy gradient has been derived and implemented for the linear-response time-dependent density functional theory (TDDFT) combined with the effective fragment potential (EFP) method. The EFP method is an efficient ab initio based polarizable model that describes the explicit solvent effects on electronic excitations, in the present work within a hybrid TDDFT/EFP scheme. The new method is applied to the excited-state MD of aqueous formaldehyde in the n-π* state. The calculated π*→n transition energy and solvatochromic shift are in good agreement with other theoretical results.

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.

Elucidating the Nature of the Streptomyces plicatus β-Hexosaminidase-Bound Intermediate Using ab initio Molecular Dynamics Simulations

By using all-atom ab initio molecular dynamics simulations, the solution pK(a) of the oxazolinium ion intermediate formed during the Streptomyces plicatus beta-hexosaminidase (SpHex)-catalyzed hydrolysis of beta-D-N-acetylglucosaminides is estimated as pK(a) = 7.7. The structure and protonation state of the enzyme-bound intermediate have also been investigated, using hybrid QM/MM methods. The protonation state and conformational properties of the enzyme bound intermediate are found to be sensitive to the protonation state of a number of ionisable residues (other than the aspartate-glutamate catalytic dyad) suggesting that the microscopic electrostatic environment of SpHex not only perturbs the relative magnitudes of the pK(a) values of the Asp side chain carboxylate and oxazolinium ion but also that SpHex binds its intermediate in a distorted conformation with respect to its ground-state conformation in solution.

Functional Derivatives of Meta-Generalized Gradient Approximation (Meta-GGA) Type Exchange-Correlation Density Functionals

Meta-generalized gradient approximation (meta-GGA) exchange-correlation density functionals depend on the Kohn-Sham (KS) orbitals through the kinetic energy density. The KS orbitals in turn depend functionally on the electron density. However, the functional dependence of the KS orbitals is indirect, i.e., not given by an explicit expression, and the computation of analytic functional derivatives of meta-GGA functionals with respect to the density imposes a challenge. The practical solution used in many computer implementations of meta-GGA density functionals for ground-state calculations is abstracted and generalized to a class of density functionals that is broader than meta-GGAs and to any order of functional differentiation. Importantly, the TDDFT working equations for meta-GGA density functionals are presented here for the first time, together with the technical details of their computer implementation. The analysis presented here also uncovers the implicit assumptions in the practical solution to computing functional derivatives of meta-GGA density functionals. The connection between the approximation that is invoked in taking functional derivatives of density functionals, the non-uniqueness with respect to the KS orbitals, and the non-locality of the resultant potential is also discussed.