George C. Berend

Vibrational relaxation of HF and DF

Relaxation times for vibration→rotation, translation deexcitation of HF(v=1) by HF(v=0) and DF(v=1) by DF(v=0) are calculated using quasiclassical trajectory techniques. An empirical interaction potential, formulated so as to give a reasonably accurate description of the hydrogen bonding in these systems, is employed in the calculations. Since the initial rotational states of the collision partners are restricted to the most probable state for each temperature investigated, only qualitative agreement with experiment is obtained. The observed temperature dependencies of the vibrational relaxation times are discussed in terms of their interdependence on the directionality of the hydrogen bonding interaction and initial molecular rotation.

Vibrational Energy Exchange of Highly Excited Anharmonic Oscillators

The probabilities of dissociation Pdis, excitation Pex, de‐excitation Pde, and the associated average energy exchanges were calculated theoretically for a highly energized, anharmonic oscillator (I2 or Br2) colliding classically with an inert gas atom C through a Morse‐type potential. The effect of varying mass and well depth was investigated.It was found that the effect of anharmonicity is to favor excitation and dissociation. However, the average ΔEv for these processes is about the same for harmonic and anharmonic oscillators and not much bigger than 1 to 2 RT. Pdis increases markedly with increasing mass. The well depth (V0) does not seem to have much effect in the range 0.004<V0/D0<0.14, where D0 is the bond dissociation energy. Exchange reactions are observed, but for shallow well depths they are rare events. From the results, it is possible to calculate λ, the probability of stabilizing an atom pair by a third‐body collision. This turns out to be independent of temperature but depends strongly on t...

Vibrational and Rotational Excitation of Diatomic Molecules. Two‐Dimensional Model

The change of energy of a diatomic molecule upon collision with an atom in two dimensions was calculated. The energy contributed to the various internal degrees of freedom of the molecule was evaluated. The vibrational transition probabilities obtained were compared to experimental data for the case of O2→Ar collisions. By contrasting these results with those of a one‐dimensional treatment, the form of a realistic three‐dimensional potential function was predicted. It was found that at lower initial rotational energies, transfer of energy from rotational to vibrational degrees of freedom is as effective as translational→vibrational transfer. For higher initial rotational energy, rotational→vibrational transfer is shown to be less probable.

Classical Theory of Rotational Relaxation of Diatomic Molecules

The classical equations of motion of colliding diatomic molecules are solved rigorously in two dimensions to obtain the energy transferred to the internal degrees of freedom during collision. The model considers up to four atoms bound by six atom‐centered Morse potentials. The effect of varying range parameters is noted. The relaxation of H2 with He and H2 collision partners, D2 with He, and pure N2 and O2 is studied. The vibration—rotation energy exchange is evaluated and accounted for. The resulting relaxation times and average collision numbers agree well with empirical findings. In the temperature range 100°—700°K, except for N2 and O2, a negative temperature dependence was obtained. The contrary is expected at higher temperatures where the relaxation times are functions of the inverse collision frequency only.

Molecular Relaxation Processes in Triatomic Molecules. I. T–V Transition Probabilities in the CO2–He System

A classical method is presented for calculating translational–vibrational energy exchange between a colliding atom and linear triatomic molecule. The method entails a rigorous solution of the equations of motion of the four particles interacting in two dimensions. The interaction potential is described by three independent, atom–atom, Morse‐type potential functions. Computer solutions provide the probabilities of the T–V energy‐transfer processes associated with the three normal vibrational modes of the triatomic molecule. The method is demonstrated on the CO2–He system. Results show good agreement with the experimental data for excitation of the bending mode and are in accord with SSH theory predictions for excitation of the longitudinal modes.

Vibration–Vibration Energy Transfer between Diatomic Molecules

A classical method is presented to calculate resonant and near‐resonant vibrational energy exchange between colliding diatomic molecules. The method entails a rigorous solution of the equations of motion of the four particles interacting in two dimensions. The interaction potential is described by six independent, atom–atom, Morse‐type potential functions. Computer solutions provide the probability of the simultaneous energy‐transfer process. Temperature‐dependent transition probabilities, relaxation times, and exchange cross sections are calculated. The method is demonstrated on two reactions: N2(υ = 1) + CO(υ = 0)→N2(υ = 0) + CO(υ = 1) and N2(υ = 2) + N2(υ = 0)→2N2(υ = 1). Results show good agreement with experimental data and other theoretical calculations.

Vibrational relaxation of HF in Ar

A quasiclassical trajectory study of the vibrational relaxation of HF (ν=1) by Ar is presented. Examination of the collision dynamics indicates that intra‐ and intermolecular vibration‐rotation energy transfer governs the vibrational relaxation rate.

Vibration‐Vibration Energy Exchange in N2 with O2 and HCl Collision Partners

A rigorous, classical solution of two colliding diatomic molecules is presented. Single quantum vibration‐vibration energy transfer probabilities are calculated for the case of N2*+O2 and N2*+HCl. Results are in excellent agreement with experimental findings. Previous findings on N2*+N2 and N2*+CO reactions are included and it is demonstrated that the energy discrepancy between the respective vibrational states which exchange their energies is not necessarily the measure of the efficiency of the process. Geometry of the collision and the matching of interacting atomic masses seem to be of equal importance.