EXCITED STATE DYNAMICS OF RETINAL PROTEINS AS STUDIED BY FOURIER TRANSFORM OF OPTICAL ABSORPTION SPECTRUM—I. DEVELOPMENT OF ANALYTICAL METHOD

Abstract— We significantly improved the analytical method for the study of excited state dynamics of pigments, by means of the time correlation function (tcf) of the vibrational wavepacket which is produced by the Fourier transform of experimentally obtained optical absorption spectra (FTOA). Applying the tcf method to the spectra of rhodopsin at 0°C and -180°C, we observed specific peaks which are slightly different between 0°C and -180°C in the early time region (1–130 fs) of the absolute value of tcf, representing a characteristic propagation of the wavepacket along a reaction coordinate pertinent to the cis-trans photoisomerization of the chromophore accompanying the motion of protein moiety. From the analysis of phase angle propagation, we obtained a rather small relaxation energy, 6–7 kcal/mol. Based on these results, we can say that FTOA analysis is useful as one of the most powerful techniques for the study of very early procedures in the excited state dynamics of pigments.     

Transport coefficients of square-well fluids

We analyze the analytical form of the velocity time correlation function of a hard sphere system obtained by employing generalized Langevin equation for a square-well fluid. The self-diffusion coefficient and shear viscosity have been calculated using this analytical form of velocity tcf for a square-well fluid. The addition of an attractive square-well potential in place of hard sphere leads to a substantial influence on transport coefficients. Unlike harmonic model diffusion coefficient no longer vanishes. A breakdown of the Stokes–Einstein relation is observed at low densities for a square-well fluid.     

Theoretical investigation of molecular properties of the first excited state of the phenoxyl radical

A theoretical study of molecular, electronic, and vibrational properties of the first excited state of the phenoxyl radical, A 2B2, is presented. The calculated molecular geometries, vertical and adiabatic excitation energies, and harmonic vibrational frequencies are compared with analogous results obtained for the ground state. The calculated excitation energies correspond well to experimental data. The harmonic vibrational frequencies of the A 2B2 and the ground state are similar except for modes involving the vibrations of the CO bond.     

Quantum chemistry study on internal conversion of diphenyldibenzofulvene in solid phase

We investigate the nonradiative decay process of diphenyldibenzofulvene (DPDBF) in solid phase by using the quantum chemistry methods. To carry out the nonradiative rate constant calculation, we construct a solid phase model based on the ONIOM method. The geometry of the DPDBF molecule is optimized for the ground state by DFT and the first excited state by TD-DFT, and the corresponding vibrational frequencies and normal coordinates are computed. Under displaced-distorted harmonic oscillator potential approximation, Huang-Rhys factors are obtained. Vibronic coupling constants are calculated as a function of the normal mode based on Domcke's scheme. We find that vibronic coupling constants of 12 modes with large reorganization energies are of similar order, and if this result is still valid for other modes, the internal conversion rate would be determined by high frequency modes because they have a significant nuclear factor that is related to Franck-Condon overlap intergrals. We also find that geometrical changes are suppressed due to the stacking effect, which yields small Huang-Rhys values in the solid phase.     

Pump-dump iterative squeezing of vibrational wave packets

The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.     

On the applicability of the Born-Oppenheimer approximation in a theory of nonadiabatic charge transfer reactions: An exactly solvable model

The question concerning the applicability of the Born-Oppenheimer approximation (BOA) for the calculation of the transition probability for a nonadiabatic process of charge transfer in a polar environment with allowance made for temperature effects is investigated theoretically. Considered is the transfer of a quantum particle (proton) that interacts with a local vibration mode in a model of bound harmonic oscillators. The model admits an exact solution for wavefunctions of the initial and final states. A calculation shows that BOA is applicable even for very large distances of the proton transfer. At the same time, the exact result and the BOA result severely differ from a probability calculated in a crude Condon approximation. It is demonstrated that the non-Condon effects are in a general case temperature-dependent and may substantially influence the calculated values of the transition probability.     

Spectroscopic investigations of Nd(3+)-doped alkali chloroborophosphate glasses

Optical absorption spectra were studied in wavelength region 400-900 nm for the Nd(3+)-doped alkali (R = Li, Na and K) chloroborophosphate glasses at room temperature. The energy level scheme of the 4f(3) electron configuration was deduced from the observed energy level data using a parametrized Hamiltonian (H(F1)) model which includes 20 free-ion interaction parameters. Reasonable correlation was obtained between the experimental and calculated energy levels. The Judd-Ofelt model for the intensity analysis of induced electric dipole transitions has been applied to the measured oscillator strengths of the absorption bands to determine the three phenomenological intensity parameters Omega(2), Omega(4) and Omega(6) for each glass. Using these parameters, the total radiative transition rates (A(T)), non-radiative relaxation rates (W(NR)), branching ratios (beta(R)), integrated cross-sections for the stimulated emission (Sigma), excited state emission intensities (f(ESE)) and excited state absorption intensities (f(ESA)) have been theoretically calculated for certain excited Nd(3+) fluorescent levels. From the results obtained, the conclusion is made about the possibility of using these glasses as laser media.     

