Energy transfer in classical collinear and perpendicular central collisions of a structureless atom with a morse oscillator

The energy transfer in classical collinear (C_∞) and perpendicular (C_2v) central collisions of an atom with a Morse oscillator is compared. These collision geometries contribute in classical collisions to experimentally observed inelastic backward scattering of alkali ions from H₂ molecules. For both collision geometries the equations of motion reduce to a set of only two coupled differential equations which can be easily solved numerically. The calculations show that the C_2v collisions are much more effective than C_∞ collisions at all but the very lowest energies. The calculated ΔE/E versus E curves for C_2v collisions using a Born-Mayer potential for the atom atom-in-molecule interaction could be fitted to the experimental results for Na⁺-D₂ yielding reasonable potential values.     

Dynamical regimes on the Cl + H2 collisions: inelastic rainbow scattering

While Cl + H(2) reactive collisions have been a subject of numerous experimental and theoretical studies, inelastic collisions leading to rotational energy transfer and/or vibrational excitation have been largely ignored. In this work, extensive quantum mechanical calculations covering the 0.5-1.5 eV total energy range and various initial rovibrational states have been carried out and used to perform a joint study of inelastic and reactive Cl + H(2) collisions. Quasiclassical trajectories calculations complement the quantum mechanical results. The analysis of the inelastic transition probabilities has revealed the existence of two distinct dynamical regimes that correlate with low and high impact parameters, b, and are neatly separated by glory scattering. It has been found that while high-b collisions are mainly responsible for |Δj| = 2 transitions which dominate the inelastic scattering, they are very inefficient in promoting higher |Δj| transitions. The effectiveness of this type of collision also drops with rotational excitation of H(2). In contrast, reactive scattering, that competes with |Δj|?> 2 inelastic transitions, is exclusively caused by low-b collisions, and it is greatly favored when the reactants get rotationally excited. Previous studies focusing on the reactivity of the Cl + H(2) system established that the van der Waals well located in the entrance channel play a key role in determining the mechanism of the collisions. Our results prove this to be also a case for inelastic processes, where the origin of the double dynamical regime can be traced back to the influence exerted by this well that shapes the topology of the entrance channel of the Cl-H(2) system.     

Collisional line shapes for low frequency vibrations of adsorbates on a metal surface

The dynamics of atoms or molecules adsorbed on a metal surface, and excited by collisions with an atomic beam, are treated within a theory that includes energy dissipation into lattice vibrations by means of a frequency and temperature dependent friction function. The theory provides dynamic structure factors for energy transfer derived from collisional time correlation functions. It describes the relaxation of a vibrationally excited atom or molecule within a model of a damped quantum harmonic oscillator bilinearly coupled to a bath of lattice oscillators. The collisional time correlation function is generalized to include friction effects and is applied to the vibrational relaxation of the frustrated translation mode of Na adsorbed on a Cu(001) surface, CO on Cu(001), and CO on Pt(111), following excitation by collisions with He atoms. Results for the frequency shift and width of line shapes versus surface temperature are in very good agreement with experimental measurements of inelastic He atom scattering. Our interpretation of the experimental results provides insight on the relative role of phonon versus electron-hole relaxation.     

Simultaneous integration of mixed quantum-classical systems by density matrix evolution equations using interaction representation and adaptive time step integrator

A density matrix evolution method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem., 97, 13464 (1993)] to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five-level quantum harmonic oscillator. We improved the numerical performance by rewriting the Liouville–von Neumann equation in the interaction representation and so eliminated the frequencies of the unperturbed oscillator. Furthermore, replacement of the fixed time step fourth-order Runge–Kutta integrator with an adaptive step size control fourth-order Runge–Kutta resulted in significantly lower computational effort at the same desired accuracy. © 1996 by John Wiley & Sons, Inc.     

