Applications of Time-Dependent and Time-Independent Density Functional Theory to Electronic Transitions in Tetrahedral d(0) Metal Oxides.

We present benchmark calculations on excitation energies based on time-dependent density functional theory (TDDFT) as well as orbital relaxed self-consistent and constricted variational DFT (RSCF-CV-DFT) with and without use of the Tamm-Dancoff approximation. The compilation contains results for the 3d complexes MnO₄⁻, CrO₄²⁻, and VO₄³⁻, as well as the 4d congeners RuO₄, TcO₄⁻, and MoO₄²⁻, and 5d homologues OsO₄, ReO₄⁻, and WO₄²⁻. Considerations have been given to the local density approximation (LDA) and the functionals BP86 and PBE based on the generalized gradient approximation (GGA), as well as the hybrids B3LYP, BHLYP, and PBE0 and the length corrected functional LCBP86.

Excited State Studies of Polyacenes Using the All-Order Constricted Variational Density Functional Theory with Orbital Relaxation.

For the polyacenes series from naphthalene to hexacene, we present the vertical singlet excitation energies 1 (1)La and 1 (1)Lb, as well as the first triplet excitation energies obtained by the all-order constricted variational density functional theory with orbital relaxation (R-CV(∞)-DFT). R-CV(∞)-DFT is a further development of variational density functional theory (CV(∞)-DFT), which has already been successfully applied for the calculation of the vertical singlet excitation energies (1)La and (1)Lb for polyacenes,15 and we show that one obtains consistent excitation energies using the local density approximation as a functional for singlet as well as for triplet excitations when going beyond the linear response theory. Furthermore, we apply self-consistent field density functional theory (ΔSCF-DFT) and compare the obtained excitation energies for the first triplet excitations T1, where, due to the character of the transition, ΔSCF-DFT and R-CV(∞)-DFT become numerically equivalent, and for the singlet excitations 1 (1)La and 1 (1)Lb, where the two methods differ.

Applications of time-dependent and time-independent density functional theory to Rydberg transitions.

We have benchmarked the performance of time-independent density functional theory (ΔSCF and RSCF-CV-DFT) in studies on Rydberg transitions employing five different standard functionals and a diffuse basis. Our survey is based on 71 triplet or singlet Rydberg transitions distributed over nine different species: CO (7), CH2O (8), C2H2 (8), H2O (10), C2H4 (13), Be (6), Mg (6), and Zn (8). The best performance comes from the long-range corrected functional LCBP86 (ω = 0.

Derivation of the RPA (Random Phase Approximation) Equation of ATDDFT (Adiabatic Time Dependent Density Functional Ground State Response Theory) from an Excited State Variational Approach Based on the Ground State Functional.

The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation.

Applications of Time Dependent and Time Independent Density Functional Theory to the First π to π* Transition in Cyanine Dyes.

The first π → π* transition in a number of cyanine dyes was studied using both time dependent and time independent density functional methods using a coupled cluster (CC2) method as the benchmark scheme. On the basis of 10 different functionals, it was concluded that adiabatic time dependent density functional theory (ATDDFT) almost independently of the functional gives rise to a singlet-triplet separation that is too large by up to 1 eV, leading to too high singlet energies and too low triplet energies. This trend is even clearer when the Tamm-Dancoff (TD) approximation is introduced and can in ATDDFT/TD be traced back to the representation of the singlet-triplet separation by a HF-type exchange integral between π and π*.

Introducing constricted variational density functional theory in its relaxed self-consistent formulation (RSCF-CV-DFT) as an alternative to adiabatic time dependent density functional theory for studies of charge transfer transitions.

We have applied the relaxed and self-consistent extension of constricted variational density functional theory (RSCF-CV-DFT) for the calculation of the lowest charge transfer transitions in the molecular complex X-TCNE between X = benzene and TCNE = tetracyanoethylene. Use was made of functionals with a fixed fraction (α) of Hartree-Fock exchange ranging from α = 0 to α = 0.5 as well as functionals with a long range correction (LC) that introduces Hartree-Fock exchange for longer inter-electronic distances.

