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While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the inter-relation of two stochastic variables X and Y, it fails for multidimensional variables, such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information I(X, Y) does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound (I ∈ [0, ∞)), i.e., it is not clear if say, I = 0.4 corresponds to a low or a high correlation. Moreover, the mutual information (MI) involves the estimation of high-dimensional probability densities (e.g., six-dimensional for Cartesian coordinates), which requires a k nearest-neighbor algorithm, such as the estimator by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. As existing methods to normalize the MI cannot be used in connection with this estimator, a new approach is presented, which uses an entropy estimation method that is invariant under variable transformations. The algorithm is numerically efficient and does not require more effort than the calculation of the (un-normalized) MI. After validating the method by applying it to various toy models, the normalized MI between the Cα-coordinates of T4 lysozyme is considered and compared to a correlation analysis of inter-residue contacts. [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]

The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. D. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale invariance of the system, which is associated with discrete and equidistant timescales on a logarithmic scale. Examples include such diverse fields as financial crashes, random diffusion, and quantum topological materials. Recent time-resolved experiments and molecular dynamics simulations suggest that discrete scale invariance may also apply to hierarchical dynamics in proteins, where several fast local conformational changes are a prerequisite for a slow global transition to occur. Employing entropy-based timescale analysis and Markov state modeling to a simple one-dimensional hierarchical model and biomolecular simulation data, it is found that hierarchical systems quite generally give rise to logarithmically spaced discrete timescales. By introducing a one-dimensional reaction coordinate that collectively accounts for the hierarchically coupled degrees of freedom, the free energy landscape exhibits a characteristic staircase shape with two metastable end states, which causes the log-periodic time evolution of the system. The period of the log-oscillations reflects the effective roughness of the energy landscape and can, in simple cases, be interpreted in terms of the barriers of the staircase landscape. [ABSTRACT FROM AUTHOR]

Markov processes provide a popular approach to construct low-dimensional dynamical models of a complex biomolecular system. By partitioning the conformational space into metastable states, protein dynamics can be approximated in terms of memory-less jumps between these states, resulting in a Markov state model (MSM). Alternatively, suitable low-dimensional collective variables may be identified to construct a data-driven Langevin equation (dLE). In both cases, the underlying Markovian approximation requires a propagation time step (or lag time) δt that is longer than the memory time τM of the system. On the other hand, δt needs to be chosen short enough to resolve the system timescale τS of interest. If these conditions are in conflict (i.e., τM > τS), one may opt for a short time step δt = τS and try to account for the residual non-Markovianity of the data by optimizing the transition matrix or the Langevin fields such that the resulting model best reproduces the observables of interest. In this work, rescaling the friction tensor of the dLE based on short-time information in order to obtain the correct long-time behavior of the system is suggested. Adopting various model problems of increasing complexity, including a double-well system, the dissociation of solvated sodium chloride, and the functional dynamics of T4 lysozyme, the virtues and shortcomings of the rescaled dLE are discussed and compared to the corresponding MSMs. [ABSTRACT FROM AUTHOR]

Recent time-resolved experiments and accompanying molecular dynamics simulations allow us to monitor the flow of vibrational energy in biomolecules. As a simple means to describe these experimental and simulated data, Buchenberg et al. [J. Phys. Chem. Lett. 7, 25 (2016)] suggested a master equation model that accounts for the energy transport from an initially excited residue to some target residue. The transfer rates of the model were obtained from two scaling rules, which account for the energy transport through the backbone and via tertiary contacts, respectively, and were parameterized using simulation data of a small α-helical protein at low temperatures. To extend the applicability of the model to general proteins at room temperature, here a new parameterization is presented, which is based on extensive nonequilibrium molecular dynamics simulations of a number of model systems. With typical transfer times of 0.5–1 ps between adjacent residues, backbone transport represents the fastest channel of energy flow. It is well described by a diffusive-type scaling rule, which requires only an overall backbone diffusion coefficient and interatom distances as input. Contact transport, e.g., via hydrogen bonds, is considerably slower (6–30 ps) at room temperature. A new scaling rule depending on the inverse square contact distance is suggested, which is shown to successfully describe the energy transport in the allosteric protein PDZ3. Since both scaling rules require only the structure of the considered system, the model provides a simple and general means to predict energy transport in proteins. To identify the pathways of energy transport, Monte Carlo Markov chain simulations are performed, which highlight the competition between backbone and contact transport channels. [ABSTRACT FROM AUTHOR]

