Coulombic couplings between pigments in the major light-harvesting complex LHC II calculated by the transition density cube method

We present ab initio transition density cube (TDC) calculations of the coulombic couplings between chlorophyll and carotenoid pigments in the major light-harvesting complex of photosystem II (LHC II) based on the 2.72 Å structure [Liu et al., Nature 428(2004) 287–292]. A comparison with couplings calculated by the ideal dipole approximation (IDA) demonstrate that for inter-pigment distances of less than 25 Å the IDA-values can deviate by up to one order of magnitude from the exact values calculated by the TDC-method. The largest deviations are observed for interactions involving Q_x states because of a significant multipole character of the corresponding Q_x transitions.     

Energy transfer in the nanostar: the role of coulombic coupling and dynamics

We present a theoretical investigation of energy transfer in the phenylene ethynelene dendrimer known as the nanostar. Data from extensive molecular dynamics simulations are used to model the dynamical effects caused by torsional motion of the phenyl groups. We compare rate constants for energy transfer between the two-ring chromophore and the three-ring chromophore obtained via the F?rster model, the ideal dipole approximation (IDA), and the transition density cube (TDC) method, which has as its limit an exact representation of the Coulombic coupling. We find that the rate constants obtained with the TDC are extremely sensitive to the phenyl group rotation, whereas the constants computed with the F?rster model and the IDA are not. The implications of these results for the interpretation of recent pump-probe experiments on the nanostar are discussed in detail. Finally, we predict the temperature dependence of the rate constant for energy transfer.     

UV spectra and excitation delocalization in DNA: influence of the spectral width.

The singlet excited states of the model DNA duplex (dA)10.(dT)10 are studied. Calculations are performed in the exciton theory framework. Molecular dynamics calculations provide the duplex geometry. The dipolar coupling is determined using atomic transition charges. The monomer transition energies are simulated by Gaussian functions resembling the absorption bands of nucleosides in aqueous solutions. Most of the excited states are found to be delocalized over at least two bases and result from the mixing of different monomer states. Their properties are only weakly affected by conformational changes of the double helix. On average, the highest oscillator strength is carried by the upper eigenstates. The duplex absorption spectra are shifted a few nanometers to higher energies with respect to the spectra of noninteracting monomers. The states with larger spatial extent are located close to the maximum of the absorption spectrum.     

光系统I（PSI）反应中心的激子耦合

运用点偶极、单极跃迁电荷和跃迁密度等经典库仑作用的方法,考察了叶绿素a分子间面心距和错位结构等因素对激子耦合的影响．结果表明,当分子间距大于分子尺寸时,上述三种方法得到的结果基本一致;但当分子间距小于分子尺寸时,点偶极方法将明显高估激子耦合,跃迁密度的方法更适合计算分子间的激子耦合．此外,还使用上述方法计算了光系统Ⅰ（PSI）反应中心叶绿素a分子间激子耦合．结果表明,用跃迁密度计算PSI晶体结构（1jb0．pdb）e700的激子耦合为75.3cm^-1,而QM．MM优化的结构P700（ecAl．ecBl）的激子耦合为23．8cm^-1,这与考虑Dexter交换项的全对角化方法的结果（20cm^-1）一致,进而说明PSI反应中心并不是传统的P700强激子耦合对,而是ecAl-ecB2和ecBl-ecA2对强耦合二聚体构成的二聚体对．     

Do coupling exciton and oscillation of electron-hole pair exist in neutral and charged pi-dimeric quinquethiophenes?

Optical physical properties of neutral and charged quinquethiophene monomer, and neutral and cationic pi-dimeric quinquethiophenes were investigated with density functional theory as well as the two dimensional (2D) site (transition density matrix) and three dimensional (3D) cube (transition density and charge difference density) representations, stimulated by the recent experimental report [T. Sakai et al., J. Am. Chem. Soc. 127, 8082 (2005)]. Transition density shows the orientation and strength of the transition dipole moment of neutral and charged quinquethiophene monomer, and charge difference density reveals the orientation and result of the charge transfer in neutral and charged quinquethiophene monomer. To study if coupling exciton and oscillation of electron-hole pair exist in neutral and cationic pi-dimeric quinquethiophenes, the coupling constants J (coupling exciton of electron-hole pair) and K (coupling oscillation of electron-hole pair) were introduced to the exciton coordinate and momentum operators, respectively, and the 2D and 3D analysis methods were further developed by extending our previous theoretical methods [M. T. Sun, J. Chem. Phys. 124, 054903 (2006)]. With the new developed 2D and 3D analysis methods, we investigated the excited state properties of neutral and cationic pi-dimeric quinquethiophenes, especially on the coupling exciton and oscillation of electron-hole pair between monomers. The 2D results show that there is neither coupling exciton (J=0) nor oscillation (K=0) of electron-hole pair in neutral pi-dimeric quinquethiophenes. For some excited states of cationic pi-dimeric quinquethiophenes, there is no coupling exciton (J=0), but there is coupling oscillation (K not equal0); while for some excited states, there are both coupling exciton and coupling oscillator simultaneously (J not equal0 and K not equal0). The strength of transition dipole moments of pi-dimeric quinquethiophenes were interpreted with 3D transition density, which reveals the orientations of their two subtransition dipole moments. The 3D charge transition density reveals the orientation and result of intermonomer and/or intramonomer charge transfer. The calculated results reveal that excited state properties of neutral pi-dimeric quinquethiophene are significantly different from those of the cationic pi-dimeric quinquethiophenes.     

