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  • 1
    Electronic Resource
    Electronic Resource
    Semiclassical-limit molecular dynamics on multiple electronic surfaces (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 4918-4930 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we present a new approach to treating many-body molecular dynamics on coupled electronic surfaces. The method is based on a semiclassical limit of the quantum Liouville equation. The formal result is a set of coupled classical-like partial differential equations for generalized distribution functions which describe both the nuclear probability densities on the coupled surfaces and the coherences between the electronic states. The Hamiltonian dynamics underlying the evolution of these distributions is augmented by nonclassical source and sink terms, which allow the flow of probability between the coupled surfaces and the corresponding formation and decay of electronic coherences. The formal results are shown analytically to reproduce the well-known Rabi and Landau–Zener results in appropriate limits. In addition, a direct numerical solution of the phase space partial differential equations is performed, and the results compared with exact quantum solutions for a model curve-crossing problem, yielding excellent agreement. Future trajectory-based implementation of the method in molecular dynamics simulations is also discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473541
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  • 2
    Electronic Resource
    Electronic Resource
    Nanoscale shock wave spectroscopy: A direct view of coherent ultrafast bath dynamics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 4343-4350 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present molecular dynamics simulations of an idealized ultrafast pump-probe experiment that is designed to allow direct observation of the real-time dynamical response of an impulsively driven many-body bath. In this scheme, a pump laser pulse excites an impurity molecule embedded in a solid host to a repulsive electronic state. The resulting photofragments collide with neighboring host atoms and create localized excitations that travel through the lattice at supersonic velocities. We refer to these excitations as a nanoscale shock wave, as they are localized on the nanometer length scale of individual atoms in the solid. The probe laser is tuned to a transient absorption in the host that is induced by the collisions between neighboring lattice atoms that accompany the propagation of the localized disturbance. The resulting signal as a function of time delay then provides a view of the creation, evolution, and decay of the nanoscale shock waves. We apply the general approach to a two-dimensional model system representing I2 photodissociation in solid Ar. Pump-probe signals are synthesized, and the observed features are interpreted in terms of the microscopic dynamics of the system. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.479733
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  • 3
    Electronic Resource
    Electronic Resource
    Simulation of nonadiabatic wave packet interferometry using classical trajectories (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 7345-7354 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we describe the application of our recently developed multistate semiclassical Liouville equation method for modeling molecular dynamics on multiple coupled electronic states [C. C. Martens and J.-Y. Fang, J. Chem. Phys. 106, 4918 (1997); A. Donoso and C. C. Martens, J. Phys. Chem. 102, 4291 (1998)] to problems where electronic coherence effects play a dominant role. We consider a model problem involving the simultaneous evolution of wave packets on two coupled electronic states. We analyze the problem qualitatively from both quantum and semiclassical perspectives using perturbation theory, and identify the roles played by coupling strength and relative phase of the initial wave packets. We then perform trajectory-based simulations on a two-state one-dimensional model problem and compare the results with those of exact quantum calculations. In marked contrast with most current methods for modeling nonadiabatic dynamics with classical trajectories, the semiclassical Liouville method is found to be capable of treating even dominant electronic coherence effects in a consistent and accurate manner. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481333
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  • 4
    Electronic Resource
    Electronic Resource
    Semiclassical multistate Liouville dynamics in the adiabatic representation (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 3980-3989 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we describe implementation of the semiclassical Liouville method for simulating molecular dynamics on coupled electronic surfaces in the electronic adiabatic representation. We cast the formalism in terms of semiclassical motion on Born–Oppenheimer potential energy surfaces with nonadiabatic coupling arising from the coordinate dependence of the adiabatic electronic eigenstates. Using perturbation theory and asymptotic evaluation of the resulting time integrals, we derive an expression for the probability of transition between adiabatic states which agrees with the result given previously by Miller and George [W. H. Miller and T. F. George, J. Chem. Phys. 56, 5637 (1972)]. We also demonstrate numerically the equivalence of semiclassical trajectory-based calculations in the adiabatic and diabatic representations by performing molecular dynamics simulations on a model two-state system and comparing with exact quantum mechanical results. Excellent agreement between the exact and semiclassical treatments is obtained in both representations. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.480948
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  • 5
    Electronic Resource
    Electronic Resource
    Simulation of ultrafast dynamics and pump–probe spectroscopy using classical trajectories (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 6919-6929 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we develop a method for accurately modeling ultrafast molecular dynamics and pump–probe spectroscopy using classical trajectory simulations. The approach is based on a semiclassical limit of the Liouville formulation of quantum mechanics. Expressions for the nonstationary classical phase space probability density created by an ultrashort laser pulse on an excited electronic state, and the observable fluorescence signal resulting from a pump–probe experiment, are derived in the weak-field limit using perturbation theory. By introducing additional approximations, these expressions are cast in a form that can be directly implemented using classical trajectory integration and ensemble averaging. The method is tested against multisurface time-dependent quantum mechanical wave packet calculations for a one-dimensional model system representing I2 photodissociation-recombination in a static Ar lattice. Nearly quantitative agreement between the exact calculations and the trajectory-based method is obtained. Although demonstrated for a one-dimensional system, the method is easily incorporated in conventional molecular dynamics programs, allowing efficient treatment of many-body ultrafast dynamics and spectroscopy. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471407
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  • 6
    Electronic Resource
    Electronic Resource
