Low temperature electron transfer in strongly condensed phase

Electron transfer coupled to a collective vibronic degree of freedom is studied in strongly condensed phase and at lower temperatures where quantum fluctuations are essential. Based on an exact representation of the reduced density matrix of the electronic + reaction coordinate compound in terms of path integrals, recent findings on the overdamped limit in quantum dissipative systems are employed. This allows us to give a consistent generalization of the well-known Zusman equations to the quantum domain. Detailed conditions for the range of validity are specified. Using the Wigner transform these results are also extended to the quantum dynamics in full phase space. As an important application electronic transfer rates are derived that comprise adiabatic and nonadiabatic processes in the low temperature regime including nuclear tunneling. Accurate agreement with precise quantum Monte Carlo data is observed.     

One-dimensional description of multidimensional electron transfer reactions in condensed phase

We derive a one-dimensional energy diffusion equation for describing the dynamics of multidimensional electron transfer reactions in condensed phase, which is conceptually simpler and computationally more economic than the conventional approaches. We also obtain an analytical expression for the rate of electron transfer reactions for a general one-dimensional effective potential as well as an energy dependent diffusitivity. As an illustrative example, we consider application to electron transfer in a contact ion pair system modeled through harmonic potentials consisting of two slow classical modes and a high frequency vibrational mode for which the numerical results calculated using the proposed one-dimensional approach are shown to be in good agreement with experimental results. The energy diffusion equation and the rate expression for electron transfer obtained from the present theory, therefore, open up the possibility of describing the dynamics of electron transfer in complex systems, through a simpler approach.     

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Fo?rster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.     

Kinetics of energy transfer processes in C-phycocyanin complexes

The antenna system of algae for photosynthesis is a functional entity composed of various phycobiliproteins and the linker polypeptides. Up to now, high-resolution crystal structure data have been available only for the isolated phycobiliproteins. To have an understanding of the functional connection between different phycobiliproteins, it is necessary to study the complexes composed of different phycobiliproteins. The energy transfer processes in C-phycocyanin complexes were studied through computer simulation because it is difficult to be studied by conventional experimental methods. The main pathways of energy flow and the dynamic property of the energy transfer were obtained. A fast transfer process between two neighboring disks was observed through analyzing the distribution curves of excitation energy over time. According to the definition of the time constants for energy transfer in time-resolved spectrum techniques, for a complex with three C-phycoeyanin hexamer disks, a fluorescence-rising comp     

A one-dimensional energy diffusion approach to multidimensional dynamical processes in the condensed phase

We propose a generalized one-dimensional energy diffusion approach for describing the dynamics of multidimensional dynamical processes in the condensed phase. On the basis of a formalism originally due to Zwanzig, we obtain a one-dimensional kinetic equation for a properly selected relevant dynamical quantity and derive new analytical results for the dynamics of a multidimensional electron-transfer process, nonequilibrium solvation, and diffusive escape from a potential well. The calculated results for electron-transfer reactions in solvent-separated and contact ion pair systems are found to be in good agreement with the experimental results. We are able to explain the rate of the electron-transfer reaction using much smaller and reasonable values of the solvent reorganization energy in contrast to earlier works that had to use a much larger value. The proposed theory is not only conceptually simpler than the conventional approaches but is also free from many of their limitations. More importantly, it provides a single theoretical framework for describing a wide class of dynamical phenomena.     

Vibrational relaxation in the condensed phase

A modified Landau-Teller equation for vibrational relaxation in the condensed phase is proposed. This equation differs from previous approaches by accounting for the fluctuations of the energies of the vibrational levels that result from the interactions with the surroundings (bath). In the conventional approach the effects of the bath are only included in the coupling between the relaxing and accepting vibrational modes. It is shown that the additional inclusion of the fluctuations of the energy levels can lead to a dramatic change of the vibrational relaxation rate.     

Kinetics of photochromic reactions in condensed phases

A review of kinetic data reported for a few organic photochromic systems is given. The kinetics of processes taking place in solid matrices and in crystals was briefly discussed. The effect of solid matrices manifests itself in the kinetics being controlled by distributions rather than by discrete rate constants. The photochromic reactions often require a substantial free volume to occur, hence they seldom take place in crystals without a destruction of the crystal lattice. The activation energies of thermally driven reactions are in this case related rather to crystal parameters than to the reactions themselves.     

On the direct calculation of the free energy of quantization for molecular systems in the condensed phase

Using the path integral formalism or the Feynman-Hibbs approach, various expressions for the free energy of quantization for a molecular system in the condensed phase can be derived. These lead to alternative methods to directly compute quantization free energies from molecular dynamics computer simulations, which were investigated with an eye to their practical use. For a test system of liquid neon, two methods are shown to be most efficient for a direct evaluation of the excess free energy of quantization. One of them makes use of path integral simulations in combination with a single-step free energy perturbation approach and was previously reported in the literature. The other method employs a Feynman-Hibbs effective Hamiltonian together with the thermodynamic integration formalism. However, both methods are found to give less accurate results for the excess free energy of quantization than the estimate obtained from explicit path integral calculations on the excess free energy of the neon liquid in the classical and quantum mechanical limit. Suggestions are made to make both methods more accurate.     

"Reduced" distributed monopole model for the efficient prediction of energy transfer in condensed phases

We propose a methodology for the realistic simulation and prediction of resonance energy transfer in condensed phases based on a combination of computer simulations of phase morphologies and of a distributed monopole model for the radiationless transfer. The heavy computational demands of the method are moderated by the introduction of a transition charges reduction scheme, originally developed for ground state interactions [Berardi, R. et al. Chem. Phys. Lett. 2004, 389, 373]. We demonstrate the scheme for a condensed glass phase formed by perylene monoimide end-capped 9,9-(di n,n)octylfluorene trimers, recently studied as light-harvesting materials, where we couple a coarse-grained Monte Carlo simulation of the molecular organization and a master equation approach modeling the energy diffusion process.     

