Why are time-dependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree-Fock-type exchange introduce excitonic effects?

We examine the time-dependent density functional theory (TD-DFT) equations for calculating excitation energies in solids with Gaussian orbitals and analytically show that for semilocal functionals, their lowest eigenvalue collapses to the minimum band orbital energy difference. With the introduction of nonlocal Hartree-Fock-type exchange (as in hybrid functionals), this result is no longer valid, and the lowest TD-DFT eigenvalue reflects the appearance of excitonic effects. Previously reported "charge-transfer" problems with semilocal TD-DFT excitations in molecules can be deduced from our analysis by taking the limit to infinite lattice constant.     

Exciting flavins: Absorption spectra and spin–orbit coupling in light–oxygen–voltage (LOV) domains

Flavins are central molecular chromophores for many photobiological processes. In this paper, several aspects of the photophysics and photochemistry of lumiflavin in a (protein) environment will be studied with the help of quantum chemical methods. In a first part of the paper, we present vertical singlet excitation energies for lumiflavin (a molecule of the isoalloxazin type), using time-dependent density functional theory (TD-DFT) in conjunction with the B3LYP hybrid functional. When calculated for isolated species, TD-DFT excitation energies are generally blue-shifted relative to the experimental absorption spectra of isoalloxazines in solution, or in a protein environment. We develop four different models to account for environmental effects, with special emphasis on the LOV1 domain of Chlamydomonas reinhardtii. It is found that the two lowest, allowed singlet excitations are sensitive to the polarizability of an environment, to hydrogen bonds, and to geometrical constraints imposed by the surrounding protein. All of this brings theory and experiment in better agreement.

In the second part of the paper the light-induced adduct formation in LOV domains, between the chromophore and a neighbouring cystein unit is investigated. Energies along a model “reaction path” are calculated on the DFT/B3LYP and MCQDPT2 level of theories. A transition state for a H-transfer between the mercapto (SH–) group of cystein, and the N(5) position of flavin is found. The reaction requires spin–orbit coupling between the S₀ and the T₁ states of the system. Spin–orbit coupling constants between S₀ and T₁ are calculated, and found to be in the range of several tens of cm⁻¹ after the transition state was passed. A biradical intermediate was observed along the reaction path.     

Computations on the A-X transition of isoprene-OH-O2 peroxy radicals

Calculations are carried out on the A state of HO2, CH3O2, and CH3CH2O2 and 10 isomers and conformers of the isoprene-OH-O2 peroxy radicals derived from OH addition to isoprene (2-methyl-1,3-butadiene). In addition to calculating vertical and adiabatic excitation energies, we consider the effect of excitation on molecular structure, and examine the OO stretching frequencies, which are known to be major features in the absorption spectra of the A states of the smaller radicals. The two methods used are the configuration interaction with single excitations (CIS) method and time-dependent density functional theory (TD-DFT), both with a range of basis sets up to 6-311++G(2df,2pd). TD-DFT overestimates excitation energies considerably, while CIS tends to underestimate them slightly. TD-DFT does seem to capture the trend in excitation energy vs. size for the smaller peroxy radicals. Conformation and configuration strongly affect the excitation energies of the peroxy radicals from isoprene. CIS calculations indicate that the intramolecular OH--O hydrogen bonds, present in the ground state of some peroxy radicals from isoprene, are weakened or broken in the excited state, while TD-DFT calculations suggest they are retained.     

CL-20 photodecomposition: ab initio foundations for identification of products

1,5-Dihydrodiimidazo[4,5-b:4'5'e]pyrazine, 1H-imidazo[4,5-b]pyrazine, and 1H-imidazole were considered as possible products of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) photodecomposition. Since we took as a reference the product obtained after CL-20 irradiation in methanol solution, the nature of intermolecular bonds between heterocycles under study and methanol molecules was analyzed in detail. Existing hydrogen bonds were found to be quite strong, so dependence of calculations results on an influence of solvent was taken into account using both the polarizable continuum model (PCM) and the supermolecular approach. Electronic spectra of 1,5-dihydrodiimidazo[4,5-b:4'5'e]pyrazine, 1H-imidazo[4,5-b]pyrazine and 1H-imidazole were simulated using time dependent density functional theory (TD-DFT) and single-excitation configuration interaction (CIS) method. We observed that TD-DFT excitation energies are lower if compared to corresponding values obtained by the CIS method. Results of calculations with PCM and the supermolecular approach are very close. It was found that differences between calculated gas phase excitation energies and those values obtained by applying solvent models increases when the number of conjugated bonds in a molecule increases. Oscillator strengths of UV bands of the considered molecules are higher in the gas phase than in modeled methanol solutions. We found that the predicted spectrum of 1H-imidazole is in close agreement with the experimental UV spectrum of the CL-20 photolysis product.     