Principal component analysis (PCA) represents a standard approach to identify collective variables {xi} = x, which can be used to construct the free energy landscape ΔG(x) of a molecular system. While PCA is routinely applied to equilibrium molecular dynamics (MD) simulations, it is less obvious as to how to extend the approach to nonequilibrium simulation techniques. This includes, e.g., the definition of the statistical averages employed in PCA as well as the relation between the equilibrium free energy landscape ΔG(x) and the energy landscapes Δ G (x) obtained from nonequilibrium MD. As an example for a nonequilibrium method, "targeted MD" is considered which employs a moving distance constraint to enforce rare transitions along some biasing coordinate s. The introduced bias can be described by a weighting function P(s), which provides a direct relation between equilibrium and nonequilibrium data, and thus establishes a well-defined way to perform PCA on nonequilibrium data. While the resulting distribution P (x) and energy Δ G ∝ ln P will not reflect the equilibrium state of the system, the nonequilibrium energy landscape Δ G (x) may directly reveal the molecular reaction mechanism. Applied to targeted MD simulations of the unfolding of decaalanine, for example, a PCA performed on backbone dihedral angles is shown to discriminate several unfolding pathways. Although the formulation is in principle exact, its practical use depends critically on the choice of the biasing coordinate s, which should account for a naturally occurring motion between two well-defined end-states of the system. [ABSTRACT FROM AUTHOR]

The accurate definition of suitable metastable conformational states is fundamental for the construction of a Markov state model describing biomolecular dynamics. Following the dimensionality reduction in a molecular dynamics trajectory, these microstates can be generated by a recently proposed density-based geometrical clustering algorithm [F. Sittel and G. Stock, J. Chem. Theory Comput. 12, 2426 (2016)], which by design cuts the resulting clusters at the energy barriers and allows for a data-based identification of all parameters. Nevertheless, projection artifacts due to the inevitable restriction to a low-dimensional space combined with insufficient sampling often leads to a misclassification of sampled points in the transition regions. This typically causes intrastate fluctuations to be mistaken as interstate transitions, which leads to artificially short life times of the metastable states. As a simple but effective remedy, dynamical coring requires that the trajectory spends a minimum time in the new state for the transition to be counted. Adopting molecular dynamics simulations of two well-established biomolecular systems (alanine dipeptide and villin headpiece), dynamical coring is shown to considerably improve the Markovianity of the resulting metastable states, which is demonstrated by Chapman-Kolmogorov tests and increased implied time scales of the Markov model. Providing high structural and temporal resolution, the combination of density-based clustering and dynamical coring is particularly suited to describe the complex structural dynamics of unfolded biomolecules. [ABSTRACT FROM AUTHOR]

The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {xi} = x that in some sense describe the essential dynamics of the system. Considering the distribution P(x) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P(x), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG(x) = −kBT ln P(x), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms. [ABSTRACT FROM AUTHOR]

