Evaluation of the excitation energies in and plastocyanin was carried out with three different density functional theory (DFT) methods: time‐dependent DFT (TDDFT), ΔDFT, and Δself consistent field (SCF)‐DFT. Use was made of two local (local density approximation and BP86), two hybrid (B3LYP and PBE0), and one long‐range corrected (LC‐BP86) functionals to probe the effect of the exact exchange on the excitation energies. Some well‐known deficiencies observed in TDDFT were explained on the basis of lacking orbital relaxation and two‐electron terms not considered in adiabatic TDDFT. Δself consistent field (SCF)‐DFT reproduces well the position of the charge‐transfer excitations and yields results in best agreement with experiment regardless of the system or functional used. We conclude that the orbital relaxation and proper account of higher‐order terms neglected in adiabatic TDDFT are of great importance for the simulation of excitation spectra. © 2014 Wiley Periodicals, Inc.

The performance of range separated functionals for the calculation of reaction profiles of organometallic compounds is considered. Sets of high-level computational results are used as reference data for the most part The benchmark data include a number of reactions involving small molecules reacting with the Pd atom, PdCl-, PdCl2, and a Ni atom, the reaction of a model Grubbs catalyst, and the ligand binding in a real Grubbs catalyst. Range-separated functionals are found to improve upon most standard local functionals especially if an optimized range-separation parameter is used They do not represent an improvement upon the better-performed global hybrid functionals or a local functional that includes a larger number of adjustable parameters. Some unusual results for molecule-molecule interaction energies are observed and explained by a detailed analysis of the contributions to the bonding energies. The influence of range separation on the barriers and reaction energies is also investigated.

A theoretical study of the bonding in ArEEAr (where E = Si, Ge, Sn, Pb; Ar = terphenyl ligand) revealed for the first time why bulky isopropyl substituents electronically are required in order to isolate stable ArEEAr species. This was accomplished by combining the natural orbitals for chemical valence (NOCV) method with the extended transition state (ETS) scheme. The NOCV-ETS analysis was based on two ArE fragments in their doublet ground state with the configuration σ(2)π(1). For E = Si, Ge, and Sn, it revealed one π-bond perpendicular to the CEEC plane and two σ/π-type bonds in the plane, whereas the ArPbPbAr system was found to have a single σ bond with a C-Pb-Pb trans-bent angle close to 90°. While similar bonding pictures have been obtained in previous model studies with Ar = H and CH3, the NOCV-ETS scheme was able to obtain quantitative estimates for the strength of various σ/π components without artificial truncations or twisting of the system. More importantly, NOCV-ETS analysis was able to show that the electronic influence of the isopropyl substituents on the σ/π components differs little from that found in a system where they are replaced by hydrogen. Instead, the favorable role of the isopropyl substituents is due to dispersive van der Waals attractions between Pr(i) groups on aryl rings attached to different E atoms as well as hyperconjugation involving donation into σ* orbitals on Pr(i). Dispersive interaction amounts to -27.5 kcal/mol (Si), -29.1 kcal/mol (Ge), -26.2 kcal/mol (Sn), and -44.0 kcal/mol (Pb). The larger dispersive stabilization for Pb reflects the fact that the longer Pb-Pb and Pb-C bonds sterically allow for more isopropyl groups with Ar = C6H3-2,6-(C6H2-2,4,6-Pr(i)3)2. This is compared to the other elements where Ar = C6H3-2,6-(C6H3-2,6-Pr(i)2)2. It is finally concluded from the analysis that real ArEEAr systems reveal little character of the EE bond in contrast to the findings of previous studies on model systems.

The peroxide intermediate (PI) is obtained in the first step of the reduction of O2 by multicopper oxidases. Earlier density functional theory (DFT) studies as well as spectral and structural comparison to a fully oxidized structural analogue of the PI known as the peroxide adduct (PA) reveal that O2 bridges all three copper atoms of the trinuclear cluster in the PI. This orientation of the oxygen moiety has been discussed as a result of the influence from the second coordination sphere. In the present study, we investigate by DFT and quantum mechanics/molecular mechanics (QM/MM) the potential energy surface (PES) of the PI as a function of the orientation of O2 within the copper cluster to examine the influence of the second coordination sphere on the structure of the PI. We use the second order spin-flip constricted variational DFT method to probe a possible multideterminantal nature of the PI and to devise a computational strategy for its treatment. Our results suggest that the PI can be approximated to a closed shell singlet. Additionally, for the determination of the oxidation states of the three copper atoms in the PI, the electron redistribution upon the formation of the PI has been investigated with the extended transition state–natural orbitals for chemical valence method. We observe a flat PES on which oxygen can easily rotate between the copper atoms. The fully bridged PI structure emerges in the absence of atoms from the second coordination sphere and has been attributed to the coordination unsaturation of the copper atoms in the cluster. The good Cu–O overlap leads to the participation of all copper atoms in the reduction of O2.

