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Recent progress in transient infrared spectroscopy has made it possible to monitor the transient flow of vibrational energy along a peptide helix [V. Botan et al., Proc. Natl. Acad. Sci. U.S.A. 104, 12749 (2007)]. To provide a theoretical description of these experiments, extensive nonequilibrium molecular dynamics simulations of the photoinduced energy transport in a photoswitchable Aib peptide are performed. By calculating the response of the molecule caused by its excitation via optical and infrared pulses as well as temperature jump and stationary heating, it is shown that these methods are equivalent in that they provide approximately the same molecular energy transfer times. The resulting thermal diffusivity of 10 Å2 ps-1 qualitatively agrees with the results of previous normal mode calculations for proteins and with experimental bulk values (e.g., 14 Å2 ps-1 for water). To compare to experiment, a new way of approximating the measured signals is suggested which leads to an improved agreement with the experimental results and explains previous discrepancies. To elucidate the mechanism of energy transfer, modifications to the molecular dynamics force field are introduced, which reveal that the energy transfer occurs mainly through the peptide backbone and depends surprisingly little on the force field parametrization. Employing a harmonic model, quantum-mechanical effects are estimated to moderately (about a factor of 2) speed up the energy transport along the peptide. [ABSTRACT FROM AUTHOR]

A systematic molecular dynamics (MD) simulation study of the photoinduced heat transfer from the model peptide N-methylacetamide (NMA) to various solvents is presented, which considers four types of solvent (water, dimethyl sulfoxide, chloroform, and carbon tetrachloride), and in total 24 different force field models for these solvents. To initiate nonstationary energy flow, an initial temperature jump of NMA is assumed and nonequilibrium MD simulations are performed. As expected from simple theoretical models of heat transfer, the cooling process is proportional to the heat capacity CV and—to some extent—to the viscosity η of the solvent. The complex interplay of Coulomb and Lennard-Jones interactions is studied by scaling these interaction energies. The study reveals that realistic changes (<=10%) of the Lennard-Jones and Coulomb parameters do not change the cooling time considerably. Including polarizibility, on the other hand, appears to enhance the energy dissipation. Moreover, the solvent’s internal degrees of freedom may significantly participate in the heat transfer. This is less so for water, which possesses only three high-frequency vibrational modes, but certainly so for the larger solvent molecules dimethyl sulfoxide and chloroform, which possess several low-frequency vibrational modes. For water, the simulated cooling rate is in excellent agreement with experiment, while only qualitative agreement (up to a factor of 2) is found for the other considered solvents. The importance of the force field model and quantum-mechanical effects to correctly describe the cooling process is discussed in some detail. [ABSTRACT FROM AUTHOR]

A systematic computational approach to describe the conformational dynamics of biomolecules in reduced dimensionality is presented. The method is based on (i) the decomposition of a high-dimensional molecular dynamics trajectory into a few “system” and (many) “bath” degrees of freedom and (ii) a Langevin simulation of the resulting model. Employing principal component analysis, the dimension of the system is chosen such that it contains all slow large-amplitude motions of the molecule, while the bath coordinates only account for its high-frequency fluctuations. It is shown that a sufficiently large dimension of the model is essential to ensure a clear time scale separation of system and bath variables, which warrants the validity of the memory-free Langevin equation. Applying methods from nonlinear time series analysis, a practical Langevin algorithm is presented which performs a local estimation of the multidimensional Langevin vector fields describing deterministic drift and stochastic driving. Adopting a 800 ns molecular dynamics simulation of the folding of heptaalanine in explicit water, it is shown that a five-dimensional Langevin model correctly reproduces the structure and conformational dynamics of the system. The virtues and limits of the approach are discussed in some detail. [ABSTRACT FROM AUTHOR]

A systematic approach to construct a low-dimensional free energy landscape from a classical molecular dynamics (MD) simulation is presented. The approach is based on the recently proposed dihedral angle principal component analysis (dPCA), which avoids artifacts due to the mixing of internal and overall motions in Cartesian coordinates and circumvents problems associated with the circularity of angular variables. Requiring that the energy landscape reproduces the correct number, energy, and location of the system’s metastable states and barriers, the dimensionality of the free energy landscape (i.e., the number of essential components) is obtained. This dimensionality can be determined from the distribution and autocorrelation of the principal components. By performing an 800 ns MD simulation of the folding of hepta-alanine in explicit water and using geometric and kinetic clustering techniques, it is shown that a five-dimensional dPCA energy landscape is a suitable and accurate representation of the full-dimensional landscape. In the second step, the dPCA energy landscape can be employed (e.g., in a Langevin simulation) to facilitate a detailed investigation of biomolecular dynamics in low dimensions. Finally, several ways to visualize the multidimensional energy landscape are discussed. [ABSTRACT FROM AUTHOR]

