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The constrained adiabatic trajectory method (CATM) is reexamined as an integrator for the Schrödinger equation. An initial discussion places the CATM in the context of the different integrators used in the literature for time-independent or explicitly time-dependent Hamiltonians. The emphasis is put on adiabatic processes and within this adiabatic framework the interdependence between the CATM, the wave operator, the Floquet, and the (t, t′) theories is presented in detail. Two points are then more particularly analyzed and illustrated by a numerical calculation describing the H2+ ion submitted to a laser pulse. The first point is the ability of the CATM to dilate the Hamiltonian spectrum and thus to make the perturbative treatment of the equations defining the wave function possible, possibly by using a Krylov subspace approach as a complement. The second point is the ability of the CATM to handle extremely complex time-dependencies, such as those which appear when interaction representations are used to integrate the system. [ABSTRACT FROM AUTHOR]

A quasi-classical study of the endoergic Au+(1S) + H2(X1Σg+) → AuH+ (2Σ+) + H(2S) reaction, and isotopic variants, is performed to compare with recent experimental results [F. Li, C. S. Hinton, M. Citir, F. Liu, and P. B. Armentrout, J. Chem. Phys. 134, 024310 (2011)]. For this purpose, a new global potential energy surface has been developed based on multi-reference configuration interaction ab initio calculations. The quasi-classical trajectory results show a very good agreement with the experiments, showing the same trends for the different isotopic variants of the hydrogen molecule. It is also found that the total dissociation into three fragments, Au++H+H, is the dominant reaction channel for energies above the H2 dissociation energy. This results from a well in the entrance channel of the potential energy surface, which enhances the probability of H-Au-H insertion. [ABSTRACT FROM AUTHOR]

Quasiclassical trajectory calculations are compared, with classical and Wigner sampling of transition state (TS) energy levels, for C2H5F≠→HF+C2H4 product energy partitioning and [Cl...CH3...Cl]- central barrier dynamics. The calculations with Wigner sampling are reported here for comparison with the previously reported calculations with classical sampling [Y. J. Cho et al., J. Chem. Phys. 96, 8275 (1992); L. Sun and W. L. Hase, J. Chem. Phys. 121, 8831 (2004)]. The C2H5F≠ calculations were performed with direct dynamics at the MP2/6-31G* level of theory. Classical and Wigner sampling give post-transition state dynamics, for these two chemical systems, which are the same within statistical uncertainties. This is a result of important equivalences in these two sampling methods for selecting initial conditions at a TS. In contrast, classical and Wigner sampling often give different photodissociation dynamics [R. Schinke, J. Phys. Chem. 92, 3195 (1988)]. Here the sampling is performed for a vibrational state of the ground electronic state potential energy surface (PES), which is then projected onto the excited electronic state’s PES. Differences between the ground and the excited PESs may give rise to substantially different excitations of the vibrational and dissociative coordinates on the excited state PES by classical and Wigner sampling, resulting in different photodissociation dynamics. [ABSTRACT FROM AUTHOR]

We report results of a classical trajectory calculation of the postquenching dynamics of OH A 2∑+ by H2. This is done by performing roughly 100 000 trajectories at previously identified conical intersections (CoIs) [B. C. Hoffman and D. R. Yarkony, J. Chem. Phys. 113, 10091 (2000)]. The initial momenta are sampled fully and partially microcanonically, corresponding to “adiabatic” and “diabatic” model of the dynamics, respectively. The trajectories are propagated on a new ground state ab initio-based potential energy surface. This surface is a permutationally invariant fit to roughly 23 000 electronic energies (multireference configuration interaction/correlation-consistent-augmented-triple-zeta basis) at configurations obtained mostly from direct-dynamics calculations (complete active space second order perturbation theory with correlation-consistent-augment double-zeta basis), also initiated at the CoIs. Final rovibrational state distributions of the ground electronic state OH product and the H-atom translational energy distributions for abstraction and insertion mechanisms are calculated and compared to experimental ones. Agreement for these observable quantities is good. The branching between reactive and nonreactive quenching is sensitive to the momenta sampling; very good agreement with experiment is obtained using the diabatic sampling but not with the adiabatic sampling. The calculated H2 rovibrational distributions (not measured experimentally) are also presented. [ABSTRACT FROM AUTHOR]

Transition path sampling has been established as a powerful tool for studying the dynamics of rare events. The trajectory generation moves of this Monte Carlo procedure, shooting moves and shifting modes, were developed primarily for rate constant calculations, although this method has been more extensively used to study the dynamics of reactive processes. We have devised and implemented three alternative trajectory generation moves for use with transition path sampling. The centering-shooting move incorporates a shifting move into a shooting move, which centers the transition period in the middle of the trajectory, eliminating the need for shifting moves and generating an ensemble where the transition event consistently occurs near the middle of the trajectory. We have also developed varied-perturbation size shooting moves, wherein smaller perturbations are made if the shooting point is far from the transition event. The trajectories generated using these moves decorrelate significantly faster than with conventional, constant sized perturbations. This results in an increase in the statistical efficiency by a factor of 2.5–5 when compared to the conventional shooting algorithm. On the other hand, the new algorithm breaks detailed balance and introduces a small bias in the transition time distribution. We have developed a modification of this varied-perturbation size shooting algorithm that preserves detailed balance, albeit at the cost of decreased sampling efficiency. Both varied-perturbation size shooting algorithms are found to have improved sampling efficiency when compared to the original constant perturbation size shooting algorithm. [ABSTRACT FROM AUTHOR]

