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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.

Based on a comparison of classical and quantum-mechanical perturbation theory, the validity of classical nonequilibrium molecular dynamics simulations to describe vibrational energy redistribution in biomolecules is studied. Adopting a small model peptide in aqueous solution as an example, the theory correctly predicts quantum correction factors that need to be applied to the results of classical simulations in order to match the correct quantum results.

Energy transport in a short helical peptide in chloroform solution is studied by time-resolved femtosecond spectroscopy and accompanying nonequilibrium molecular dynamics (MD) simulations. In particular, the heat transport after excitation of an azobenzene chromophore attached to one terminus of the helix with 3 eV (UV) photons is compared to the excitation of a peptide C=O oscillator with 0.2 eV (IR) photons. The heat in the helix is detected at various distances from the heat source as a function of time by employing vibrational pump-probe spectroscopy. As a result, the carbonyl oscillators at different positions along the helix act as local thermometers. The experiments show that heat transport through the peptide after excitation with low-energy photons is at least 4 times faster than after UV excitation. On the other hand, the heat transport obtained by nonequilibrium MD simulations is largely insensitive to the kind of excitation. The calculations agree well with the experimental results for the low-frequency case; however, they give a factor of 5 too fast energy transport for the high-energy case. Employing instantaneous normal mode calculations of the MD trajectories, a simple harmonic model of heat transport is adopted, which shows that the heat diffusivity decreases significantly at temperatures initially reached by high-energy excitation. This finding suggests that the photoinduced energy gets trapped, if it is deposited in high amounts. The various competing mechanisms, such as vibrational T(1) relaxation, resonant transfer between excitonic states, cascading down relaxation, and low-frequency mode transfer, are discussed in detail.

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.

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]

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]

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]

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 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]

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.

Employing extensive quantum-chemical calculations at the DFT/B3LYP and MP2 level, quartic force fields of isolated N-methylacetamide are constructed. Taking into account 24 vibrational degrees of freedom, the model is employed to perform numerically exact vibrational configuration interaction calculations of the vibrational energy relaxation of the amide I mode. It is found that the energy transfer pathways may sensitively depend on details of the theoretical description. Moreover, the exact reference calculations were used to study the applicability and accuracy of (i) the quasiclassical trajectory method, (ii) time-dependent second-order perturbation theory, and (iii) the instantaneous normal mode description of frequency fluctuations. Based on the results, several strategies to describe vibrational energy relaxation in biomolecular systems are discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [ABSTRACT FROM AUTHOR]

A recently proposed semiclassical approach to the description of nonadiabatic quantum dynamics [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997), X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997)] is applied to the S[sub 1]-S[sub 2] conical intersection in pyrazine. This semiclassical method is based on a transformation of discrete quantum variables to continuous variables, thereby bypassing the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states. Extending previous work on small systems, we investigate the applicability of the semiclassical method to larger systems with strong vibronic coupling. To this end, we present results for several pyrazine models of increasing dimensionality and complexity. In particular, we discuss the quality and performance of the semiclassical approach when the number of nuclear degrees of freedom is increased. Comparison with quantum-mechanical calculations and experimental results shows that the semiclassical method is able to describe the ultrafast dynamics in this system. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract: The mapping formulation of nonadiabatic quantum dynamics is applied to obtain a classical description of the ultrafast dynamics and time-resolved spectroscopy of a photochemical reaction. Adopting a previously studied dissipative two-state two-mode model of nonadiabatic cis–trans photoisomerization, classical mapping simulations are compared to quantum-mechanical reduced density matrix calculations. Overall, the simple classical method is found to reproduce the quantum reference calculations quite well. In particular, it is studied if the classical approach yields the correct long-time cis/trans localization of the wave packet and therefore the correct quantum yield of the photoreaction. As the long-time behavior of the classical mapping formulation suffers from the well-known zero point energy problem of classical mechanics, a new practical method is proposed to determine a zero point energy correction. Employing a second-order Franck–Condon-type approximation, the capability of the classical method to simulate time- and frequency-resolved pump–probe spectra of the nonadiabatic photoreaction is studied. The potential of the classical approach as a practical method to describe condensed-phase photoreactions is discussed. [Copyright &y& Elsevier]

Based on a given time series, data-driven Langevin modeling aims to construct a low-dimensional dynamical model of the underlying system. When dealing with physical data as provided by, e.g., all-atom molecular dynamics simulations, effects due to small damping may be important to correctly describe the statistics (e.g., the energy landscape) and the dynamics (e.g., transition times). To include these effects in a dynamical model, an algorithm that propagates a second-order Langevin scheme is derived, which facilitates the treatment of multidimensional data. Adopting extensive molecular dynamics simulations of a peptide helix, a five-dimensional model is constructed that successfully forecasts the complex structural dynamics of the system. Neglect of small damping effects, on the other hand, is shown to lead to significant errors and inconsistencies. [ABSTRACT FROM AUTHOR]