We show how to apply a general theoretical approach to nonequilibrium statistical mechanics, called Maximum Caliber, originally suggested by E. T. Jaynes [Annu. Rev. Phys. Chem. 31, 579 (1980)], to a problem of two-state dynamics. Maximum Caliber is a variational principle for dynamics in the same spirit that Maximum Entropy is a variational principle for equilibrium statistical mechanics. The central idea is to compute a dynamical partition function, a sum of weights over all microscopic paths, rather than over microstates. We illustrate the method on the simple problem of two-state dynamics, A↔B, first for a single particle, then for M particles. Maximum Caliber gives a unified framework for deriving all the relevant dynamical properties, including the microtrajectories and all the moments of the time-dependent probability density. While it can readily be used to derive the traditional master equation and the Langevin results, it goes beyond them in also giving trajectory information. For example, we derive the Langevin noise distribution rather than assuming it. As a general approach to solving nonequilibrium statistical mechanics dynamical problems, Maximum Caliber has some advantages: (1) It is partition-function-based, so we can draw insights from similarities to equilibrium statistical mechanics. (2) It is trajectory-based, so it gives more dynamical information than population-based approaches like master equations; this is particularly important for few-particle and single-molecule systems. (3) It gives an unambiguous way to relate flows to forces, which has traditionally posed challenges. (4) Like Maximum Entropy, it may be useful for data analysis, specifically for time-dependent phenomena. [ABSTRACT FROM AUTHOR]

It has recently been suggested by Mu et al. [Proteins 58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and interpretation of the free energy landscape of a biomolecule undergoing large structural rearrangements. To account for the circular statistics of angular variables, a transformation from the space of dihedral angles {φn} to the metric coordinate space {xn=cos φn,yn=sin φn} was employed. To study the validity and the applicability of the approach, in this work the theoretical foundations underlying the dihedral angle principal component analysis (dPCA) are discussed. It is shown that the dPCA amounts to a one-to-one representation of the original angle distribution and that its principal components can readily be characterized by the corresponding conformational changes of the peptide. Furthermore, a complex version of the dPCA is introduced, in which N angular variables naturally lead to N eigenvalues and eigenvectors. Applying the methodology to the construction of the free energy landscape of decaalanine from a 300 ns molecular dynamics simulation, a critical comparison of the various methods is given. [ABSTRACT FROM AUTHOR]

A quantum-classical description of the amide I vibrational spectrum of trialanine cation in D2O is given that combines (i) a classical molecular dynamics simulation of the conformational distribution of the system, (ii) comprehensive density functional theory calculations of the conformation-dependent and solvent-induced frequency fluctuations, and (iii) a semiclassical description of the vibrational line shapes which includes nonadiabatic transitions between vibrational eigenstates. Various assumptions that are usually employed in the calculation of condensed-phase vibrational spectra are tested, including the adiabatic, the Franck-Condon, and the second-order cumulant approximations, respectively. All three parts of the theoretical formulation are shown to have a significant impact on the simulated spectrum, suggesting that the interpretation of peptide amide I spectra may require substantial theoretical support. [ABSTRACT FROM AUTHOR]

A method is presented to improve the speed of convergence of Wang-Landau simulations as used to calculate the density of states of continuous systems. The density of states is first crudely estimated with calculations employing a smoothed potential-energy surface. This estimate is then used as a seed for subsequent Wang-Landau simulations using the original potential. The performance of the method is demonstrated by employing several simple models, including an analytically solvable harmonic system as well as a Gō model of a protein. For all systems considered, the seeded simulations were found to converge significantly faster and with higher accuracy than the standard Wang-Landau simulations. [ABSTRACT FROM AUTHOR]

