A Simple Model Indicating the Origin of the Angular Momentum Gap Law in Rotational Transfer

Abstract

In the recently proposed angular momentum (AM) theory of collision-induced rotational transfer, the probability distribution of effective impact parameter (or torque arm) plays a central role as the means via which linear momentum is converted to AM. This was found empirically to be best represented by the function P(b n ) ) b n -γ . Here we show that the ubiquitous inverse power function is readily explained as resulting from the combined contributions to P(b n ) that come from considering both angular and radial variability in a realistic intermolecular potential.

A new approach to molecular collision dynamics

“…15 and Osborne et al 34 have demonstrated that the above expression predicts an exponential-like fall of RT crosssections with increasing Dj. These two articles also stress the importance of the range of integration over effective impact parameter to the state-to-state probability, i.e.…”

“…The form of P(b n ) obtained from analysis of extensive RT data, quite accurately follows a b n Àg dependence in the case of pure RT 15 and was shown to represent the probability density of the repulsive anisotropy of a typical atom-diatom intermolecular potential. 34 Note that here and in other publications we use the expression P(b n ) as shorthand for P(b perp n ,cos f) where b perp n is the effective impact parameter generated by the perpendicular component of incident relative momentum and f is the angle this momentum subtends to the normal. 34 Both elements contribute to the b n Àg form of P(b n ) that gives RT its characteristic inverse power dependence on transferred AM, 34 a shape referred to here as exponential-like to provide an easily visualised description.…”

“…34 Note that here and in other publications we use the expression P(b n ) as shorthand for P(b perp n ,cos f) where b perp n is the effective impact parameter generated by the perpendicular component of incident relative momentum and f is the angle this momentum subtends to the normal. 34 Both elements contribute to the b n Àg form of P(b n ) that gives RT its characteristic inverse power dependence on transferred AM, 34 a shape referred to here as exponential-like to provide an easily visualised description. Detailed empirical studies 39 established the inverse power relationship that is clearly discernible when RT is extensive.…”

“…A value somewhat less than this quantity will bring the A-plot within the boundaries set by energy conservation. This revised maximum value of b n is readily calculated 34,45 and by this means, the mechanism constrained to work within the bounds of energy conservation. Limits of this nature on accessible values of b n constitute a different form of inefficiency to that revealed in Fig.…”

From Ligand Field Theory to Molecular Collision Dynamics: A Common Thread of Angular Momentum

“…These include rotational transfer (RT) [24,26,36,[38][39][40], i.e., state change within a vibrational manifold, vibration-rotation transfer (VRT) [41,42], i.e., transitions between vibrational states and electronic energy transfer [43], i.e., transitions between discrete levels of different electronic states. An example is given in Fig.…”