Wave-packet method

Mowrey R C and Kouri D J 1987 Application of the close coupling wave packet method to long lived resonance states in molecule-surface scattering J. Chem. Phys. 86 6140... 

Garcia-Vela, A., Gerber, R. B. Hybrid quantum-semiclassical wave packet method for molecular dynamics Application to photolysis of Ar...HCl. J. Chem. Phys. 98 (1993) 427-43... 

In the DC-biased structures considered here, the dynamics are dominated by electronic states in the conduction band [1]. A simplified version of the theory assumes that the excitation occurs only at zone center. This reduces the problem to an n-level system (where n is approximately equal to the number of wells in the structure), which can be solved using conventional first-order perturbation theory and wave-packet methods. A more advanced version of the theory includes all of the hole states and electron states subsumed by the bandwidth of the excitation laser, as well as the perpendicular k states. In this case, a density-matrix picture must be used, which requires a solution of the time-dependent Liouville equation. Substituting the Hamiltonian into the Liouville equation leads to a modified version of the optical Bloch equations [13,15]. These equations can be solved readily, if the k states are not coupled (i.e., in the absence of Coulomb interactions). 

II. THE REAL WAVE PACKET METHOD A. General Ideas... 

The real wave packet (RWP) method, developed by Gray and Bahnt-Kuiti [ 1], is an approach for obtaining accurate quantum dynamics information. Unlike most wave packet methods [2] it utilizes only the real part of the generally complex-valued, time-evolving wave packet, and the effective Hamiltonian operator generating the dynamics is a certain function of the actual Hamiltonian operator of interest. Time steps in the RWP method are accomphshed by a simple three-term Chebyshev... 

The RWP method also has features in common with several other accurate, iterative approaches to quantum dynamics, most notably Mandelshtam and Taylor s damped Chebyshev expansion of the time-independent Green s operator [4], Kouri and co-workers time-independent wave packet method [5], and Chen and Guo s Chebyshev propagator [6]. Kroes and Neuhauser also implemented damped Chebyshev iterations in the time-independent wave packet context for a challenging surface scattering calculation [7]. The main strength of the RWP method is that it is derived explicitly within the framework of time-dependent quantum mechanics and allows one to make connections or interpretations that might not be as evident with the other approaches. For example, as will be shown in Section IIB, it is possible to relate the basic iteration step to an actual physical time step. 

A general description of the time-dependent wave packet approach is presented for N variables (degrees of freedom) represented by the vector R = r, f2,..., r /. The time-dependent wave packet method is based on the solution of the TDSE describing the coupling between M electronic states... 

Another indirect technique, which enables one to calculate the resonance spectrum for many energies simultaneously, is the wave packet method [163-168], used, for example, in studies of non-rotating [47,169] and rotating [52] HCO, HO2 [170] and H2O [71]. One iteratively solves the time-dependent Schrodinger equation, Eq. (10),... 

Agrawal. P.M. and Raff. L.M. (1981) Calculation of reaction probabilities and rate cocfficicnrs for collincar three-body exchange reactions using time-dependent wave packet methods J. Chem. Phys. 74. 5076-5081. 

Goldfield, E.M. and Gray. S.K. (2002) A quantum dvnamics study of H2-rOH H2O-PH employing the Wu-Schatz-Lendvay-Fang-Hardiug potential function and a four-atom implementation of the real wave packet method. J. Cham. Phys. 117. 1604-1613. 

Abstract. Over the last deeade, advances in quantum dynamics, notably the development of the initial state selected time-dependent wave packet method, coupled with advances in constructing ab initio potential energy surfaces, have made it possible for some four-atom reactions to be addressed from first principles, in their full six internal degrees of freedom. Attempts have been made to extend the time-dependent wave packet method to reactions with more internal degrees of freedom. Here, we review the full-dimensional theory for the A + BCD four-atom reaction and use it to guide the reduced-dimensionality treatment of the X + YCZ3 reaction. Comparison of rigorous calculations with recent experiments are presented for (a) the benchmark H + H2O abstraction reaction, and (b) the H + CH4 H2 + CH3 reaction. 

The time-dependent wave packet method has been outlined to solve the A + BCD and the X -I- YCZ3 reactions. The tetraatomic system could be solved in full-dimensionality, but to solve the hexaatomie system we followed the method of Palma and Clary,40 where the CD bond is replaced by CZ3 with C3V symmetry throughout the reaction, with reduced dimensionality. Caleulations were performed for the H -l- H2O reaction in full-dimensionality, and the H -l- CFL reaction in seven dimensions. 

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