We use the fewest switches nonadiabatic trajectory surface hopping approach to study the photodissociation of methane on its lowest singlet excited state potential surface (1 1T2) at 122 nm, with emphasis on product state branching and energy partitioning. The trajectories and couplings are based on CASSCF(8,9) calculations with an aug-cc-pvdz basis set. We demonstrate that nonadiabatic dynamics is important to describe the dissociation processes. We find that CH3(X 2A2″)+H and CH2(ã 1A1)+H2 are the major dissociation channels, as have been observed experimentally. CH3+H is mostly formed by direct dissociation that is accompanied by hopping to the ground state. CH2+H2 can either be formed by hopping to the ground state to give CH2(ã 1A1)+H2 or by adiabatic dissociation to CH2(b 1B1)+H2. In the latter case, the CH2(b 1B1) can then undergo internal conversion to the ground singlet state by Renner–Teller induced hopping. Less important dissociation mechanisms lead to CH2+H+H and to CH+H2+H. Intersystem crossing effects, which are not included, do not seem essential to describe the experimentally observed branching behavior. About 5% of trajectories involve a roaming atom mechanism which can eventually lead to formation of products in any of the dissociation channels. Branching fractions to give H and H2 are in good agreement with experiment, and the H atom translational energy distribution shows bimodal character which also matches observations. [ABSTRACT FROM AUTHOR]

We demonstrate that the ring-polymer molecular dynamics (RPMD) method is equivalent to an automated and approximate implementation of the “Im F” version of semiclassical instanton theory when used to calculate reaction rates in the deep-tunneling regime. This explains why the RPMD method is often reliable in this regime and also shows how it can be systematically improved. The geometry of the beads at the transition state on the ring-polymer potential surface describes a finite-difference approximation to the “instanton” trajectory (a periodic orbit in imaginary time βh on the inverted potential surface). The deep-tunneling RPMD rate is an approximation to the rate obtained by applying classical transition-state theory (TST) in ring-polymer phase-space using the optimal dividing surface; this TST rate is in turn an approximation to a free-energy version of the Im F instanton rate. The optimal dividing surface is in general a function of several modes of the ring polymer, which explains why centroid-based quantum-TSTs break down at low temperatures for asymmetric reaction barriers. Numerical tests on one-dimensional models show that the RPMD rate tends to overestimate deep-tunneling rates for asymmetric barriers and underestimate them for symmetric barriers, and we explain that this is likely to be a general trend. The ability of the RPMD method to give a dividing-surface-independent rate in the deep-tunneling regime is shown to be a consequence of setting the bead-masses equal to the physical mass. [ABSTRACT FROM AUTHOR]

A potential energy surface that describes the title reaction has been constructed by interpolation of ab initio data. Classical trajectory studies on this surface show that the total reaction rate is close to that predicted by a Langevin model, although the mechanism is more complicated than simple ion-molecule capture. Only the HCO++H product is observed classically. An estimate of the magnitude of rotational inelastic scattering is also reported. [ABSTRACT FROM AUTHOR]

The transition to spatial-temporal complexity exhibited by spiral waves under the effect of gravitational field in the Belousov–Zhabotinsky reaction is numerically studied on the basis of spiral tip dynamics. Successive transformations in tip trajectories are characterized as a function of the hydrodynamical parameter and attributed to a Ruelle–Takens–Newhouse scenario to chaos. The analysis describes the emergence of complexity in terms of the interplay between the evolution of the velocity field and concentration waves. In particular, (i) by mapping the tip motion in relation to some hydrodynamical pseudopotentials, the general mechanism by which the velocity field affects the tip trajectory is pointed out, and, (ii) by comparing the dynamical evolutions of local and mean properties associated with the inhomogeneous structures and to the velocity field, a surprising correlation is found. The results suggest that the reaction-diffusion-convection (RDC) coupling addresses the system to some general regimes, whose nature is imposed by the hydrodynamical contribution. More generally, RDC coupling would be formalized as the phenomenon that governs the system and drives it to chaos. [ABSTRACT FROM AUTHOR]

Multiconfiguration molecular mechanics (MCMM) was previously applied to calculate potential energies, gradients, and Hessians along a reaction path and in the large-curvature tunneling swath, and it was shown that one could calculate variational transition state theory rate constants with optimized multidimensional tunneling without requiring more than a few electronic structure Hessians. It was also used for molecular dynamics simulations of liquid-phase potentials of mean force as functions of a reaction coordinate. In the present article we present some improvements to the formalism and also show that with these improvements we can use the method for the harder problem of trajectory calculations on gas-phase bimolecular reactive collisions. In particular, we apply the MCMM algorithm to the model reaction OH+H2→H2O+H, for which we construct the global full-dimensional interpolated potential energy surfaces with various numbers of electronic structure Hessians and various molecular mechanics force fields, and we assess the quality of these fits by quasiclassical trajectory calculations. We demonstrate that chemical accuracy (1–2 kcal/mol) can be reached for a MCMM potential in dynamically important regions with a fairly small number of electronic structure Hessians. We also discuss the origins of the errors in the interpolated energies and a possible way to improve the accuracy. [ABSTRACT FROM AUTHOR]