A theoretical description of transient vibrational spectra following the impulsive optical excitation of a molecular system is presented. The approach combines the nonsecular evaluation of the Redfield equations to describe the dissipative dynamics of the system with an efficient implementation of the doorway-window formalism to calculate optical pump/infrared probe (vis/IR) spectra. Both parts of the calculation scale with N2, thus facilitating the treatment of systems with a dimension up to 104. The formulation is applied to a simple model of photoinduced electron transfer, which takes into account two coupled electronic states and a single anharmonic vibrational mode. Despite its simplicity, the model is found to exhibit quite complex electronic and vibrational relaxation dynamics, which in turn give rise to rather complex time- and frequency-resolved vis/IR spectra. Interestingly, the calculated IR spectra of the electron-transfer system predict the appearance of novel vibronically induced sidebands, which may even dominate the spectrum at early times. [ABSTRACT FROM AUTHOR]

Various aspects of the ab initio-based parametrization of an exciton model of amide I vibrations in peptides are discussed. Adopting “glycine dipeptide” (Ac-Gly-NHCH3) as a simple building-block model that describes the vibrational interaction between two peptide units, we perform comprehensive quantum-chemical calculations to investigate the effect and importance of the level of theory, the choice of local coordinates, and the localization method. A solvent continuum model description turns out important to obtain planar CONH peptide units when a full geometry optimization (which is necessary to obtain the correct frequencies) is performed. To study the conformational dependence of the amide I vibrations, we calculate ([lowercase_phi_synonym],ψ) maps of the local-mode frequencies and couplings. Performing conformational averages of the ([lowercase_phi_synonym],ψ) maps with respect to the most important peptide conformational states in solution (α, β, PII, and C5), we discuss the relation between these measurable quantities and the corresponding conformation of the peptide. Finally, the transferability of these maps to dipeptides with hydrophilic and hydrophobic side chains as well as to tripeptides with charged end groups is investigated. [ABSTRACT FROM AUTHOR]

A nonequilibrium description of the vibrational-energy relaxation of solvated flexible molecules such as small peptides in aqueous solution is outlined. Having in mind to employ standard biomolecular molecular-dynamics program packages, several methodological developments are introduced. To calculate the vibrational normal-mode energies for a system undergoing large-amplitude motion, an instantaneous normal-mode analysis is employed. To mimic the laser excitation of a given vibrational mode in its excited states, a computational scheme is proposed which allows us to calculate the nonequilibrium phase-space initial conditions for the solute and the solvent atoms. It is demonstrated that the vibrational relaxation dynamics sensitively depends on the accurate representation of the initially excited normal mode. In particular, effects of the quantum-mechanical zero-point energy contained by the initial state are investigated, thus elucidating the importance of quantum fluctuations. To study the validity and the performance of the method, the laser-induced amide I ν=1→0 energy relaxation of N-methylacetamid in D[sub 2]O is considered. The vibrational energy relaxation rate obtained from the nonequilibrium simulations is in qualitative agreement with experiment, whereas a Landau–Teller-type calculation underestimates the rate considerably. The virtues and problems of the nonequilibrium description are discussed in some detail. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The capability of quasiclassical and semiclassical methods to describe quantum dynamics in a periodic potential is investigated. Due to the periodicity of the potential, such systems may exhibit prominent quantum interference effects and, therefore, provide a particular challenge to methods based on classical approximations. Adopting a simple model for an isomerization reaction, we study the dynamics for different initial preparations as well as different dynamical observables. The quasiclassical calculations are based on the classical Wigner method and the semiclassical approach utilizes the Herman–Kluk (coherent state) initial-value representation, generalized to properly take into account the boundary conditions of the wave functions in a periodic potential. The results of the study show that the quasiclassical method can only describe the quantum dynamics in situations where the system is confined to the potential well and for highly averaged observables but fails otherwise. The semiclassical method, on the other hand, provides an excellent description of the quantum dynamics as long as the initial state is energetically separated from the torsional barrier. The reasons why the quasiclassical and semiclassical methods perform well in some situations but fail for others are discussed in some detail. Furthermore, the relation between the performance of the quasiclassical and semiclassical methods and the eigenvalue structure of the participating eigenstates is analyzed. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Adopting a multidimensional model of nonadiabatic cis–trans photoisomerization, quantum-mechanical and classical simulations of the ultrafast wave-packet dynamics associated with this photoreaction are presented. The quantum calculations demonstrate that nonadiabatic photoisomerization typically leads to a largely delocalized and diffuse wave function, which hampers an intuitive understanding of the dynamics in terms of specific nuclear motion. To facilitate a classical description, a recently proposed theoretical formulation is employed that affords an exact mapping of discrete electronic states onto continuous degrees of freedom and therefore provides a well-defined classical limit of a nonadiabatically coupled system. It is shown that a simple quasiclassical implementation of the mapping formulation is able to reproduce at least qualitatively the complex quantum dynamics of the system. In addition, the classical description allows us to characterize the nonadiabatic photoisomerization dynamics in terms of a few “quasiperiodic orbits.” These orbits are close to a true unstable periodic orbit but are exactly periodic only with respect to the slow reaction coordinate of the system. Various types of quasiperiodic orbits of nonadiabatic photoisomerization are identified and analyzed. It is shown that the diffuse appearance of the quantum-mechanical wave function can be directly connected to irregular classical orbits propagating on vibronically coupled potential-energy surfaces. The chaotic behavior of the system is mainly caused by the relatively high energy corresponding to photoexcitation, the large anharmonicity of the isomerization potentials, and the reflection of the trajectory at surface crossings. The results demonstrate that quasiperiodic orbits represent a concept well suited to analyze the quantum dynamics of complex systems in terms of classical trajectories without the cumbersome search for periodic orbits. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Nonlinear time-resolved vibrational spectroscopy is used to compare spectral broadening of the amide I band of the small peptide trialanine with that of N-methylacetamide, a commonly used model system for the peptide bond. In contrast to N-methylacetamide, the amide I band of trialanine is significantly inhomogeneously broadened. Employing classical molecular-dynamics simulations combined with density-functional-theory calculations, the origin of the spectral inhomogeneity is investigated. While both systems exhibit similar hydrogen-bonding dynamics, it is found that the conformational dynamics of trialanine causes a significant additional spectral broadening. In particular, transitions between the poly(Gly)II and the α[SUBR] conformations are identified as the main source of the additional spectral inhomogeneity of trialanine. The experimental and computational results suggest that trialanine adopts essentially two conformations: poly(Gly)II (80%) and α[SUBR] (20%). The potential of the joint experimental and computational approach to explore conformational dynamics of peptides is discussed. [ABSTRACT FROM AUTHOR]

