Charles W. Eaker

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.

A surface hopping quasiclassical trajectory study of the H2+ + H2 and (H2 + D2)+ systems

Abstract In this work we use a complete surface hopping quasiclassical trajectory method to determine cross sections for the reactions H 2 + + H 2 → H 3 + + H and the isotopic variants (H 2 + + D 2 and D 2 + + H 2 ). Initial translational energies ranged between 0.5 and 6 eV. The vibrational quantum number ( v + ) of the charged diatom is either 0 or 3. Comparing these results with our previous results with a partial treatment of surface hopping, we find essentially no change for v + = 0 and reductions in cross sections of up to 30% for v + = 3 trajectories.

A fast Fourier transform method for quasiclassical selection of initial coordinates and momenta for rotating diatoms

This paper describes a new fast Fourier transform technique to determine the transformations from action‐angle variables to Cartesian coordinates for a rotating diatomic molecule. This allows one to obtain the initial values of the coordinates and momenta for a given v and J from properly weighted radial and angular distributions as required in quasiclassical trajectory calculations. This method offers a number of advantages over previous methods for obtaining initial values. It is very accurate, even for cases of high J. This method works equally well for all types of diatomic potentials. Results are reported for Morse potentials and extended Rydberg potentials.

Metastable H+3 formation and decay in the reaction of highly excited H+2 with H2

This paper presents the detailed results of a quasiclassical trajectory surface hopping study of reaction of highly vibrationally excited H+2 with ground state H2 (and isotopic counterparts H+2 +D2, D+2 +H2, and D+2 +D2 ), with particular emphasis on the formation and decay of metastable H+3 products. A diatomics‐in‐molecules surface is used which has been successful in previous studies of H+2 (v) + H2 at low v. In the present study, we consider v=0–17, and find that metastable H+3 ’s are a major product for v≥13. Some of these metastables decay rapidly, showing exponential lifetime distributions with 2–7 ps lifetimes depending on v and on isotope. The remaining H+3 ’s have much longer lifetimes, and a number of methods are used to determine the origin of their stability. In no cases are any of these molecules found to be quasiperiodic, but a Fourier spectral analysis reveals some decoupling of H+ –H2 orbital motion from H2 rotational motion, and we find that many molecules have long lifetimes even though...

Collision induced dissociation of H+2 and D+2 with H2 using a surface hopping trajectory method

The collision induced dissociation (CID) and charge transfer (CT) cross sections have been determined for H+2 and D+2 colliding with H2 using a surface hopping trajectory method. Approximately 40 000 trajectories have been analyzed for collisions at 4.0, 6.0, and 8.0 eV (center of mass) and for H+2 (D+2 ) in vibrational states from 0 to 10. Our results are consistent with the recent experiments of Guyon, Baer, Cole, and Govers [Chem. Phys. 119, 145 (1988)]. However we have come to a different understanding of the mechanism for dissociation. We find that there are two pathways for CID: (1) formation of a H+3 intermediate followed by dissociation and (2) direct dissociation of a H+4 transition state via vibrational excitation. The H+3 intermediate pathway predominates at low collisional and low H+2 (D+2 ) vibrational energies.

A quasiclassical trajectory study of the (H2 + D2)+ system

Abstract We have applied the quasiclassical trajectory method to investigate the effect of vibration and translational energy on the reaction dynamics of H + 2 + D 2 and D + 2 + H 2 . Two vibrational states (ν + = 0 and 3) of the charged diatom and five translational energies ( E T = 0.23, 1.1, 2.1, 4.1, and 6.1 eV) are examined in this study. Using diatomics-in-molecules potential energy surfaces, the reaction is assumed to be diabatic (no charge hopping) until the reactants are within 8.0 bohr and then adiabatic. This simple theoretical description of the reaction gives good agreement with the experimental results.

Hermitian formulation of diatomics‐in‐molecules theory

The Hermitian formulation of the diatomics‐in‐molecules (DIM) theory is capable of reproducing the results of the non‐Hermitian DIM procedure developed by Tully and Truesdale [J. Chem. Phys. 65, 1002 (1976)]. This is shown for the collinear H3 and H1 systems for which the two methods are in excellent agreement. The conclusion of this work is that it is neither necessary nor desirable to invoke a non‐Hermitian formulation of DIM.

Generalized diatomics‐in‐molecules potential energy surfaces for H3 and H4

The generalized diatomics‐in‐molecules method has been applied to calculate potential energies of H3 and H4. This modification of the diatomics‐in‐molecules equations significantly improves the calculated energies for nonlinear geometries of these systems.

A fast Fourier transform method for the quasiclassical selection of initial rovibrational states of triatomic molecules

This paper describes the use of an exact fast Fourier transform method to prepare specified vibrational–rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating–rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial Cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational–rotational state selected. For example, in the case of the ground vibrational state of a nonrotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001ℏ of the specified quantization values and energies within 5 cm−1 of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However, for states for which the fundamental frequencies become comm...

A quasiclassical, surface hopping trajectory study of the reaction Na(2P)+HCl→NaCl+H(2S)

The reaction of electronically excited Na(2P) with HCl to produce NaCl and H has been studied using a quasiclassical surface hopping trajectory program. Two translational energies (5.6 and 16.3 kcal/mol) and two HCl vibrational states (v=0 and 1) were investigated. We find that the reaction cross section increases with vibrational excitation and decreases with increasing translational energy. The calculated reaction cross section of 3.02±0.25 A2 at 5.6 kcal/mol and v=0 agrees with the results of recent molecular‐beam experiments on this system. The ground and first excited state potential‐energy surfaces and the nonadiabatic coupling between these surfaces were calculated using the diatomic‐in‐molecules (DIM) method. Reactive trajectories which occur on these surfaces remain in the interaction region for nearly 1 ps and must pass through a perpendicular geometry. This critical geometry corresponds to the avoided crossing seam region.