Direct modeling of the electrochemistry in the three-phase boundary of solid oxide fuel cell anodes by density functional theory: a critical overview.

The first principles modeling of electrochemical reactions has proven useful for the development of efficient, durable and low cost solid oxide full cells (SOFCs). In this account we focus on recent advances in modeling of structural, electronic and catalytic properties of the SOFC anodes based on density functional theory (DFT) first principle calculations. As a starting point, we highlight that the adequate analysis of cell electrochemistry generally requires modeling of chemical reactions at the metal/oxide interface rather than on individual metal or oxide surfaces.

Self-consistent Formulation of Constricted Variational Density Functional Theory with Orbital Relaxation. Implementation and Applications.

We introduce here a new version of the constricted nth order variational density functional method (CV(n)-DFT) in which the occupied excited state orbitals are allowed to relax in response to the change of both the Coulomb and exchange-correlation potential in going from the ground state to the excited state. The new scheme is termed the relaxed self-consistent field nth order constricted variational density functional (RSCF-CV(n)-DFT) method. We have applied the RSCF-CV(n)-DFT scheme to the nσ→π* transitions in which an electron is moved from an occupied lone-pair orbital nσ to a virtual π* orbital.

Modeling Transition Metal Reactions with Range-Separated Functionals.

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.

Accurate Theoretical Description of the (1)La and (1)Lb Excited States in Acenes Using the All Order Constricted Variational Density Functional Theory Method and the Local Density Approximation.

We present the results of calculations on the vertical singlet (1)La and (1)Lb excitation energies in acenes within time dependent density functional theory (TDDFT), second order constricted variational DFT (CV(2)-DFT), and all order constricted variational DFT (CV(∞)-DFT) using the local density approximation LDA(VWN). For the linear acenes it is shown that the application of the Tamm-Dancoff (TD) approximation to TDDFT (TDDFT-TD) substantially improves the agreement with experiment compared to pure TDDFT. This improvement leads to the correct ordering of the (1)La and (1)Lb excitation energies in naphthalene.

The implementation of a self-consistent constricted variational density functional theory for the description of excited states.

We present here the implementation of a self-consistent approach to the calculation of excitation energies within regular Kohn-Sham density functional theory. The method is based on the n-order constricted variational density functional theory (CV(n)-DFT) [T. Ziegler, M.

Range-Separated Exchange Functionals with Slater-Type Functions.

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.

Molecular and vibrational structure of tetroxo d0 metal complexes in their excited states. a study based on time-dependent density functional calculations and Franck-Condon theory.

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.

The Application of Constricted Variational Density Functional Theory to Excitations Involving Electron Transitions from Occupied Lone-Pair Orbitals to Virtual π* Orbitals.

We have applied the constricted variational density functional method (CV(n)-DFT) to n → π* transitions in which an electron is moved from an occupied lone-pair orbital n to a virtual π* orbital. A total of 34 transitions involving 16 different compounds were considered using the local density approximation (LDA), Becke, three-parameter, Lee-Yang-Parr (B3LYP), and BHLYP functionals. The DFT-based results were compared to the "best estimates" (BE) from high-level ab initio calculations.

On the calculation of charge transfer transitions with standard density functionals using constrained variational density functional theory.

It is well known that time-dependent density functional theory (TD-DFT) based on standard gradient corrected functionals 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 terms readily affords a qualitatively correct picture even for simple functionals based on the local density approximation.

On the relation between time-dependent and variational density functional theory approaches for the determination of excitation energies and transition moments.

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.

A revised electronic Hessian for approximate time-dependent density functional theory.

Time-dependent density functional theory (TD-DFT) at the generalized gradient level of approximation (GGA) has shown systematic errors in the calculated excitation energies. This is especially the case for energies representing electron transitions between two separated regions of space or between orbitals of different spatial extents. It will be shown that these limitations can be attributed to the electronic ground state Hessian G(GGA).

Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism. III. Temperature-dependent magnetic circular dichroism induced by spin-orbit coupling.