A trajectory surface hopping algorithm is proposed, which stems from a mathematically rigorous analysis of propagation through conical intersections of potential energy surfaces. Since nonadiabatic transitions are only performed when a classical trajectory attains one of its local minimal surface gaps, the algorithm is called single switch surface hopping. Numerical experiments for a two mode Jahn–Teller system are presented, which illustrate the asymptotic justification of the method as well as its good performance in the physically relevant parameter range. [ABSTRACT FROM AUTHOR]

Projection of a Markov process with constant rates of transition to a small number of observable aggregated states can result in complex kinetics with memory. Here, we define the entropy production along a single sequence of aggregated states and show that it obeys detailed and integral fluctuation theorems. More importantly, we prove that projection shifts the distribution of entropy production over the ensemble of paths for a nonequilibrium process toward one characteristic of a system at equilibrium. This statement represents an analog of the second law of thermodynamics for path-dependent entropies and thus a new form of constraint of irreversible systems. Numeric examples are presented to illustrate these ideas. [ABSTRACT FROM AUTHOR]

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action S is taken to be complex [Y. Goldfarb et al., J. Chem. Phys. 125, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex action is able to overcome the main computational limitation of conventional Bohmian methods—the propagation of wave functions once nodes set in. In the vicinity of nodes, the quantum force in conventional Bohmian formulations exhibits rapid oscillations that present a severe numerical challenge. We show that within complex Bohmian mechanics, multiple complex initial conditions can lead to the same real final position, allowing for the accurate description of nodes as a sum of the contribution from two or more crossing trajectories. The idea is illustrated on the reflection amplitude from a one-dimensional Eckart barrier. We believe that trajectory crossing, although in contradiction to the conventional Bohmian trajectory interpretation, provides an important new tool for dealing with the nodal problem in Bohmian methods. [ABSTRACT FROM AUTHOR]

The absolute integral cross sections for the formation of HeH+ and HeD+ from the collisions of HD+(v,j=1)+He have been examined over a broad range of vibrational energy levels v=0–13 at the center-of-mass collision energies (ET) of 0.6 and 1.4 eV using the vacuum ultraviolet (VUV) pulsed field ionization photoelectron secondary ion coincidence method. The ET dependencies of the integral cross sections for products HeH+ and HeD+ from HD+(v=0–4)+He collisions in the ET range of 0–3 eV have also been measured using the VUV photoionization guided ion beam mass spectrometric technique, in which vibrationally selected HD+(v) reactant ions were prepared via excitation of selected autoionization resonances of HD. At low total energies, a pronounced isotope effect is observed in absolute integral cross sections for the HeH++D and HeD++H channels with significant favoring of the deuteron transfer channel. As v is increased in the range of v=0–9, the integral cross sections of the HeH++D channel are found to approach those of HeD++H. The observed velocity distributions of products HeD+ and HeH+ are consistent with an impulsive or spectator-stripping mechanism. Detailed quasiclassical trajectory (QCT) calculations are also presented for HD+(v,j=1)+He collisions at the same energies of the experiment. The QCT calculations were performed on the most accurate ab initio potential energy surface available. If the zero-point energy of the reaction products is taken into account, the QCT cross sections for products HeH+ and HeD+ from HD+(v)+He are found to be significantly lower than the experimental results at ET values near the reaction thresholds. The agreement between the experimental and QCT cross sections improves with translational energy. Except for prethreshold reactivity, QCT calculations ignoring the zero-point energy in the products are generally in good agreement with experimental absolute cross sections. The experimental HeH+/HeD+ branching ratios for the HD+(v=0–9)+He collisions are generally consistent with QCT predictions. The observed isotope effects can be rationalized on the basis of differences in thermochemical thresholds and angular momentum conservation constraints. [ABSTRACT FROM AUTHOR]

Quasiclassical trajectory calculations have been carried out for H2(v1=high)+H2(v2=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v1’s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H2(v1=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined. [ABSTRACT FROM AUTHOR]

We use a constant velocity steered molecular dynamics (SMD) simulation of the stretching of deca-alanine in vacuum to demonstrate a technique that can be used to create a surrogate processes approximation (SPA) using the time series that come out of SMD simulations. In this article, the surrogate processes are constructed by first estimating a sequence of local parametric diffusion models along a SMD trajectory and then a single global model is constructed by piecing the local models together through smoothing splines (estimation is made computationally feasible by likelihood function approximations). The SPAs are then “bootstrapped” in order to obtain a plausible range of work values associated with a particular SMD realization. This information is then used to assist in estimating a potential of mean force constructed by appealing to the Jarzynski equality. When this procedure is repeated for a small number of SMD paths, it is shown that the global models appear to come from a single family of closely related diffusion processes. Possible techniques for exploiting this observation are also briefly discussed. The findings of this paper have potential relevance to computationally expensive computer simulations and experimental works involving optical tweezers where it is difficult to collect a large number of samples, but possible to sample accurately and frequently in time. [ABSTRACT FROM AUTHOR]

