760 research outputs found
Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method
The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom–diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10^–8. For such low-probability events the anteater sampling scheme requires a large number of trajectories (~10^10) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10^5 trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm
Uniform approximation of barrier penetration in phase space
A method to approximate transmission probabilities for a nonseparable
multidimensional barrier is applied to a waveguide model. The method uses
complex barrier-crossing orbits to represent reaction probabilities in phase
space and is uniform in the sense that it applies at and above a threshold
energy at which classical reaction switches on. Above this threshold the
geometry of the classically reacting region of phase space is clearly reflected
in the quantum representation. Two versions of the approximation are applied. A
harmonic version which uses dynamics linearised around an instanton orbit is
valid only near threshold but is easy to use. A more accurate and more widely
applicable version using nonlinear dynamics is also described
The quantum-classical correspondence principle for work distributions
For closed quantum systems driven away from equilibrium, work is often
defined in terms of projective measurements of initial and final energies. This
definition leads to statistical distributions of work that satisfy
nonequilibrium work and fluctuation relations. While this two-point measurement
definition of quantum work can be justified heuristically by appeal to the
first law of thermodynamics, its relationship to the classical definition of
work has not been carefully examined. In this paper we employ semiclassical
methods, combined with numerical simulations of a driven quartic oscillator, to
study the correspondence between classical and quantal definitions of work in
systems with one degree of freedom. We find that a semiclassical work
distribution, built from classical trajectories that connect the initial and
final energies, provides an excellent approximation to the quantum work
distribution when the trajectories are assigned suitable phases and are allowed
to interfere. Neglecting the interferences between trajectories reduces the
distribution to that of the corresponding classical process. Hence, in the
semiclassical limit, the quantum work distribution converges to the classical
distribution, decorated by a quantum interference pattern. We also derive the
form of the quantum work distribution at the boundary between classically
allowed and forbidden regions, where this distribution tunnels into the
forbidden region. Our results clarify how the correspondence principle applies
in the context of quantum and classical work distributions, and contribute to
the understanding of work and nonequilibrium work relations in the quantum
regime.Comment: 22 pages, 9 figure
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008)
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Parallel Implementation of Semiclassical Transition State Theory
This paper presents the parsctst code, an efficient parallel implementation of the semiclassical transition state theory (SCTST) for reaction rate constant calculations. Parsctst is developed starting from a previously presented approach for the computation of the vibrational density of states of fully coupled anharmonic molecules (Nguyen et al. Chem. Phys. Lett. 2010, 499, 915). The parallel implementation makes it practical to tackle reactions involving more than 100 fully coupled anharmonic vibrational degrees of freedom and also includes multidimensional tunneling effects. After describing the pseudocode and demonstrating its computational efficiency, we apply the new code for estimating the rate constant of the proton transfer isomerization reaction of the 2,4,6-tri-tert-butylphenyl to 3,5-di-tert-butylneophyl. Comparison with both theoretical and experimental results is presented. Parsctst code is user-friendly and provides a significant computational time saving compared to serial calculations. We believe that parsctst can boost the application of SCTST as an alternative to the basic transition state theory for accurate kinetics modeling not only in combustion or atmospheric chemistry, but also in organic synthesis, where bigger reactive systems are encountered
Atomic and molecular data for spacecraft re-entry plasmas
The modeling of atmospheric gas, interacting with the space vehicles in re-entry conditions in planetary exploration missions, requires a large set of scattering data for all those elementary processes occurring in the system. A fundamental aspect of re-entry problems is represented by the strong non-equilibrium conditions met in the atmospheric plasma close to the surface of the thermal shield, where numerous interconnected relaxation processes determine the evolution of the gaseous system towards equilibrium conditions. A central role is played by the vibrational exchanges of energy, so that collisional processes involving vibrationally excited molecules assume a particular importance. In the present paper, theoretical calculations of complete sets of vibrationally state-resolved cross sections and rate coefficients are reviewed, focusing on the relevant classes of collisional processes: resonant and non-resonant electron-impact excitation of molecules, atom-diatom and molecule-molecule collisions as well as gas-surface interaction. In particular, collisional processes involving atomic and molecular species, relevant to Earth (N2, O2, NO), Mars (CO2, CO, N2) and Jupiter (H2, He) atmospheres are considered
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