Centrifugal distortions

The centrifugal distortion constant depends on the stifthess of the bond and it is not surprising that it can be related to the vibration wavenumber co, in the harmonic approximation (see Section 1.3.6), by 

Quantum mechanically, this expression for the rotational energy becomes 

Like B , D decreases as v increase its -dependence has often been fitted for diatomics using expressions of the form [6] 

When Dg 0, the rotational lines in a pure rotational spectrum (or in a vibration-rotation spectrum) are no longer equally spaced, but become more closely spaced at higher J. However, is usually not particularly large. In I2, which has one of the weaker vibrational force constants among ordinary 

The energy eigenvalue expression for the vibration-rotation of a diatomic molecule can be improved by including more terms from Equation 6-18. If one additional term is added, the approximation becomes  

If the vibrational potential is assumed to be harmonic, the effective potential becomes the following quadratic polynomial  

The two-body vibrating/rotating Schroedinger equation becomes  

One method for solving Equation 646 is to use perturbation theory. The term in the brackets in Equation 646 can be recognized as the Schroedinger equation for the RRHO approximation (Equation 6-19), and the term bs can be taken as a first-order perturbation. The first-order and higher order corrections to the energy eigenvalues to the RRHO approximation can then be computed using Perturbation Theory. 

An easier approach to solving Equation 646 is recognize that the effective potential in Equation 645 is still a quadratic equation resulting in a parabola. As can be seen in Eigure 6-7, the only difference between parabola Aks and the parabola from the effective potential in Equation 6-45 is that the minimum potential is no longer at s = 0. The minimum is shifted by amount 5, and the minimum potential is now Vq. 

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The vibrational dependence of the centrifugal distortion constant is too small to concern us further. 

When the effects of centrifugal distortion are included the term values of a prolate symmetric rotor are given by... 

Figure 5.7 Eight components, with AT = 0 to 7 and separated by centrifugal distortion, of the 7 = 8 — 7 microwave transition of SiH3NCS...

When centrifugal distortion is faken info accounf fhe rofafional term values are given by Equation (5.19) and we have... 

The approximate symmetry of the band is due to the fact that Bi — Bq, that is, the vibration-rotation interaction constant (Equation 5.25) is small. If we assume that B = Bq = B and neglect centrifugal distortion the wavenumbers of the i -branch transitions, v[i (J)], are given by... 

Any effects of centrifugal distortion will show up as slight curvature of the A2F(J) versus... 

More accurately, we can use the method of combination differences, while still neglecting centrifugal distortion, to obtain B" and B. Transitions having wavenumbers v[5(J — 2)] and v[0 J + 2)] have a common upper state so that the corresponding combination difference A4F(J) is a function of B" only ... 

Neglecting centrifugal distortion, the rotational term values for a spherical rotor in an A j vibrational state are... 

Beckmann P. A., Burnell E. E. Nuclear spin relaxation and centrifugal distortion effects in dilute silane gas, Can. J. Phys. 55, 1354-5 (1977). 

Actually, symmetrical tetrahedral molecules like methane do have extremely small dipole moments, caused by centrifugal distortion effects these moments are so small that they can be ignored for all practical purposes. For CH4, p is 5.4 x 10 D Ozier, I. Phys. Rev. Lett., 1971, 27, 1329 Rosenberg, A. Ozier, I. Kudian, A.K. J. Chem. Phys., 1972, 57, 568. 

Evidence for a significant contribution from the ionic form [BX] + - -Y in a gas-phase complex B- XY was first deduced from the spectroscopic constants of H3N- -ClF, as obtained by analysis of its rotational spectrum [63]. In particular, the value ka = 34.3 N m 1 of the intermolecular stretching force constant (obtained from the centrifugal distortion constant Dj in the man-... 

Values were also reported for the rotational constants, centrifugal distortion constants, and the chlorine nuclear quadrupole coupling constants of the three isotopic species F C1 02, F CF 02, and i F CF 0 0. The molecular dipole moment was found to be 1.722 0.03 D. 

The dipole moment is a fundamental property of a molecule (or any dipole unit) in which two opposite charges are separated by a distance . This entity is commonly measured in debye units (symbolized by D), equal to 3.33564 X 10 coulomb-meters, in SI units). Since the net dipole moment of a molecule is equal to the vectorial sum of the individual bond moments, the dipole moment provides valuable information on the structure and electrical properties of that molecule. The dipole moment can be determined by use of the Debye equation for total polarization. Examples of dipole moments (in the gas phase) are water (1.854 D), ammonia (1.471 D), nitromethane (3.46 D), imidazole (3.8 D), toluene (0.375 D), and pyrimidine (2.334 D). Even symmetrical molecules will have a small, but measurable dipole moment, due to centrifugal distortion effects. Methane " for example, has a value of about 5.4 X 10 D. 

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