Vibration-rotation contributions rotational constants

The vibration-rotation constants af are complicated functions of the harmonic (quadratic) and an-harmonic (mainly cubic) potential constants [9] and depend on the masses of the component atoms. Since a rotational constant is inversely proportional to a moment of inertia, a/ does not simply represent averaged vibrational contributions. It has, however, been proven [10] that the rotational constant corrected for the harmonic part of af gives the moment of inertia which corresponds to the real vibrational average. The corrected rotational constant is often denoted as B, i. e.. 

For bimolecular reactions (i.e. where the reactant is two separate molecules) and contribute a constant —4 RT. The translational and rotational enttopy changes are substantially negative, —30 to —50 e.u., due to the fact that there are six translational and six rotational modes in the reactants but only three of each at the TS. The six remaining degrees of freedom are transformed into the reaction coordinate and five new vibrations at the TS. These additional vibrations usually make a few kcal/mol... 

The above treatment has made some assumptions, such as harmonic frequencies and sufficiently small energy spacing between the rotational levels. If a more elaborate treatment is required, the summation for the partition functions must be carried out explicitly. Many molecules also have internal rotations with quite small barriers, hi the above they are assumed to be described by simple harmonic vibrations, which may be a poor approximation. Calculating the energy levels for a hindered rotor is somewhat complicated, and is rarely done. If the barrier is very low, the motion may be treated as a free rotor, in which case it contributes a constant factor of RT to the enthalpy and R/2 to the entropy. 

The vibration-rotation contribution to rotational constants is given (through... 

In a previous study of cyclic SiCs, a residual inertial defect of only slightly smaller magnitude was found, despite the fact that an extremely high level of calculation (surpassing that in the present study) was used to determine the vibration-rotation interaction contributions to the rotational constants. This was subsequently traced to the so-called electronic contribution, which arises from a breakdown of the assumption that the atoms can be treated as point masses at the nuclear positions. Corrections for this somewhat exotic effect were carried out in that work and reduced the inertial defect from about 0.20 to less than 0.003 amu A. However, the associated change in the rotational constants had an entirely negligible effect on the inferred structural parameters. Hence, this issue is not considered further in this work. 

Recently, an extensive study regarding a possible prediction of the association patterns of 1, 1-ionic surfactants in solvents with low dielectric constants has been proposed by Muller151,1S2. His model calculations are based upon a comparison between surfactant association patterns in solution and the formation of ionic lattices by (gaseous) alkali halides. The application of this latter process to the aggregation of detergent molecules in solution is certainly questionable with regard to many details, particularly, the considerations of internal rotational and vibrational entropic contributions in evaluating the stability of molecular clusters in solution. 

Equation (10) follows from the fact that, to a very good approximation, the sum Dq+ Gq = Dg is isotopically invariant. Equation (10) is useful because it allows one to use accurate Gq values rather than the more poorly determined Dq bond energies in calculating A °, and it is seen that the only input data needed to compute are isotopic masses and vibrational-rotational parameters. Since the g s appear as ratios in Eq. (2), most of the constants in fact cancel and Kp consists of four factors (the electronic contribution is essentially unity) ... 

The microwave spectrum of oxetanone-3 has been studied by Gibson and Harris 1S In the case of small-amplitude harmonic vibrations, the rotational constants should vary linearly with vibrational quantum number. For a single-minimum anharmonic potential representing a large-amplitude coordinate, deviation from this linear dependence is expected on two accounts. If we express the dependence on the large-amplitude coordinate in a power series, it may be necessary to carry the series past the quadratic term. Also, the contribution of the quartic term in the potential energy may cause deviations from linearity. 

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