Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

Relativistic time-dependent density functional theories

The foundations, formalisms, technicalities, and practicalities of relativistic time-dependent density functional theories (R-TD-DFT) for spinor excited states of molecular systems containing heavy elements are critically reviewed.

Spin-state energies of heme-related models from spin-flip TDDFT calculations

The spin-state energies of heme-related models were calculated by using the spin-flip TDDFT method avoiding spin contamination.

Jahn-Teller effect in VCl4

A theoretical study is made of the Jahn-Teller and other properties of vanadium tetrachloride. Relativistic effective core potentials and corresponding valence spin-orbit operators are used with Gaussian atomic orbitals to compute self-consistent-field and spin-orbit configuration-interaction wave functions. Energy-surface parameters, electronic excitation energies, vibronic energy levels, and g factors are computed. Electron correlation is shown to have a substantial effect on the Jahn-Teller properties. As have others, we find the Jahn-Teller effect in VCl4 to be of the dynamic form.

Progress in time-dependent density-functional theory

The classic density-functional theory (DFT) formalism introduced by Hohenberg, Kohn, and Sham in the mid-1960s is based on the idea that the complicated N-electron wave function can be replaced with the mathematically simpler 1-electron charge density in electronic structure calculations of the ground stationary state. As such, ordinary DFT cannot treat time-dependent (TD) problems nor describe excited electronic states. In 1984, Runge and Gross proved a theorem making TD-DFT formally exact. Information about electronic excited states may be obtained from this theory through the linear response (LR) theory formalism. Beginning in the mid-1990s, LR-TD-DFT became increasingly popular for calculating absorption and other spectra of medium- and large-sized molecules. Its ease of use and relatively good accuracy has now brought LR-TD-DFT to the forefront for this type of application. As the number and the diversity of applications of TD-DFT have grown, so too has our understanding of the strengths and weaknesses of the approximate functionals commonly used for TD-DFT. The objective of this article is to continue where a previous review of TD-DFT in Volume 55 of the Annual Review of Physical Chemistry left off and highlight some of the problems and solutions from the point of view of applied physical chemistry. Because doubly-excited states have a particularly important role to play in bond dissociation and formation in both thermal and photochemistry, particular emphasis is placed on the problem of going beyond or around the TD-DFT adiabatic approximation, which limits TD-DFT calculations to nominally singly-excited states.

Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory

The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin-flip configuration interaction approaches can easily be spin-adapted via the tensor-coupling scheme.

Exploring the ground and excited state potential energy landscapes of the mixed-valence biferrocenium complex

Density functional theory (DFT) and time-dependent DFT (TDDFT) have been used to explore the potential energy landscapes in the class II (in Robin and Day classification) mixed-valence biferrocenium mono-cation (BF(+)) in an effort to evaluate factors affecting optical and thermal intramolecular electron transfer rates. Both energy- and spectroscopy-based benchmarks were used to explore the adiabatic potential energy surfaces (PESs) of the mixed-valence BF(+) cation along with the optimization of appropriate ground-, excited-, and transition-state geometries. The calculation of Mossbauer isomer shifts and quadrupole splittings, UV-vis excitation energies, and the electronic coupling matrix element, H(ab), corroborate the PES analyses. The adiabatic electron transfer pathway is also analyzed with respect to several possible vibronic coordinates. The degree of the electronic coupling between iron sites, the value of H(ab), and the nature of the electron transfer pathway correlate with the amount of Hartree-Fock exchange involved in the DFT calculation with hybrid (approximately 20% of Hartree-Fock exchange) methods providing the best agreement between theory and experiment. DFT (B3LYP) predicted values of H(ab) (839, 1085, and 1265 cm(-1)) depend on the computational method and are in good agreement with experimental data.