S1 and S2 excited states of gas-phase Schiff-base retinal chromophores: a time-dependent density functional theoretical investigation

In concert with the recent photoabsorption experiments of gas-phase Schiff-base retinal chromophores (Nielsen et al. Phys. Rev. Lett. 2006, 96, 018304), quantum chemical calculations using time-dependent density functional theory coupled with different functionals and under the Tamm-Dancoff approximation were made on the first two excited states (S1 and S2) of two retinal chromophores: 11-cis and all-trans protonated Schiff bases. The calculated vertical excitation energies (Tv) and oscillator strengths (f) are consistent with the experimental absorption bands. The experimentally observed phenomenon that the transition dipole moment (mu) of S2 is much smaller that of S1 was interpreted by 3D representation of transition densities. The different optical behaviors (linear and nonlinear optical responds) of the excited states were investigated by considering different strengths of external electric fields.     

A density functional theory study of vibrational coupling in the amide I band of beta-sheet models

We report the first molecular orbital/density functional theory (DFT) calculations on the vibrational frequencies involved in the amide I band of completely geometrically optimized models for beta-sheet peptides based upon (up to 16) glycine residues. These calculations use the B3LYP/D95** level of DFT. The primary means of vibrational coupling occurs through H bond, rather than through space, interactions, which is consistent with a previous report on alpha-helical polyalanines and H-bonding chains of both formamides and 4-pyridones. We decoupled the C=O stretching vibrations using selected 14C substitutions to probe the coupling mechanism and to determine "natural" frequencies for individual 14C=Os. The intermolecular H-bonding interactions affect the geometries of the amide groups. Those near the center of H-bonding chains have long C=O bonds. The C=O bond lengths correlate with these "natural" frequencies, The frequencies obtained from the DFT calculations are generally more coupled, and the most intense are more red shifted than those calculated by transition dipole coupling (TDC). TDC inverts the order of the shifted frequencies compared to DFT in several cases.     

Bis(merocyanine) Hetero-Folda-Dimers: Evaluation of Exciton Coupling between Different Types of π-Stacked Chromphores

Exciton coupling between different types of chromophores has been rarely investigated. Herein, a systematic study on the exciton coupling between merocyanine chromophores of different conjugation length with varying excited state energies is presented. In this work well-defined hetero-dimer stacks were obtained upon folding of bis(merocyanine) dyes in nonpolar solvents. They show distinctly different absorption properties in comparison with the spectra of the single chromophores, revealing a significant coupling between the different chromophores. The simulated absorption spectra obtained from time-dependent density functional theory (TD-DFT) calculations are in good agreement with the experimental spectra. Our theoretical analysis based on an extension of Kasha's exciton theory discloses strong coupling between the dyes’ transition dipole moments despite of an excited-state energy difference of 0.60 eV between the chromophores.     

Parameters for excess electron transfer in DNA. Estimation using unoccupied Kohn-Sham orbitals and TD DFT

We show that the energetics and electronic couplings for excess electron transfer (EET) can be accurately estimated by using unoccupied Kohn-Sham orbitals (UKSO) calculated for neutral pi stacks. To assess the performance of different DFT functionals, we use MS-PT2 results for seven pi stacks of nucleobases as reference data. The DFT calculations are carried out by using the local spin density approximation SVWN, two generalized gradient approximation functionals BP86 and BLYP, and two hybrid functionals B3LYP and BH&HLYP. Best estimations within the UKSO approach are obtained by the B3LYP and SVWN methods. TD DFT calculations provide less accurate values of the EET parameters as compared with the UKSO data. Also, the excess charge distribution in the radical anions is well described by the LUMOs of neutral systems. In contrast, spin-unrestricted DFT calculations of radical anions considerably overestimate delocalization of the excess electron. The excellent results obtained for the ground and excited states of the radical anions (excitation energy, transition dipole moment, electronic coupling, and excess electron distribution) by using UKSO of neutral dimers suggest an efficient strategy to calculate the EET parameters for DNA pi stacks.     

