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  • 1
    Electronic Resource
    Electronic Resource
    Approximate calculation of femtosecond pump–probe spectra monitoring nonadiabatic excited-state dynamics (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 4910-4922 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck–Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time- and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing (i) the nonadiabatic cis–trans isomerization of an electronic two-state system, and (ii) the S2→S1 internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe–pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump–probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481045
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  • 2
    Electronic Resource
    Electronic Resource
    Ultrafast cis-trans photoswitching: A model study (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 1085-1091 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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 ((approximately-less-than)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 (Yc→t) and the trans-cis backward reaction (Yt→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 Yt→c=1−Yc→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. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1428344
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  • 3
    Electronic Resource
    Electronic Resource
    Classical phase-space analysis of vibronically coupled systems (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 69-78 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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 Poincaré 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1421067
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  • 4
    Electronic Resource
    Electronic Resource
    Quantum-classical Liouville description of multidimensional nonadiabatic molecular dynamics (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 2001-2012 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The quantum-classical Liouville formulation gives a quantum-mechanical density-matrix description of the "quantum" particles of a problem (e.g., the electrons) and a classical phase-space-density description of the "classical" particles (e.g., the nuclei). In order to employ this formulation to describe multidimensional nonadiabatic processes in complex molecular systems, this work is concerned with an efficient Monte Carlo implementation of the quantum-classical Liouville equation. Although an exact stochastic realization of this equation is in principle available, in practice one has to cope with two major complications: (i) The representation of nonlocal phase-space operators in terms of local classical trajectories and (ii) the convergence of the Monte Carlo sampling which is cumbersome due to complex-valued trajectories with rapidly oscillating phases. Several strategies to cope with these problems are discussed, including various approximations to determine the momentum shift associated with a nonadiabatic transition, the on-the-fly generation of new trajectories at curve-crossings, and the localization of trajectories after irreversible electronic transitions. Employing several multidimensional model systems describing ultrafast photoinduced electron transfer and internal conversion, detailed numerical studies are performed which are compared to exact quantum calculations as well as to the "fewest-switches" surface-hopping method. In all cases under consideration, the Liouville calculations are in good agreement with the quantum reference. In particular, the approach is shown to provide a correct quantum-classical description of the electronic coherence. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1336576
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  • 5
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    Communication: Microsecond peptide dynamics from nanosecond trajectories: A Langevin approach (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-12-23
    Description: 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.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 6
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    Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-07-08
    Description: 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.
    Electronic ISSN: 1931-9223
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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  • 7
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    Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates (2014)
    American Institute of Physics (AIP)
    Details
    Publication Date: 2014-07-08
    Description: 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.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics (AIP)
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