Energy Transfer In Molecular Collisions Research Articles

On the adequacy of perturbed stationary state formulations in molecular energy transfers. The classical-path treatment

We have analysed the accuracy of the perturbed stationary state description of energy transfer in molecular collisions. The perturbed basis decreases the time overlapping of the various coupling terms and appears better adapted to simplified treatments, i.e. the exponential approximation. We determine the optimum trajectory in PSS semiclassical calculations. Our expressions are tested on vibrational energy transfer.

A distorted wave calculation for electronic energy transfer in molecular collisions. Application to the N2(A 3Σu+)+CO(X 1Σ+) →N2(X 1Σg+) +CO(a 3Π) system

The electronic energy transfer in collisions between two diatomic molecules at thermal energy is treated by a distorted-wave type calculation. The predominating role of short-range interactions is assumed. Potential energy curves and coupling terms have been estimated by configuration interaction between locally excited states. The method is applied to the system: N2(A 3Σu+)+CO(X 1Σ+) →N2(X 1Σg+) +CO(a 3Π). The results are compared with the available experimental data. A general study of the dependence of the rate constants and cross sections on the energy gap and temperature is given. Finally a comparison with the golden-rule model and other quantum mechanical approximate calculations is presented.

Electronic-to-rotational energy transfer in molecular collisions

Abstract A quantum mechanical study of collision induced electronic-to-rotational energy transfer in the fluorine—para-hydrogen system (F + H 2 ) is reported. The three potential energy surfaces of the system, constrained to lie in a fixed plane, are obtained by the diatomics-in-molecules approach, and close-coupling calculations are performed in a diabatic representation. An enhancement of rotationally inelastic (compared to rotationally elastic) transitions is observed when fluorine makes a transition from its upper to its lower spin—orbit state.

Vibrational energy transfer in molecular collisions: An information theoretic analysis and synthesis

State-to-state rate constants for vibrational energy transfer (both V–V and V–T) are characterized using an ’’exponential gap’’ representation. The collisions analyzed include experimental results for both V–T and V–V transfer rates, trajectory computations for V–T transfer rates (via both inelastic and reactive, atom exchange, collisions) and quantal computations for V–V transfer rates. The results are analyzed in terms of the surprisal, a measure of deviation of the actual rate from the prior (or reference) rate. The prior rates are computed on the basis of the assumption that (at a given collision energy) all final states are equally probable. For almost all cases the surprisal could be characterized by a single parameter. The magnitude of this parameter (and its temperature dependence) could be predicted using bulk averages only. Such predictions are demonstrated for both experimental and trajectory computed rates. The link between the microscopic dynamics and macroscopic kinetics is forged by the use of sum rules (which provide constraints on the rates) and of the principle of maximal entropy (which is used to determine the least biased set of rate constants subject to the constraints).

Energy transfer in molecular collisions far from resonance

Transfer of one quantum of vibrational excitation from a CO molecule initially in vibrational level 10 to another CO molecule initially in its ground vibrational level, a process endothermic by about 236 cm −1, is explained by a second-order distorted-wave Born calculation. The distortion potential is taken to be the spherically symmetric Lennard-Jones (6-12) potential, and the potential causing the energy transfer is assumed to be the multipolar interaction. A key factor in the explanation is the inclusion of the phase shifts due to elastic scattering by the multipolar potential. The calculated value for the cross section may differ from the true value by about 50% due to the uncertainty in the value of the molecular quadrupole moment. The computed cross section in the exothermic direction is 3.0 × 10 −18 cm 2 compared to the experimental value of 2.6 × 10 −18 cm 2.

Quantum resonance effects in electronic-to-vibrational energy transfer in molecular collisions

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Quasi-resonance energy transfer in molecular collisions. Vibrational energy exchange between N 2 and CO 2 molecules

Possible reasons for the non-monotonous temperature dependence of the quasi-resonance energy transfer probability and relative contributions of short-range and long-range forces are discussed. Particular calculations are made for the case N 2-CO 2(ν 3) vibrational energy exchange.

On a First-Order Electronic Dipole–Dipole Mechanism for Energy Transfer in Molecular Collisions

On a First-Order Electronic Dipole–Dipole Mechanism for Energy Transfer in Molecular Collisions

Energy Transfer in Molecular Collisions

AbstractComputational studies of energy transfer in models of molecular collisions are presented and analyzed qualitatively and semi‐quantitatively. Particular attention is given to those approximations where the leading term is already in good qualitative agreement with the exact numerical results. In particular, results for the distorted wave approximation in an adiabatic basis are reported and compared with the exact results. It is argued that for slow molecular collisions, the efficiency of the transfer is determined by the “Franck Condon” overlap near the repulsive part of the intermolecular potential.

Vibrational Energy Transfer in High-Energy Collisions

Time-dependent wavefunctions are used to evaluate the exact transition probabilities for a forced harmonic oscillator. The forcing is represented by a time-dependent potential, where this potential has a linear dependence on the oscillator coordinate. The results are compared with available numerical solutions for a harmonic oscillator forced with a potential which has an exponential dependence on the oscillator coordinate. The comparison is made for the collision of an N2 molecule with another particle, and it is found that although the results for the two cases are similar, the linear potential gives higher values for the multiquantum transitions. It is then shown that time-dependent wavefunctions which contain the corresponding classical motion as a parameter provide a good set of functions for a perturbation calculation. The energy transfer to these oscillating wavefunctions is always identical to the energy transfer to the classical oscillator. Thus the perturbation value of the energy transfer represents the difference between the classical and the quantum-mechanical result. It is shown that this value, which is zero for the linear forcing potential, is very small for higher-order potentials, even at high velocity of impact. This demonstrates that classical calculations can be used to obtain the energy transfer in molecular collisions at high temperature.