The use of the Ehrenfest method to simulate the relaxation of molecules in solution is explored. Using the cyanide ion dissolved in water as a test model, the independent trajectory (IT) and the bundle of trajectories (BT) approximations are shown to provide very different results for the time evolution of the vibrational populations of the solute. None of these approximations reproduce the Boltzmann equilibrium vibrational populations accurately. A modification of the Ehrenfest method based on the use of quantum correction factors is thus proposed to solve this problem. The simulations carried out using the modified Ehrenfest method provide IT and BT relaxation times which are closer to each other and which agree quite well with previous hybrid perturbative results. [ABSTRACT FROM AUTHOR]

The temporal evolution of the entropy of a mechanical system as described by a single trajectory is computed using the Clausius [Philos. Mag. 40, 122 (1868)] equality. This requires computing the maximal work that can be done by the system and comparing it to the actual work performed. A single trajectory suffices to determine the entropy when it is “typical,” meaning that average values of mechanical variables will not be different when computed using trajectories with different initial conditions. The results are illustrated for small rare gas clusters heated and compressed by an impact at a hard surface. [ABSTRACT FROM AUTHOR]

Trajectory calculations of collisional energy transfer between excited azulene and Kr are reported, and the results are compared with recent crossed molecular beam experiments by Liu et al. [J. Chem. Phys. 123, 131102 (2005); 124, 054302 (2006)]. Average energy transfer quantities are reported and compared with results obtained before for azulene-Ar collisions. A collisional energy transfer probability density function P(E,E′), calculated at identical initial conditions as experiments, shows a peak at the up-collision branch of P(E,E′) at low initial relative translational energy. This peak is absent at higher relative translational energies. There is a supercollision tail at the down-collision side of the probability distribution. Various intermolecular potentials are used and compared. There is broad agreement between experiment and computation, but there are some differences as well. [ABSTRACT FROM AUTHOR]

The effect of finite trajectory length on single molecule rotational correlation functions has been studied by utilizing time series analysis and numerical simulations. Correlation functions obtained from the trajectories of length less than 100 times the correlation time constant (τℓ) exhibit significant deviations from the true correlation function. The distributions of sample time constants (τF) and stretching exponents (βF) are mapped by fitting a large number of rotational trajectories to stretched exponentials. As the trajectory length gets smaller, the distributions become broader and asymmetric and their mean values deviate from the true value predicted by pure rotational diffusion. Analysis based on higher order spherical harmonics is suggested as a method for minimizing the effect of the trajectory length. The distributions of time constants for different higher order spherical harmonics are also compared. While the focus of the paper is on rotational correlation functions, the general conclusions apply to any dynamical process that yields an exponentially decaying correlation function. [ABSTRACT FROM AUTHOR]

Trajectory calculations run on global potential energy surfaces have shown that the topology of the entrance channel has strong implications on the dynamics of the title reactions. This may explain why huge differences are observed between the rate constants calculated from global dynamical methods and those obtained from local methods that employ the same potential energy surfaces but ignore such topological details. Local dynamics approaches such as transition state-based theories should then be used with caution for fine-tuning potential energy surfaces, especially for fast reactions with polyatomic species since the key statistical assumptions of the theory may not be valid for all degrees of freedom. [ABSTRACT FROM AUTHOR]

A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic two-dimensional system confirm the efficiency of this approach. The results are compared to the standard fixed transition state dividing surface that is well-known to suffer from recrossings and therefore requires trajectories to be evolved over a long time interval before they can reliably be classified as reactive or nonreactive. The moving dividing surface can be used to identify reactive trajectories in harmonic or moderately anharmonic systems with considerably lower numerical effort or even without any simulation at all. [ABSTRACT FROM AUTHOR]

We present a generalized formulation of the trajectory surface hopping method applicable to a general multidimensional system. The method is based on the Zhu-Nakamura theory of a nonadiabatic transition and therefore includes the treatment of classically forbidden hops. The method uses a generalized recipe for the conservation of angular momentum after forbidden hops and an approximation for determining a nonadiabatic transition direction which is crucial when the coupling vector is unavailable. This method also eliminates the need for a rigorous location of the seam surface, thereby ensuring its applicability to a wide class of chemical systems. In a test calculation, we implement the method for the DH2+ system, and it shows a remarkable agreement with the previous results of C. Zhu, H. Kamisaka, and H. Nakamura, [J. Chem. Phys. 116, 3234 (2002)]. We then apply it to a diatomic-in-molecule model system with a conical intersection, and the results compare well with exact quantum calculations. The successful application to the conical intersection system confirms the possibility of directly extending the present method to an arbitrary potential of general topology. [ABSTRACT FROM AUTHOR]

Jarzynski’s [Phys. Rev. Lett. 78, 2690 (1997)] identity for the free-energy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phase-space mappings. Solving a system’s equation of motion by approximate means generates a mapping that is perfectly valid for this purpose, regardless of how closely the solution mimics true time evolution. We exploit this fact, using crudely dynamical trajectories to compute free-energy differences that are in principle exact. Numerical simulations show that Newton’s equation can be discretized to low order over very large time steps (limited only by the computer’s ability to represent resulting values of dynamical variables) without sacrificing thermodynamic accuracy. For computing the reversible work required to move a particle through a dense liquid, these calculations are more efficient than conventional fast-switching simulations by more than an order of magnitude. We also explore consequences of the phase-space mapping perspective for systems at equilibrium, deriving an exact expression for the statistics of energy fluctuations in simulated conservative systems. [ABSTRACT FROM AUTHOR]