We have applied time dependent density functional theory to study excited state structures of the tetroxo d(0) transition metal complexes MnO(4)(-), TcO(4)(-), RuO(4), and OsO(4). The excited state geometry optimization was based on a newly implemented scheme [Seth et al. Theor. Chem. Acc. 2011, 129, 331]. The first excited state has a C(3v) geometry for all investigated complexes and is due to a "charge transfer" transition from the oxygen based HOMO to the metal based LUMO. The second excited state can uniformly be characterized by "charge transfer" from the oxygen HOMO-1 to the metal LUMO with a D(2d) geometry for TcO(4)(-), RuO(4), and OsO(4) and two C(2v) geometries for MnO(4)(-). It is finally found that the third excited state of MnO(4)(-) representing the HOMO to metal based LUMO+1 orbital transition has a D(2d) geometry. On the basis of the calculated excited state structures and vibrational modes, the Franck-Condon method was used to simulate the vibronic structure of the absorption spectra for the tetroxo d(0) transition metal complexes. The Franck-Condon scheme seems to reproduce the salient features of the experimental spectra as well as the simulated vibronic structure for MnO(4)(-) generated from an alternative scheme [Neugebauer J. J. Phys. Chem. A 2005, 109, 1168] that does not apply the Franck-Condon approximation.

An implementation of range-separated density functionals utilizing the Yukawa potential and Slater-type functions is described. The density-functional part of the range-separated regime is straightforward. The exact exchange part makes use of established methods for evaluating exchange integrals over Slater-type functions but still requires new one- and two-center integrals. Equations for the one-center integrals are derived. The two-center integrals are evaluated through a combination of new equations and techniques taken from procedures for evaluating two-center Coulomb integrals over Slater-type functions. In a first application, the performance of range-separated functionals in the prediction of transition metal thermochemistry is evaluated using a database of average ligand removal energies. The range-separated functionals perform better than a GGA parent and similarly to commonly used hybrid and meta-hybrid functionals. The results were relatively insensitive to the chosen value of the attenuation parameter.

The performance of the second-order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) for the calculation of the exchange coupling constant (J) is assessed by application to a series of triply bridged Cu(II) dinuclear complexes. A comparison of the J values based on SF-CV(2)-DFT with those obtained by the broken symmetry (BS) DFT method and experiment is provided. It is demonstrated that our methodology constitutes a viable alternative to the BS-DFT method. The strong dependence of the calculated exchange coupling constants on the applied functionals is demonstrated. Both SF-CV(2)-DFT and BS-DFT affords the best agreement with experiment for hybrid functionals.

The theory of calculating magnetic circular dichroism in the presence of zero-field splitting is presented and illustrated with applications to small and medium-sized systems.

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH2 and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C–C bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.

We have recently developed a methodology for the calculation of exchange coupling constants J in weakly interacting polynuclear metal clusters. The method is based on unrestricted and restricted second order spin-flip constricted variational density functional theory (SF-CV(2)-DFT) and is here applied to eight binuclear copper systems. Comparison of the SF-CV(2)-DFT results with experiment and with results obtained from other DFT and wave function based methods has been made. Restricted SF-CV(2)-DFT with the BH&HLYP functional yields consistently J values in excellent agreement with experiment. The results acquired from this scheme are comparable in quality to those obtained by accurate multi-reference wave function methodologies such as difference dedicated configuration interaction and the complete active space with second-order perturbation theory.

We present a test of a recently developed density functional theory (DFT) based methodology for the calculation of magnetic circular dichroism (MCD) spectra in the presence of zero-field splitting (ZFS). The absorption and MCD spectra of the trinuclear copper complex μ(3)O ([Cu(3)(L)(μ(3)-O)](4+)), which models the native intermediate produced in the catalytic cycle of the multicopper oxidases, have been simulated from first principle within the framework of adiabatic time dependent density functional theory. The effects of the ZFS of the quartet (4)A(2) ground state on the theoretical MCD spectrum of μ(3)O have been analyzed. The simulated spectra are consistent with the experimental ones. The theoretical assignments of the MCD spectra are based on direct simulation as well as a detailed analysis of the molecular orbitals in μ(3)O. Some of the assignments differ from those given in previous studies. The ZFS effects in the presence of a strong external magnetic field (7 T) prove negligible. The change of the sign of the ZFS changes systematically the intensity of the MCD bands of the z-polarized excitations. The effect of the ZFS on the x,y-polarized excitations is not uniform.