Measurement of Energy Transfer in Molecular Collisions

Experimental data were reviewed critically for four types of intermolecular energy transfer in the gas phase:(1) exchange of vibrational energy, (2) interchange of vibrational and electronic energy, (3) exchange of electronic energy, and (4) interchange of electronic and translational energy. The rate of exchange of vibrational energy between NO and a number of diatomic molecules has been measured by fluorescence and by flash photolysis. The probability of energy transfer decreases rapidly with increasing discrepancy between the vibrational frequencies of the two colliding molecules, and the results are in satisfactory quantitative agreement with predictions of Schwartz, Slawsky, and Herzfeld theory. The spin-orbit relaxation of Hg(63P), Hg(63P1) + M → Hg(63P0) + M*, was investigated by flash spectroscopy, and was shown to occur with M = N2, CO, H2O, or D2O. There is no systematic variation of quenching cross section with the minimum energy which cannot be converted to vibration in the quenching molecule. It was suggested that if a substantial transfer of electronic energy occurs, e.g., Na(32P) + M→Na(32S)+M *, the yield of vibrational energy in the quenching molecule is generally small. Quenching occurs because of a strong interaction between Na(32P) and M which permits near crossing of potential curves in the collision complex. It was pointed out that the apparent electronic relaxation time of a metal atom in a shock-heated gas will be approximately equal to the vibrational relaxation time if quenching produces a finite yield into any one of the vibrationally excited levels of the quenching molecule. Exchange of electronic energy between atoms was reviewed and it was shown that to a first approximation transfer occurs to minimize the change in internal energy. If several opportunities occur with ΔE < ∼1000 cm−1, the course of the energy transfer cannot be predicted either from the magnitude of ΔE or from the optical rules. The quenching of an excited atom by a polyatomic molecule depends on the reactivity of the polyatomic molecule, which again suggests that strong interaction facilitates transitions between potential surfaces in the collision complex. Hg(63P0) is curiously stable to collisional deactivation. The probability of electronic−translational energy transfer was shown to decrease rapidly with increasing magnitude of the energy to be transferred. It was suggested that several types of energy transfer conform approximately to the law log P = A ΔE + B, where P is the probability of transfer per collision and ΔE is the energy to be converted to translation. For fixed masses and temperature, A is the same constant for several different types of energy transfer, and B can be neglected except for vibrational exchange.

Vibrational Energy Transfer in Molecular Collisions Involving Large Transition Probabilities

The usual calculations of vibrational energy exchange in a diatomic gas make use of first-order perturbation theory and are therefore limited to low transition probabilities. In actual practice, the thermally averaged transition probabilities in most gases are indeed small. However, this is partly because it is the relatively few molecules in the high-velocity ``tail'' of the velocity distribution which account for most of the energy exchange. The actual microscopic transition probabilities in these collisions may be too great to justify the perturbation method for many gases at high temperatures. We have therefore solved the time-dependent Schrödinger equation based on a semiclassical collision, subject to an assumed form of potential, to get exact transition probabilities in a molecular collision. At low velocities, our result reduces to the perturbation result. A thermal average of our transition probabilities should eliminate errors due to use of the perturbation solution in previous calculations. For N2, these errors only become important above 5000°K. For gases with lower vibrational frequencies such as O2, or strong attractive forces such as NO, these effects become important at much lower temperatures.

Rotational energy transfer in molecular collisions : transitions in parahydrogen

Rotational energy transfer in molecular collisions : transitions in parahydrogen

Molecular Collisions. III. Symmetric Top Molecules

The question of rotational energy transfer in molecular collisions is treated for the case of symmetric top molecules. The Schrödinger equation for this problem, which can be taken as an integral equation over nine variables, is reduced to a set of coupled one dimensional integral equations by means of expansions over the irreducible representations of the three-dimensional rotation group. Various selection rules are found, of which two, in indices (in the matrix elements of the potential) related to the quantum number k, have no counterpart in the previously developed theory for diatomic molecules. The results are exhibited as cross sections for the excitation of rotational states, given the states before the collision. The rotational states for the symmetric top rotors are specified by the usual quantum numbers k, l, m, and the translational states by the velocity and direction of motion. The angular dependence of the cross section is treated by means of an expansion in spherical harmonics which is new in this context and which promises to be extremely useful in the application to transport processes.

Influence of adiabatic interactions on the energy transfer in molecular collisions

Synopsis A description of slow molecular collisions is given, based on the assumption that the molecular interaction can be divided into an “adiabatic” and a “non-adiabatic” part. The adiabatic interaction has in general the twofold effect of changing the relative motion of the collision partners and of perturbing their internal states. The non-adiabatic interaction gives rise to transitions between the perturbed internal states. Each of the effects due to the adiabatic interaction can contribute to an increased probability of energy transfer between the translation and the internal states. The method is applied to head-on collisions of HCl molecules with dipole-dipole interaction and of CO molecules with quadrupole-quadrupole interaction as adiabatic forces. Increases in the vibrational deactivation probabilities by factors of 4 and 2, respectively, are found as a result of these interactions. The interactions give rise only to the “acceleration” effect; they are not strong enough to induce internal perturbations.

Influence of adiabatic interactions on the energy transfer in molecular collisions)

Influence of adiabatic interactions on the energy transfer in molecular collisions)