Hydrogen bonding and reactivity of water to azines in their S1 (n,π*) electronic excited states in the gas phase and in solution

A unified picture is presented of water interacting with pyridine, pyridazine, pyrimidine, and pyrazine on the S(1) manifold in both gas-phase dimers and in aqueous solution. As (n,π*) excitation to the S(1) state removes electrons from the ground-state hydrogen bond, this analysis provides fundamental understanding of excited-state hydrogen bonding. Traditional interpretations view the excitation as simply breaking hydrogen bonds to form dissociated molecular products, but reactive processes such as photohydrolysis and excited-state proton coupled electron transfer (PCET) are also possible. Here we review studies performed using equations-of-motion coupled-cluster theory (EOM-CCSD), multireference perturbation theory (CASPT2), time-dependent density-functional theory (TD-DFT), and excited-state Monte Carlo liquid simulations, adding new results from symmetry-adapted-cluster configuration interaction (SAC-CI) and TD-DFT calculations. Invariably, gas-phase molecular dimers are identified as stable local minima on the S(1) surface with energies less than those for dissociated molecular products. Lower-energy biradical PCET minima are also identified that could lead to ground-state recombination and hence molecular dissociation, dissociation into radicals or ions, or hydration reactions leading to ring cleavage. For pyridine.water, the calculated barriers to PCET are low, suggesting that this mechanism is responsible for fluorescence quenching of pyridine.water at low energies rather than accepted higher-energy Dewar-benzene based "channel three" process. Owing to (n,π*) excitation localization, much higher reaction barriers are predicted for the diazines, facilitating fluorescence in aqueous solution and predicting that the as yet unobserved fluorescence from pyridazine.water and pyrimidine.water should be observable. Liquid simulations based on the assumption that the solvent equilibrates on the fluorescence timescale quantitatively reproduce the observed spectral properties, with the degree of (n,π*) delocalization providing a critical controlling factor.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.     

Electronic excitation energies of molecules in solution within continuum solvation models: investigating the discrepancy between state-specific and linear-response methods

In a recent article [R. Cammi, S. Corni, B. Mennucci, and J. Tomasi, J. Chem. Phys. 122, 104513 (2005)], we demonstrated that the state-specific (SS) and the linear-response (LR) approaches, two different ways to calculate solute excitation energies in the framework of quantum-mechanical continuum models of solvation, give different excitation energy expressions. In particular, they differ in the terms related to the electronic response of the solvent. In the present work, we further investigate this difference by comparing the excitation energy expressions of SS and LR with those obtained through a simple model for solute-solvent systems that bypasses one of the basic assumptions of continuum solvation models, i.e., the use of a single Hartree product of a solute and a solvent wave function to describe the total solute-solvent wave function. In particular, we consider the total solute-solvent wave function as a linear combination of the four products of two solute states and two solvent electronic states. To maximize the comparability with quantum-mechanical continuum model the resulting excitation energy expression is recast in terms of response functions of the solvent and quantities proper for the solvated molecule. The comparison of the presented expressions with the LR and SS ones enlightens the physical meaning of the terms included or neglected by these approaches and shows that SS agrees with the results of the four-level model, while LR includes a term classified as dispersion in previous treatments and neglects another related to electrostatic. A discussion on the possible origin of the LR flaw is finally given.     

Detailed analysis of polyad-breaking spectroscopic Hamiltonians for multiple minima with above barrier motion: isomerization in HO2

We present a two-dimensional model for isomerization in the hydroperoxyl radical (HO(2)). We then show that spectroscopic fitting Hamiltonians are capable of reproducing large scale vibrational structure above isomerization barriers. Two resonances, the 2:1 and 3:1, are necessary to describe the pertinent physical features of the system and, hence, a polyad-breaking Hamiltonian is required. We further illustrate, through the use of approximate wave functions, that inclusion of additional coupling terms yields physically unrealistic results despite an improved agreement with the exact energy levels. Instead, the use of a single diagonal term, rather than "extra" couplings, yields good fits with realistic results. Insight into the dynamical nature of isomerization is also gained through classical trajectories. Contrary to physical intuition the bend mode is not the initial "reaction mode," but rather isomerization requires excitation in both the stretch and bend modes. The dynamics reveals a Farey tree formed between the 2:1 and 3:1 resonances with the prominent 5:2 (2:1 + 3:1) feature effectively dividing the tree into portions. The 3:1 portion is associated with isomerization, while the 2:1 portion leads to "localization" and perhaps dissociation at higher energies than those considered in this work. Simple single resonance models analyzed on polyad phase spheres are able to account in a qualitative way for the spectral, periodic orbit, and wave function patterns that we observe.     