The title compound, abbreviated as 5'ThiomethylImmA, is a potent inhibitor of methylthioadenosine phosphorylase [Singh et al. (2004). Biochemistry, 43, 9-18]. The synchrotron study reported here shows that the hydrochloride salt crystallizes with two independent, nearly superimposable, dications as a monohydrate with formula 2C(12)H(19)N(5)O(2)S(2+)·4Cl(-)·H(2)O. Hydrogen bonding utilizing the H atoms of the dication is found to favour certain molecular conformations in the salt, which are significantly different from those found as bound in the enzyme. Ligand docking studies starting from either of these dications or related neutral structures successfully place the conformationally revised structures in the enzyme active site but only under particular hydrogen-bonding and molecular flexibility criteria. Density functional theory calculations verify the energy similarity of the independent cations and confirm the significant energy cost of the required conformational change to the enzyme bound form. The results suggest that using crystallographically determined free ligand coordinates as starting parameters for modelling may have serious limitations.

We report a density functional theory (DFT) study of electron paramagnetic resonance (EPR) parameters for complexes modeling the paramagnetic center Mo(V) of the molybdoenzyme dimethyl sulfoxide reductase. We pay special attention to the Mo-OH link to find the most likely geometry and orientation of the metal center in the enzyme and provide an analysis of the physical origin of the g-values in terms of magnetically induced orbital mixing. We also present a study of the magnetic circular dichroism (MCD) spectrum for a complex that models the Mo(V) center of the enzyme. The calculation of the MCD-parameters that give rise to the spectrum was performed using a newly implemented method based on time-dependent DFT. On the basis of the theoretical calculations, it was possible to give a full assignment of the bands of the MCD spectrum for the enzyme.

The excitation, circular dichroism, magnetic circular dichroism (MCD) and electron paramagnetic resonance (EPR) spectra of small models of four blue copper proteins are simulated on the TDDFT/BP86 level. X-Ray diffraction geometries are used for the modeling of the blue copper sites in azurin, plastocyanin, cucumber basic protein, and nitrite reductase. Comparison with experimental data reveals that the calculations reproduce most of the qualitative trends of the observed experimental spectra with some discrepancies in the orbital decompositions and the values of the excitation energies, the g( parallel) components of the g tensor, and the components of the A tensor. These discrepancies are discussed relative to deficiencies in the time-dependent density functional theory (TDDFT) methodology, as opposed to previous studies which address them as a result of insufficient model size or poor performance of the BP86 functional. In addition, attempts are made to elucidate the correlation between the MCD and EPR signals.

We report a density functional theory (DFT) study of the magnetic circular dichroism (MCD) spectra for four molybdenyl complexes: [MoOCl4](-), [MoO(S2C2H4)(2)](-), [(Tp*)MoO(bdt)], and [(L3S)MoO(bdt)] (Tp* = hydrotris (3,5-dimethyl-1-pyrazolyl) borate; L3S = (2-dimethylethane-thiolate)bis(3,5-dimethylpyrazolyl)-methane; bdt =1,2-benzenedithiolate). The simulation of the temperature dependent MCD-bands (C-terms) that give rise to the spectra was performed using a method based on time-dependent DFT. In this method, the C-parameters are calculated by including spin orbit perturbations. On the basis of the theoretical calculations, new or additional assignments are made for the MCD spectra of the complexes; specially for [(L3S)MoO(bdt)], for which case only tentative assignments of the excitations have been proposed in recent years.

It is well known that standard time-dependent density functional theory (TD-DFT) affords both a quantitative and qualitative incorrect picture of charge transfer transitions between two spatially separated regions. It is shown here that the well-known failure can be traced back to the use of linear response theory. Further, it is demonstrated that the inclusion of higher order response terms readily affords a qualitatively correct picture even for simple functionals based on the local density approximation. By using the higher order response terms, we finally derive a correction that can be added as a perturbation to charge transfer excitation energies calculated by standard TD-DFT.

We present a theoretical study of the temperature-dependent magnetic circular dichroism (MCD) spectrum for complexes modeling the molybdoenzyme sulfite-oxidase (1) in its Mo(V) oxidation state. The theoretical study was based on a newly implemented time-dependent density functional method that takes into account first-order perturbations due to spin-orbit coupling and a constant magnetic field. It was possible, on the basis of the theoretical calculations, to give a full assignment of the MCD spectrum for 1 and interpret the C term of each band in the experimental MCD spectrum in terms of spin-orbit couplings between specific excited states and between excited states and the ground state.

It is shown that it is possible to derive the basic eigenvalue equation of adiabatic time-dependent density functional theory within the Tamm-Dancoff approximation (TD-DFT/TD) from a variational principle. The variational principle is applied to the regular Kohn-Sham formulation of DFT energy expression for a single Slater determinant and leads to the same energy spectrum as TD-DFT/TD. It is further shown that this variational approach affords the same electric and magnetic transition moments as TD-DFT/TD. The variational scheme can also be applied without the Tamm-Dancoff approximation. Practical implementations of TD-DFT are limited to second order response theory which introduces errors in transition energies for charge transfer and Rydberg excitations. It is indicated that higher order terms can be incorporated into the variational approach. It is also discussed how the current variational method is related to traditional DFT schemes based on variational principles such as DeltaSCF-DFT, and how they can be combined.