Single-photon ionization dynamics of two conformers of glycine is studied by classical trajectory simulations using the semiempirical PM3 potential surface in “on the fly” calculations. Initial conditions for the trajectories are weighted according to the Wigner distribution function computed for the initial vibrational ground state. Vertical ionization in the spirit of the classical Franck–Condon principle is assumed. The dynamics of the two conformers are compared during the first 10 ps. The comparison shows very different dynamical behavior for the two conformers. In particular, the chemical fragmentation pathways differ in part. Also, one of the conformers gives much higher rates of conformational transitions, while the other conformer gives larger chemical fragmentation yields. The example shows significantly different chemical dynamics for two conformers close in energy and separated by a low barrier. [ABSTRACT FROM AUTHOR]

The triplet channel in the photodissociation of ozone in the Hartley band, O3+hν→O(3P)+O2(3Σ), is investigated by means of a classical trajectory surface hopping method using ab initio diabatic potential energy surfaces for the B and the R states. Because of the strong recoil in the R state along the breaking O–O bond, O2(3Σ) is produced with a high rotational energy. The nonadiabatic transition probability depends markedly on the coordinate along the crossing seam. As a consequence a unique correlation is found between the internuclear geometry at the crossing and the final vibrational state of O2(3Σ). The calculated distribution of the translational energy is in good accord with the measured distribution. [ABSTRACT FROM AUTHOR]

We utilize classical trajectory calculations to study the reaction dynamics of the dissociative adsorption of H2 on the stepped Pt(211) surface. The potential-energy surface has been obtained through an accurate interpolation of density-functional theory data at the generalized gradient approximation level, using the corrugation reduction procedure. New techniques for visualizing the collective dynamics of trajectories are introduced to elucidate the reaction mechanisms involved. Reaction exhibits a nonmonotonic dependence on collision energy, first decreasing with energy, and then increasing. A strong component of direct nonactivated reaction exists at the top edge of the step over the entire range of energies. The inverse relationship between reaction and collision energy at low energies is attributed to trapping in weak chemisorption wells. These wells also influence the direct reaction at the step, leading to a strong asymmetric dependence on incidence angle. Reaction on the terrace is activated, and only contributes significantly at high energies. Agreement with experiments on Pt(533) [A. T. Gee, B. E. Hayden, C. Mormiche, and T. S. Nunney, J. Chem. Phys. 112, 7660 (2000); Surf. Sci. 512, 165 (2002)] is good, and we are able to suggest new interpretations of the experimental data. [ABSTRACT FROM AUTHOR]

Quasiclassical trajectory calculations were carried out to determine product energy distributions for the HCl and HF eliminations that take place in the photodissociation of 2-chloro-1,1-difluoroethylene at 193 nm. The trajectories were initiated at the transition states of the HCl and HF elimination channels under microcanonical, quasiclassical conditions, and were propagated with the energies and gradients taken directly from density functional theory calculations. Good agreement with experiment is found, except for the translational energy distribution of the HF elimination channel and the average vibrational energy of the HCl fragment. Possible sources of disagreement are discussed. [ABSTRACT FROM AUTHOR]

The effect of zero-point energy differences (ΔZPE) between the possible fragmentation channels of highly excited O3 complexes on the isotope dependence of the formation of ozone is investigated by means of classical trajectory calculations and a strong-collision model. ΔZPE is incorporated in the calculations in a phenomenological way by adjusting the potential energy surface in the product channels so that the correct exothermicities and endothermicities are matched. The model contains two parameters, the frequency of stabilizing collisions ω and an energy dependent parameter Δdamp, which favors the lower energies in the Maxwell–Boltzmann distribution. The stabilization frequency is used to adjust the pressure dependence of the absolute formation rate while Δdamp is utilized to control its isotope dependence. The calculations for several isotope combinations of oxygen atoms show a clear dependence of relative formation rates on ΔZPE. The results are similar to those of Gao and Marcus [J. Chem. Phys. 116, 137 (2002)] obtained within a statistical model. In particular, like in the statistical approach an ad hoc parameter η≈1.14, which effectively reduces the formation rates of the symmetric ABA ozone molecules, has to be introduced in order to obtain good agreement with the measured relative rates of Janssen et al. [Phys. Chem. Chem. Phys. 3, 4718 (2001)]. The temperature dependence of the recombination rate is also addressed. [ABSTRACT FROM AUTHOR]

The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill behaved at caustics. In contrast, quantum trajectory methods—based on Bohmian mechanics (quantum hydrodynamics)—are characterized by divergent forces and erratic trajectories near nodes, but also well-behaved, single-valued representational functions. In this paper, we unify these two approaches into a single method that captures the best features of both, and in addition, satisfies the correspondence principle. Stationary eigenstates in one degree of freedom are the primary focus, but more general applications are also anticipated. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