A quantum-mechanical model description of a molecular photoswitch is developed. It takes into account (i) the electronic curve crossing arising from the cis-trans twisting of a double bond, resulting in an ultrafast internal-conversion process of the system and (ii) the coupling of the initially excited chromophore (the "system") to the remaining degrees of freedom (the "bath"), affecting a vibrational cooling of the hot photoproducts. The latter mechanism is responsible for the localization of the molecule in the cis and trans configuration, respectively, thus determining the quantum yield of the photoreaction. Following a discussion of the validity and the numerical implementation of the Redfield formulation employed, detailed numerical studies of the time-dependent dissipative photoisomerization dynamics are presented. While the short-time dynamics (... 1 ps) is dominated by the coherent wave-packet motion of the system, the time evolution at larger times mainly reflects the interaction between system and bath. The quantum yield of the cis-trans forward reaction (Y[sub c→t) and the trans-cis backward reaction (Y[sub t→c]) is shown to depend on the energy storage of the photoreaction and, in particular, on the form of the system-bath coupling. On the other hand, it is found that Y[sub t→c] = 1 - Y[sub c→t], that is the population probabilities of the cis and trans configuration at long times do not depend on the initial preparation of the system. [ABSTRACT FROM AUTHOR]

Based on a recently introduced mapping formulation [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], a classical phase-space description of vibronically coupled molecular systems is developed. In this formulation the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states is bypassed by transforming the discrete quantum variables to continuous variables. Here the mapping formalism is applied to a spin-boson-type system with a single vibrational mode, e.g., representing the situation of a photo-induced electron transfer promoted by a high-frequency vibrational mode. Studying various Poincare´ surfaces-of-section, a detailed phase-space analysis of the mapped two-state problem is given, showing that the model exhibits mixed classical dynamics. Furthermore, a number of periodic orbits (PO’s) of the nonadiabatic system are identified. In direct extension of the usual picture of trajectories propagating on a single Born-Oppenheimer surface, these vibronic PO’s describe nuclear motion on several coupled potential-energy surfaces. A quasiclassical approximation is derived that expresses time-dependent quantities of a vibronically coupled system in terms of the PO’s of the system. As an example, it is demonstrated that vibronic PO’s may be used to calculate the time-dependent population probability of the initially excited electronic state. For the system under consideration, already two PO’s are sufficient to qualitatively describe the short-time evolution of the nonadiabatic process. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The time-resolved femtosecond spectroscopy in conjunction with nonequilibrium molecular dynamics (MD) simulations was used to study the energy transport in a short helical peptide in chloroform solution. A simple harmonic model of heat transport adopted on the bases of results showed that the heat diffusivity decreased significantly at temperatures initially reached by high-energy excitation.

