Centrifugal distortion effects

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. 

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. 

Our conclusions about dipole moments are all within the context of the Bom-Oppenheimer approximation and methane, for example, has in reality a small permanent moment whose magnitude is the order of 10 to 10 D. This moment is caused by centrifugal distortion effects. ... 

We now turn to the second-order perturbation terms they are rather numerous since all possible combinations of squared and cross terms can contribute. In practice, we can often be selective and take only those terms which are significant into consideration. For example, the second-order terms produce only minor modifications of the fine structure patterns and are often difficult to separate from the effects of the first-order terms. Probably the most easily observable of the second-order terms are the centrifugal distortion effects associated with the off-diagonal matrix elements of Bn(R). There are two reasons for this. First, Btl(R) has a fairly strong dependence on r ... 

These values differ slightly from those given by Meerts [149]. Since the J = 3/2 level of the 2n3/2 state is particularly important, we commence our analysis with this level. We may anticipate that the mixing of different J levels should be even less important than it was in NO, since the rotational levels are much more widely spaced. Centrifugal distortion effects should also be small for the low J levels. 

For ordinary molecules the rigid rotor model works quite succussfully in explaining pure rotation spectra as well as the rotational fine structure obtained in other fields of spectroscopy. The vibrational perturbations appear mostly in the change of effective rotational constants with the vibrational state and in the centrifugal distortion effects. Much useful information can be found from these perturbation effects, however5. ... 

In calculation II the centrifugal distortion effects from the operator of Eq. (5.42) were rigorously evaluated. It is seen that the rotational series, QS, V 0, are very well reproduced. This is also the case for the °Qljl>2-series (at the rather low /-values included) whereas the Qo,o,2 -series still show significant systematic deviations. 

Centrifugal distortion effects are small but have been observed in nuclear quadmpole hyperfine structures of asymmetric tops. They can be analyzed with the aid of simple expansions in J and K, see, for example, [04Leu] ... 

In the fit of some data sets for light molecules which display large centrifugal distortion effects, it has been necessary to include the leading octic terms also. In the present compilation, these effects are described by... 

The fundamental absorption band of PH in its ground state X was observed at high resolution using a tunable diode laser spectrometer eighteen lines betwen 2224.4125 and 2107.8160 cm" (4.50 to 4.74 pm) have been identified as P-branch transitions with N" = 3 to 7 and 9, where each transition exhibits the fine-structure triplet splitting due to AJ = AN transitions between the three sublevels (J = N +1, N, N -1) of the respective rotational levels N" and N. Two further lines at 2292.1918 and 2308.1542 cm" (-4.3 pm) have been identified as the R-branch transitions with N", J " = 0,1 and 1,0. Hyperfine splitting could not be resolved. The analysis, which included rotational and centrifugal distortion effects as well as spin-spin... 

The molecule PH3 (C3V symmetry) is an oblate symmetric top (Crotational constants C (refers to rotation around the C3 axis) and B (perpendicular to C3). Since the permanent electric dipole moment is pointed parallel to the C3 axis, only pure rotational transitions with the selection rule AK=0 are allowed (K is the quantum number of the component about the C3 axis of the total angular momentum J). Their analysis leads to the parameters B, Dj, Djk, and Hjk. From the perturbation-allowed transitions AK= 3n (n=1,2,...), which become weakly allowed by centrifugal distortion effects (inducing a small dipole moment of about 8x10 D perpendicular to the C3 axis [1, 2, 3]), the K-related constants (C, Dk, Hk) were obtained see, e.g. [1, 3, 4]. 

Well-agreeing sets of constants from three detailed analyses of the spectrum [4, 5, 6] are presented in Table 6, p. 162. Jhe distortion constants are defined by the effective rotational Hamiltonian for a nondegenerate vibrational state of a symmetric-top C y, molecule, including terms up to the eighth power in the angular momentum (according to [7]). An effective rotational Hamiltonian in form of a Pad operator was derived [8 to 11]. Optimum versions of a rational expansion of the effective rotational Hamiltonian for C3V molecules were developed and some of them critically discussed [12 to 17]. For an ab initio calculation of centrifugal distortion effects for phosphane, see [18]. 

Puttkamer, Quack, and Suhml l07 also explained the dependence of tunneling splittings on rotational and vibrational excitation with simple models. They explained the effect of K as a centrifugal distortion effect that tends to move the H-F bonds into positions closer to perpendicular to the F-F axis, which is the same direction as required to initiate... 

Centrifugal distortion effects can be conveniently treated by means of perturbation theory ... 

Although the most fundamental selection rule for rotational spectroscopy is that the molecule should have a nonvanishing permanent dipole moment, we note that molecules without a permanent dipole moment can have perturbation-allowed rotational spectrum [22]. For spherical tops, for example, centrifugal distortion effects can produce a small permanent dipole moment that allows the observation of the rotational spectrum [1, 37]. 

The analysis, so far, has assumed that the molecules are rigid, but this is only an approximation. The molecules are vibrating, and so the rotational constants represent a vibrational average of structural parameters. Also, as in the case of diatomic molecules, molecular rotation may give rise to centrifugal distortion effects. 

Experimental Techniques Evaluation of the Moments of Inertia Rigid-Rotor Energy Levels and Spectra Centrifugal Distortion Effects Rotation-Vibration Interactions Internal Rotation... 

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