For two methods commonly used to achieve canonical-ensemble sampling in a molecular-dynamics simulation, the Langevin thermostat and the Andersen [H. C. Andersen, J. Chem. Phys. 72, 2384 (1980)] thermostat, we observe, as have others, synchronization of initially independent trajectories in the same potential basin when the same random number sequence is employed. For the first time, we derive the time dependence of this synchronization for a harmonic well and show that the rate of synchronization is proportional to the thermostat coupling strength at weak coupling and inversely proportional at strong coupling with a peak in between. Explanations for the synchronization and the coupling dependence are given for both thermostats. Observation of the effect for a realistic 97-atom system indicates that this phenomenon is quite general. We discuss some of the implications of this effect and propose that it can be exploited to develop new simulation techniques. We give three examples: efficient thermalization (a concept which was also noted by Fahy and Hamann [S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)]), time-parallelization of a trajectory in an infrequent-event system, and detecting transitions in an infrequent-event system. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Termolecular collisions between a benzene molecule and two Ar atoms were studied by quasiclassical trajectory calculations. The calculations show that termolecular collisions form termolecular complexes and occur by three mechanisms: (a) the Chaperon mechanism, in which the first Ar in is the first Ar out of the termolecular complex, is the dominant one at high pressures. Two-thirds of all termolecular collisions go by this mechanism. (b) The energy transfer mechanism, in which the first Ar in is the last Ar out of the termolecular complex, comprises about a quarter of all termolecular collisions at high pressures. (c) The concerted channel, in which both argon atoms depart from the benzene simultaneously and does not lead to products in reactive systems, comprises about 10% of all termolecular collisions. Energy transfer quantities and collision complex lifetimes in binary and termolecular collisions are evaluated and their dependence on inter- and intramolecular harmonic and anharmonic potentials, temperature, pressure, and internal energy of the benzene molecule are reported. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report experiments where hexapole focusing is combined with stimulated emission pumping in a molecular beam, providing control over the molecule's rovibronic quantum numbers, its laboratory frame velocity and its transverse divergence. Hexapole focusing profiles can be quantitatively reproduced by classical trajectory simulations. These experiments provide new ways of manipulating beams of vibrationally excited molecules including: (1) transverse refocusing and concomitant improved efficiency for transport of the vibrationally excited molecules, (2) relative enrichment of the concentration of the vibrationally excited molecules with respect to the unexcited portion of the beam and, (3) orientation of vibrationally excited molecules. [ABSTRACT FROM AUTHOR]

This article constructs trajectories associated with various boundary conditions for the Smoluchowski equation on an interval. Single-particle diffusion processes are first constructed by taking the diffusion limits of random walks. The diffusion limit gives both boundary conditions which enforce the single-particle constraint and properties of underlying trajectories at those boundaries. Mean-field diffusions are then obtained as limits of sums of single-particle processes. The results help to interpret the application of diffusion models to both ion channels and wider pores that facilitate molecular transport across membranes. Potential applications to Brownian dynamics simulations are discussed. [ABSTRACT FROM AUTHOR]

Channel-specific transit time distributions for a two-level model system exhibiting simple avoided crossing are computed and interpreted in terms of a general semiclassical analysis which expresses wave packet evolution in terms of sums over complex trajectories. Novel effects observed include "quantum speedup" (the Hartman effect), for tunneling, and "quantum slowdown" for above-barrier reflection. Nonadiabatic effects are found to appear only at times for which their exponentially small amplitude is comparable or greater than the amplitude of adiabatic contributions. This is in accord with the semiclassical treatment provided. Nonadiabatic effects include, most notably, the appearance of slowly leaking resonances in the excited level potential energy well. [ABSTRACT FROM AUTHOR]

We present a modification of Tully's fewest-switches (TFS) trajectory surface-hopping algorithm (also called molecular dynamics with quantum transitions) that is called the fewest-switches with time uncertainty (FSTU) method. The FSTU method improves the self-consistency of the fewest-switches algorithm by incorporating quantum uncertainty into the hopping times of classically forbidden hops. This uncertainty allows an electronic transition that is classically forbidden at some geometry to occur by hopping at a nearby classically allowed geometry if an allowed hopping point is reachable within the Heisenberg interval of time uncertainty. The increased accuracy of the FSTU method is verified using a challenging set of three-body, two-state test cases for which accurate quantum-mechanical results are available. The FSTU method is shown to be more accurate than the TFS method in predicting total nonadiabatic quenching probabilities and product branching ratios. [ABSTRACT FROM AUTHOR]

We report quasiclassical trajectory calculations for the reaction O(¹D)+HCl using a recent modification of the potential of Peterson et al. [J. Chem. Phys. 111, 7446 (1999)] based on extensive additional ab initio calculations. The cross sections and branching ratio for the OH and C10 products are examined for HCI(v=0,j=0) at relative translational energies up to 0.53 eV. Comparisons are made with previous quantum calculations of this reaction using the same potential energy surface. The effects of vibrational and rotational excitation of the diatomic target and of the orientation of the rotational angular momentum on this branching ratio are also investigated. [ABSTRACT FROM AUTHOR]

