Qiyan Sun

A method to constrain vibrational energy in quasiclassical trajectory calculations

In this paper, we present a general method to constrain the classical energy of a vibrational mode to be greater than a specifled amount. In particular, zero‐point energy constraints can be applied with this method to (zero‐order) vibrational modes of a polyatomic system or complex. A demonstration of the method is made for a model two‐mode Henon–Heiles Hamiltonian.

Reduced dimensionality quantum reactive scattering : H2+CN→H+HCN

We apply a recently developed, reduced dimensionality quantum theory of diatom–diatom reactive scattering [Q. Sun and J. M. Bowman, Int. J. Quantum Chem., Symp. 23, 115 (1989] to the exoergic H2+CN→H+HCN reaction, for zero total angular momentum. A new semiempirical, three‐dimensional potential surface, which is based in part on ab initio calculations of the saddle point properties is also reported. Reaction probabilities for the ground and first excited bending states of HCN are calculated for total energies up to 1.0 and 1.06 eV, respectively. The results show a strong preference for formation of HCN (0vb1) and HCN (0vb2), vb=0 and 1, starting with ground vibrational state reactants. Reaction probabilities for vibrational excitation of H2 or CN are also reported for both bending states of HCN. Vibrational excitation of H2 is found to be far more effective in promoting reaction than vibrational excitation of CN.

Experimental and reduced dimensionality quantum rate coefficients for H2(D2)+CN→H(D)CN+H(D)

New experimental rate coefficients are reported for the H2(D2)+CN→H(D)CN+H(D) reactions over the temperature range 209 to 740 K for H2 and 250 to 740 K for D2. Previous reduced dimensionality reaction probabilities for the reaction with H2, and new ones for the reaction with D2 are used to obtain analogous rate coefficients. In addition, reaction probabilities and rate coefficients for vibrationally excited reactants H2(v=1), D2(v=1), or CN(v=1) are presented. Comparisons of the calculated rate coefficients are made with the new and previous experiments, especially those of Sims and Smith [Chem. Phys. Lett. 149, 565 (1988)].

Reduced‐dimensionality quantum calculations of the thermal rate coefficient for the Cl+HCl→ClH+Cl reaction: Comparison with centrifugal‐sudden distorted wave, coupled channel hyperspherical, and experimental results

Reduced dimensionality (RD) cumulative reaction probabilities (CRPs) are reported for the Cl+HCl→ClH+Cl reaction using two semiempirical extended London–Eyring–Polanyi–Sato potential energy surfaces. Comparison is made with CRPs from centrifugal‐sudden distorted wave (CSDW) calculations, and with accurate coupled channel hyperspherical (CCH) CRPs for total angular momentum quantum number J=0. Rotational and bending energy‐shift approximations are applied to the CCH CRPs for J=0 to obtain approximate CRPs for J>0. A test of this approximation is made using CSDW partial wave CRPs. New expressions for the thermal rate coefficient are derived using these approximations. The rate coefficients calculated from RD and energy‐shifted CCH CRPs are in excellent agreement with each other. They also agree well with the CSDW and experimental rate coefficients.

Reduced dimensionality diatom–diatom reactive scattering: Application to a model H2+A2→H+HA2 reaction

We apply a recently formulated quantum theory of diatom–diatom reactions [Q. Sun and J. M. Bowman, Int. J. Quant. Chem., Quant. Chem. Symp. 23, 9 (1989)] to a model collinear H2+A2→H+HA2 reaction, where A has the mass of a hydrogen atom. The theory assumes one diatom bond is nonreactive, and the reactive scattering Hamiltonian is written in terms of hyperspherical and cylindrical coordinates. The potential‐energy surface used is the PK2 H+H2 surface augmented by a harmonic degree of freedom describing the nonreactive A2. Details of the formulation and solution of the coupled‐channel equations are given, along with convergence tests, and a discussion of the new state‐to‐state transition probabilities. In particular, the partial quenching of the well‐known collinear H+H2 resonances is noted.

A comparison of scattering and L2 photodetachment Franck–Condon factors for reduced dimensionality ClHCl–→ Cl + HCl + e–

We present two calculations of the Franck–Condon factors describing the photodetachment of ClHCl– to form Cl + HCl plus an electron. Both calculations are made using a reduced dimensionality Hamiltonian based on an adiabatic treatment of the three-atom, internal bending motion. One calculation, the rigorous one, is a reactive scattering calculation, employing hyperspherical coordinates. The other calculation is based on an L2 approximation to the continuum Cl + HCl wavefunctions. The Franck–Condon factors, resonance energies and wave-functions from both calculations are compared.

Application of adiabatic switching to vibrational energies of three‐dimensional HCO, H2O, and H2CO

Semiclassical vibrational energies are calculated for nonrotating, three‐dimensional HCO, H2O, and H2CO by the adiabatic switching method. For HCO and H2O the Hamiltonian is given in a body‐fixed frame in terms of Jacobi coordinates. Several zero‐order Hamiltonians for adiabatic switching to the full Hamiltonian are considered. The simple, ‘‘obvious’’ choices do not yield stable results; however, a nonseparable zero‐order Hamiltonian, which can be transformed to a simple normal form, does give stable results. Semiclassical quantization is done with the transformed zero‐order Hamiltonian, initial conditions are obtained in terms of the Jacobi coordinates, and adiabatic switching is done in these coordinates. The Watson Hamiltonian is used for H2CO in a straightforward fashion. In all cases, the semiclassical energies are in good agreement with quantum mechanical results, and for H2O in excellent agreement with other semiclassical results.

Rotational rainbows in high energy H+CO scattering

Abstract Large-scale coupled-channel scattering calculations are reported for collisions of H with CO for zero total angular momentum and total energies between 0.60 and 1.00 eV, where two to three vibrational states of CO and many rotational states are open. An ab initio global potential surface is used in these calculations. Rotational rainbows are observed in the final rotational distributions, thermally averaged over initial rotational states for 300 K, for the ground and first excited final vibrational states of CO. The energy dependence of these rainbows is determined and shown to be well described by a simple hard-shell model. In addition, classical trajectory calculations are reported at 1.0 eV total energy and compared to the quantum results.

Classical energy transfer in forced oscillator models of inelastic scattering

A compact formalism is presented to solve the classical equations of motion for a general linearly driven parametric oscillator. It is shown that quantum transition probabilities obtained from an operator algebraic technique can be expressed in terms of classical energy transfers. The success and limitations of the DECENT method for vibration–translation energy transfer in molecular collisions is discussed and illustrated numerically in a simple model.