Vibration-rotation contributions

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

The vibration-rotation contribution has been computed from the experimentally reported value of xj [124] for CH3I while for CHCI3 the small moment of inertia associated with the proton stretch renders the vibration-rotation... 

Figure 12. Theoretically obtained plots of In (Q(f) 2(0)) versus t (where t is scaled by t 2, isc = [mcH cHii/kBT]1 2 1.1 ps ) for the first three quantum levels (n = 1,2,3) of the CH3-I mode in CH3I from the friction estimates (shown in Figs. 10 and 11) and the vibration-rotation contribution. The equilibrium CH3-I bond length was set to re = 2.14 A. The results show an increasing Gaussian behavior in the short-time scale with increasing quantum number n. This figure has been taken from Ref. 133.

Then it is clear that if e is a slowly varying function of atomic mass, the vibration-rotation contributions to the moments of inertia will at least partially cancel out, leaving a result closer to the equilibrium result. Indeed, if e e, then... 

In Watson s treatment, these small or imaginaiy coordinates are not dropped, set equal to zero, or recomputed by some other method (such as COM relation) in fact, the values from Kraitchman s equations (Eq. (31) for the linear molecule) provide the essential mass-dependent vibration-rotation contributions to the moments of inertia. 

Le Guennec et al. determined equilibrium rotational constants and moments of inertia for FCIO3 [51] and 74gcH3F [52] and calculated the vibration-rotation contributions s for each principal axis. They used them to estimate s for other isotopomers of FCIO3 and 74gcH3F using the relation... 

We recommend that experimental uncertainties in the coordinates be assessed by Eq. (10) and the vibration/rotation contributions be assessed by the Costain rule [Eq. (14)1 or by first moment or product of inertia relations. Then, either the procedure introduced by Tobiason and Schwendeman20 should be used to propagate the uncertainties into distances or angles, or the two contributions should be added together and used with Eq. (18) to generate distance and angle uncertainties. 

Vibrational-rotational contribution to Gibbs free energy for HC1 from variational and AOSS-U calculations. 

Figure 6. Computed vibration-rotation contributions to the Gibbs free energy and 4th-order polynomial curve fits for H20, HDO, and D20 as a function of temperature. AH computations were carried out using the AOSS-U Monte Carlo method in mass-weighted Jacobi coordinates. Three hundred Fourier coefficients were used per degree of freedom and 106 Monte Carlo samples were used for each calculation. Error bars at the 95% confidence level, as weU as all free energy fluctuations, are smaller than the width of the lines showing the curve fits. An increment of 10 was used over the temperature interval (1000-4000 K).

Figure 7. Computed vibration-rotation contributions to the Gibbs free energy and fourth-...

Figure 8. Vibration-rotation contributions to the entropy for H20 as a function of temperature. The lower curve (O, solid line) shows the entropy predicted by the classical rigid rotator-quantum harmonic oscillator (RR/HO) model, the intermediate curve ( , dashed line) shows data taken from the JANAF Thermochemical Tables, and the upper curve (0> solid line) is obtained from differentiating the fourth-order fit to the AOSS-U free energy calculations shown in Figure 6. Note that (as expected) all three curves coincide at low temperatures and that the JANAF and AOSS-U results are in dose agreement throughout the entire temperature range.

Figure 9. Vibration-rotation contributions to the entropy for H20, HDO, D20, H2S, and H2Se as a function of temperature. All curves are obtained by differentiating the fourth-order fits to the AOSS-U free-energy calculations shown in Figures 6 and 7.

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