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  • 1
    Electronic Resource
    Electronic Resource
    Time-evolution of molecular states in electronically diabatic phenomena (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 8173-8180 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We describe the propagation in time of quantal molecular states for electronically diabatic phenomena involving the coupling of two or more electronic states. We first show how the time propagation of a wave packet can be broken up into several stages corresponding to regions through which the wave packet moves with or without electronic couplings. This is done with a generalization of the interaction picture procedure recently shown to be quite efficient for numerical work. We next consider the propagation of total molecular states in regions with couplings by using sequences of transformations between adiabatic and diabatic electronic representations for a finite number of coupled electronic states. This requires the introduction of a general and efficient way of transforming between the two representations, that is the main concern of this contribution. The transformation is constructed using Lie-algebraic methods; it leads to simple expressions suitable for computations, and contains as a special case the coupling of two electronic states. The propagation in time through the electronically diabatic region is described using a split-operator propagator procedure suitable for electronically diabatic phenomena. We concentrate on only one molecular variable, which could be a bond distance or a bond angle, to focus on the construction of the adiabatic–diabatic transformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463439
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  • 2
    Electronic Resource
    Electronic Resource
    Alternative approach to stationary perturbation theory for separable problems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 8465-8469 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new implementation of stationary perturbation theory for separable quantum-mechanical problems is presented which allows the calculation of perturbation corrections for all the states simultaneously, so that the results are expressed in terms of the quantum numbers of the unperturbed system. The anharmonic oscillator, the Stark effect in a rigid rotor, and a caged harmonic oscillator are considered as illustrative examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463973
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  • 3
    Electronic Resource
    Electronic Resource
    On the bilinear approximation for time-dependent Hamiltonians (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1188-1193 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The transition probabilities for a one-dimensional harmonic oscillator with a time-dependent interaction potential are obtained. Two different bilinear approximations to the interaction potential are obtained by expanding it in Taylor series around two reference coordinate values, namely, the equilibrium position q0=0 and the expectation value of the coordinate q0=〈q〉, keeping only first- and second-order terms. The effect of the choice of q0 on the accuracy of the results is investigated for several values of the interaction potential parameters. The model posed by the semiclassical approach to the collision between a structureless particle and a harmonic oscillator via an exponential interaction potential is chosen as an illustrative example. The expansion around 〈q〉 is found to be related to an iterative procedure, based on Lie algebraic methods, recently proposed to treat time-dependent quantum-mechanical problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458127
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  • 4
    Electronic Resource
    Electronic Resource
    Construction of effective Hamiltonians for time-dependent phenomena from variational principles (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 3607-3613 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We develop a variational method for constructing the effective Hamiltonian that best propagates the state of a system, based on the minimization of a temporal error functional. As an illustrative example the procedure is used to derive the effective Hamiltonian in the time-dependent self-consistent-field method. The present variational approach is particularly useful to build the best effective Hamiltonian that is a linear combination of the generators of a Lie algebra. We explicitly consider systems having classical analogs with many degrees of freedom and calculate transition probabilities for a simple semiclassical model of the collinear collision between an atom and a diatomic molecule. We show that our variational approach is more general and accurate than the widely used local harmonic approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460811
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  • 5
    Electronic Resource
    Electronic Resource
    A generalized intermediate picture of quantal time evolution using operator algebraic methods. Application to translational–vibrational energy transfer in molecular collisions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3537-3541 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method for solving the time-dependent Schrödinger equation in an intermediate picture defined by an effective time-dependent Hamiltonian is discussed. The state function in this intermediate picture is written as a linear combination of time-independent basis functions with time-dependent coefficients. It is shown how to use Lie algebraic methods to build the interaction potential in the intermediate picture and calculate physical observables. The construction of the interaction potential is explicitly discussed in the case of one degree of freedom with a classical coordinate analog. The effective Hamiltonian is obtained by expanding the potential energy function around a reference value of the coordinate. Effective Hamiltonians for He–H2 collisions obtained for equilibrium and average reference values of the vibrational coordinate of H2 are compared and the expansion convergence in the resulting intermediate pictures are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459775
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  • 6
    Electronic Resource
    Electronic Resource
    Multidimensional harmonic oscillator matrix elements (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 5505-5508 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Multidimensional harmonic oscillator matrix elements of arbitrary products of exponentials for operators containing only linear and quadratic terms in the creation and annihilation operators are obtained. A simple and straightforward method is presented that leads to recurrence relations and generating functions for such matrix elements. Results are shown to be general enough to cover the cases of Franck–Condon overlaps, transition probabilities for time-dependent harmonic oscillators, and correlation functions for electronic spectra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457553
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  • 7
    Electronic Resource
    Electronic Resource
    Calculation of vibrational transition probabilities in molecular collisions: A recursive algebraic procedure (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 924-928 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The vibrational energy transfer in collinear collisions between diatomic molecules is studied by means of a recursive algebraic approach applicable to several degrees of freedom. Introducing classical relative trajectories the problem is reduced to solving the Schrödinger equation with a time-dependent bilinear Hamiltonian. On using the equations of motion for the creation and annihilation operators, simple recurrence relations for the transition amplitudes are obtained. Transition probabilities between several vibrational states are calculated for N2+O2 to illustrate the advantages of the computational approach for high vibrational quantum numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457143
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  • 8
    Electronic Resource
    Electronic Resource
    A new implementation of stationary perturbation theory for separable quantum-mechanical problems (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 6392-6394 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We improve a recently developed implementation of perturbation theory for separable problems. On choosing a new ansatz for the perturbed wave function that takes into account the singularities of the eigenvalue equation explicitly, the resulting perturbation equations become simpler. As an illustrative example, we consider the Stark shift of the microwave spectra of a polarizable symmetric-top molecule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.464836
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  • 9
    Electronic Resource
    Electronic Resource
    Exponential time-evolution operator for the time-dependent harmonic oscillator (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2908-2908 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The time-evolution operator for the time-dependent harmonic oscillator H= (1)/(2) {α(t)p2 +β(t)q2} is exactly obtained as the exponential of an anti-Hermitian operator. The method is based on the equations of motion for the coordinate and momentum operators in the Heisenberg representation. The problem is reduced to solving the classical equations of motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527819
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  • 10
    Electronic Resource
    Electronic Resource
    Renormalized perturbation series and the semiclassical limit of quantum mechanics (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 3922-3930 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The accuracy of the renormalized perturbation series for anharmonic oscillators and other simple quantum-mechanical models increases with the quantum number when the adjustable parameter is determined by a simple variational criterion. In the semiclassical limit of quantum mechanics such an expansion converges towards the result of the Jeffreys–Wentzel–Kramers–Brillouin method to all orders. The hypervirial and Hellmann–Feynman theorems facilitate the derivation of the semiclassical series from Rayleigh–Schrödinger perturbation theory. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530938
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