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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Quantum theory of planar four-atom reactions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 402-422 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An exact quantum mechanical theory is developed to treat four-atom reactions of the type AB+CD↔(BCD+A, ACD+B), where the atoms are constrained to move in a plane. The theory makes use of an unbiased set of hyperspherical coordinates. A method is proposed for implementing the theory that exploits the potential optimized discrete variable representation. Application is made to the calculation of rovibrational state-to-state reaction probabilities for the reaction H2+OH↔H2O+H, in which the length of the OH spectator bond is held fixed. The results show that a rotating bond approximation, in which the H2 molecule is not allowed to rotate, gives good results for vibrationally selected reaction probabilities. The effect of reactant rotation and vibration on the reactivity and product distributions is discussed for the reactions H2+OH→H2O+H and H2O+H→H2+OH.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466954
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  • 6
    Electronic Resource
    Electronic Resource
    The planar reaction OH+H2→H2O+H: A quasiclassical trajectory study (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 2841-2846 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We report a quasiclassical trajectory (QCT) study of the reaction OH+H2→H2O+H performed on the same model as that used in a recent exact quantum treatment. The reaction is constrained to occur on a plane, with the OH bond frozen. We used Clary's modification to the Schatz–Elgersma potential energy surface. Initial state selected reaction probabilities and cross sections were calculated at several energies between 0.31 and 0.65 eV. The effect of rotational excitation of H2 and OH on reaction probabilities was studied and QCT results were compared with exact quantum results for the same model. We found very good quantitative agreement between quantum and QCT results. Furthermore, QCT calculations confirm the qualitative effects predicted by the quantum treatment; exciting the rotation of H2 decreases reactivity while the rotation of OH has almost no effect. Similarities and differences between the present QCT results with 2D and 3D quantum and classical results by other authors are discussed. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471107
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  • 7
    Electronic Resource
    Electronic Resource
    Time-dependent reactive scattering in hyperspherical coordinates: A close coupled wave packet approach (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 1380-1386 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a close coupled wave packet method to treat reactive collisions in hyperspherical coordinates. Within this approach, the information needed for the time-dependent propagation is the same as that required for a time-independent close coupling treatment. The method is tested on the simple collinear D+H2 reaction. We compare the time-dependent technique with the more established time-independent close coupling treatment. Finally, we show that time-dependent properties are useful to gain insight into the detailed mechanism of the reaction. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470795
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  • 8
    Electronic Resource
    Electronic Resource
    On the convergence of the Magnus expansion in the Schrödinger representation (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 338-341 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The convergence properties of the Magnus expansion in the Schrödinger representation are investigated. A quite general result is rigorously derived from first-order perturbation theory. A finite matrix representation is presented for obtaining the exponential time-evolution operator more easily. Two time-dependent models, an oscillator and a spin system, are considered as illustrative examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528919
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  • 9
    Electronic Resource
    Electronic Resource
    Baker-Campbell-Hausdorff relations for finite-dimensional lie algebras (1992)
    Springer
    Journal of mathematical chemistry 9 (1992), S. 87-94 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A method is proposed for disentangling exponentials of operators that belong to finite-dimensional Lie algebras. A straightforward matrix representation is combined with a widely used parameter-differentiation method, giving rise to a simpler and more systematic procedure. The SU(1, 1), SU(2) and double photon algebras are explicitly considered as illustrative examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01172932
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  • 10
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    Molecular Dynamics Study of the Active Site of Methylamine Dehydrogenase (2006)
    American Chemical Society
    Details
    Publication Date: 2006-06-01
    Print ISSN: 1520-6106
    Electronic ISSN: 1520-5207
    Topics: Chemistry and Pharmacology , Physics
    Published by American Chemical Society
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