The [phis], [psi] backbone angle distribution of small homopolymeric model peptides are examined by a joint molecular dynamics (MD) simulation and heteronuclear NMR study. It is found that the alanine peptides [Ala.sub.n] exhibit the same conformational distribution.

The calculation of transient absorption spectra of cis-trans photoreactive system in the condensed phase is described theoretically. The formulation consists of a multidimensional model of nonadiabatic photoisomerization, a Redfield treatment of the environment within the secular approximation, and a doorway-window formulation to calculate transient pump-probe spectra.

A method for site-directed spin labeling of oligonucleotides with TPA and a precise 4-pulse electron double resonance (PELDOR) based nanometer distance ruler, in the range from 19 to 53 A for folded DNA/RNA in aqueous buffer solution, is presented.

Analyzes the flow of zero-point energy and exploration of phase space in classical simulations of quantum relaxation dynamics. Modeling of relaxation in classical and quantum mechanics; Classical description of nondiabatic quantum dynamics; Relaxation of strongly coupled few-mode systems.

Analyzes necessary conditions under which a classical description will give the correct quantum relaxation behavior. Expression of mean values of observables in terms of spectral density and state-specific level densities; Flow of zero-point energy in classical mechanics.

A classical-path approach to the description of photoinduced isomerization dynamics as well as the interrelated electronic and vibrational relaxation processes is outlined. Adopting a three-mode model of photoisomerization that has been recently proposed by Seidner and Domcke (Chem. Phys. 186, 27 (1994)), we perform detailed numerical studies and compare the results of the classical simulations to available exact quantum-mechanical results. It is shown that the classical model reproduces semiquantitatively time-dependent diabatic and adiabatic electronic population probabilities, state-specific torsional wave functions, and energy contents of vibrational degrees of freedom. Furthermore it is demonstrated that the classical approach is able to simulate at least qualitatively time- and frequency-resolved pump-probe spectra of these processes. In accordance with exact quantum calculations, the classical simulations reveal the decay of the stimulated emission of the reactants and the delayed onset of the absorption of the photoproducts. To demonstrate the capability of the classical approach, the three-mode model of Seidner et al. is augmented by a hundred weakly-coupled harmonic modes. This allows to roughly simulate the relaxation dynamics of a chromophore interacting with a solvent. The simulations reveal that the time evolution of the full system within the first few hundred femtoseconds is quite similar to the case of the bare three-mode model. For later times, however, the dynamics of the three-mode model becomes quasistationary, whereas the calculations for the full system reflect the redistribution of the excess energy of the reaction mode into the bath nuclear degrees of freedom. It is found that the quantum yield of the cis-trans photoreaction depends to a large extent on the specific chromophore-solvent coupling employed, as it governs directly the competition of the various relaxation pathways. Simulations of the corresponding time- and... [ABSTRACT FROM AUTHOR]