Description of quantum effects in the condensed phase

Recent experiments on light harvesting complexes have shown clear indication of coherent transport of excitations in these aggregates. We review the theoretical models that have been used to study energy transfer in molecular aggregates, beginning with the early models of Förster and Davydov. We cover the Redfield and Haken Strobl models in some detail, in order to set the nomenclature and because they are the most common and easiest models to understand and work with. We briefly discuss more complex models.     

Positive muons in condensed phase ammonia

The chemical behavior of positive muons in condensed phase ammonia has been investigated in order to elucidate the phase and temperature effects on the chemical and physical behavior of the muon and muonium formation in a simple binary compound. Diamagnetic muon yield (P_D) was constant at 0.67±0.01 in both solid and liquid above 125 K. Muonium formation in solids were observed above 100 K with slow muonium spin relaxation. In liquids, the muonium yield and its spin relaxation rate showed temperature dependence. Addition of metallic sodium increased P_D in liquids.     

Radical-olefin addition reactions in condensed phase

A study has been made of the rate constant for the reaction The states of the product have quasilevels E_n — i_n, which, depending on the heat of reaction, may be in resonance with the state of the reactants after surmounting the activation barrier. Because of this, there is no monotonic variation of the propagation rate constant, even as a function of the heat of reaction; the behavior of the rate constant has a resonance character. The results obtained in this investigation are in good agreement with experimental data.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 1, pp. 25–32, January–February, 1990.     

Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: a model for enzymatic catalysis

A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.     

Intermolecular force constants of hcn in the condensed phase

A simple theory of linear lattice is applied to the hydrogen bonded linear chain system of HCN to calculate the intermolecular force constants at different temperatures in the condensed phase. The strong CN bond is assumed to remain unperturbed in the hydrogen bond formation. The sharp change in intermolecular force constant while passing from the crystalline to the liquid phase is interpreted as a characteristic of this phase transition (fusion).     

Comparison between the Landau-Teller and flux-flux methods for computing vibrational energy relaxation rate constants in the condensed phase

The calculation of vibrational energy relaxation (VER) rate constants in the condensed phase is usually based on the Landau-Teller formula, which puts them in terms of the Fourier transform, at the vibrational frequency, of the autocorrelation function of the force exerted on the relaxing mode by the bath modes. An alternative expression for the VER rate constant puts it in terms of the autocorrelation function of the vibrational energy flux. In this paper, we compare the predictions obtained via those two methods in the case of iodine in liquid xenon. We find that the computational cost underlying both methods is comparable and that they predict similar VER rates. However, while the calculation of the VER rate via the Landau-Teller formula is somewhat more direct, the predictions obtained via the flux-flux formula are in somewhat better agreement with the VER rates obtained from nonequilibrium molecular dynamics simulations.     

相转移催化反应中界面性能的研究

过去在研究相转移催化反应机理时仅考虑在相转移催化剂作用下反应物、中间体(离子)、产物在两相间的转移,并导致两相间反应进行。我们以研究结果证明水相的表面能和两相的界面能与相转移催化反应的结果有密切关系。     

Triplet-triplet optical energy transfer from benzophenone to naphthalene in the vapor phase

In principle the optical energy absorbed by a complex molecule raises that molecule to one of its excited states, and afterwards this excitation energy decays through the different relaxation channels. Initially, electronically excited benzophenone emits photons in the phosphorescence band of benzophenone and these emitted photons, as a stream of particles, are absorbed by the acceptor molecule naphthalene, then excited naphthalene phosphoresces. In this investigation, sensitized phosphorescence decay times in different conditions were measured for benzophenone-naphthalene system in the vapor phase. The ultraviolet-visible spectra of the system in the vapor phase at room temperature conditions were broad and structureless.     

Femtosecond intermolecular electron transfer in condensed systems

We have investigated the ultrafast intermolecular electron transfer (ET) from an electron-donating solvent (aniline (AN) or N, N-dimethylaniline (DMA)) to an excited dye molecule (oxazines (Nile blue and oxazine 1) or coumarins). A non-exponential time dependence was observed in AN and can be explained by solvent reorientation and nuclear motion of the reactants. However, in DMA, a single exponential process was observed for Nile blue (160 fs) and oxazine 1 (280 fs), which can be explained by assuming that the rate of ET is limited mainly by ultrafast nuclear motion. A clear substituent effect on intermolecular ET was observed for the 7-aminocoumarins. When the alkyl chain on the 7-amino group is extended and a hexagonal ring with the benzene moiety is formed, the rate of ET is reduced by three orders of magnitude. This effect can be explained by a change in the free energy difference of the reaction and by the vibrational motion of the amino group.     

Nonperturbative quantum simulation of time-resolved nonlinear spectra: Methodology and application to electron transfer reactions in the condensed phase

A quantum dynamical method is presented to accurately simulate time-resolved nonlinear spectra for complex molecular systems. The method combines the nonpertubative approach to describe nonlinear optical signals with the multilayer multiconfiguration time-dependent Hartree theory to calculate the laser-induced polarization for the overall field–matter system. A specific nonlinear optical signal is obtained by Fourier decomposition of the overall polarization. The performance of the method is demonstrated by applications to photoinduced ultrafast electron transfer reactions in mixed-valence compounds and at dye–semiconductor interfaces.