Towards understanding performance differences between approximate density functionals for spin states of iron complexes

Density functional theory has been widely used to investigate the structural and electronic properties of heme-containing proteins such as cytochrome P450. Nevertheless, recent studies have shown that approximate exchange-correlation energy density functionals can incorrectly predict the stability order of spin states in, for instance, iron-containing pyridine and imidazole systems. This raises questions about the validity of earlier theoretical studies. In this work, we systematically investigate a few typical inorganic and organic iron-containing complexes and try to understand the performance difference of various density functionals. Two oxidation states of iron, Fe(II) and Fe(III), with different spin states and both adiabatic and vertical structures are considered. A different description of the outmost molecular orbital is found to play the crucial role. Local density and generalized gradient based functionals bias the lower spin state and produce a more localized frontier orbital that is higher in energy than the hybrid functionals. Energy component analysis has been performed, together with comparison of numerous structural and electronic properties. Implications of the present work to the theoretical study of heme-containing biological molecules and other spin-related systems are discussed.

Microscopic insight into properties and electronic instabilities of impurities in cubic and lower symmetry insulators: the influence of pressure

This article reviews the microscopic origin of properties due to transition-metal (TM) impurities, M, in insulator materials. Particular attention is paid to the influence of pressure upon impurity properties. Basic concepts such as the electronic localization in an MX(N) complex, the electrostatic potential, V(R), arising from the rest of the lattice ions or the elastic coupling of the complex to the host lattice are initially exposed. The dependence of optical and magnetic parameters on the impurity-ligand distance, R, in cubic lattices is discussed in a first step. Emphasis is put on the actual origin of the R dependence of 10Dq. Examples revealing that laws for strict cubic symmetry cannot in general be transferred to lower symmetries are later given. This relevant fact is shown to come from allowed hybridizations like nd-(n+1)s as well as the influence of V(R). As a salient feature the different colour in ruby and emerald is stressed to arise from distinct V(R) potentials in Al(2)O(3) and Be(3)Si(6)Al(2)O(18). The last part of this review deals with electronic instabilities. The phenomena associated with the Jahn-Teller (JT) effect in cubic lattices, the origin of the energy barrier among equivalent minima and the existence of coherent tunnelling in systems like MgO:Cu(2+) are discussed. An increase of elastic coupling is pointed out to favour a transition from an elongated to a compressed equilibrium conformation. Interestingly the equilibrium geometry of JT ions in non-cubic lattices is shown to be controlled by mechanisms different to those in cubic systems, V(R) playing again a key role. The relevance of first principles calculations for clarifying the subtle mechanisms behind off-centre instabilities is also pointed out. Examples concern monovalent and divalent TM impurities in lattices with the CaF(2) structure. The instability due to the transition from the ground to an excited state is finally considered. For complexes with significant elastic coupling vibrational frequencies and the Stokes shift are expected to undergo bigger changes through a chemical rather than a hydrostatic pressure. The reduction of Huang-Rhys factors upon increasing the pressure is discussed as well.

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. II. Transformed reference via intermediate configuration Kohn-Sham time dependent density functional theory oscillator strengths and magnetic circular dichroism C terms

An extension of the transformed reference via an intermediate configuration Kohn-Sham time dependent density functional theory (TRICKS-TDDFT) method for calculating the transition energies of molecules with spatially degenerate ground states is proposed that enables oscillator strengths to also be evaluated. The oscillator strengths are calculated starting from a description of the degenerate ground state and the excited states of interest in terms of linear combinations of Slater determinants based upon the F-vectors obtained in the TRICKS-TDDFT calculation. This approach for calculating oscillator strengths can also be applied to several other properties that involve excited states. An example of such a property, the C term of magnetic circular dichroism (MCD), is presented. The new method is illustrated through example calculations of the absorbance and MCD spectra of several octahedral and C(4v) d(5) transition metal complexes. The calculated transition energies and oscillator strengths are somewhat too low and too high, respectively, but these errors are within the range that would normally be expected for TDDFT calculations of this type. The calculations help to resolve some previously unexplained problems with the MCD spectra of the C(4v) complexes.