A new implementation of the trajectory surface hopping (TSH) method is proposed to treat multidimensional nonadiabatic dynamics by incorporating the analytical Zhu–Nakamura semiclassical theory of nonadiabatic transition. The problem of classically forbidden hops in the TSH method can now be solved and dealt with just as easily as the classically allowed hops by introducing nonvertical hopping techniques. This is made possible, because the theory can treat both classically allowed and forbidden hops accurately in a unified way. The Zhu–Nakamura theory also enables us to predetermine important regions of potential energy surface before carrying out any dynamics calculations, and thus to save a lot of computational efforts. The charge transfer processes in the collinear H[sub 3][sup +] system are studied numerically to test the new TSH method. Comparing the new and old versions of TSH with exact quantum calculations, the new method shows much better agreement with the exact calculations. It also works well when all trasitions are classically forbidden and the old method fails completely. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Studies the ab initio classical trajectories on the Born-Oppenheimer surface. Outline of the Hessian-based integration scheme for classical trajectory calculations; Similarity between the electronic structure work per step and the second order Hessian based integrator; Fifth order polynomial fit to the potential energy surface.

Studies the ab initio classical trajectories on the Born-Oppenheimer surface through the Hessian-based integrators using fifth-order polynomial and rational function fits. Chemical reaction used to examine the behavior of the Hessian based integration schemes; Comparison of different step sizes in the integration of a trajectory.

Examines planar benzene overtone relaxation through quassiclassical trajectories computation. Description of the coordinate system, Hamiltonian and force field models; Conditions of trajectory simulation; Results of energy flow and survival probabilities calculation.

The problem of zero point energy in classical trajectory computations is discussed and illustrated by an example of dissociation where the zero point energy is used to provide the required energy. This is not possible in quantal dynamics. A proposed route to the alleviation of the problem, based on using classical-like trajectories which mimic the solution of the (expectation values) of Heisenberg equations of motion, is discussed. In general, one cannot simultaneously correct for all possible expectation values, so the remedy is at best partial. The variable whose expectation value and variance is to be handled correctly is examined in detail for a one-dimensional anharmonic potential, and is identified with the logarithmic derivative of the wave function in the Wentzel–Kramers–Brillouin (WKB) approximation. The multidimensional case is also discussed and it is pointed out that the zero point energy problem can be particularly severe for systems which exhibit a locally unstable classical motion. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Classical trajectory calculations of ion–permanent quadrupole+induced dipole capture processes are performed over wide ranges of conditions. The results are expressed in two-parametric analytical form, and analyzed with respect to the transition from sudden to adiabatic dynamics. The results are compared with the statistical adiabatic channel model (SACM). For this purpose, adiabatic channel potential curves are expressed in approximate analytical form. The agreement between classical trajectory and SACM results is excellent in the range of adiabatic quasiclassical motion of the collision partners. Analytical expressions can well describe the temperature variation of the capture rate constant in the transition range between the quantum and classical limits. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The nonstatistical behavior of a unimolecular reaction at energies well in excess of the threshold is examined. This behavior is sometimes referred to as ‘‘intrinsically non-Rice–Ramsperger–Kassel–Marcus’’ (RRKM). It is well known that microcanonical unimolecular rates computed by using classical mechanics can deviate from the predictions of statistical theories, particularly at high energies. The simplest manifestation of this behavior is that rate constants as a function of energy cannot be represented by simple expressions such as the RRK equation, k(E)=ν(1-E*/E)s-1, with a single set of parameter values over a wide energy range; more specifically, fits of the classical RRK expression to trajectory results frequently yield values for the effective number of degrees of freedom s that are significantly smaller than the ‘‘theoretical’’ values 3N-6. In the present study, rates were calculated for the unimolecular dissociation of dimethylnitramine, (CH3)2NNO2, by simple N–N bond rupture over wide energy ranges by using classical trajectories and Monte Carlo transition-state theory. The formalism of a diffusional theory of chemical reactions is used to develop a model that relates classical reaction rates to intramolecular vibrational energy redistribution (IVR). This model is based on the assumption that the molecular modes can be separated into reaction coordinate and energy reservoir modes. It is shown how this model can be used to extrapolate high-energy, nonstatistical classical trajectory rates to the low-energy, statistical region. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effect of linearly chirped pulses in condensed phase ultrafast pump–probe experiments is investigated by classical simulations for the model system of I2 isolated in a Kr matrix. The central frequency of the probe laser is selected to monitor exclusively the event of first collision and recoil of atoms from the host cage. It is shown that a chirped probe pulse enables characterization of the magnitude and sign of the momentum of the evolving trajectory flux. This can be understood by transforming the frequency–time profile of the probe pulse to coordinate–time space, and noting that the observable signal is a function of the relative group velocities of the traveling wave packet and the traveling window function. The effect of the pump pulse chirp, is a measure of the controllability of the evolving dynamics. In the particular case studied, breaking and remaking of the I2 bond near the dissociation limit of the bare molecule, it is shown that the memory of the system outlasts the collision with the cage. Negatively chirped pulses produce a more tightly focused wave packet during recoil, leading to a stronger population coherence in the subsequent dynamics. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Classical trajectory studies of CD2HNC isomerization have been carried out using a simple potential energy function. Mode-specific effects are found to be small, and the fastest rate of reaction is observed for a microcanonical ensemble. Comparison with the CH3NC isomerization reaction reveals an unexpected inverse secondary isotope effect. Rotational excitation about the molecular axis is found to enhance the rate of reaction more than rotation perpendicular to this axis. [ABSTRACT FROM AUTHOR]

