Rigid-rotor approximation

The first three Stokes lines in the rotational Raman spectrum of 02 are separated by 14.4 cm, 25.8 cm and 37.4 cm from the exciting radiation. Using the rigid rotor approximation obtain a value for tq. 

The R(0) transition in 12CO is at 115.271 GHz. Calculate the position of the R(0) transition in 13CO in the rigid rotor approximation. The separation between the energy levels in the R-branch is between levels E(J + 1) — E(J) and in the rigid-rotor approximation is given by ... 

In the rigid rotor approximation, the radial wave function is independent of /. The total wave function is... 

This simplification was already introduced in Chapter 2. In the rigid rotor approximation there is no rotational-vibrational interaction. The molecular Schrodinger... 

The partition function ratios needed for the calculation of the isotope effect on the equilibrium constant K will be calculated, as before, in the harmonic-oscillator-rigid-rotor approximation for both reactants and transition states. One obtains in terms of molecular partition functions q... 

The thermodynamic properties were computed with the molecular geometry and vibrational frequencies given above assuming an ideal gas at 1 atm pressure and using the harmonic-oscillator rigid-rotor approximation. These properties are given for the range 0-2000°K in the Appendix (Table AI). 

The simplest approach to modeling rotational spectroscopy is the so-called rigid-rotor approximation. In this approximation, the geometry of the molecule is assumed to be constant at the equilibrium geometry qeq. In that case, V(qeq) in Eq. (9.37) becomes simply a multiplicative constant, so that we may write the rigid-rotor rotational Schrodinger equation as... 

Less symmetric molecules require a considerably more complicated treatment, but in the end their spectral transitions arc functions of their three moments of inertia (see Section 10.3.5). From a computational standpoint, then, prediction of rotational spectral lines depends only on the moments of inertia, and hence only on the molecular geometry. Thus, any method which provides good geometries will permit an accurate prediction of rotational spectra within the regime where tlie rigid-rotor approximation is valid. 

Theory. The theory of collision-induced absorption profiles of systems with anisotropic interaction [43, 269] is based on Arthurs and Dalgamo s close coupled rigid rotor approximation [10]. Dipole and potential functions are approximated as rigid rotor functions, thus neglecting vibrational and centrifugal stretching effects. Only the H2-He and H2-H2 systems have been considered to date, because these have relatively few channels (i.e., rotational levels of H2 to be accounted for in the calculations). The... 

I. Elastic scattering of ground state para- and ortho-H2 in the rigid rotor approximation. J. Chem. Phys., 70 344, 1979. 

For simplicity of the presentation we will hereafter employ the rigid-rotor approximation in which r is fixed at the equilibrium bond distance re of BC.t Note that the potential energy surface (PES) V depends only on the two distances R and r and on the orientation angle 7. 

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... 

The torsional solutions are then determined variationally by using this potential (116), together with B constants (114) evaluated in the rigid rotor approximation, and by developing the solutions on the basis of 961 double products of trigonometric functions. 

This result was obtained in the rigid rotor approximation, i.e, with B and B 2 constant in equation (111). When non-rigidity will be introduced in the calculations, the B constants have to be developed also in Fourier expansions just as the potential. Better results may then be expected [59]. 

For that purpose the potential energy functions are determined, at 4-31 G levels + d orbitals on the sulphur atom, into the RHF and UHF approximations, for the singlet and triplet states, respectively [51], In addition, the B constants are calculated separately into the rigid rotor approximation, taking into account the geometrical changes. 

The vibrational qv) and rotational (q r) partition functions may be calculated within the harmonic and rigid rotor approximations, respectively. In addition, in this work, the qy values were corrected by replacing some of the large amplitude vibrations by the corresponding hindered internal rotations, when necessary. 

P13.14 The set of peaks to the left of center are the P branch, those to the right are the R branch. Within the rigid rotor approximation the two sets are separated by 4B. The effects of the interactions between vibration and rotation and of centrifugal distortion are least important for transitions with small J values hence the separation between the peaks immediately to the left and right of center will give good approximate values of B and bond length. 

The simplest approach for treating the rotational motion of a molecule is to make the rigid-rotor approximation so that the third and fourth terms in Eq. (2.23) are zero. In Cartesian coordinates the second term becomes... 

We consider the PD of CH3I by a multipath two-photon process from the 0,0,0) = 0) of the X Ai surface via excited states l,Vci,v) of the same surface. The J,Vci,v) states on the iPAi surface are obtained using the potential surface of Ref. [254] within the rigid-rotor approximation the corresponding... 

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