Transition probabilities of a string oscillator subject to impulsive collisions with a heavy mass point

Impulsive linear collisions between a string oscillator (a one-dimensional particle in a box) and a mass point are studied quantum mechanically. In the limit of a very heavy mass point (which corresponds classically to many collisions during a single encounter) the transition probabilities are determined exactly. The result permits a discussion of the mixed quantum-classical regime where the collider becomes almost classical while the oscillator remains quantum mechanical. While the average transition probabilities P(m-->n) are well reproduced by the Ehrenfest mean-field approximation, the prediction for the superimposed high-frequency resonance structure is qualitatively wrong for a genuine quantum oscillator. Only if the oscillator is also almost classical and if (m-n)2 square root(mu) < m, where mu is the mass ratio collider/oscillator, this structure is correctly predicted by the Ehrenfest approximation.     

Interaction and dynamics of collisional energy transfers in simple ion-molecule systems

The possible selective pathways for the excitations of vibrational and/or rotational modes of the hydrogen molecule in collisions with two, apparently simple, ionic projectiles (H⁺ and H^-) are studied in detail using quantum-mechanical coupled channels methods and a sudden-type of partial decoupling approximation discussed in the main text. The relevant potential energy surfaces (PES’s) are obtained from the existing literature and an extensive comparison of their features in relation of possible outcomes from inelastic collisions is carried out. The final state-to-state inelastic cross sections, partial integral and differential, are computed and compared with earlier calculations and with the existing experiments. The behaviour of such observables, and their relations with the PES features, help us to shed light on the microscopic mechanisms of collisional energy transfers in some of the simplest ion-molecule and to underline the dynamical effects which stem from their structural differences.     

Quantum dynamics of rovibrational transitions in H2-H2 collisions: internal energy and rotational angular momentum conservation effects

We present a full dimensional quantum mechanical treatment of collisions between two H(2) molecules over a wide range of energies. Elastic and state-to-state inelastic cross sections for ortho-H(2)?+ para-H(2) and ortho-H(2)?+ ortho-H(2) collisions have been computed for different initial rovibrational levels of the molecules. For rovibrationally excited molecules, it has been found that state-to-state transitions are highly specific. Inelastic collisions that conserve the total rotational angular momentum of the diatoms and that involve small changes in the internal energy are found to be highly efficient. The effectiveness of these quasiresonant processes increases with decreasing collision energy and they become highly state-selective at ultracold temperatures. They are found to be more dominant for rotational energy exchange than for vibrational transitions. For non-reactive collisions between ortho- and para-H(2) molecules for which rotational energy exchange is forbidden, the quasiresonant mechanism involves a purely vibrational energy transfer albeit with less efficiency. When inelastic collisions are dominated by a quasiresonant transition calculations using a reduced basis set involving only the quasiresonant channels yield nearly identical results as the full basis set calculation leading to dramatic savings in computational cost.     

Non-exponential correlation function in DPR: A comparison of experiment and the distorted wave born approximation

The recently observed non-exponential decay of the correlation function for the depolarized Rayleigh (DPR) line in N₂ is examined by a partial calculation of the cross section. The calculation, which is based upon a distorted wave Born approximation (DWBA), shows that the presence of inelastic collisions is necessary to account for the experimental results. Moreover, the inclusion of inelastic collisions has the consequence that the diagonal elements of the relaxation matrix are virtually constant rather than dying off as [j(j + 1)]^?1.     

Cold collisions of an open-shell S-state atom with a 2Π molecule: N(4S) colliding with OH in a magnetic field

We present quantum-theoretical studies of collisions between an open-shell S-state atom and a (2)Π-state molecule in the presence of a magnetic field. We analyze the collisional Hamiltonian and discuss possible mechanisms for inelastic collisions in such systems. The theory is applied to the collisions of the nitrogen atom ((4)S) with the OH molecule, with both collision partners initially in fully spin-stretched (magnetically trappable) states, assuming that the interaction takes place exclusively on the two high-spin (quintet) potential energy surfaces. The surfaces for the quintet states are obtained from spin-unrestricted coupled-cluster calculations with single, double, and noniterative triple excitations. We find substantial inelasticity, arising from strong couplings due to the anisotropy of the interaction potential and the anisotropic spin-spin dipolar interaction. The mechanism involving the dipolar interaction dominates for small magnetic field strengths and ultralow collision energies, while the mechanism involving the potential anisotropy prevails when the field strength is larger (above 100 G) or the collision energy is higher (above 1 mK). The numerical results suggest that sympathetic cooling of magnetically trapped OH by collisions with ultracold N atoms will not be successful at higher temperatures.     