The photodissociation reaction of ICN in the A continuum has been theoretically studied based on ab initio potential energy surfaces and classical trajectories. Ab initio contracted spin–orbit configuration interaction calculations have been carried out to obtain potential energy surfaces (PES’s) of 3Π1, 3Π0+ and 1Π1 excited states, where results are fit to five diabatic potential functions and their couplings as functions of all three internal degrees of freedom. The transition dipoles at the Franck–Condon region have also been calculated. All the PES’s involved in photodissociation are bent near the Franck–Condon region. Classical trajectory calculations performed on these potential surfaces have produced results that are in agreement with various experimental findings and provide a basis for their interpretation. The calculations indicate that the absorption is a mixture of parallel and perpendicular transition. A reasonable I/I* branching ratio can be obtained by considering the effect of initial bending vibrations in addition to the character of mixed transitions. The I/I* channel selectivity of the CN rotation can be compared to the shape of PES’s with respect to the bending angle. The rotational excitation of the CN fragment is determined by the shape of PES’s on which trajectories travel before and after the transition.The higher rotational component in the I channel is attributed to the energy gradient of 1Π1 with respect to the bending angle at the transition region where the C–I distance is between 5.0 and 8.0 a.u. The lower component in the I channel emerges from 3Π1. The average rotational distribution obtained with the proper weight of Boltzmann populations and transition intensities is in agreement with the experiment. This interpretation can also be applied to the rotational quantum number dependence of anisotropy parameters. Trajectory calculations on the 3Π1... [ABSTRACT FROM AUTHOR]

The atom–cluster association reaction I(Ar)n+I→I2+nAr (n=12) is studied theoretically as a prototypical model of the effect of microscopic solvation on reaction dynamics. Classical trajectory methods are employed to model the dynamics. This paper focuses on the initial capture of I by the I(Ar)12 cluster. Two distinct minimum energy configurations for I(Ar)12 are considered: Ar6(I)Ar6, an icosahedron with I located at the center of the cluster; and IAr12, an icosahedron with I replacing one of the vertex Ar atoms. Both the structure and the temperature dependence of the capture cross section are investigated. Capture rate constants at temperatures of 10 and 30 K are computed. Capture cross sections for Ar6(I)Ar6+I predicted by a Langevin model agree well with those computed by classical trajectory simulation, revealing that the capture process under investigation is determined by the long range interaction potential. In comparison with its gas phase counterpart I+I, Ar6(I)Ar6+I has a much larger capture cross section. One of the most important roles played by the microscopic solvation of chemical reactants in clusters is this enhancement of the cross section for the initial capture process. [ABSTRACT FROM AUTHOR]

Classical trajectory calculations are performed to determine differences in the microscopic dynamics for two fundamental processes for the Cla-+CH3Clb→ClaCH3+Clb- reactive system: Cla-–CH3Clb complex formation and directly attaining the [Cla–CH3–Clb]- central barrier without first forming the complex. This latter process becomes important when the C–Clb stretch mode is excited in the CH3Clb reactant. The total cross section for complex formation and directly attaining the central barrier increases as nC–Clb is increased. The value for the Cla-—C–Clb angle θ as the reactants interact, the dynamical stereochemistry, is found to be a very important property for distinguishing between the mechanisms for the two fundamental processes. Directly attaining the central barrier requires oriented reactants with θ≊π, while orientation suppresses complex formation. Substantial reactant orientation only occurs for CH3Clb rotational temperatures less than 300 K. The complex is formed by a T→R energy transfer process which involves coupling between the reactant orbital angular momentum and CH3Clb rotational angular momentum. Complex formation does not involve energy transfer to the CH3Clb vibrational modes, which is consistent with an earlier finding that the CH3Clb intramolecular modes are inactive during decomposition of the Cla-–CH3Clb complex. Orientation of CH3Clb enhances coupling between the Cla-+CH3Clb radial motion and the C–Clb stretch mode. This coupling leads to the above direct substitution process and extensive deactivation of the excited C–Clb stretch during direct unreactive collisions. Considerably less deactivation results from Cla-–CH3Clb complex formation followed by dissociation to the reactants. Rotationally exciting CH3Clb eliminates orientation and, thus, suppresses deactivation of the C–Clb stretch. [ABSTRACT FROM AUTHOR]

The O++H2 prototypic ion–molecule reaction was recently studied in our group using the quasiclassical trajectory method on a ground model potential-energy surface of the system inferred from both experimental and theoretical information and reasonable assumptions, fitted using a London–Eyring–Polanyi–Sato surface modified to include an ion–induced-dipole interaction term. The theoretical results previously reported agreed rather well with the available experimental information. In view of the latest experimental findings, we present in this contribution the results of new trajectory calculations on the above-mentioned surface, covering a wide range of relative translational energies of reactants. The accord between the experimental determinations and the present theoretical evaluations is excellent at relative energies below 1.0 eV, while for higher energies the potential-energy surface, even though still yielding reasonably good results, provides a worse agreement. The observed discrepancies should be attributed either to the too attractive character of the surface or to the interfering influence of the competing O++H2→O+H2+ charge-transfer process. [ABSTRACT FROM AUTHOR]