Trajectory Surface Hopping Method Research Articles

Comparison of trajectory surface-hopping and Monte Carlo phase-space theory predissociation rate constants for N 2O

We demonstrate that the Monte Carlo evaluation of a phase-space integral is a viable alternative to the more computationally expensive classical trajectory surface-hopping method for calculating unimolecular electronic predissociation rate constants. Rate constants for N 2O( 1Σ +)→N 2( 1Σ g ++O( 3P) calculated by classical trajectory surface-hopping and Monte Carlo phase-space theory methods are compared for angular momentum resolved microcanonical distributions.

Semiclassical calculation of state-selective electronic predissociation rate constants

State-selected rate constants for predissociation in collinear N 2O( 1Σ +)→N 2( 1Σ + g)+O( 3O) have been calculated by a classical trajectory surface-hopping method. Specific states (tori), corresponding to semiclassical states given by EBK theory, were found by using adiabatic switching. Potential-energy surfaces that cross were assumed since the nonadiabatic interaction is small. Most trajectories on the initial potential-energy surface are quasiperiodic. The rate constants computed for the various tori show fluctuations.

Classical path surface-hopping dynamics. I. General theory and illustrative trajectories

A formulation of a trajectory surface-hopping method is presented which starts with some of the basic ideas of the standard method, extends these to include more than two states, and enlists the classical-path equations not only to propagate through the nonadiabatic region but also to effect the transitions, or surface hops, themselves. The latter is accomplished by letting the Hamiltonian matrix elements in the time-dependent Schrödinger equation become complex, allowing manipulation of the fluctuation in the various adiabatic state populations. The procedure automatically conserves total energy and angular momentum as well as probability, and ensures that energetically inaccessible states are not significantly populated. In regions of extended degeneracy, the method resembles the standard classical-path approach with no surface hopping. In fact, the evolution of the wave function can be controlled to behave either as in the surface-hopping extreme or in the pure semiclassical extreme, allowing the method to be tailored to suit individual systems. The procedure is illustrated by application to a well-studied collision induced predissociation, Ne+He+2→Ne++He+He, where vibration in the entrance channel, Ne+He+2, leads to the strong nonadiabatic behavior responsible for the large observed cross sections. A few preliminary calculations for singly charged argon trimer ions produced in the ionization process Arn→Ar+n→Ar+2+(n−2)Ar, demonstrate that the formulation can be easily extended to include many degrees of freedom.

A three-dimensional quantum mechanical study of vibrationally resolved charge transfer processes in H++H2 at Ecm=20 eV

A three-dimensional quantum mechanical study of vibrational state resolved differential cross sections for the direct inelastic and charge transfer channels of the H++H2 system has been carried out at Ecm =20 eV using the infinite order sudden approximation (IOSA). Steric factors, opacity functions, angular distributions, and integral cross sections are calculated. The integral cross sections are in very good agreement with recent experimental results, whereas the angular distributions agree only partially with the experiments. A further comparison of both the theoretical and experimental results with semi-classical calculations based on the usual trajectory surface hopping method revealed that the present quantum results provide a better description of the experimental observations. The likely shortcomings of the semiclassical method are discussed.

A comparison between theoretical and experimental state-to-state charge transfer cross sections for H++H2 at 20 eV: Evidence for quantum effects

A three−dimensional close coupling quantum mechanics calculation is performed for hydrogen ion−molecule collisions. The results are compared to those obtained from the trajectory surface hopping method. (AIP)

A comparison of two classical trajectory surface hopping methods for Na(2P)+H2,D2 quenching

Trajectory surface hopping calculations were performed on optimized diatomics-in-molecules surfaces to study Na(2P) collisions with H2 and D2 molecules (v=0, j=1) at four different translational energies (0.039, 0.062, 0.101, and 0.140 eV). Two methods were used to predict surface hopping: (1) transformation of the multidimensional surface intersection to a local one-dimensional curve crossing and calculation of the Landau–Zener transition probability, and (2) integration of the coefficients of the adiabatic electronic states to determine transition probability. For all initial conditions used in this work, we found that method (2) gave significantly larger quenching cross sections. Also in this paper we present results that show nonadiabatic coupling terms calculated by the diatomics-in-molecules method are in good agreement with ab initio values.

Proton-Hydrogen collisions:

The trajectory surface hopping (TSH) method is used to compute product cross sections for the reactions H+ + D2, D+ + D2 and D+ + H2. They are compared with (mostly) integral cross sections obtained with a guided beam apparatus. The agreement is excellent in view of the absolute character of this comparison. Some systematic deviations of the computation can be traced to deficiencies of the potential (DIM), and of the TSH method.

The formation of highly excited H in the reaction H2+(v) + H2 → H + H

AbstractA quasiclassical trajectory surface hopping method has been used to study H(v) + H2 → H + H for v = 0, 3, 7, 10, 13, and 17 with an emphasis on determining the H internal energy and angular momentum distributions for high v. For v = 13 and 17, significant cross sections are found for producing H at energies above its dissociation energy. An average metastable H lifetime of 11.5 ps for v = 13 and 4.7 ps for v = 17 is found, but there is also a much longer lived component to the lifetime distributions that is more important for v = 13 than for v = 17. Some of the longer lived metastables correspond to high angular momentum orbiting states of H, but other sources of metastability are also present.

Critical evaluation of classical trajectory surface-hopping methods as applied to the hydrogen molecular ion (H2+) + hydrogen molecule (H2) system

Critical evaluation of classical trajectory surface-hopping methods as applied to the hydrogen molecular ion (H2+) + hydrogen molecule (H2) system

Dynamics of nonadiabatic reactions (theory). I. Branching ratios for early and late seams

The 3D classical trajectory surface hopping (TSH) method has been applied in a ‘‘model’’ study of factors governing nonadiabatic reaction, A+BC→AB+C* and →AB+C. In the diabatic approximation the potential-energy surfaces (pes) were a LEPS surface for F+H2 (→AB+C*) and a repulsive pes Vrep (→AB+C). These intersected in the exit valley to give an early or a late seam (E or L, perpendicular to the exit valley). The splitting at the avoided crossing 2ε was adjusted to ε=1.26 or 5.02 kcal/mol. The ratio of reactive cross sections onto the upper and lower adiabatic pes ρ* was investigated for mass combinations H+HL, L+HL, L+HH, and H+LL with E and L seams, and for small and large ε. The effect on ρ* of reapportioning a constant total energy (ETOT=13.84 kcal/mol) between reagent translation T and vibration V was examined for these 16 cases. Since the velocity in the coordinate of separation increased with increased T (yielding increased product translation; ΔT→ΔT′) ρ* also tended to increase with T. The extreme mass combinations H+HL and L+HH exhibited modified ρ* due to markedly differing widths in the entry and exit valley. The strongly skewed pes for H+LL led to multiple crossing of the seam which reduced ρ*. For other mass combinations ρ* was reduced by the inability of the low T′ component of the product to hop across the 2ε gap. In all cases ρ* was an index of the local dynamics at the seam, and hence shed light on the intermediate motions en route to the asymptotic outcome V′, R′, T′.