    Nanoscale shock wave generation by photodissociation of impurities in solids: A molecular dynamics study (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 1905-1916 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The dynamics of shock wave generation, propagation, and decay in an Ar lattice following photodissociation of an I2 impurity are studied using molecular dynamics simulation. A two-dimensional model is treated to allow the modeling of shock wave propagation over larger distances than easily accessible in full three-dimensional calculations. The shock waves are created on atomic length scales by binary collisions between the nascent photofragments and adjacent lattice atoms, and propagate long distances through the crystal in a highly directed, quasi-one-dimensional manner. As a consequence of the I/Ar mass ratio, the I fragments undergo multiple collisions with the adjacent Ar atoms situated along the I–I bond axis, generating pulse trains of shock waves, each with a characteristic initial energy, velocity, and decay rate. The dynamics of the system are interpreted using a simple one-dimensional hard sphere model. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468756
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  • 7
    Electronic Resource
    Electronic Resource
    One-atom cage effect in collinear I2(B)–Ar complexes: A time-dependent wave packet study (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 9072-9082 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Two-dimensional time-dependent wave packet calculations are carried out on a collinear model of the I2(B)–Ar complex to investigate the possible kinematic origin of the one-atom cage effect in small van der Waals molecules. Three different excitation wavelengths are considered (496.5, 488, and 476.5 nm), and the dynamics are assumed to be restricted to the I2 B state electronic surface, with no nonadiabatic transitions following the pump excitation. Good agreement with experiment is obtained. To investigate the sensitivity of observable final state distributions on the weak intermolecular potential between I2 and Ar, three slightly different B state I–Ar interactions are employed for the case of 488 nm excitation. It is found that relatively small changes in the form and magnitude of the weak van der Waals interactions can have a large effect on the final state distributions. These results suggest that the experimental data on I2–Ar photodissociation–recombination can be explained by a purely kinematic one-atom cage effect on the B state electronic surface for a collinear population of I2–Ar clusters, without the need to introduce nonadiabatic electronic effects. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.472741
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  • 8
    Electronic Resource
    Electronic Resource
    Classical, quantum mechanical, and semiclassical representations of resonant dynamics: A unified treatment (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 284-302 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper addresses the general problem of zeroth order representation of resonant dynamics. We investigate the classical, quantum mechanical, and semiclassical transformation properties of two-dimensional isotropic and anisotropic uncoupled harmonic oscillators. The classical and quantal theories are presented in a manner that emphasizes the strong correspondence between the two, and in particular, the SU(2) symmetry exhibited by both the classical and quantum oscillators. The classical canonical transformations relating the action-angle variables appropriate for normal, local, and precessional motion of the isotropic oscillator are derived by explicit calculation of the generating functions. By employing a simple mapping relating the anisotropic and isotropic oscillators, expressions for action-angle variables appropriate for the topology of an arbitrary m:n resonance are determined. The resulting invariant tori are compared with the corresponding quantum mechanical wave functions and phase space densities. The relationship between the classical and quantum mechanical theories is illustrated by determining semiclassical approximations to the unitary transformation matrix elements, which are given in terms of the classical generating functions. Applications to problems of current interest, such as the adiabatic switching method for semiclassical quantization of nonseparable systems, are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453625
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  • 9
    Electronic Resource
    Electronic Resource
    Classical and semiclassical mechanics of strongly resonant systems: A Fourier transform approach (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 86 (1987), S. 279-307 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Fourier transform approach to EBK quantization, previously applied to nonresonant systems with up to four degrees of freedom [J. Chem. Phys. 83, 2990 (1985)], is extended to the case of strongly resonant classical motion. The classical mechanics of systems with 3:4, 1:2, and 1:1 resonances is examined in detail from the Fourier transform point of view, and the results of nonlinear resonance analysis used to interpret numerical trajectory Fourier spectra. Calculation of classical actions and numerical construction of the angle parametrization of invariant tori is described, and the relation between spectral frequency assignments and the choice of good action-angle variables investigated. It is shown that correct quantization conditions for arbitrary resonant motion can be determined by direct numerical evaluation of Maslov indices. Semiclassical eigenvalues are reported for the 3:4, 1:2, and 1:1 resonant systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.452618
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  • 10
    Electronic Resource
    Electronic Resource
    Qualitative dynamics of generalized Langevin equations and the theory of chemical reaction rates (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 2516-2528 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we present an analysis of condensed phase chemical reactions from the perspective of qualitative dynamical systems theory. Our approach is based on a phenomenological phase space representation of the generalized Langevin equation (GLE). In general, the GLE with memory requires an infinite-dimensional phase space for its description. The phenomenological phase space is constructed by augmenting the physical phase plane (q,p) with additional variables defined as the convolution of the system momentum with the memory kernel and its time derivatives. The qualitative dynamics in this representation are then characterized in terms of the eigenvalues and eigenvectors of the linear system near the barrier top. The phase space decomposes into a single unstable direction and a complementary stable subspace. The rate of exponential growth along the unstable eigenvector is directly related to the rate of chemical reaction, and our linear analysis reproduces the Grote–Hynes expression for the reaction rate [R. F. Grote and J. T. Hynes, J. Chem. Phys. 73, 2715 (1980)]. In the presence of noise, the stable subspace can be identified with the stochastic separatrix, a manifold of initial conditions with a reaction probability of 0.5. Other dynamical processes, such as solvent caging, can also be given a simple geometric interpretation in terms of the qualitative dynamical analysis. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1436116
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