Adimensionality reduction method for high-dimensional circular data is developed, which is based on a principal component analysis (PCA) of data points on a torus. Adopting a geometrical view of PCA, various distance measures on a torus are introduced and the associated problem of projecting data onto the principal subspaces is discussed. The main idea is that the (periodicity-induced) projection error can be minimized by transforming the data such that the maximal gap of the sampling is shifted to the periodic boundary. In a second step, the covariance matrix and its eigendecomposition can be computed in a standard manner. Adopting molecular dynamics simulations of two well-established biomolecular systems (Aib9 and villin headpiece), the potential of the method to analyze the dynamics of backbone dihedral angles is demonstrated. The new approach allows for a robust and well-defined construction of metastable states and provides low-dimensional reaction coordinates that accurately describe the free energy landscape. Moreover, it offers a direct interpretation of covariances and principal components in terms of the angular variables. Apart from its application to PCA, the method of maximal gap shifting is general and can be applied to any other dimensionality reduction method for circular data. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations of biomolecular processes are often discussed in terms of diffusive motion on a low-dimensional free energy landscape F(x). To provide a theoretical basis for this interpretation, one may invoke the system-bath ansatz á la Zwanzig. That is, by assuming a time scale separation between the slow motion along the system coordinate x and the fast fluctuations of the bath, a memory-free Langevin equation can be derived that describes the system's motion on the free energy landscape F(x), which is damped by a friction field and driven by a stochastic force that is related to the friction via the fluctuation-dissipation theorem. While the theoretical formulation of Zwanzig typically assumes a highly idealized form of the bath Hamiltonian and the system-bath coupling, one would like to extend the approach to realistic data-based biomolecular systems. Here a practical method is proposed to construct an analytically defined global model of structural dynamics. Given a molecular dynamics simulation and adequate collective coordinates, the approach employs an ?empirical valence bond?-type model which is suitable to represent multidimensional free energy landscapes as well as an approximate description of the friction field. Adopting alanine dipeptide and a three-dimensional model of heptaalanine as simple examples, the resulting Langevin model is shown to reproduce the results of the underlying all-atom simulations. Because the Langevin equation can also be shown to satisfy the underlying assumptions of the theory (such as a delta-correlated Gaussiandistributed noise), the global model provides a correct, albeit empirical, realization of Zwanzig's formulation. As an application, the model can be used to investigate the dependence of the system on parameter changes and to predict the effect of site-selective mutations on the dynamics. [ABSTRACT FROM AUTHOR]

To interpret molecular dynamics simulations of complex systems, systematic dimensionality reduction methods such as principal component analysis (PCA) represent a well-established and popular approach. Apart from Cartesian coordinates, internal coordinates, e.g., backbone dihedral angles or various kinds of distances, may be used as input data in a PCA. Adopting two well-known model problems, folding of villin headpiece and the functional dynamics of BPTI, a systematic study of PCA using distance-based measures is presented which employs distances between Ca-atoms as well as distances between inter-residue contacts including side chains. While this approach seems prohibitive for larger systems due to the quadratic scaling of the number of distances with the size of the molecule, it is shown that it is sufficient (and sometimes even better) to include only relatively few selected distances in the analysis. The quality of the PCA is assessed by considering the resolution of the resulting free energy landscape (to identify metastable conformational states and barriers) and the decay behavior of the corresponding autocorrelation functions (to test the time scale separation of the PCA). By comparing results obtained with distance-based, dihedral angle, and Cartesian coordinates, the study shows that the choice of input variables may drastically influence the outcome of a PCA. [ABSTRACT FROM AUTHOR]

Based on extensive ab initio calculations and the time-propagation of the nuclear Schrödinger equation, we study the vibrational relaxation dynamics and resulting spectral signatures of the OH stretch vibration of a hydrogen-bonded complex, HCO2- · H2O. Despite their smallness, it has been shown experimentally by Johnson and coworkers that the gas-phase infrared spectra of these types of complexes exhibit much of the complexity commonly observed for hydrogen-bonded systems. That is, the OH stretch band exhibits a significant red shift together with an extreme broadening and a pronounced substructure, which reflects its very strong anharmonicity. Employing an adiabatic separation of time scales between the three intramolecular high-frequency modes of the water molecule and the three most important intermolecular low-frequency modes of the complex, we calculate potential energy surfaces (PESs) of the ground and the first excited states of the high-frequency modes and identify a vibrational conical intersection between the PESs of the OH stretch fundamental and the HOH bend overtone. By performing a time-dependent propagation of the resulting system, we show that the conical intersection affects a coherent population transfer between the two states, the first step of which being ultrafast (60 fs) and irreversible. The subsequent relaxation of vibrational energy into the HOH bend and ground state occurs incoherently but also quite fast (1 ps), although the corresponding PESs are well separated in energy. Owing to the smaller effective mass difference between light and heavy degrees of freedom, the adiabatic ansatz is consequently less significant for vibrations than in the electronic case. Based on the model, we consider several approximations to calculate the measured Ar-tag action spectrum of HCO2- · H2O and achieve semiquantitative agreement with the experiment. [ABSTRACT FROM AUTHOR]

