Biomedical subjects

Michael F Herman

Publications and source records attributed to Michael F Herman.

7 recordsLinked to original sources

PubMed2006

A justification for a nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation of the time evolution operator.

A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [J. Chem. Phys. 84, 326 (1986)] and Herman's nonadiabatic semiclassical surface hopping theory [J. Chem. Phys. 103, 8081 (1995)], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrodinger equation to the first order of variant Planck's over 2pi and the error is O(variant Planck's over 2pi(2)). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term variant Planck's over 2pi(1) order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tully's three model systems in low energies is improved.

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PubMed2006

An analysis of the accuracy of an initial value representation surface hopping wave function in the interaction and asymptotic regions.

The behavior of an initial value representation surface hopping wave function is examined. Since this method is an initial value representation for the semiclassical solution of the time independent Schrodinger equation for nonadiabatic problems, it has computational advantages over the primitive surface hopping wave function. The primitive wave function has been shown to provide transition probabilities that accurately compare with quantum results for model problems. The analysis presented in this work shows that the multistate initial value representation surface hopping wave function should approach the primitive result in asymptotic regions and provide transition probabilities with the same level of accuracy for scattering problems as the primitive method.

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PubMed2005

Toward an accurate and efficient semiclassical surface hopping procedure for nonadiabatic problems.

The derivation of a semiclassical surface hopping procedure from a formally exact solution of the Schrodinger equation is discussed. The fact that the derivation proceeds from an exact solution guarantees that all phase terms are completely and accurately included. Numerical evidence shows the method to be highly accurate. A Monte Carlo implementation of this method is considered, and recent work to significantly improve the statistical accuracy of the Monte Carlo approach is discussed.

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PubMed2005

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems.

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.

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PubMed2005

Matching-pursuit/split-operator Fourier-transform simulations of nonadiabatic quantum dynamics.

A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuitsplit-operator Fourier-transform (MPSOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MPSOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.

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PubMed2005

Numerical study of the accuracy and efficiency of various approaches for Monte Carlo surface hopping calculations.

A one-dimensional, two-state model problem with two well-separated avoided crossing points is employed to test the efficiency and accuracy of a semiclassical surface hopping technique. The use of a one-dimensional model allows for the accurate numerical evaluation of both fully quantum-mechanical and semiclassical transition probabilities. The calculations demonstrate that the surface hopping procedure employed accounts for the interference between different hopping trajectories very well and provides highly accurate transition probabilities. It is, in general, not computationally feasible to completely sum over all hopping trajectories in the semiclassical calculations for multidimensional problems. In this case, a Monte Carlo procedure for selecting important trajectories can be employed. However, the cancellation due to the different phases associated with different trajectories limits the accuracy and efficiency of the Monte Carlo procedure. Various approaches for improving the accuracy and efficiency of Monte Carlo surface hopping procedures are investigated. These methods are found to significantly reduce the statistical sampling errors in the calculations, thereby increasing the accuracy of the transition probabilities obtained with a fixed number of trajectories sampled.

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PubMed2004

Globally uniform semiclassical surface-hopping wave function for nonadiabatic scattering.

A globally uniform time-independent semiclassical wave function for nonadiabatic scattering is presented. This wave function, which takes the form of a surface-hopping expansion, is motivated by the globally uniform semiclassical wave function of Kay and co-workers for the single-surface case. The surface-hopping expansion is similar to a previously presented primitive semiclassical wave function for nonadiabatic problems. This earlier wave function has the important feature that it correctly incorporates all phase terms, allowing for an accurate treatment of quantum interference effects. The globally uniform expression has important numerical advantages over the primitive formulation. The globally uniform wave function does not have caustic singularities, and the globally uniform calculation avoids a root search for trajectories obeying double-ended boundary conditions that is required by the primitive semiclassical calculation.

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