Rotor parameters, vibration-rotation

In, for example, the planar asymmetric rotor molecule formaldehyde, IT2CO, shown in Figure 5.1(f), it is possible by obtaining, say, and B in the zero-point level and in the V = 1 level of all six vibrations to determine and B. Two rotational constants are insufficient, however, to give the three structural parameters rg(CFI), rg(CO) and (ZFICFI)e necessary for a complete equilibrium structure. It is at this stage that the importance of... 

Surprisingly, the enthalpy of combustion of isoxazole was determined only very recently.270 For isoxazole, AH° (298.15 K) = —(394.70 + 0.12) kcalth mol-1, from which the enthalpy of formation in the gas phase was derived as AHf (g) = 18.78 0.13 kcalth mol-1. The enthalpies of combustion of 3-amino-5-methylisoxazole and 5-amino-3,4-dimethylisoxazole have also been determined.271 Thermodynamic parameters for isoxazole have been derived from vibrational spectra using the harmonic oscillator-rigid rotor approximation.272,273 Analysis of the rotational spectra of isotopic forms of isoxazole, studied by double resonance modulated microwave spectroscopy, has given the molecular dimensions shown in Fig. 1.274,275... 

If we compare Eq. (4.78) with Eq. (4.73), it is clear that the algebraic three-dimensional model provides the correct rotational spectrum of a rigid linear rotor, where the (vibrational) angular momentum coefficient, ggg, is described by the algebraic parameters A 2 and A j2- The J-rotational band is obtained by recalling in Eq. (4.12), the branching law... 

The three rotational constants completely determine the energy level scheme of a rigid asyrmnetric top. This scheme may be considerably more complex than that of a synunetric rotor, especially if n is close to zero. Like it has already been shown for hnear and synunetric-top molecules, the number of parameters required to theoretically reproduce accmately measured rotational spectra may increase considerably if effects of rotation-vibration interaction, spin coupling, or internal rotation must be taken into account. Details of practical importance will be considered below. 

Finally, hindered-rotor potentials have to be taken into account when there are internal rotations. As long as no precise information on these often uncertain molecular parameters is available, the use of the simplified expressions (20)—(26) is recommended. One generally obtains agreement of better than a factor of 2 with the corresponding complete RRKM calculations (without sqxiration of vibrations and rotations). 

J. Chao, R. C. Wilhoit and B. J. Zwolinski, Ideal gas thermodynamic properties of ethane and propane , J. Phys. Chem. Ref. Data, 2, 427 (1973). Review and evaluation of structural parameters (including vibrational frequencies and internal rotation properties) tabulation of thermodynamic properties [C°, S°, H° — H°), (H° — H )/T, - G°-Hl)/T, AfG°,AfH°, logK ] for 0< T (K)< l500 calculated by statistical thermodynamic methods [rigid-rotor harmonic oscillator (RRHO) approximation]. 

In the previous section the rigid-rotor approximation has been applied, while in the following we account for the nonrigidity of the molecules, which means that the nuclear positions are no longer fixed at their equilibrium values. We first address the effect of the rotation itself on the energy levels (centrifugal distortion), and then the effect of molecular vibrations on the spectroscopic parameters is presented. 

NH2 Radical. The NH2 radical Is an asymmetric top with the asymmetry parameter k = (2 B-A-C)/(A-C)= -0.38 (axes b C2, c molecular plane). An increase of the rotational quantum number N leads to a change from prolate- to oblate-top behavior. The rotational constants A, B, and C, the centrifugal distortion constants Ak, A k, A, 5k, and 5, and the spin-rotational coupling constants Ag, Bg, and Cg, for the vibrational ground and excited states are listed in Table 10, p. 182. The rotational Hamiltonian used for fitting the spectroscopic data is a combination of the A-reduced asymmetric rotor Hrot [1] and the spin-rotation Hamiltonian figR [2] ... 

The three rotational eonstants eompletely determine the energy level seheme of a rigid asymmetrie top. This seheme may be eonsiderably more eomplex than that of a symmetrie rotor, espeeially if k is elose to zero. Like it has already been shown for linear and symmetrie-top moleeules, the number of parameters required to theoretieally reproduee aeeurately measured rotational speetra may inerease eonsiderably if effeets of rotation-vibration interaetion, spin eoupling, or internal rotation must be taken into aeeount. Details of praetieal importanee will be eonsidered below. 

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