New experimental and theoretical data on the resonance Raman (RR) spectroscopy of the S1 and S2 states of pyrazine are presented. Based on recent ab initio CASSCF (complete- active-space-self-consistent-field) and MRCI (multireference configuration interaction) calculations of Woywod et al. [J. Chem. Phys. 100, 1400 (1994)], we construct a vibronic coupling model of the conically intersecting S1 and S2 states of pyrazine, which includes the seven most relevant vibrational degrees of freedom of the molecule. Employing a time-dependent approach that treats the intramolecular couplings in a nonperturbative manner, we calculate RR cross sections for this model, taking explicitly into account the nonseparability of all vibrational modes. The combination of high-level ab initio calculations and multimode propagation techniques makes it possible, for the first time, to make first-principles predictions of RR spectra for vibronically coupled electronic states of an aromatic molecule. The theoretical data are compared to experimental gas-phase RR spectra which have been obtained for five different excitation wavelengths. The comparison reveals that the ab initio predictions match the experimental results in almost every detail. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A general nonperturbative approach to calculate femtosecond pump-probe (PP) signals is proposed, which treats both the intramolecular couplings and the field-matter interaction (numerically) exactly. Experimentally as well as in a perturbative calculation it is straightforward to distinguish between different spectroscopic processes through the direction of the wave vector of the emitted radiation. A nonperturbative calculation, on the other hand, yields the overall polarization of the system, which is the sum of all these contributions. We present a general and practical method that allows to extract the individual spectroscopic signals, which are resolved in time, frequency, and direction of the emission, from the overall polarization. We briefly derive the basic expressions for the time- and frequency-resolved PP signals under consideration, and discuss in detail the simplifications that arise when the usual assumptions (i.e., weak laser fields, nonoverlapping pulses, slowly-varying envelope assumption and rotating-wave approximation) are invoked. The computational procedure is illustrated by nonperturbative calculations of the polarizations and PP signals for a one-dimensional shifted harmonic oscillator. To demonstrate the capability of the approach we have evaluated the polarization as well as PP signals for a three-dimensional model system with vibronically coupled potential-energy surfaces, which describes ultrafast nonadiabatic isomerization dynamics triggered by the twisting of a double bond. We consider various wavelengths and pulse durations of the laser fields and study integral and dispersed PP spectra as well as coherent photon-echo signals. It is shown that the time- and frequency-resolved PP signals reflect in real time the disappearance of the reactants and the delayed appearance of the products. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A semiclassical time-dependent self-consistent-field (TDSCF) formulation is developed for the description of internal conversion (IC) processes in polyatomic molecules. The total density operator is approximated by a semiclassical ansatz, which couples the electronic degrees of freedom to the nuclear degrees of freedom in a self-consistent manner, whereby the vibrational density operator is described in terms of Gaussian wave packets. The resulting TDSCF formulation represents a generalization of familiar classical-path theories, and is particularly useful to make contact to quantum-mechanical formulations. To avoid problems associated with spurious phase factors, we assume rapid randomization of the nuclear phases and a single vibrational density operator for all electronic states. Classically, the latter approximation corresponds to a single trajectory propagating along a ‘‘mean path’’ instead of several state-specific trajectories, which may become a critical assumption for the description of IC processes. The validity and the limitations of the mean-path approximation are discussed in detail, including both theoretical as well as numerical studies. It is shown that for constant diabatic coupling elements Vkk′ the mean-path approximation should be appropriate in many cases, whereas in the case of coordinate-dependent coupling Vkk′(x) the approximation is found to lead to an underestimation of the overall relaxation rate.As a remedy for this inadequacy of the mean-path approximation, we employ dynamical corrections to the off-diagonal elements of the electronic density operator, as has been suggested by Meyer and Miller [J. Chem. Phys. 70, 3214 (1979)]. We present detailed numerical studies, adopting (i) a two-state three-mode model of the S1-S2 conical intersection in pyrazine, and (ii) a three-state five-mode and a five-state sixteen-mode model of the C→B→X IC process in the benzene cation. The... [ABSTRACT FROM AUTHOR]

A semiclassical time-dependent self-consistent-field approach for the description of dissipative quantum phenomena is proposed. The total density operator is approximated by a semiclassical ansatz, which couples the system degrees of freedom to the bath degrees of freedom in a self-consistent manner, and is thus in the spirit of a classical-path description. The capability of the approach is demonstrated by comparing semiclassical calculations for a spin–boson model with an Ohmic bath to exact path-integral calculations. It is shown that the semiclassical model nicely reproduces the complex dissipative behavior of the spin–boson model for a large range of model parameters. The validity and accuracy of the semiclassical approach is discussed in some detail. It is shown that the method is essentially based on the assumption of complete randomization of nuclear phases. In particular, the assumption of phase randomization allows one to perform the trace over the bath variables through quasiclassical sampling of the nuclear initial conditions without invoking any further approximation. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