Theoretical study of singlet and triplet excitation energies in oligothiophenes

We have analyzed singlet and triplet excitation energies in oligothiophenes (up to five rings) using time-dependent density-functional theory (TD-DFT) with different exchange-correlation functionals and compared them with results from the approximate coupled-cluster singles and doubles model (CC2) and experimental data. The excitation energies have been calculated in geometries obtained by TD-DFT optimization of the lowest excited singlet state and in the ground-state geometries of the neutral and anionic systems. TD-DFT methods underestimate photoluminescence energies but the energy difference between singlet and triplet states shows trends with the chain-length similar to CC2. We find that the second triplet excited state is below the first singlet excited state for long oligomers in contrast with the previous assignment of Rentsch et al. (Phys.Chem. Chem. Phys. 1999, 1, 1707). Their photodetachment photoelectron spectroscopy measurements are better described by considering higher triplet excited states.     

Electronic Structure and Photophysical Properties of 2-(N,N-diethylanilin-4-yl)-4,6-bis(3,5-dimethylpyrazol-1-yl)-1,3,5-triazine

Electronic structure and photophysical properties of 2-(N,N-diethylanilin-4-yl)-4,6-bis(3,5-dimethylpyrazol-1-yl)-1,3,5-triazine are studied theoretically with quantum chemical methods as well as 2D site and 3D cube representations. The theoretical results reveal that the first excited state is an intramolecular charge transfer excited state. The change in dipole moment for the first excited state of the excitation is fitted, and the calculated result the change in dipole moment ￠1=6.40 D is consistent with the experimental result ￠1=6.90 D. The polarizability is also fitted. The large changes in dipole moment and the polarizability of the excitation show that S1 is of large nonlinear optical (NLO) effect. The NLO will promote efficient two-photon-absorption cross sections. The excited state properties of dpbt with different external electronic fields are also discussed theoretically.     

Novel infrared spectra for intermolecular dihydrogen bonding of the phenol-borane-trimethylamine complex in electronically excited state

The intermolecular dihydrogen bonding in the electronically excited states of the dihydrogen-bonded phenol-BTMA complex in gas phase was theoretically investigated using the time-dependent density functional theory method for the first time. It was theoretically demonstrated that the S(1) state of the dihydrogen-bonded phenol-BTMA complex is a locally excited state, in which only the phenol moiety is electronically excited. The infrared spectra of the dihydrogen-bonded phenol-BTMA complex in ground state and the S(1) state were calculated at both the O-H and B-H stretching vibrational regions. A novel infrared spectrum of the dihydrogen-bonded phenol-BTMA complex in the electronically excited state was found. The stretching vibrational absorption bands of the dihydrogen-bonded O-H and B-H groups are very strong in the ground state, while they are disappeared in the S(1) state. At the same time, a new strong absorption band appears at the C[Double Bond]O stretching region. From the calculated bond lengths, it was found that both the O-H and B-H bonds in the dihydrogen bond O-H...H-B are significantly lengthened in the S(1) state of the dihydrogen-bonded phenol-BTMA complex. However, the C-O bond in the phenol moiety is markedly shortened in the excited state, and then has the characteristics of C[Double Bond]O group. Furthermore, it was demonstrated that the intermolecular dihydrogen bonds in the electronically excited state of the dihydrogen-bonded phenol-BTMA complex are strengthened, since calculated H...H distance is drastically shortened in the S(1) state.     

The influence of ultrashort excitations on the vibrational dynamics in a diatomic molecule

The problem of vibrational wave packet dynamics in the system of two electronic states of a diatomic molecule, where the states are coupled by infinitely short light pulses, is solved. The electronic states were modeled by shifted harmonic oscillators with different frequencies. Exact expressions for the probability densities of the wave packets in the ground and excited states were derived. The spatial, spectral, and temporal characteristics of the wave packets, namely, the range of motion, spatial width, mean energy, spectral width (the mean number of vibrational states in a wave packet), and the autocorrelation function, were calculated as functions of the molecular parameters (the frequency ratio and the distance between the potential minima) and of the delay time between the light pulses. The possibility of controlling the mean energy and spectral width of the wave packets in the ground electronic state by varying the delay time is considered. It was shown that "squeezed" wave packets can be prepared in the ground electronic state if the upper electronic state is shallow.     

