A time dependent density functional theory study of alpha-84 phycocyanobilin chromophore in C-phycocyanin

The optical characteristics of absorption and circular dichroism (CD) spectroscopy of an alpha-subunit of C-phycocyanin (C-PC) were investigated by using time dependent density functional theory (TDDFT) combined with the polarizable continuum model (PCM). When the protonation of alpha-84 phycocyanobilin (PCB) and its interaction with the protein moiety in C-PC have been taken into account, satisfactory assignment of the absorption and CD spectra of alpha-84 PCB can be achieved. The TDDFT-PCM calculations conclude that in the visible absorption region the main peak arises from the pi electron excitation of the pyrrole rings and the shoulder peak comes from the charge transfer from Asp87 (a nearby amino acid residue) to PCBH(+).     

Excited-state calculations with TD-DFT: from benchmarks to simulations in complex environments

In this perspective, we present an overview of recent progress on Time-Dependent Density Functional Theory (TD-DFT) with a specific focus on its accuracy and on models able to take into account environmental effects, including complex media. To this end, we first summarise recent benchmarks and define an average TD-DFT accuracy in reproducing excitation energies when a conventional approach is used. Next, coupling of TD-DFT with models able to account for different kinds of interactions between a central chromophore and nearby chemical objects (solvent, organic cage, metal as well as semi-conducting surface) is investigated. Examples of application to excitation properties are presented, allowing to briefly describe several recent computational strategies. In addition, an extension of TD-DFT to describe a phenomenon involving interacting chromophores, e.g. the electronic energy transfer (EET), is presented to illustrate that this methodology can be applied to processes beyond the vertical excitation. This perspective therefore aims to provide to non-specialists a flavour of recent trends in the field of simulations of excited states in "realistic" situations.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

稠环芳烃菲电子激发态的含时密度泛函理论研究

用含时密度泛函理论TD-DFT及组态相关CIS、含时TD-HF方法对菲的UV光谱进行了理论研究,在几何构型优化的基础上,计算了其垂直电子激发能．计算表明,基函数的选择对激发能的计算影响较大,而不同的密度泛函交换一相关势对其影响较小,这和轨道能级的系统误差相互抵消有关．对菲的电子跃迁能的计算,与实验结果比较相一致,理论与实验的误差和不同的实验之间的误差在同一个数量级之内,显示TD-DFT方法比CIS,TD-HF方法更适合电子激发能的计算．     

Impact of the computational method on the geometric and electronic properties of oligo(phenylene vinylene) radical cations

We report on a quantum-chemical study of the electronic and optical properties of unsubstituted oligo(phenylene vinylene) (OPV) radical cations. Our goal is to distinguish the impact of the choice of molecular geometry from the impact of the choice of quantum-chemical method, on the calculated optical transition energies. The geometry modifications upon ionization of the OPV chains are found to depend critically on the theoretical formalism: Hartree-Fock (HF) geometry optimizations lead to self-localization of the charged defects while pure density functional theory (DFT) results in a complete delocalization of the geometric modifications over the whole conjugated backbone. The electronic structure and vertical transition energy associated with the lowest excited state of the radical cations have been calculated at the post-Hartree-Fock level within a configuration interaction (HF-CI) scheme and using the time-dependent DFT (TD-DFT) formalism for different radical cation geometries. Interestingly, the changes in the calculated optical properties obtained when using different geometric structures are less important within a given method than the differences between methods for a given structure. The optical excitation is localized with HF-CI and delocalized with TD-DFT, almost irrespective of the molecular geometry; as a result, HF-CI excitation energies tend to saturate as the chain length increases, in contrast to the results from TD-DFT.     

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.     

