Vibration-rotation coupling constant

The only tenn in this expression that we have not already seen is a, the vibration-rotation coupling constant. It accounts for the fact that as the molecule vibrates, its bond length changes which in turn changes the moment of inertia. Equation B1.2.2 can be simplified by combming the vibration-rotation constant with the rotational constant, yielding a vibrational-level-dependent rotational constant. 

The fifth term in (4.67) represents an interaction between vibration and rotation, and ae is called a vibration-rotation coupling constant. [Do not confuse ae with a in (4.26).] As the vibrational quantum number increases, the average internuclear distance increases, because of the anharmonicity of the potential-energy curve (Fig. 4.4). This increases the effective moment of inertia, and therefore decreases the rotational energy. We can define a mean rotational constant Bv for states with vibrational quantum number v by... 

P. Botschwina and J. Fliigge, Chem. Phys. Lett., 180, 589 (1991). Ab Initio Vibration-Rotation Coupling Constants and the Equilibrium Geometries of NCCN and CNCN. 

Vibration-rotation coupling constant Distortion polarizability... 

E/cR,cRj Force constants fundamental vibrational frequencies infrared and Raman spectra vibrational amplitudes vibration-rotation coupling constants... 

Defined in this way, the vibration-rotation coupling constant will usually be positive, because By, which includes the effect of the vibrational motion, will usually be smaller than 5g, which depends only on the equilibrium bond length. If rotational constants are measured in several vibrational states, then we add higher order terms with coupling constants such as (3 to fit Eq. 9.8 to the experimental data. 

The equilibrium geometry of C2N2 was calculated from experimental Bq values [1] of 5 iso-topomers and ab initio values for the vibration-rotation coupling constants [3,4]. Later 4 new isotopomers [2] help to confirm previous values. 

The third term is the centrifugal distortion term, and the constant a is called the vibration-rotation coupling constant. Note that the vibration-rotation coupling term involves both the vibrational and rotational quantum states v and J. 

It should be noted that the spacings between the experimentally observed peaks in HC1 are not constant as would be expected based on the above P- and R- branch formulas. This is because the moment of inertia appropriate for the v = 1 vibrational level is different than that of the v = 0 level. These effects of vibration-rotation coupling can be modeled by allowing the v = 0 and v = 1 levels to have rotational energies written as... 

The RRKM rate constant as given by equation (6.73) in the previous chapter is expressed as a ratio of the sum of states in the transition state and the density of states in the reactant molecule. An accurate calculation of this rate constant requires that all vibrational anharmonicity and vibrational/rotational coupling be included in calculating the sum and density. The vibrational energy levels in units of wavenumbers can be represented by a power series ... 

Np2(X2Bi). Rotational Constants A, B, C, and Spin-Rotation Coupling Constants e a for the Vibrational Ground State and the Excited States Vi=1 and V3 = 1. 

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 constants c, that arc generated by the expansion of Equation 6-60 can be assigned to the various physical constants such as the first anharmonicity, centrifugal distortion, vibration-rotation coupling, and so on. 

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