Rotation, internal quantum number

J and Vrepresent the rotational angular momentum quantum number and tire velocity of tire CO2, respectively. The hot, excited CgFg donor can be produced via absorjDtion of a 248 nm excimer-laser pulse followed by rapid internal conversion of electronic energy to vibrational energy as described above. Note tliat tire result of this collision is to... 

After the separation of the kinetic energy operator due to the center-of-mass motion from the Hamiltonian, the Hamiltonian describes the internal motions of electrons and nuclei in the system. These in the BO approximation can be separated into the vibrational and rotational motions of the nuclear frame of the molecule and the electronic motion that only parametrically depends on the instantenous positions of the nuclei. When the BO approximation is removed, the electronic and nuclear motions become coupled and the only good quantum numbers, which can be used to quantize the stationary states of the system, are the principle quantum number, the quantum number quantizing the square of the total (nuclear and electronic) squared angular momentum, and the quantum number quantizing the projection of the total angular momentum vector on a selected direction (usually the z axis). The separation of different rotational states is an important feamre that can considerably simplify the calculations. 

Inversion doubling has been observed in microwave spectrum of methylamine CH3NH2. This splitting depends on the quantum numbers of rotation and torsion vibrations [Shimoda et al., 1954 Lide, 1957 Tsuboi et al., 1964]. Inversion of NH2 alone leads to the eclipsed configuration corresponding to the maximum barrier for torsion. Thus, the transition between equilibrium configurations involves simultaneous NH2 inversion and internal rotation of CH3 that is, inversion appears to be strongly coupled with internal rotation. The inversion splits each rotation-vibration (n, k) level into a doublet, whose components, in turn, are split into three levels with m = 0, 1 by internal rotation of the... 

The OH radical is produced in a particular vibrational and rotational quantum state specified by the quantum numbers n and j. The corresponding energies are denoted by tnj. The probabilities with which the individual quantum states are populated are determined by the forces between the translational mode (the dissociation coordinate) and the internal degrees of freedom of the product molecule along the reaction path. Final vibrational and rotational state distributions essentially reflect the dynamics in the fragment channel. They are one major source of information about the dissociation process. 

Until recently, few attempts have been made to extend the theory of the ammonia inversion to account for the dependence of the inversion splittings on the vibrational and rotational quantum numbers [e.g. )]. These attempts differed not only from the standard approach to the vibration—rotation problem of rigid molecules but also from the approach to the problem of nonrigid molecules with internal rotation [for example )]. 

The immediate remedy to this problem was to take account of the quantum states of the internal modes of motion (vibration and rotation). Suppose that P E)5E is the number of internal quantum states for a molecule in the energy interval from E to E + 5E, and that the probability of activation into this energy range follows the Boltzmann distribution then... 

Internal energy partitioning between vibration and rotation is very different for Ai and A2 symmetries 18% of the internal energy goes into rotation for the Ai symmetry, in contrast with 50% for the A2 symmetry. This reflects itself in the product state distributions of Fig. 11, which have a maximum for low rotational quantum number j in the Ai symmetry, but for j near 15 for the A2 case. 

K equilibrium constant rotational quantum number (bulk modulus of elasticity [= ]) radius of gyration radiation intensity internal pressure. 

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