Spectral tuning of photoactive yellow protein

We report a theoretical study on the optical properties of a small, water-soluble photosensory receptor, photoactive yellow protein (PYP). A hierarchical ab initio molecular orbital calculation accurately evaluated the optical absorption maximum of the wild-type, as well as the lambda(max) values of 12 mutants. Electronic excitation of the chromophore directly affects the electronic state of nearby atoms in the protein environment. This effect is explicitly considered in the present study. Furthermore, the spectral tuning mechanism of PYP was investigated at the atomic level. The static disorder of a protein molecule is intimately related to the complex nature of its energy landscape. By using molecular dynamics simulation and quantum mechanical structure optimization, we obtained multiple minimum energy conformations of PYP. The statistical distribution of electronic excitation energies of these minima was compared with the hole-burning experiment (Masciangioli, T. [2000] Photochem. Photobiol. 72, 639), a direct observation of the distribution of excitation energies.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Time-dependent density functional theory predictions of the vertical excitation energies of silanones as models for the excitation process in porous silicon

Time-dependent density functional theory calculations with a proper treatment of the asymptotic form of the exchange-correlation potential have been performed on R(R')Si=O to predict vertical excitation energies. The species R(R')Si=O is used as a model for the binding of the -(R)Si=O chromophore to a porous silicon surface. The calculated vertical excitation energies are substantially lower than those determined previously and show that vertical excitation of the lone chromophore is possible for all types of substituents including electronegative ones with KrF laser excitation in contrast to other predictions. If the substituents are electropositive, the chromophore can also be excited by a nitrogen laser. These results, in concert with the effect of the porous silicon surface on the R(R')Si=O excited states, confirm our previous explanation of the photoluminescence of porous silicon as being due to the presence of Si=O chromophores and provide new insights into the photoexcitation process. The results show that the differences in the vertical and adiabatic excitation energies are strongly dependent on whether the substituents are electronegative or electropositive with the former leading to larger differences and the latter leading to smaller differences. The results for the energy differences are explained in terms of the changes in the Si=O bond length on vertical excitation and on the changes in bond angles, which are related to the ability of the Si center in the excited state to undergo an inversion process.     

Excited state properties, fluorescence energies, and lifetime of a poly(fluorene-pyridine) copolymer, based on TD-DFT investigation

The structural and electronic properties of the fluorene-pyridine copolymer (FPy)(n), (n = 1-4) were investigated theoretically by means of quantum mechanical calculations based on density functional theory (DFT) and time-dependent DFT (TD-DFT) using the B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest excited state. It was found that (FPy)(n) is nonplanar in its ground state, whereas a more pronounced trend toward planarity is observed in the S(1) state. Absorption and fluorescence energies have been extrapolated to infinite chain length making use of their good linearity with respect to 1/n. An extrapolated value of 2.64 eV is obtained for vertical excitation energy. The S(1)<--S(0) electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is dominating in terms of oscillator strength. Fluorescence energies and radiative lifetime were calculated as well. The obtained results indicate that the fluorescence energy and radiative lifetime of (FPy)(n) are 2.16 eV and 0.38 ns, respectively. The decrease of fluorescence energy and radiative lifetime with the increase in the chain length is discussed.     

UV-vis spectra of <Emphasis Type="Italic">p</Emphasis>-benzoquinone anion radical in solution by a TD-DFT/PCM approach

Excited electronic states of the anion radical of para-benzoquinone were studied by time dependent density functional theory (TD-DFT) including bulk solvent effects by the polarizable continuum model (PCM). The computed vertical excitation energies for the first four low-lying doublet states are in good agreement with previous post-Hartree–Fock computations. Geometry optimization of excited states and inclusion of solvent effects lead to a remarkable agreement between computed adiabatic transition energies and experimental band maxima. Together with their specific interest, the results point out the reliability of TD-DFT/PCM approach for valence excitations and the need to take geometry relaxation and solvent effects into the proper account for a meaningful comparison between computed and experimental absorption spectra.     

Photo absorption of ‐coumaric acid in aqueous solution: RISM‐SCF‐SEDD theory approach

Photo absorption properties of p‐coumaric acid, the chromophore of photoactive yellow protein, in aqueous solution were investigated by means of reference interaction site model self‐consistent field with spatial electron density distribution (RISM‐SCF‐SEDD) method. RISM‐SCF‐SEDD is a combination methodology of electronic structure theory and statistical mechanics for molecular liquids. Here, time‐dependent density functional theory was coupled with RISM equation to study the electronic structure of p‐coumaric acid in aqueous system. Excitation energies of the chromophore in its neutral, two monoanionic and dianionic forms were computed to elucidate the effect of the deprotonation and solvation on the spectroscopic properties. We found that solvation strongly affects the excitation character of the chromophore, especially for phenolate anion and dianion. The free energy difference among the four protonation states is also discussed. © 2017 Wiley Periodicals, Inc.     