A methodology for calculating the temperature-dependent magnetic circular dichroism (MCD) of open-shell molecules with time-dependent density functional theory (TDDFT) is described. The equations for the MCD of an open-shell molecule including spin-orbit coupling in the low- and high-temperature limits are reviewed. Two effects lead to the temperature-dependent MCD: the breaking of degeneracies and the perturbation of transition dipoles by spin-orbit coupling.

Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism. II. Calculation of A terms.

The magnetically perturbed time-dependent density functional theory is used to derive equations for the magnetic circular dichroism (MCD) of degenerate transitions of closed shell molecules. The MCD of this type of transition can be divided into two contributions. The dominant contribution is usually that from A terms that arise because of the breaking of the degeneracy of the excited state in the presence of the magnetic field.

Magnetic circular dichroism of phthalocyanine (m=mg, zn) and tetraazaporphyrin (m=mg, zn, ni) metal complexes. A computational study based on time-dependent density functional theory.

We present here simulated magnetic circular dichroism (MCD) spectra of MTAP (M=Mg, Ni, Zn) and MPc (M=Mg, Zn) where TAP=tetraazaporphyrin and Pc=phthalocyanine. The study is based on magnetically perturbed time-dependent density functional theory (MP-TDDFT) and a newly implemented method for the calculation of A and B terms from the theory of MCD. It follows from our investigation that the MCD spectrum for the MTAP and MPc systems in the Q-band region consists of a single positive A term augmented by a positive B term, in agreement with experiment where available.

Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism: calculation of B terms.

Magnetically perturbed time-dependent density functional theory is applied to the calculation of the magnetic circular dichroism (MCD) B terms of closed shell molecules. Two approaches to evaluating B term parameters are described: a sum-over-states-type approach and an approach based on the direct solution of the matrix equations. The advantages and disadvantages and technical challenges of each approach are described.

Formulation of magnetically perturbed time-dependent density functional theory.

A formulation of time-dependent density functional theory (TDDFT) in the presence of a static imaginary perturbation is derived. A perturbational approach is applied leading to corrections to various orders in the quantities of interest, namely, the excitation energies and transition densities. The perturbed TDDFT equations are relatively straightforward to derive but the resulting expressions are rather cumbersome.

Magnetic circular dichroism of porphyrins containing M = Ca, Ni, and Zn. A computational study based on time-dependent density functional theory.

A theoretical study is presented on the magnetic circular dichroism (MCD) exhibited by the porphyrin complexes MP (M = Mg,Ni,Zn), MTPP (M = Mg,Ni,Zn), and NiOEP, where P = porphyrin, TPP = tetraphenylporphyrin, and OEP = octaethylporphyrin. The study makes use of a newly implemented method for the calculation of A and B terms from the theory of MCD and is based on time-dependent density functional theory (TD-DFT). It is shown that the MCD spectrum is dominated by a single positive A term in the Q-band region in agreement with experiment where available.

Calculation of the Term of Magnetic Circular Dichroism. A Time-Dependent Density Functional Theory Approach.

A method for calculating the ℬ term of magnetic circular dichroism utilizing time-dependent density functional theory is presented. The expression for the ℬ term is formulated through the standard sum-over-states approach, and all necessary matrix elements and transition energies are provided by the time-dependent density functional theory calculation. Test calculations of the magnetic circular dichroism spectra of ethene, propene, furan and its heavier homologues, and pyrrole and two of its derivatives are presented.

1,3 Geminal interactions as the possible trend setting factors for C-H and C-C bond energies in alkanes. Support from a density functional theory based bond energy decomposition study.

A bond energy decomposition analysis has been carried out to rationalize the well-established experimental fact that C-C and C-H bond energies decrease with increasing substitution on the carbon. It is shown that this trend is set by steric 1,3 repulsive interactions (geminal repulsion) that increase in the order 1,3 hydrogen-hydrogen < 1,3 hydrogen-carbon < 1,3 carbon-carbon. On the other hand, the radical stabilization energy has little influence on the observed trend for the C-H bond energy in H-CR(1)R(2)R(3) or the C-C bond energy in H(3)C-CR(1)R(2)R(3).