It is demonstrated that photoinduced large amplitude (LA) dynamics on a picosecond time scale may result in electronic pure dephasing on a time scale of a few tens of femtoseconds. It is shown that LA photodynamics affects continuous-wave (cw) spectra (e.g., absorption and resonance-Raman) and transient spectra (e.g., photon-echo and pump–probe) in a rather different way. Calculations are presented for a two-dimensional model problem, consisting of a fast vibrational mode and a slow LA mode, which is considered as a simple model for isomerization. The spectroscopic signals for this model are compared to the results for a complementary model, where the fast vibrational mode interacts with a bath (e.g., the environment). It is shown that standard cw techniques such as absorption and resonance-Raman spectroscopy fail to clearly distinguish the two (physically rather different) model problems, as the ultrafast optical dephasing results in strong line broadening of these spectra. Time-resolved pump–probe spectroscopy, on the other hand, is not limited by electronic pure dephasing and thus allows for a clear discrimination of the two photophysical processes. Simulations of photon-echo experiments furthermore elucidate that slow intramolecular LA motion results in inhomogeneous broadening of optical spectra. Finally a novel time-resolved technique is proposed that is capable to reveal ‘‘sub-linewidth’’ information on electronic transitions which are strongly broadened by homogeneous and inhomogeneous pure dephasing processes. [ABSTRACT FROM AUTHOR]

A general classical formulation of the spectroscopy of nonadiabatically coupled electronic states is developed within the theoretical framework of the classical electron analog model due to Meyer and Miller. Adopting the Heisenberg representation for the calculation of the electric polarization, several approaches are presented to establish a quantum-classical correspondence. It is shown that a consistent classical formulation is obtained by replacing the quantum-mechanical commutators, which appear in quantum-mechanical perturbation theory, by the corresponding classical Poisson brackets which come from classical perturbation theory. The more usual practice of replacing the Heisenberg dipole operators directly by the corresponding classical dipole functions is shown to be an approximation to classical perturbation theory. For a coupled electronic three-state system explicit expressions are derived for the nonlinear polarization. Furthermore the practical application to femtosecond pump-probe spectroscopy is discussed in some detail. [ABSTRACT FROM AUTHOR]

Presents a mixed quantum-classical formulation of nonadiabatic molecular processes. Introduction of mapping approach to interpret the intricate concept of vibrational motion; Description of electronic and nuclear degrees of freedom results in the mapping formalism; Virtues and limitations of various mixed quantum-classical descriptions.

Outlines a mixed quantum-classical description of nonadiabatic photoreactions such as internal conversion and electron transfer. Validity and limitations of Tully's surface-hopping model for photoinduced relaxation processes; Characteristic features of a mixed quantum-classical descriptions of photoinduced bound-state dynamics.

The classical periodic orbits of an electron-transfer system are studied. Femtosecond time-resolved experiments on chemical and biophysical electron-transfer systems are conducted for this purpose and it is demonstrated that transient oscillations observed in electron-transfer femtosecond experiments may be explained in terms of a few classical trajectories.

The conformational structure and dynamics of trialanine in water are studied with the help of a molecular dynamics (MD) study. The MD study reveals that the conformational structures and dynamics show good overall agreement with experimental data.

While the theory of protein folding is well developed, including concepts such as rugged energy landscape, folding funnel, etc., the same degree of understanding has not been reached for the description of the dynamics of allosteric transitions in proteins. This is not only due to the small size of the structural change upon ligand binding to an allosteric site, but also due to challenges in designing experiments that directly observe such an allosteric transition. On the basis of recent pump-probe-type experiments (Buchli et al. 2013 Proc. Natl Acad. Sci. USA 110, 11 725-11 730. (doi:10.1073/ pnas.1306323110)) and non-equilibrium molecular dynamics simulations (Buchenberg et al. 2017 Proc. Natl Acad. Sci. USA 114, E6804-E6811. (doi:10.1073/pnas.1707694114)) studying an photoswitchable PDZ2 domain as model for an allosteric transition, we outline in this perspective how such a description of allosteric communication might look. That is, calculating the dynamical content of both experiment and simulation (which agree remarkably well with each other),we find that allosteric communication shares some properties with downhill folding, except that it is an 'order-order' transition. Discussing themultiscale and hierarchical features of the dynamics, the validity of linear response theory as well as the meaning of 'allosteric pathways', we conclude that non-equilibrium experiments and simulations are a promising way to study dynamical aspects of allostery. [ABSTRACT FROM AUTHOR]

A novel mixed quantum–classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees of freedom with Langevin dynamics for the classical degrees of freedom, namely, low-frequency vibrational modes within the molecule. The approach extends previous mixed quantum–classical methods based on Langevin equations to models containing strong electron–electron or quantum electronic–vibrational interactions, while maintaining a nonperturbative and non-Markovian treatment of the molecule–metal coupling. To demonstrate the approach, nonequilibrium transport observables are calculated for a molecular nanojunction containing strong interactions. [ABSTRACT FROM AUTHOR]