Based on extensive ab initio calculations and the time-propagation of the nuclear Schrödinger equation, we study the vibrational relaxation dynamics and resulting spectral signatures of the OH stretch vibration of a hydrogen-bonded complex, HCO2- · H2O. Despite their smallness, it has been shown experimentally by Johnson and coworkers that the gas-phase infrared spectra of these types of complexes exhibit much of the complexity commonly observed for hydrogen-bonded systems. That is, the OH stretch band exhibits a significant red shift together with an extreme broadening and a pronounced substructure, which reflects its very strong anharmonicity. Employing an adiabatic separation of time scales between the three intramolecular high-frequency modes of the water molecule and the three most important intermolecular low-frequency modes of the complex, we calculate potential energy surfaces (PESs) of the ground and the first excited states of the high-frequency modes and identify a vibrational conical intersection between the PESs of the OH stretch fundamental and the HOH bend overtone. By performing a time-dependent propagation of the resulting system, we show that the conical intersection affects a coherent population transfer between the two states, the first step of which being ultrafast (60 fs) and irreversible. The subsequent relaxation of vibrational energy into the HOH bend and ground state occurs incoherently but also quite fast (1 ps), although the corresponding PESs are well separated in energy. Owing to the smaller effective mass difference between light and heavy degrees of freedom, the adiabatic ansatz is consequently less significant for vibrations than in the electronic case. Based on the model, we consider several approximations to calculate the measured Ar-tag action spectrum of HCO2- · H2O and achieve semiquantitative agreement with the experiment. [ABSTRACT FROM AUTHOR]

We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1-10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water. [ABSTRACT FROM AUTHOR]

Based on a given time series, the data-driven Langevin equation (dLE) estimates the drift and the diffusion field of the dynamics, which are then employed to reproduce the essential statistical and dynamical features of the original time series. Because the propagation of the dLE requires only local information, the input data are neither required to be Boltzmann weighted nor to be a continuous trajectory. Similar to a Markov state model, the dLE approach therefore holds the promise of predicting the long-time dynamics of a biomolecular system from relatively short trajectories which can be run in parallel. The practical applicability of the approach is shown to be mainly limited by the initial sampling of the system's conformational space obtained from the short trajectories. Adopting extensive molecular dynamics simulations of the unfolding and refolding of a short peptide helix, it is shown that the dLE approach is able to describe microsecond conformational dynamics from a few hundred nanosecond trajectories. In particular, the dLE quantitatively reproduces the free energy landscape and the associated conformational dynamics along the chosen five-dimensional reaction coordinate. [ABSTRACT FROM AUTHOR]

Vibrational energy transfer (VET) is essential for protein function. It is responsible for efficient energy dissipation in reaction sites, and has been linked to pathways of allosteric communication. While it is understood that VET occurs via backbone as well as via non-covalent contacts, little is known about the competition of these two transport channels, which determines the VET pathways. To tackle this problem, we equipped the β-hairpin fold of a tryptophan zipper with pairs of non-canonical amino acids, one serving as a VET injector and one as a VET sensor in a femtosecond pump probe experiment. Accompanying extensive non-equilibrium molecular dynamics simulations combined with a master equation analysis unravel the VET pathways. Our joint experimental/computational endeavor reveals the efficiency of backbone vs. contact transport, showing that even if cutting short backbone stretches of only 3 to 4 amino acids in a protein, hydrogen bonds are the dominant VET pathway. Vibrational energy transfer (VET) is essential for protein function as it is responsible for efficient energy dissipation in reaction sites and is linked to pathways of allosteric communication. Here authors equipped a tryptophan zipper with a VET injector and a VET sensor for femtosecond pump probe experiments to map the VET. [ABSTRACT FROM AUTHOR]

When developing coarse‐grained models of complex processes out of equilibrium, one encounters the non‐stationary generalized Langevin equation. The most important feature of this equation is the presence of a non‐stationary memory kernel. Here, a method is presented to infer this memory kernel from MD simulation data in non‐equilibrium processes. The method provides an improvement of a previously published numerical scheme, the applicability of which is limited by a truncation problem. As an illustration, the method is applied to ion dissociation of NaCl in water, for which non‐trivial dampened oscillations are observed in the memory kernel. [ABSTRACT FROM AUTHOR]

Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional free energy landscape. Using Cartesian coordinates, first the translation and overall rotation need to be removed from the trajectory. Since the rotation depends via the moment of inertia on the molecule's structure, this separation is only straightforward for relatively rigid systems. Adopting millisecond molecular dynamics simulations of the folding of villin headpiece and the functional dynamics of BPTI provided by D. E. Shaw Research, it is demonstrated via a comparison of local and global rotational fitting that the structural dynamics of flexible molecules necessarily results in a mixing of overall and internal motion. Even for the small-amplitude functional motion of BPTI, the conformational distribution obtained from a Cartesian principal component analysis therefore reflects to some extend the dominant overall motion rather than the much smaller internal motion of the protein. Internal coordinates such as backbone dihedral angles, on the other hand, are found to yield correct and well-resolved energy landscapes for both examples. The virtues and shortcomings of the choice of various fitting schemes and coordinate sets as well as the generality of these results are discussed in some detail. [ABSTRACT FROM AUTHOR]

Based on a given time series, the data-driven Langevin equation proposed by Hegger and Stock [J. Chem. Phys. 130, 034106 (2009)] aims to construct a low-dimensional dynamical model of the system. Adopting various simple model problems of biomolecular dynamics, this work presents a systematic study of the theoretical virtues and limitations as well as of the practical applicability and performance of the method. As the method requires only local information, the input data need not to be Boltzmann weighted in order to warrant that the Langevin model yields correct Boltzmann-distributed results. Moreover, a delay embedding of the state vector allows for the treatment of memory effects. The robustness of the modeling with respect to wrongly chosen model parameters or low sampling is discussed, as well as the treatment of inertial effects. Given sufficiently sampled input data, the Langevin modeling is shown to successfully recover the correct statistics (such as the probability distribution) and the dynamics (such as the position autocorrelation function) of all considered problems. [ABSTRACT FROM AUTHOR]

While allostery is of paramount importance for protein regulation, the underlying dynamical process of ligand (un)binding at one site, resulting time evolution of the protein structure, and change of the binding affinity at a remote site are not well understood. Here the ligand-induced conformational transition in a widely studied model system of allostery, the PDZ2 domain, is investigated by transient infrared spectroscopy accompanied by molecular dynamics simulations. To this end, an azobenzene derived photoswitch is linked to a peptide ligand in a way that its binding affinity to the PDZ2 domain changes upon switching, thus initiating an allosteric transition in the PDZ2 domain protein. The subsequent response of the protein, covering four decades of time, ranging from ∼1 ns to ∼10 µs, can be rationalized by a remodeling of its rugged free-energy landscape, with very subtle shifts in the populations of a small number of structurally well-defined states. It is proposed that structurally and dynamically driven allostery, often discussed as limiting scenarios of allosteric communication, actually go hand-in-hand, allowing the protein to adapt its free-energy landscape to incoming signals. [ABSTRACT FROM AUTHOR]

Coarse-graining of fully atomistic molecular dynamics simulations is a long-standing goal in order to allow the description of processes occurring on biologically relevant timescales. For example, the prediction of pathways, rates and rate-limiting steps in protein-ligand unbinding is crucial for modern drug discovery. To achieve the enhanced sampling, we perform dissipation-corrected targeted molecular dynamics simulations, which yield free energy and friction profiles of molecular processes under consideration. Subsequently, we use these fields to perform temperature-boosted Langevin simulations which account for the desired kinetics occurring on multisecond timescales and beyond. Adopting the dissociation of solvated sodium chloride, trypsin-benzamidine and Hsp90-inhibitor protein-ligand complexes as test problems, we reproduce rates from molecular dynamics simulation and experiments within a factor of 2–20, and dissociation constants within a factor of 1–4. Analysis of friction profiles reveals that binding and unbinding dynamics are mediated by changes of the surrounding hydration shells in all investigated systems. Protein-ligand unbinding processes are out of reach for atomistic simulations due to time-scale involved. Here the authors demonstrate an approach relying on dissipation-corrected targeted molecular dynamics that enables to provide binding and unbinding rates with a speed-up of several orders of magnitude. [ABSTRACT FROM AUTHOR]