Optical excitations of defects in realistic nanoscale silica clusters: comparing the performance of density functional theory using hybrid functionals with correlated wavefunction methods

Optical excitations of low energy silica (SiO(2))(4) clusters obtained by global optimization, as opposed to constructed by hand, are studied using a range of theoretical methods. By focusing on the lowest energy silica clusters we hope to capture at least some of the characteristic ways by which the dry surfaces of silica nanosystems preferentially terminate. Employing the six lowest energy (SiO(2))(4) cluster isomers, we show that they exhibit a surprisingly wide range of geometries, defects, and associated optical excitations. Some of the clusters show excitations localized on isolated defects, which are known from previous studies using hydrogen-terminated versions of the defect in question. Other clusters, however, exhibit novel charge-transfer excitations in which an electron transfers between two spatially separated defects. In these cases, because of the inherent proximity of the constituent defects due to the small cluster dimensions, the excitation spectrum is found to be very different from that of the same defects in isolation. Excitation spectra of all clusters were calculated using time-dependent density functional theory (TD-DFT) and delta-SCF DFT (DeltaDFT) methods employing two different hybrid density functionals (B3LYP and BB1K) differing essentially in the amount of incorporated Hartree-Fock-like exchange (HFLE). In all cases the results were compared with CASPT2 calculated values which are taken as a benchmark standard. In line with previous work, the spatially localized excitations are found to be well described by TD-DFT/B3LYP but which gives excitation energies that are significantly underestimated in the case of the charge-transfer excitations. The TD-DFT/BB1K combination in contrast is found to give generally good excitation energies for the lowest excited states of both localized and charge-transfer excitations. Finally, our calculations suggest that the increased quality of the predicted excitation spectra by adding larger amounts of HFLE is mainly due to an increased localization of the excited state associated with the elimination of spurious self-interaction inherent to (semi-)local DFT functionals.     

Vibronic coupling and double excitations in linear response time-dependent density functional calculations: dipole-allowed states of N2

The present study serves two purposes. First, we evaluate the ability of present time-dependent density functional response theory (TDDFRT) methods to deal with avoided crossings, i.e., vibronic coupling effects. In the second place, taking the vibronic coupling effects into account enables us, by comparison to the configuration analysis in a recent ab initio study [J. Chem. Phys. 115, 6438 (2001)], to identify the neglect of double excitations as the prime cause of limited accuracy of these linear response based TDDFRT calculations for specific states. The "statistical averaging of (model) orbital potentials (SAOP)" Kohn-Sham potential is used together with the standard adiabatic local-density approximation (ALDA) for the exchange-correlation kernel. We use the N2 molecule as prototype, since the TDDFRT/SAOP calculations have already been shown to be accurate for the vertical excitations, while this molecule has a well-studied, intricate vibronic structure as well as significant double excitation nature in the lowest 1Pi(u) state at elongated bond lengths. A simple diabatizing scheme is employed to obtain a diabatic potential energy matrix, from which we obtain the absorption spectrum of N2 including vibronic coupling effects. Considering the six lowest dipole allowed transitions of 1Sigma(u)+ and 1Pi(u) symmetry, we observe a good general agreement and conclude that avoided crossings and vibronic coupling can indeed be treated satisfactorily on the basis of TDDFRT excitation energies. However, there is one state for which the accuracy of TDDFRT/ALDA clearly breaks down. This is the state for which the ab initio calculations find significant double excitation character. To deal with double excitation character is an important challenge for time-dependent density functional theory.     

Evaluation of mutual information and genetic programming for feature selection in QSAR

Feature selection is a key step in Quantitative Structure Activity Relationship (QSAR) analysis. Chance correlations and multicollinearity are two major problems often encountered when attempting to find generalized QSAR models for use in drug design. Optimal QSAR models require an objective variable relevance analysis step for producing robust classifiers with low complexity and good predictive accuracy. Genetic algorithms coupled with information theoretic approaches such as mutual information have been used to find near-optimal solutions to such multicriteria optimization problems. In this paper, we describe a novel approach for analyzing QSAR data based on these methods. Our experiments with the Thrombin dataset, previously studied as part of the KDD (Knowledge Discovery and Data Mining) Cup 2001 demonstrate the feasibility of this approach. It has been found that it is important to take into account the data distribution, the rule "interestingness", and the need to look at more invariant and monotonic measures of feature selection.     