Exciton-phonon self-trapping: A continuous transition

An exciton-phonon system of a linear aggregate is investigated in the intermediate-coupling regime. For sufficiently large intermolecular coupling. the variational approach predicts a discontinuous transition from a mobile exciton at weak exciton-phonon coupling to an immobile exciton at strong coupling. Fully converged numerical calculations exhibit strong deviations from the variational approach at intermediate exciton-phonon coupling strength and do not show a discontinuous transition. In the strong-coupling regime, results from the variational approach (which are closely related to the small polaron theory) deviate considerably from numerically converged calculations and an appropriate perturbation approximation.     

Heme-Peptide Models for Hemoproteins. 2. N-Acetylmicroperoxidase-8: Study of the pi-pi Dimers Formed at High Ionic Strength Using a Modified Version of Molecular Exciton Theory

AcMP8 is the Cys-14-acetylated water-soluble heme-octapeptide fragment obtained proteolytically from cytochrome c. Two successive dimerization equilibria are observed with increasing ionic strength in aqueous solution at neutral pH (part 1, preceding article). The electronic spectra of the two pi-pi dimers were extracted from the absorption envelopes at 2.01 and 4.02 M ionic strength and resolved by Gaussian analysis. The principal transitions were assigned using a tailored version of molecular exciton theory based on coupling of the main x- and y-polarized transition dipole moments of the interacting heme groups. The spectra of both pi-pi dimers indicate that the y-polarized exciton states are blue-shifted relative to the excited states of the monomer, while the x-polarized exciton states exhibit a red shift. These shifts were correctly predicted by a simple dipole-dipole coupling model. From an analysis of the resultant transition dipole moments to the exciton states with B(x)()(0,0) and B(y)()(0,0) character and the magnitudes of their red and blue exciton shifts, respectively, we have determined the dipole-dipole interaction geometries for both dimers. The principal difference between the interaction geometry in the first dimer and that in the second is a stronger interaction for the y-polarized transition dipoles and somewhat weakened interaction for the x-polarized transition dipoles. From an analysis of available crystallographic data for porphyrin and metalloporphyrin pi-pi dimers (Scheidt, W. R.; Lee, Y. J. Struct. Bonding 1987, 64, 1) and the results of our exciton model, we conclude that the origin of the coordinate system for the Soret transition dipole moments of AcMP8 is not metal-centered. Furthermore, since the true directions of the x- and y-axes of the low-symmetry heme chromophore in AcMP8 are unknown, we have not been able to determine the structures of the pi-pi dimers from a knowledge of their transition dipole-dipole interaction geometries. This study therefore highlights one of the shortfalls of molecular exciton theory.     

Using molecular dynamics and quantum mechanics calculations to model fluorescence observables

We provide a critical examination of two different methods for generating a donor-acceptor electronic coupling trajectory from a molecular dynamics (MD) trajectory and three methods for sampling that coupling trajectory, allowing the modeling of experimental observables directly from the MD simulation. In the first coupling method we perform a single quantum-mechanical (QM) calculation to characterize the excited state behavior, specifically the transition dipole moment, of the fluorescent probe, which is then mapped onto the configuration space sampled by MD. We then utilize these transition dipoles within the ideal dipole approximation (IDA) to determine the electronic coupling between the probes that mediates the transfer of energy. In the second method we perform a QM calculation on each snapshot and use the complete transition densities to calculate the electronic coupling without need for the IDA. The resulting coupling trajectories are then sampled using three methods ranging from an independent sampling of each trajectory point (the independent snapshot method) to a Markov chain treatment that accounts for the dynamics of the coupling in determining effective rates. The results show that the IDA significantly overestimates the energy transfer rate (by a factor of 2.6) during the portions of the trajectory in which the probes are close to each other. Comparison of the sampling methods shows that the Markov chain approach yields more realistic observables at both high and low FRET efficiencies. Differences between the three sampling methods are discussed in terms of the different mechanisms for averaging over structural dynamics in the system. Convergence of the Markov chain method is carefully examined. Together, the methods for estimating coupling and for sampling the coupling provide a mechanism for directly connecting the structural dynamics modeled by MD with fluorescence observables determined through FRET experiments.     

Probing multiple core-hole interactions in the nitrogen K-edge of DNA base pairs by multidimensional attosecond X-ray spectroscopy. A simulation study

Two-dimensional X-ray correlation spectroscopy (2DXCS) signals of the isolated DNA bases and Watson-Crick base pairs which contain multiple absorbing nitrogen atoms are calculated. Core-hole excited states are calculated using density functional theory with the B3LYP functional and 6-311G** basis set. Sum over states calculations of the signals reveal changes in cross-peak intensities between hydrogen-bonded and stacked base pairs. Nucleobase analogues are proposed for investigating base-stacking and hydrogen-bonding interactions.     

A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.     