Spectroscopic consequences of a mixed valence excited state: quantitative treatment of a dihydrazine diradical dication

A model for the quantitative treatment of molecular systems possessing mixed valence excited states is introduced and used to explain observed spectroscopic consequences. The specific example studied in this paper is 1,4-bis(2-tert-butyl-2,3-diazabicyclo[2.2.2]oct-3-yl)-2,3,5,6-tetramethylbenzene-1,4-diyl dication. The lowest energy excited state of this molecule arises from a transition from the ground state where one positive charge is associated with each of the hydrazine units, to an excited state where both charges are associated with one of the hydrazine units, that is, a Hy-to-Hy charge transfer. The resulting excited state is a Class II mixed valence molecule. The electronic emission and absorption spectra, and resonance Raman spectra, of this molecule are reported. The lowest energy absorption band is asymmetric with a weak low-energy shoulder and an intense higher energy peak. Emission is observed at low temperature. The details of the absorption and emission spectra are calculated for the coupled surfaces by using the time-dependent theory of spectroscopy. The calculations are carried out in the diabatic basis, but the nuclear kinetic energy is explicitly included and the calculations are exact quantum calculations of the model Hamiltonian. Because the transition involves the transfer of an electron from the hydrazine on one side of the molecule to the hydrazine on the other side and vice versa, the two transitions are antiparallel and the transition dipole moments have opposite signs. Upon transformation to the adiabatic basis, the dipole moment for the transition to the highest energy adiabatic surface is nonzero, but that for the transition to the lowest surface changes sign at the origin. The energy separation between the two components of the absorption spectrum is twice the coupling between the diabatic basis states. The bandwidths of the electronic spectra are caused by progressions in totally symmetric modes as well as progressions in the modes along the coupled coordinate. The totally symmetric modes are modeled as displaced harmonic oscillators; the frequencies and displacements are determined from resonance Raman spectra. The absorption, emission, and Raman spectra are fit simultaneously with one parameter set. The coupling in the excited electronic state H(ab)(ex) is 2000 cm(-1). Excited-state mixed valence is expected to be an important contributor to the electronic spectra of many organic and inorganic compounds. The energy separations and relative intensities enable the excited-state properties to be calculated as shown in this paper, and the spectra provide new information for probing and understanding coupling in mixed valence systems.     

CHARGE TRANSFER COMPLEXES OF PHEOPHYTIN a WITH NITROAROMATICS. ELECTRON TRANSFER FROM EXCITED SINGLET OF PHEOPHYTIN a TO NITROAROMATICS

Abstract— The interaction of pheophytin a (Pheo) with seven nitroaromatic acceptors of varying ring sizes and electron acceptor abilities has been studied both in the ground and excited states. The ground state association constants ( K ) of the 1: 1 complexes of donor (Pheo) and acceptors were found to increase with increasing electron affinities of the different acceptors. All the nitroaromatic compounds efficiently quench the singlet emission of Pheo and the quenching follows the Stern-Volmer (SV) relationship. The SV constants ( K _sv) for different quenchers follow the same order as that of the K values. The reduction potential of Pheo₊/Pheo_* obtained from the quenching data agrees well with the theoretically predicted value. A charge transfer interaction between the singlet excited state of Pheo and the nitroaromatics is suggested from the dependence of quenching rate constants on the electron affinities of the acceptors.     

Theoretical investigation of molecular properties of the first excited state of the thiophenoxyl radical

Accurate ab initio study of the lowest excited state (A (2)B(2)) of the thiophenoxyl radical is presented. The calculated equilibrium geometries, excitation energies, and harmonic vibrational frequencies show that the A (2)B(2) <-- X (2)B(1) excitation in C(6)H(5)S has different characteristics than the analogous transition in the phenoxyl radical. Vertical excitation energies for other low-lying (<4.5 eV) excited states of the thiophenoxyl radical are also presented and compared with available experimental data.     

PROTON TRANSFER IN THE PRIMARY PROCESS OF VISION

Abstract— Proton transfer was theoretically examined as a possible primary process of vision. The motion of protons in the adiabatic potential of the Schiff base hydrogen bond was investigated in terms of quantum mechanics. The probability of proton transfer from the Schiff base nitrogen (i.e. the unprotonation of Schiff base) was found to increase as the retinal rotated around 11–12. double bond by 90°. The results also suggested that the proton transfer can take place before or during the transition from the excited to ground state (excited state proton transfer). We proposed that such excited state proton transfer is one of the elementary processes in primary visual photochemistry, and this process leads to the unprotonated visual pigment, hyposorhodopsin, which has been experimentally verified as one of the primary photoproducts of rhodopsin. The probability of this process could be comparable to the conventional process leading to the protonated intermediate, bathorhodopsin. The relation of these results with the recent experimental data is discussed.     