In transient infrared (IR) experiments, a molecular system may be photoexcited in a nonstationary conformational state, whose time evolution is monitored via IR spectroscopy with high temporal and structural resolution. As a theoretical formulation of these experiments, this work derives explicit expressions for transient one- and two-dimensional IR spectra and discusses various levels of approximation and sampling strategies. Adopting a photoswitchable octapeptide in water as a representative example, nonequilibrium molecular dynamics simulations are performed and the photoinduced conformational dynamics and associated IR spectra are discussed in detail. Interestingly, it is found that the time scales of dynamics and spectra may differ from residue to residue by up to an order of magnitude. Considering merely the cumulative spectrum of all residues, the contributions of the individual residues largely compensate each other, which may explain the surprisingly small frequency shifts and short photoproduct rise times found in experiment. Even when a localized amide I mode is probed (e.g., via isotope labeling), the vibrational frequency shift is shown to depend in a complicated way on the conformation of the entire peptide as well as on the interaction with the solvent. In this context, various issues concerning the interpretation of transient IR spectra and conformational dynamics in terms of a few exponential time scales are discussed. [ABSTRACT FROM AUTHOR]

To measure the transport of vibrational energy along a peptide helix, Hamm and co-workers [J. Phys. Chem. B 112, 9091 (2008)] performed time-resolved vibrational experiments, which showed that the energy transport rate increases by at least a factor of 4, when a localized C=O mode of the peptide instead of an attached chromophore is excited. This finding raises the question if coherent excitonic energy transfer between the C=O modes may be of importance for the overall energy transport in peptides. With this idea in mind, nonequilibrium molecular dynamics simulations as well as quantum-classical calculations are performed, which qualitatively reproduce the experimental findings. Moreover, the latter model (an exciton Hamiltonian whose matrix elements depend on the instantaneous positions of the peptide and solvent atoms) indeed exhibits the signatures of coherent quantum energy transport, at least within the first few picoseconds and at low temperatures. The origin of the observed decoherence, the absence of vibrational self-trapping, and the possibility of quantum interference between various transport paths are discussed in some detail. [ABSTRACT FROM AUTHOR]

Recent two-dimensional infrared (2D-IR) experiments on a short peptide 310-helix in chloroform solvent [E. H. G. Backus et al., J. Phys. Chem. B 113, 13405 (2009)] revealed an intriguing temperature dependence of the homogeneous line width, which was interpreted in terms of a dynamical transition of the peptide. To explain these findings, extensive molecular dynamics simulations at various temperatures were performed in order to construct the free energy landscape of the system. The study recovers the familiar picture of a glass-forming system, which below the glass transition temperature Tg is trapped in various energy basins, while it diffuses freely between these basins above Tg. In fact, one finds at Tg≈270 K a sharp rise of the fluctuations of the backbone dihedral angles, which reflects conformational transitions of the peptide. The corresponding C==O frequency fluctuations are found to be a sensitive probe of the peptide conformational dynamics from femtosecond to nanosecond time scales and lead to 2D-IR spectra that qualitatively match the experiment. The calculated homogeneous line width, however, does not show the biphasic temperature dependence observed in experiment. [ABSTRACT FROM AUTHOR]

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays. [ABSTRACT FROM AUTHOR]

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 computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y. Zhang, and J. E. Straub, J. Chem. Phys. 124, 144910 (2006)], second-order time-dependent perturbation theory is employed which includes the fluctuations of the parameters in the Hamiltonian within the vibrational adiabatic approximation. This means that the time-dependent vibrational frequencies along a molecular dynamics trajectory are obtained via a partial geometry optimization of the solute with fixed solvent and a subsequent normal mode calculation. Adopting the amide I mode of N-methylacetamide in heavy water as a test problem, it is shown that the inclusion of dynamic fluctuations may significantly change the vibrational energy relaxation. In particular, it is found that relaxation occurs in two phases, because for short times (<=200 fs) the spectral density appears continuous due to the frequency-time uncertainty relation, while at longer times the discrete nature of the bath becomes apparent. Considering the excellent agreement between theory and experiment, it is speculated if this behavior can explain the experimentally obtained biphasic relaxation the amide I mode of N-methylacetamide. [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]

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.

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.

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]