Calculation of optical rotatory dispersion and electronic circular dichroism for tris-bidentate groups 8 and 9 metal complexes, with emphasis on exciton coupling

The optical rotatory dispersion (ORD, both non-resonant and resonant) and the electronic circular dichroism (CD) of tris-bidentate transition metal complexes of the form [M(L)(3)](n+) (M = Fe, Ru, Os, Co, Rh, Ir; n = 2, 3; L = 1,10-phenanthroline, 2,2'-bipyridine) are calculated using time-dependent density functional theory (TDDFT). The exciton CD band resulting from the coupling of ligand π-to-π* transitions is investigated in detail and analyzed in terms of exciton coupling of long-axis transitions using a dipole coupling model that takes TDDFT data for a single ligand as input. Results of the coupling model agree well with the full TDDFT CD spectra. The usefulness and reliability of this model is discussed. The resonant ORDs calculated directly from analytical damped linear TDDFT response compare well with Kramers-Kronig transformations of the calculated CD spectra. For comparisons of resonant ORD with experiment, one needs to consider wavelength shifts.     

Theoretical modeling of peptide α-helical circular dichroism in aqueous solution

Reliable modeling of protein and peptide circular dichroism (CD) spectra in the far UV presents a challenge for current theoretical approaches. In this study, the time-dependent density functional theory (TDDFT), configuration interaction with single excitation (CIS), and transition dipole coupling (TDC) were used to assess the most important factors contributing to the CD spectra of the α-helical secondary structure. The dependence on the peptide chain length and also the role of the flexibility and solvent environment were investigated with a model oligopeptide Ac-(Ala)(N)-NH-Me, (N = 1, ..., 18). Both the TDDFT and TDC-like methods suggest that the CD curve typical for the α-helix arises gradually, but its basic characteristic is discernible already for peptides with 4-5 amino acid residues. The calculated dependence was in a qualitative agreement with experimental spectra of short α-helices stabilized by the histidine-metal binding. The TDDFT computations of the CD were found to be unusually sensitive to the basis set and solvent model. Explicit hydration and temperature fluctuations of the peptide geometry, simulated with the aid of molecular dynamics (MD), significantly influenced the CD and absorption spectral shapes. An extensive averaging over MD configurations is thus required to obtain a converged spectral profile in cluster simulations. On the other hand, both the TDDFT and TDC models indicate only a minor influence of the alanine side chains. The CIS and TDC calculations also point toward a relatively small effect of the helix-helix interaction on the CD spectral profiles. For a model system of two helices, the CIS method predicted larger changes in the spectra than TDC. This suggests other than interactions between peptide chains, such as mutual polarization, can have a minor, but measurable, effect on the CD spectrum.     

Thermostimulated depolarization currents in thermorheologically simple materials

A theory is presented which makes possible the calculation of the dielectric parameters for a distributed dipole relaxation from thermostimulated depolarization current (TDC) data. The theory is applicable to dielectrics which obey the time–temperature superposition principle, i.e., for thermorheologically simple materials. The shift factor, the activation energy, the dielectric relaxation strength, the density of the isothermal displacement current, and the distribution function of relaxation times of the β relaxation in poly(methyl methacrylate) are calculated. The TDC investigations were carried out over the temperature range of ?136 to 90°C. The values for the activation energy U = 26.4 kcal/mole and the dielectric relaxation strength Δ_?β = 2 are in good agreement with values obtained from dynamic measurements. A criterion for checking the validity of the time–temperature superposition principle by TDC is suggested.     

Beyond exciton theory: a time-dependent DFT and Franck-Condon study of perylene diimide and its chromophoric dimer

The diimide perylene motif exhibits a dramatic intensity reversal between the 0 --> 0 and 0 --> 1 vibronic bands upon pi-pi stacking; this distinct spectral property has previously been used to measure folding dynamics in covalently bound oligomers and synthetic biological hybrid foldamers. It is also used as a tool to assess organization of the pi-stacking, indicating the presence of H- or J-aggregation. The zeroth-order exciton model, often used to describe the optical properties of chromophoric aggregates, is solely a transition dipole coupling scheme, which ignores the explicit electronic structure of the system as well as vibrational coupling to the electronic transition. We have therefore examined the optical properties of gas-phase perylene tetracarboxylic diimide (PTCDI) and its chromophoric dimer as a function of conformation to relate the excited-state distributions predicted by exciton theory with that of time-dependent density functional theory (TDDFT). Using ground- and excited-state geometries, the Franck-Condon (FC) factors for the lowest energy molecular nature electronic transition have been calculated and the origin of the intensity reversal of 0 --> 0 and 0 --> 1 vibronic bands has been proposed.     

Calculation of the exciton band structure of the lowest energy singlet state of fluorene

The exciton band structure of the 33000 cm⁻¹ transition of fluorene has been calculated in the dipole approximation. It is shown that the interac