Quantum wave packet study of N(2D) + H2 reactive scattering

N(²D) + H₂ → NH + H reaction at zero total angular momentum is studied by using a time dependent quantum wave packet method. State‐to‐state and state‐to‐all reactive scattering probabilities for a broad range of energy are calculated. The probabilities show many sharp peaks that ascribed to reactive scattering resonances. The probabilities for J > 0 are estimated by using the J‐shifting method. The integral cross sections and thermal rate constants are then calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Time-dependent wave packet propagation using quantum hydrodynamics

A new approach for propagating time-dependent quantum wave packets is presented based on the direct numerical solution of the quantum hydrodynamic equations of motion associated with the de Broglie–Bohm formulation of quantum mechanics. A generalized iterative finite difference method (IFDM) is used to solve the resulting set of non-linear coupled equations. The IFDM is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a “smart” Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is generalized to treat higher-dimensional problems and anharmonic potentials. The method is applied to a one-dimensional Gaussian wave packet scattering from an Eckart barrier, a one-dimensional Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. The 2D scattering results represent the first successful application of an accurate direct numerical solution of the quantum hydrodynamic equations to an anharmonic potential energy surface.     

Molecular wave packet interferometry and quantum entanglement

We study wave packet interferometry (WPI) considering the laser pulse fields both classical and quantum mechanically. WPI occurs in a molecule after subjecting it to the interaction with a sequence of phase-locked ultrashort laser pulses. Typically, the measured quantity is the fluorescence of the molecule from an excited electronic state. This signal has imprinted the interference of the vibrational wave packets prepared by the different laser pulses of the sequence. The consideration of the pulses as quantum entities in the analysis allows us to study the entanglement of the laser pulse states with the molecular states. With a simple model for the molecular system, plus several justified approximations, we solve for the fully quantum mechanical molecule-electromagnetic field state. We then study the reduced density matrices of the molecule and the laser pulses separately. We calculate measurable corrections to the case where the fields are treated classically.     

Hyperspherical coordinates in quantum mechanical collinear reactive scattering

A new hyperspherical coordinate method for performing atom—diatom quantum mechanical collinear reactive scattering calculations is described. The method is applicable at energies for which breakup channels are open. Comparison with previous results and new results at high energies for H H₂ are given. The usefulness of this approach is discussed.     

Overview of reduced dimensionality quantum approaches to reactive scattering

 In this overview I discuss recent advances as well as outstanding issues in reduced dimensionality quantum approaches to reactive scattering. “Reduced dimensionality” in the present context signifies treating a subset of all degrees of freedom (the most strongly coupled ones) by rigorous quantum methods and treating the remaining (weakly coupled) degrees of freedom by a variety of approximate methods, ranging from simple, so-called energy shifts to more elaborate adiabatic treatments. The most widely used example of this approach is termed “J-shifting”, and this overview will concentrate on this method and discuss its application and generalization to both “direct” and “complex” reactions, exemplified by O(³P) + HCl and O(¹D) + HCl, respectively. In addition, for O(³P) + HCl, resonances in the tunneling region, due to van der Waals wells, are discussed and their challenge to reduced dimensionality methods is stressed. Another new aspect of the reduced dimensionality treatment of polyatomic reactions is the need to describe anharmonicity in a consistent fashion. This is exemplified by the H + CH₄ reaction. Received: 3 February 2002 / Accepted: 8 April 2002 / Published online: 19 August 2002     

A dynamical Lie algebraic mehtod for quantum reactive scattering

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Two‐dimensional reactive scattering with transmitted quantum trajectories

A simple and easy‐to‐implement method is presented for the study of time‐dependent reaction dynamics by propagating an ensemble of transmitted quantum trajectories. During the trajectory evolution, reflected trajectories are gradually removed and all the remaining trajectories represent the transmitted subensemble. The removal process of reflected trajectories avoids numerical instabilities arising from node formation in the reactant region, and allows stable long‐time propagation of transmitted trajectories. This method is applied to a two‐dimensional model chemical reaction. Excellent computational results are obtained for the time‐dependent reaction probabilities evaluated by the time integration of the probability flux. © 2014 Wiley Periodicals, Inc.     

Non-Hermitian quantum mechanics: wave packet propagation on autoionizing potential energy surfaces

The correspondence between the time-dependent and time-independent molecular dynamic formalisms is shown for autoionizing processes. We demonstrate that the definition of the inner product in non-Hermitian quantum mechanics plays a key role in the proof. When the final state of the process is dissociative, it is technically favorable to introduce a complex absorbing potential into the calculations. The conditions which this potential should fulfill are briefly discussed. An illustrative numerical example is presented involving three potential energy surfaces.     

