Rotational energy levels constants

The energy and symmetry properties of rotational levels have been discussed comprehensively by Herzberg (1945). The principles are unchanged as between the different classes, although the details vary somewhat from one class to another. Here we shall consider only the case of a near-prolate asymmetric top (lcxlb >la), a class which contains formaldehyde, propynal, and (raws-bent acetylene among other examples. In first approximation the rotational energy levels are expressed in terms of the rotational constants A, B, and C, where... 

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... 

It will be noticed in Table III that the rate constant for complex 3 has a maximum value, relative to complex I, at ef = 15 kcal., and relative to complex 2, at ef = 5 kcal. These comparisons give the differential effect of four Ci tumblings relative to four vibration modes at 1190(2) and 822(2), for complex 1, or 595(2) and 410(2), for complex 2. The effect of the quadratic dependence of rotational energy levels on the quantum number J is thus evident. This is what makes the statement of the footnote on p. 12 valid there, only two tumblings were represented by two vibration modes at 300 cm.-1, and the effect on the rate is estimated at less than a factor of 10 (even at a value of ef as low as 0-5 kcal.), while variation of rate with ef will be crudely correct. 

There is a large class of molecules for which all three rotational constants are dilTerent, although such molecules do not necessarily lack all symmetry. The rotational energy levels and the spectra of such molecules are rather complex. As a consequence of the asymmetry, the K degeneracy of the symmetric top levels is lifted, so that (2/ + 1) levels of different energy for each J value exist. The degree of asymmetry can be expressed by different parameters, a common one is defined by... 

For a nonrigid symmetric top molecule there are three different centrifugal distortion constants 1, D", and ). The rotational energy levels of the vibrational level v of an oblate symmetric top can be represented by... 

A diatomic molecule has two axes around which it can physically rotate see Figure 2. These axes are equivalent, and correspond to a single moment of inertia L I determines the spacing of rotational energy levels of the molecule, and is used to define the rotational constant B, where B = h/(8ai I) and h is Planck s constant. According to quantum mechanics, rotational energy levels can only take on certain discrete values, i.e. they are quantized, and we label them with a quantum number called J. The energies of the rotational levels are ... 

The preceding presentation describes how the collision impact parameter and the relative translational energy are sampled to calculate reaction cross sections and rate constants. In the following, Monte Carlo sampling of the reactant s Cartesian coordinates and momenta is described for atom + diatom collisions and polyatomic + polyatomic collisions. Initial energies are chosen for the reactants, which corresponds to quantum mechanical vibrational-rotational energy levels. This is the quasi-classical model [2-4]. 

Rotational constants - In molecular spectroscopy, the constants appearing in the expression for the rotational energy levels as a function of the angular momentum quantum numbers. These constants are proportional to the reciprocals of the principal moments of inertia, averaged over the vibrational motion. 

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