Free molecules, vibration-rotation

Figure 2.6-2 Variation of the frequencies by the incorporation of a tetraatomic molecule with two degenerate vibrational states ( ) in a crystal lattice, a spectrum of the free molecule, R = rotations, T = translations b static influence of the crystal lattice. The degenerate states split, the free rotations change into librations L c dynamic coupling of the vibrations of molecules within a primitive unit cell with z = 2 molecules. Each vibrational level of a molecule splits into z components and 3 z - 3 translational vibrations TS and 3 z librations L appear d dependence of the vibrational frequencies on the wave vector k of the coupled vibrations of all unit cells in the lattice. The three acoustic branches arise from the three free translations with = 0 (for k 0) of the unit cell all vibrations of the unit cells with / 0 (for k 0) give optical branches .

Plenary 9. J W Nibler et al, e-mail address niblerj chem.orst.edu (CARS and SRS). High resolution studies of high lymg vibration-rotational transitions in molecules excited in electrical discharges and low density monomers and clusters in free jet expansions. Ionization detected (REMPI) SRS or IDSRS. Detect Raman... 

If the rotational motion of the molecules is assumed to be entirely unhindered (e.g., by any environment or by collisions with other molecules), it is appropriate to express the time dependence of each of the dipole time correlation functions listed above in terms of a "free rotation" model. For example, when dealing with diatomic molecules, the electronic-vibrational-rotational C(t) appropriate to a specific electronic-vibrational transition becomes ... 

The semi-classical expression shown in Eq. (54) for the rate of ejection of electrons from a specified initial vibration-rotation state Xi (Q) induced by non BO coupling to all accessible neutral-molecule-plus-free-electron final states (labeled f) gives this rate as ... 

Microwave spectroscopy is generally defined as the high-resolution absorption spectroscopy of molecular rotational transitions in the gas phase. Microwave spectroscopy observes the transitions between the quantised rotational sublevels of a given vibrational state in the electronic ground state of free molecules. Molecular... 

Figure 2.6 A free molecule has three degrees of translational entropy and three degrees of overall rotational entropy. When two molecules condense to form one, the resulting adduct has only three degrees of translational and three degrees of rotational entropy overall, a loss of three degrees of each. A compensating gain of internal vibrational and rotational entropy partly offsets this loss.

The frequencies of rotational transitions are much smaller than vibrational frequencies, which means that the rotational motion is slower than the vibrational one. For a free molecule, the period of rotational motion is within 10 12-10 9 s. In condensed media the rotational motion is even slower, its period being respectively greater. At this stage it is more correct to speak of the relaxation time of the molecules. The latter essentially depends on the phase state of the medium. For example, in liquid water the relaxation time of molecular dipoles in an external electric field is about 10 11 s, whereas in ice (at 0°C) it is — 1 () 5 s. 

The appearance of additional peaks in the monolayer spectrum suggests the existence of surface vibratory modes associated with rotations and translations of the free molecule hindered by adsorption. To identify these modes, it is necessary to perform normal mode calculations of the vibrational spectrum of the adsorbed molecule. These calculations are also of interest because of the sensitivity of the frequency and intensity of the surface vibratory modes to the molecular orientation and the location and strength of its bonds to the substrate. 

The impulse model is applied to the interpretation of experimental results of the rotational and translational energy distributions and is effective for obtaining the properties of the intermediate excited state [28, 68, 69], where the impulse model has widely been used in the desorption process [63-65]. The one-dimensional MGR model shown in Fig. 1 is assumed for discussion, but this assumption does not lose the essence of the phenomena. The adsorbate-substrate system is excited electronically by laser irradiation via the Franck-Condon process. The energy Ek shown in Fig. 1 is the excess energy surpassing the dissociation barrier after breaking the metal-adsorbate bond and delivered to the translational, rotational and vibrational energies of the desorbed free molecule. 

For HCN the situation is somewhat better, because the data on DCN are much more effectively independent of the HCN data. This molecule has also been the subject of much high-resolution spectroscopic study, so that the vibration-rotation energy levels are particularly well known and its vibrational spectrum is free of accidental resonances. Table 8 compares the results of three quite different calculations. The calculation by Strey and Mills is the most recent, and was based on the latest spectroscopic data the refinement was made to a and x values rather than to the vibrational levels and rotational constants as used by both the earlier workers. Strey and Mills also constrained 3 of the quartic interaction constants to zero, and refined to cubic and quartic force constants in a separate calculation to the quadratic refinement. The level of agreement between the calculations leads to conclusions rather similar to those made above for C02 in particular, standard errors should be multiplied by at... 

Analysis of the symmetry of the chemical species under study (i.e. the point group for a free molecule, the space and factor groups for a crystal [44]), according to the site symmetry of every atom, allows the determination of the irreducible representation of the total modes and, after the subtraction of the translational and rotational modes (the acoustic modes for the crystals), the irreducible representation of the vibrational (or optical ) modes can be obtained. This means that the number of vibrational modes belonging to the symmetry species associated with the molecular or crystal symmetry can be counted. Consequently, the number of active modes can be counted, according to the symmetry selection rules of the different techniques (in particular IR and Raman). 

For diatomic molecules the configurational entropy remains the same but the vibrational term has to be modified and now a rotational term, also proportional to N, has to be included. For physlsorptlon the intramolecular vibration is usually not significantly perturbed. Hence, this contribution to S Ivibr) may be disregarded. To identify the entropy with the excess entropy, rotation-free molecules must be taken as the reference. 

The solution of the simultaneous differential Equations 11 and 12 has already been discussed in detail in Reference 16. Only the four lowest rotational-vibrational energies, as a function of y and D, for all of the isotopic hydrogens have been calculated and tabulated. These are the states which correlate, in the case of the free molecule, with the states... 

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