Calculating absorption shifts for retinal proteins: computational challenges

Rhodopsins can modulate the optical properties of their chromophores over a wide range of wavelengths. The mechanism for this spectral tuning is based on the response of the retinal chromophore to external stress and the interaction with the charged, polar, and polarizable amino acids of the protein environment and is connected to its large change in dipole moment upon excitation, its large electronic polarizability, and its structural flexibility. In this work, we investigate the accuracy of computational approaches for modeling changes in absorption energies with respect to changes in geometry and applied external electric fields. We illustrate the high sensitivity of absorption energies on the ground-state structure of retinal, which varies significantly with the computational method used for geometry optimization. The response to external fields, in particular to point charges which model the protein environment in combined quantum mechanical/molecular mechanical (QM/MM) applications, is a crucial feature, which is not properly represented by previously used methods, such as time-dependent density functional theory (TDDFT), complete active space self-consistent field (CASSCF), and Hartree-Fock (HF) or semiempirical configuration interaction singles (CIS). This is discussed in detail for bacteriorhodopsin (bR), a protein which blue-shifts retinal gas-phase excitation energy by about 0.5 eV. As a result of this study, we propose a procedure which combines structure optimization or molecular dynamics simulation using DFT methods with a semiempirical or ab initio multireference configuration interaction treatment of the excitation energies. Using a conventional QM/MM point charge representation of the protein environment, we obtain an absorption energy for bR of 2.34 eV. This result is already close to the experimental value of 2.18 eV, even without considering the effects of protein polarization, differential dispersion, and conformational sampling.     

Time-dependent density functional theory as a tool for isomer assignments of hydrogen-bonded solute.solvent clusters

Can isomer structures of hydrogen-bonded solute x solvent clusters be assigned by correlating gas-phase experimental S0 <--> S1 transitions with vertical or adiabatic excitation energies calculated by time-dependent density functional theory (TD-DFT)? We study this question for 7-hydroxyquinoline (7HQ), for which an experimental database of 19 complexes and clusters is available. The main advantage of the adiabatic TD-B3LYP S0 <--> S1 excitations is the small absolute error compared to experiment, while for the calculated vertical excitations, the average offset is +1810 cm(-1). However, the empirically adjusted vertical excitations correlate more closely with the experimental transition energies, with a standard deviation of sigma = 72 cm(-1). For the analogous correlation with calculated adiabatic TD-DFT excitations, the standard deviation is sigma = 157 cm(-1). The vertical and adiabatic TD-DFT correlation methods are applied for the identification of isomers of the 7-hydroxyquinoline.(MeOH) n , n = 1-3 clusters [Matsumoto, Y.; Ebata, T.; Mikami, N. J. Phys. Chem. B 2002, 106, 5591]. These confirm that the vertical TD-DFT/experimental correlation yields more effective isomer assignments.     

Ultraviolet absorption spectra of substituted phenols: a computational study

Vertical excitation energies for electronic transitions from the ground state to the first two excited states of phenol, mono- and disubstituted methoxyphenols and methyl-substituted phenols have been characterized with the Time-Dependent Density Functional Theory (TD-DFT), the Complete Active Space Self-Consistent Field method (CASSCF) and the Coupled Cluster with Single and Double Excitations Equation-of-Motion approach (CCSD-EOM) to simulate and interpret experimental ultraviolet absorption spectra. While CASSCF excitation energies for the first two transitions either are grossly overestimated or exhibit a weak correlation with experimental data, both TD-DFT and CCSD-EOM perform very well, reproducing the spectral shifts of both the primary band and secondary band observed upon substitution. The conformational dependence of the calculated excitation energies is generally smaller than the shifts caused by substitution.     

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.     

Investigation of the S<Subscript>0</Subscript>S<Subscript>1</Subscript> excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

 We have investigated the S₀ and S₁ electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin. Received: 13 October 2001 / Accepted: 6 September 2002 / Published online: 3 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: K. Morokuma e-mail: morokuma@emory.edu     

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.