Analytical solution for optimal squeezing of wave packet of a trapped quantum particle

Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final state is presented for a case of an infinite well trapping potential. The presented solution may be applied to increase the resolution of atom lithography.     

Laser control of vibrational excitation in carboxyhemoglobin: a quantum wave packet study

A coherent control algorithm is applied to obtain complex-shaped infrared laser pulses for the selective vibrational excitation of carbon monoxide at the active site of carbonmonoxyhemoglobin, modeled by the six-coordinated iron-porphyrin-imidazole-CO complex. The influence of the distal histidine is taken into account by an additional imidazole molecule. Density-functional theory is employed to calculate a multidimensional ground-state potential energy surface, and the vibrational dynamics as well as the laser interaction is described by quantum wave-packet calculations. At each instant in time, the optimal electric field is calculated and used for the subsequent quantum dynamics. The results presented show that the control scheme is applicable to complex systems and that it yields laser pulses with complex time-frequency structures, which, nevertheless, have a clear physical interpretation.     

An extension of the grid empowered molecular simulator to quantum reactive scattering

Within the activities of the D37 COST Action, we have further developed the quantum dynamics framework of the grid empowered molecular simulator (GEMS) implemented on the segment of the European grid available to the COMPCHEM (computational chemistry) virtual organization. GEMS does now include in a full ab initio approach, the evaluation of the detailed quantum (both time dependent and time independent) dynamics of small systems starting from the calculation of the electronic structure properties as well as the direct calculation of thermalized properties. Illustrative, full dimensional applications of the extended simulator to the H + H(2) , N + N(2) , and O + O(2) systems are presented.     

Resonances in three-dimensional H + HLi scattering: a time-dependent wave packet dynamical study

This paper examines the resonances in H + HLi scattering. The signature of these resonances is obtained from the oscillations in its reaction probability versus energy curves. They are identified here from a set of pseudospectra calculated for different initial locations of a stationary Gaussian wave packet on the ab initio potential energy surface (PES) reported by Dunne, Murrel, and Jemmer. The nuclear motion on this PES is monitored with the aid of a time-dependent wave packet method and the pseudospectrum are calculated by Fourier transforming the time autocorrelation function of the initial wave packet. The resonances are further examined and assigned by computing their eigenfunctions through spectral quantization algorithm. Both the linewidth as well as decay lifetimes of the resonances are reported.     

Extended wave packet dynamics; exact solution for collinear atom,diatomic molecule scattering

The semiclassical wave packet dynamics method of Heller is extended to provide a formally exact theory of quantum mechanical motion for multidimensional anharmonic systems by introducing a complete, orthonormal, time-dependent basis of generalized oscillator functions. The exact wavefunction is expressed in terms of this basis and the expansions are shown to develop according to linear, coupled first-order differential equations. Application to collinear inelastic atom-diatomic molecule scattering demonstrates the feasibility and convergence of the new method.     

Multidimensional reactive scattering with quantum trajectories: dynamics with Morse vibrational modes

The reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the time-dependent Schrodinger equation.     

A quantum wave packet dynamical study of the electronic and spin-orbit coupling effects on the resonances in Cl(2P) + H2 scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.     

Benchmark studies of the BCRLM reactive scattering code: Implications for accurate quantum calculations

Summary The Bending Corrected Rotating Linear Model (BCRLM), developed by Hayes and Walker, is a simple approximation to the true multidimensional scattering problem for reactions of the type: A + BC AB + C. While the BCRLM method is simpler than methods designed to obtain accurate three-dimensional quantum scattering results, this turns out to be a major advantage in terms of our benchmarking studies. The computer code used to obtain BCRLM scattering results is written for the most part in standard FORTRAN and has been ported to several scalar, vector, and parallel architecture computers including the IBM 3090-600J, the Cray XMP and YMP, the Ardent Titan, IBM RISC System/6000, Convex C-1 and the MIPS 2000. Benchmark results will be reported for each of these machines with an emphasis on comparing the scalar, vector, and parallel performance for the standard code with minimum modifications. Detailed analysis of the mapping of the BCRLM approach onto both shared and distributed memory parallel architecture machines indicates the importance of introducing several key changes in the basic strategy and algorithms used to calculate scattering results. This analysis of the BCRLM approach provides some insights into optimal strategies for mapping three-dimensional quantum scattering methods, such as the Parker-Pack method, onto shared or distributed memory parallel computers.     

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.