一维精确量子散射研究——H+ClH(u)在反应势能面上的振动去激

HCl化学激光中存在振动激发的HCl及游离的H和Cl,故HCl在H原子和Cl原子碰撞下振动弛豫速率过程的研究很重要。不久前我们报道了Cl原子对HCl碰撞去激的一维精确量子散射研究,本文用类似方法,讨论H原子对激发态的HCl的碰撞去激。     

Monte Carlo Simulation of Electron Transport and X-Ray Generation. II. Radiative Processes and Examples in Electron Probe Microanalysis

Theoretical models for Monte Carlo simulation of radiative processes, i.e. bremsstrahlung and characteristic x-ray emission, are presented. Possible strategies for simulating electron transport are briefly described. For mechanisms involving energy loss and angular deflections, difficulties for strict implementation of accurate numerical differential cross sections still remain due to the strong correlations between these variables. Practical solutions for the case of inelastic collisions and bremsstrahlung emission are described. Comparisons of simulation results with experimental data for several problems of interest in electron probe microanalysis are presented.     

Theoretical study of inelastic collisions of hot atoms

In this work, use is made of the integral-equation approach to study inelastic collisions so frequently encountered in hot-atom chemistry. To do this a few assumptions are made which on the one hand enable the analytic derivation and on the other hand are still real enough in the sense that the solution obtained is valid and meaningful. It is found that the inelasticity in the collision between a hot atom and a reactive molecule manifests itself as a parameter which can be defined only by analogy as the average energy loss in an inelastic collision.     

Numerical solution for itinerant libration in two dimensions

The planar itinerant oscillator model of molecular motion in a structured fluid, developed recently by Coffey et al., is simulated by invoking collisions between 120 rough annuli within which are harmonically bound disks carrying a dipole unit vector u. It is found that the stochastic equations of motion of the analytical treatment produce results which can be reproduced very accurately with the deterministic equations of motion used in the computer simulation. This implies that the simulation may be extended to problems beyond analytical tractability, such as itinerant libration in three dimensions, and libration combined with centre of mass oscillation. The use of a model such as this is considered as intermediate between simple brownian-motion theory and a full scale simulation of polyatomics.     

DynamO: a free O(N) general event-driven molecular dynamics simulator

Molecular dynamics algorithms for systems of particles interacting through discrete or "hard" potentials are fundamentally different to the methods for continuous or "soft" potential systems. Although many software packages have been developed for continuous potential systems, software for discrete potential systems based on event-driven algorithms are relatively scarce and specialized. We present DynamO, a general event-driven simulation package, which displays the optimal O(N) asymptotic scaling of the computational cost with the number of particles N, rather than the O(N) scaling found in most standard algorithms. DynamO provides reference implementations of the best available event-driven algorithms. These techniques allow the rapid simulation of both complex and large (>10(6) particles) systems for long times. The performance of the program is benchmarked for elastic hard sphere systems, homogeneous cooling and sheared inelastic hard spheres, and equilibrium Lennard-Jones fluids. This software and its documentation are distributed under the GNU General Public license and can be freely downloaded from http://marcusbannerman.co.uk/dynamo.     

Orientation effects in Cl + H2 inelastic collisions: characterization of the mechanisms

Based on quantum mechanical scattering (QM) calculations, we have analyzed the polarization of the product hydrogen molecule in Cl + H(2) (v = 0, j = 0) inelastic collisions. The spatial arrangements adopted by the rotational angular momentum and internuclear axis of the departing molecule have been characterized and used to prove that two distinct mechanisms, corresponding to different dynamical regimes, are responsible for the inelastic collisions. Such mechanisms, named as low-b and high-b, correlate with well defined ranges of impact parameter values, add in an essentially incoherent way, and can be clearly differentiated through the quantum mechanical polarization moment that measures the orientation of the products rotational angular momentum with respect to the scattering plane. Other directional effects turn out to fail when it comes to distinguishing the mechanisms. Quasiclassical trajectories (QCT) calculations have been used as a supplement to the purely quantum mechanical analysis. By combining QM and QCT results, which are in very good agreement, we have succeeded in obtaining a clear and meaningful picture of how the two types of collisions take place.     

