Collisions molecular orientations

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

In the MF equation (A7.20) can be simplified essentially only in the particular case of non-adiabatic collisions, which do not change the molecular orientation y(g) = <5(g). In this case operator T = /, and the relaxation part of (A7.20) can be diagonalized over index q ... 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

Estimates of the rotational diffusivity may be made from MD calculations by fitting an exponential function to Legendre polynomials that express the decorrelation of a unit vector that is fixed in the methane coordinate frame (11). The rotational diffusivity was found to increase with concentration (as a result of sorbate-sorbate collisions which act to decorrelate the molecular orientation). The values are of the same order as those for liquid methane and are 2 orders of magnitude larger than those found by Jobic et al. (73) from a quasi-elastic neutron scattering study of methane in NaZSM-5. 

Thus it seems clear that no direct transitions between essentially repulsive covalent potential surfaces Na + BC and Na + BC are possible. This view is also supported by calculations.68 Under such circumstances an additional ionic potential surface has been postulated,69-70 namely, Na+ + BC, which was supposed to be strongly attractive and to couple with the covalent surfaces. All potentials depend on the molecular distance RM, on the atom-molecule distance Rc during the collision, and on the molecular orientation relative to Rc measured by the angle y. A two-dimensional cut through these surfaces along Rc is shown schematically in Fig. 3 for the... 

Since the scope of this article is purely theoretical, we just outline below the state of the experimental situation. The ideal experiment in Chemical Dynamics would be that in which starting with reactants in definite intramolecular quantum-states and running towards each other in a definite way (relative velocity and orbital angular momentum) the distribution of the products over the various intramolecular quantum-states and the state of the relative motion (direction and velocity) would be measured. Such an experiment would show whether there is a preferential molecular orientation at the heart of the collision, what the lifetime of the intermediate complex is, how the excess energy is distributed over the various degrees of freedom of... 

To start the mathematical integration of the equations of motion for one particular trajectory, a set of initial values of coordinates and either velocities or momenta must be specified. These, however, are dependent on the experimental conditions which need be reproduced, such as collision energy, intramolecular vibrational energies etc... In addition, some other variables, for instance intramolecular instantaneous elongations, molecular orientations, impact parameter, etc..., are necessarily specified in classical mechanics but are not observable microscopically because of the Uncertainty Principle. The ensemble of these result in a set of trajectories associated with a given set of observable initial conditions. 

The answer lies in the molecular orientations during collisions. We can illustrate this effect by using the reaction between two BrNO molecules, as shown in Fig. 15.13. Some collision orientations can lead to reaction, and others cannot. Therefore, we must include a correction factor to allow for collisions with nonproductive molecular orientations. 

Molecular orientations (kinetics) orientations of molecules during collisions, some of which can lead to a reaction and some of which cannot. (15.8)... 

To obtain the reaction attributes for a particular set of vibrational, rotational and translational energies, many trajectories were simulated at given values of N2 vibrational and rotational quantum numbers and N2-O relative translational energy. The N2 molecular orientation, vibrational phase and impact parameter were chosen randomly for each trajectory. The reaction attributes were then determined by averaging the outcomes of all collisions. The information obtained is state-specific, so for example, the energy distributions of the reactant and product molecules can be determined. The method used to calculate the vibrational and rotational state of the product molecule is outlined in Ref. 67. With the QCT approach, reaction cross sections were determined solely from the precollision state. The method knows nothing of the fluid flow environment and so... 

Figure 16.14 The importance of molecular orientation to an effective collision.

Another model of rotational reorientation is the jump-diffusion model first described by Ivanov (1964). In this model the molecule reorients by a series of discontinuous jumps (with an arbitrary distribution of jump angles). This should be contrasted with the Debye model, which involves infinitesimal jumps, and the Gordon model, which involves continuous free rotations between collisions. This model is probably applicable to the situation where the molecular orientation is frozen until a volume fluctuation occurs, at which time the molecular orientation jumps to a new frozen value. We present our own version of the jump model here. It is assumed that (a) the jump takes place instantaneously, (b) successive jumps are uncorrelated in time with an average time tv between jumps, and (c) the dihedral angle between the two planes defined by the orientation vector u in two successive jumps is randomized. 

Interactive Figure To see an animation of the effect of molecular orientation on collision effectiveness, visit glencoe.com. 

Correlation times for common organic molecules can be thought of as rotational diffusion times. The correlation times indicate the time it takes for the molecular orientation to be randomized relative to the starting orientation. A common organic molecule rotates in solvents very much in the same manner that it diffuses. Constant and continual collisions ran-... 

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