Quantum mechanics calculations, rotational motion

Further work will be needed to ascertain whether their conclusions about diffraction intensities remain valid even when rotations of the Hj and motion of the surface atoms are included. This will require quantum mechanical calculations, not classical simulations. A recent method has been developed to treat simultaneous rotations and diffraction via a set of close-coupled TDSE (Mowrey and Kouri 1986 Mowrey et al. 1987) which are solve using the FFT procedure. This approach could be combined with a modification... 

The theory of R-R transfer requires complex quantum mechanical calculations, and well-defined selection rules can be obtained. In a sense, the problem is easier than V-V transfer since to a good approximation the vibrational motion of the molecule can be ignored, whereas V-V transfer is almost always accompanied by extensive rotational transfer so that V-R and R-R processes must be considered. 

In traditional quantum mechanical calculations the inclusion of rotational motion, particularly to high orders, has proved difficult because of the consequent increase in the size of the secular matrix. For Van der Waals systems, the so-called helicity approximation has often been invoked. This approximation assumes that the projection, k, of the total angular momentum,. J, onto some body-fixed z-axis is a constant of motion for the system. The approximation is often good for energy levels but is less reliable for properties such as transition intensities. 

Much of the theoretical work in molecular dynamics has been based on potential energy surfaces that have been calculated for individual reactions. Dynamical calculations are then carried out for various initial states of the reacting molecules. For a reaction A + B—C, for example, one chooses a particular vibrational and rotational state for the molecule B-C, and particular translational states for A and B-C. Other details of the collision between the two are also selected. One then calculates, on the basis of dynamics, the path that the system takes on the potential energy surface. A diagram or mathematical description that describes the motion of a reaction system over a potential energy surface is known as a trajectory. Ideally the dynamical calculations are based on quantum mechanics, but this presents difficulty and more often classical calculations are made there is good reason to conclude that not much error is then introduced. Even when the trajectories are obtained classically, the initial states of the reactants are usually selected on the basis of quantum theory. 

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