Theoretical investigation of hyperthermal reactions at the gas-liquid interface: O (3P) and squalane

Hyperthermal collisions (5 eV) of ground-state atomic oxygen [O ((3)P)] with a liquid-saturated hydrocarbon, squalane (C(30)H(62)), have been studied using QM/MM hybrid "on-the-fly" direct dynamics. The surface structure of the liquid squalane is obtained from a classical molecular dynamics simulation using the OPLS-AA force field. The MSINDO semiempirical Hamiltonian is combined with OPLS-AA for the QM/MM calculations. In order to achieve a more consistent and efficient simulation of the collisions, we implemented a dynamic partitioning of the QM and MM atoms in which atoms are assigned to QM or MM regions based on their proximity to "seed" (open-shell) atoms that determine where bond making/breaking can occur. In addition, the number of seed atoms is allowed to increase or decrease as time evolves so that multiple reactive events can be described. The results show that H abstraction is the most important process for all incident angles, with H elimination, double H abstraction, and C-C bond cleavage also being important. A number of properties of these reactive channels, as well as inelastic nonreactive scattering, are investigated, including angular and translational energy distributions, the effect of incident collision angle, variation with depth of the reactive event within the liquid, with the reaction site on the hydrocarbon, and the effect of dynamics before and after reaction (direct reaction versus trapping reaction-desorption).     

Generalization of the Forster resonance energy transfer theory for quantum mechanical modulation of the donor-acceptor coupling

The Forster resonance energy transfer theory is generalized for inelastic situations with quantum mechanical modulation of the donor-acceptor coupling. Under the assumption that the modulations are independent of the electronic excitation of the donor and the acceptor, a general rate expression is derived, which involves two dimensional frequency-domain convolution of the donor emission line shape, the acceptor absorption line shape, and the spectral density of the modulation of the donor-acceptor coupling. For two models of modulation, detailed rate expressions are derived. The first model is the fluctuation of the donor-acceptor distance, approximated as a quantum harmonic oscillator coupled to a bath of other quantum harmonic oscillators. The distance fluctuation results in additional terms in the rate, which in the small fluctuation limit depend on the inverse eighth power of the donor-acceptor distance. The second model is the fluctuation of the torsional angle between the two transition dipoles, which is modeled as a quantum harmonic oscillator coupled to a bath of quantum harmonic oscillators and causes sinusoidal modulation of the donor-acceptor coupling. The rate expression has new elastic and inelastic terms, depending sensitively on the value of the minimum energy torsional angle. Experimental implications of the present theory and some of the open theoretical issues are discussed.     

Direct determination of collision rates beyond the Lennard-Jones model through state-resolved measurements of strong and weak collisions

We describe a new approach for measuring absolute rates for molecular collisions including contributions of both strong and weak collisions. Elastic and inelastic collisions are monitored using high-resolution transient IR spectroscopy by measuring increases in the velocity distributions of individual rotational states of scattered molecules. Weak collisional energy transfer is detected by measuring velocity increases for the low-energy rotational states. This technique is illustrated for the collisional relaxation of highly vibrationally excited pyrazine (108 kcal/mol) with HOD. The observed collision rate is nearly twice the Lennard-Jones collision rate.     

The inelastic hard dimer gas: a nonspherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution alpha<1, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting nonequilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalize to inelastic systems a recently method introduced [G. Ciccotti and G. Kalibaeva, J. Stat. Phys. 115, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres held together by rigid bonds. Each dimer consists of two hard disks of diameter d, whose centers are separated by a fixed distance a. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event-driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law t(-2), describing how the kinetic energy of an inelastic hard-sphere system with a constant coefficient of restitution decreases in time, holds even in the case of these nonspherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.