We have formulated a law for state‐to‐state rotational transfer (RT) in diatomic molecules based on the angular momentum (AM) theory proposed by McCaffery et al. [J. Chem. Phys. 98, 4586 (1993)]. In this, the probability of angular momentum change in the rotor is calculated by assuming the dominant process to be the conversion of linear to angular momentum at the repulsive wall of the intermolecular potential. The result is a very simple expression containing three variable parameters, each of which has physical significance in the context of the model. Fits to known RT data are very good and suggest strongly that linear to angular momentum change is indeed the controlling process in RT. The parameters of the fit are sufficiently available to give the model predictive power. Using this formulation, RT probabilities may be calculated for an unknown system with little more than the atomic masses, bond length, and velocity distribution. We feel that this represents an important step in the development of a s...

A fitting law for rotational transfer rates: An angular momentum model with predictive power

The highly resolved experiments of modern collision and reaction dynamics indicate that momentum change provides the principal motive force for change at the single molecule level. A description of collisions is developed from two basic equations, one representing the conservation of angular momentum and the other conservation of energy. Linear (or orbital angular) momentum of relative motion is converted to rotational angular momentum under constraints imposed by state-to-state and overall energy conservation. The result is a simple, transparent form of mechanics the parameters of which are familiar to chemists, with bond length playing a central role. The approach is illustrated by predicting the outcome of the elementary collisions of physical and chemical change. Graphical representation of the principal equations allows insight into the physical principles as well as giving a qualitative guide to final rotational distributions. Quantitative calculations accurately reproduce experimental data from inelastic and reactive processes using input data consisting of mass, bond length, spectroscopic constants and velocity distribution. Reactive collisions require some changes in the formalism but the basic principles remain unchanged. The method is shown to be of wide application in diatomics and an initial treatment of collision-induced transitions in polyatomic molecules is outlined. Vibrational pre-dissociation in van der Waals molecules is also analysed within the momentum exchange formalism. An approach to modelling the multi-collision environment without invoking statistical assumptions is described. The concept of molecular efficiency is developed in terms of the ability of species to convert linear-to-angular momentum. This and other findings allow some generalisations to be made regarding the optimisation of chemical processes.

A new approach to molecular collision dynamics

Stimulated emission pumping state preparation and laser induced fluorescence state detection in the CN(B 2Σ+–X 2Σ+) violet system have been employed to study relaxation of single rotational states of CN(X 2Σ+, v=2) in collisions with He at 295 K. Approximately 2/3 of the value of the total removal rate constant for CN(X 2Σ+, v=2, N=2, 11, or 14) corresponds to changes in the rotational quantum number of ‖ΔN‖≤3 and a strong propensity is evident which favors even changes in N for ‖ΔN‖≤4. The measured rate constants are consistent with detailed balance, can be described with statistical power‐gap and exponential energy‐gap fitting functions and, where compared, are in accord with an IOS‐based scaling function. No significant difference is found between a sum of state‐to‐state rate constants and separately measured total removal rate constants for N=2, 11, and 14. The total removal rate constants decrease monotonically between N=0 and N=41 to about 1/3 of their value at N=0.

Direct measurement of thermal rate constants for state‐to‐state rotational energy transfer in collisions of CN(X 2Σ+, v=2, N) with He

State-to-state rotationally inelastic scattering cross sections of H2O with Ar are measured under single-collision conditions in crossed supersonic jets at a collision energy of 480(90) cm−1. The H2O is initially prepared in its lowest ortho (101) and para (000) rotational levels by supersonic cooling in a Ne expansion, and then excited in the intersection region by single collisions with a second pulsed jet of Ar atoms. Column-integrated densities of H2O in both initial and final scattering states are monitored via direct absorption of narrow bandwidth (Δν≈0.0001 cm−1) infrared light from a continuous wave (cw) F-center laser. Absolute inelastic cross sections for state-to-state collisional energy transfer out of para and ortho initial states are determined from the dependence of infrared absorption signals on collider gas densities. Overall, the results can be approximately characterized by an exponential decrease in cross section with the magnitude of rotational energy transferred, i.e., as suggested b...

Rotationally inelastic scattering of jet cooled h2o with ar : state-to-state cross sections and rotational alignment effects

One-colour polarization spectroscopy (PS) on the OH A 2Σ+
				− X 2Π(0,0) band has been used to measure the removal of bulk rotational angular momentum alignment of ground-state OH(X 2Π) in collisions with He and Ar. Pseudo-first-order PS signal decays at different collider partial pressures were used to determine second-order decay rate constants for the X 2Π3/2, J = 1.5–6.5, e states. The PS signal decay rate constant, kPS, is sensitive to all processes that remove population and destroy polarization. The contribution to kPS from pure (elastic) alignment depolarization within the initial level, kDEP, can be extracted by subtracting the independently measured or predicted sum of the rate constants for total rotational energy transfer (RET), kRET, and for Λ-doublet changing, kΛ, collisions from kPS. Literature values of kRET and kΛ are available from experiments with He and Ar, and from quantum scattering calculations for Ar only. We therefore also present the results of new, exact, fully quantum mechanical calculations of kRET and kΛ on the most recent ab initio OH(X)–He potential energy surface of Lee et al. [J. Chem. Phys. 2000, 113, 5736]. The results for kDEP from this subtraction for He are found to be modest, around 0.4 × 10−10 cm3 s−1, whereas for Ar kDEP is found to range between 0.6 ± 0.2 × 10−10 cm3 s−1 and 1.7 ± 0.3 × 10−10 cm3 s−1, comparable to total population removal rate constants. The differences between kDEP for the two colliders are most likely explained by the presence of a substantially deeper attractive well for Ar than for He. The measurement of kDEP may provide a useful new tool that is more sensitive to the form of the long-range part of the intermolecular potential than rotational state-changing collisions.

Inelastic scattering of OH(X 2Π) with Ar and He: a combined polarization spectroscopy and quantum scattering study

We have re‐examined critical experiments on collision induced rotational transfer (RT) and conclude that the probability of RT is controlled by the factors that control the probability of angular momentum (AM) change. The probability of energy change seems less important in this respect. In the light of this we suggest a model for RT in which the probability of AM change is calculated directly and present a formalism for this purpose. We demonstrate that such a calculation leads to an exponential‐like fall of RT probabilities with transferred AM, a consequence of the radial dependence of the repulsive part of the intermolecular potential. Thus in this AM model, the exponential gap law has a simple physical origin. The AM model we describe may be used as the basis of an inversion routine through which it is possible to convert RT data into a probability density of the repulsive anisotropy. Through this model therefore it is possible to relate experimental RT data directly to the forces that are responsible for rotational transfer. The hard ellipse model is used in this work to relate calculated anisotropies to a form that includes an isotropic component. The result is a representation of the intermolecular potential through which new insights into the RT process are gained.

Colin J. Williams

Papers

Rotational transfer, an angular momentum model