On the nature of the low-lying singlet states of 4-(Dimethyl-amino)benzonitrile

4-(N,N-Dimethyl-amino)benzonitrile (DMABN) is a prototype molecule for dual fluorescence. The anomalous emission has been attributed to an intramolecular charge-transfer (ICT) state, and the structure of the latter is still subject to some controversy. We applied a recently developed analytical gradient code for the approximate coupled-cluster singles-and-doubles method CC2 in combination with accurate basis sets to address this problem. Fully optimized excited state structures are presented for the ICT state and the so-called locally excited state, and recent transient IR and Raman measurements on the excited states are interpreted by means of calculated harmonic frequencies. Strong evidence is found for an electronic decoupling of the phenyl and the dimethyl-amino moiety, resulting in a minimum structure for the ICT state with a twisted geometry. In contrast to previous findings, the structure of this state is, at least in the gas phase, not C(2v) symmetric but distorted towards C(s) symmetry. The distortion coordinate is a pyramidalization of the phenyl carbon atom carrying the dimethyl-amino group. The results from the CC2 model are supported by single-point calculations using more elaborate coupled-cluster models (CCSD, CCSDR(3)) and by CASSCF calculations.     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

Molecular dynamics effects on luminescence properties of oligothiophene derivatives: a molecular mechanics-response theory study based on the CHARMM force field and density functional theory

CHARMM force field parameter values for a class of oligothiophene derivatives have been derived with reference to density functional theory/B3LYP potential energy surfaces. The force field parametrization of these luminescent conjugated polyelectrolytes includes the electronic ground state as well as the strongly light absorbing first excited state. In conjunction with quantum chemical response theory calculations of transition state properties, a molecular dynamical model of the Stokes shift is obtained. The theoretical model is benchmarked against experimental data recorded at room temperature which refer to sodium salts of p-HTAA and p-FTAA with distilled water as a solvent. For p-HTAA the theoretically predicted Stokes shift of 112 nm is in good agreement with the experimental result of 124 nm, given the approximations about exciton localization that were introduced to obtain a force field for the excited state.     

Dimeres composes de molecules dont l'excitation electronique entraine un deplacement de la configuration nucleaire d'equilibre accompagne d'un changement de constante de force

We have studied the validity of the traditional model of a dimer that has been treated exactly by Merrifield and Fulton and Gouterman, solving the vibronic coupled equations by a numerical method. This model takes into account the modification of the nuclear equilibrium configuration, but it neglects the variation of the force constant when the monomer is electronically excited from the fundamental to a given excited state (the corresponding electronic potentials are both considered as harmonic). We have shown by inspection of the absorption and fluorescence spectra calculated by solving the vibronic equation exactly that the variation force constant cannot be neglected, even if it is weak, particularly in the weak coupling region. The weak, intermediate and strong coupling criteria have been deduced, for the model studied, by examination of the dimeric electronic potential surfaces for different cases of intermolecular interactions.     

Analysis of time resolved femtosecond and femtosecond/picosecond coherent anti-Stokes Raman spectroscopy: application to toluene and Rhodamine 6G

The third-order polarization for coherent anti-Stokes Raman scattering (CARS) from a pure state is described by 48 terms in perturbation theory, but only 4 terms satisfy the rotating wave approximation. They are represented by Feynman dual time-line diagrams and four-wave mixing energy level diagrams. In time-resolved (tr) fs and fs/ps CARS from the ground vibrational state, one resonant diagram, which is the typical CARS term, with three field interactions-pump, Stokes, followed by probe-on the ket is dominant. Using the separable, displaced harmonic oscillators approximation, an analytic result is obtained for the four-time correlation function in the CARS third-order polarization. Dlott's phenomenological expression for off-resonance CARS from the ground vibrational state is derived using a three-state model. We calculated the tr fs and fs/ps CARS for toluene and Rhodamine 6G (R6G), initially in the ground vibrational state, to compare with experimental results. The observed vibrational features and major peaks for both tr fs and fs/ps CARS, from off-resonance (for toluene) to resonance (for R6G) pump wavelengths, can be well reproduced by the calculations. The connections between fs/ps CARS, fs stimulated Raman spectroscopy, and impulsive stimulated scattering for toluene and R6G are discussed.