Polyatomic systems selection rules

Calculations for the time required to reach equilibrium can be made for selected systems using the kinetic data in Tables I-III. For systems for which no kinetic data are available, estimates can be made. Thus for ion-solvent molecule equilibria studies in which the clustering molecules are polyatomic, as a rule of thumb one can assume that the achievement of equilibrium is determined by the rate of the slowest reaction, which has a rate constant k 10 cm molecule sec This value corresponds to the rate constant for the attachment of HjO to Cl with O2 as third body (Table I). With this value one calculates a half-life for the reaction at 0.5 Torr HjO and 5 Torr third body equal to 4 x 10 sec. The subsequent steps in the clustering sequence require considerably less time since... 

The probabilities of absorption by structures larger than an atom are determined in essentially the same way. For diatomic and linear polyatomic molecules the orbital momentum selection rule becomes AA = 0, 1, where A is the symbol for molecular total orbital angular momentum. For systems with appropriate symmetry, the rules are g m, -I- <-> H-, —. For non-linear polyatomic molecules... 

The results presented in this chapter show that the use of proper effective models, in combination with calculations based on the exact vibrational Hamiltonian, constitutes a promising approach to study the laser driven vibrational dynamics of polyatomic molecules. In this context, the MCTDH method is an invaluable tool as it allows to compute the laser driven dynamics of polyatomic molecules with a high accuracy. However, our models still contain simplifications that prevent a direct comparison of our results with potential experiments. First, the rotational motion of the molecule was not explicitly described in the present work. The inclusion of the rotation in the description of the dynamics of the molecule is expected to be important in several ways. First, even at low energies, the inclusion of the rotational structure would result in a more complicated system with different selection rules. In addition, the orientation of the molecule with respect to the laser field polarization would make the control less efficient because of the rotational averaging of the laser-molecule interaction and the possible existence of competing processes. On the other hand, the combination of the laser control of the molecular alignment/orientation with the vibrational control proposed in this work could allow for a more complete control of the dynamics of the molecule. A second simplification of our models concerns the initial state chosen for the simulations. We have considered a molecule in a localized coherent superposition of vibrational eigenstates but we have not studied the preparation of this state. We note here that a control scheme for the localiza-... 

In the previous chapter, vibrational/rotational (i.e. infrared) spectroscopy of diatomic molecules was analyzed. The same analysis is now applied to polyatomic molecules. Polyatomic molecules have more than one bond resulting in additional vibrational degrees of freedom. Rotation of linear polyatomic molecules is mechanically equivalent to that of diatomic molecules however, the rotation of non-linear polyatomic molecules results in more than one degree of rotational freedom. The result of the additional vibrational and rotational degrees of freedom for polyatomic molecules is to complicate the vibrational/rotational spectra of polyatomic molecules relative to spectra of diatomic molecules. Though the spectra of polyatomic molecules are more complicated, many of the same features exist as in the spectra of diatomic molecules. As a result, a similar approach wiU be used in this chapter. The mechanics of a model system will be solved, determine the selection rules, and the features of a spectrum will be predicted. 

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