Theoretical study of Ln(III) complexes with polyaza-aromatic ligands: geometries of [LnL(H2O)n]3+ complexes and successes and failures of TD-DFT

The accuracy and the usefulness of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations for the theoretical study of Ln (La, Eu, Lu) complexes have been investigated. The geometries calculated at the DFT level for [Ln(H2O)nL]3+ complexes have been successfully compared with crystallographic data. TD-DFT is able to offer valuable insights into VUV spectra of lanthanide complexes. However, the results obtained on the largest ligand (i.e., 2,4,6-tri-(pyridin-2-yl)-1,3,5-triazine (Tptz)) have to be considered as a failure of TD-DFT.     

Double-hybrid density functional theory for excited electronic states of molecules

Double-hybrid density functionals are based on a mixing of standard generalized gradient approximations (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), respectively. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chemistry applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent density functional theory (TD-DFT) or the closely related Tamm-Dancoff approximation (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to configuration interaction with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. [Chem. Phys. Lett. 219, 21 (1994)] is computed on the basis of density functional data and added to the TD(A)-DFTGGA excitation energy. The method is implemented by applying the resolution of the identity approximation and the efficiency of the code is discussed. Extensive tests for a wide variety of molecules and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from reference data typically <0.2 eV) are obtained that are mostly better than those from standard functionals. Still, systematic errors are obtained for Rydberg (too low on average by about 0.3 eV) and charge-transfer transitions but due to the relatively large ax parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases.     

On the Road Toward More Efficient Biocompatible Two-Photon Excitable Fluorophores

Red-to-NIR absorption and emission wavelengths are key requirements for intravital bioimaging. One of the way to reach such excitation wavelengths is to use two-photon excitation. Unfortunately, there is still a lack of two-photon excitable fluorophores that are both efficient and biocompatible. Thus, we design a series of biocompatible quadrupolar dyes in order to study their ability to be used for live-cell imaging, and in particular for two-photon microscopy. Hence, we report the synthesis of 5 probes based on different donor cores (phenoxazine, acridane, phenazasiline and phenothiazine) and the study of their linear and non-linear photophysical properties. TD-DFT calculations were performed and were able to highlight the structure-property relationship of this series. All these studies highlight the great potential of three of these biocompatible dyes for two-photon microscopy, as they both exhibit high two-photon cross-sections (up to 3650 GM) and emit orange to red light. This potential was confirmed through live-cell two-photon microscopy experiments, leading to images with very high brightness and contrast.     

A probabilistic approach to classifying metabolic stability

Metabolic stability is an important property of drug molecules that should-optimally-be taken into account early on in the drug design process. Along with numerous medium- or high-throughput assays being implemented in early drug discovery, a prediction tool for this property could be of high value. However, metabolic stability is inherently difficult to predict, and no commercial tools are available for this purpose. In this work, we present a machine learning approach to predicting metabolic stability that is tailored to compounds from the drug development process at Bayer Schering Pharma. For four different in vitro assays, we develop Bayesian classification models to predict the probability of a compound being metabolically stable. The chosen approach implicitly takes the "domain of applicability" into account. The developed models were validated on recent project data at Bayer Schering Pharma, showing that the predictions are highly accurate and the domain of applicability is estimated correctly. Furthermore, we evaluate the modeling method on a set of publicly available data.     

Theoretical investigation of the excited states of coumarin dyes for dye-sensitized solar cells

Using time-dependent density functional theory (TD-DFT), configuration interaction single (CIS) method, and approximate coupled cluster singles and doubles (CC2) method, we investigated the absorption spectra of coumarin derivative dyes (C343, NKX-2388, NKX-2311, NKX-2586, and NKX-2677), which have been synthesized for efficient dye-sensitized solar cells. The CC2 calculations are found in good agreement with the experimental results except for the smallest coumarin dye (C343). TD-DFT underestimates the vertical excitation energy of the larger coumarin dyes (NKX-2586 and -2677). Solvents (methanol) are found to induce a red shift of the vertical excitation energies, and their effects on the molecular geometry and the electronic structure are examined in detail. The deprotonated form of coumarin is also investigated, where a blue shift of the vertical excitation energies is observed.