Rotation interaction

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... 

If B can be obtained for at least two vibrational levels, say Bq and Bi, then B and the vibration-rotation interaction constant a can be obtained from Equation (5.25). Values for and a, together with other constants, are given for H CI in Table 6.2. 

From the following wavenumbers of the P and R branches of the 1-0 infrared vibrational band of H Cl obtain values for the rotational constants Bq, Bi and B, the band centre coq, the vibration-rotation interaction constant a and the intemuclear distance r. Given that the band centre of the 2-0 band is at 4128.6 cm determine cOg and, using this value, the force constant k. 

By obtaining values for B in various vibrational states within the ground electronic state (usually from an emission spectrum) or an excited electronic state (usually from an absorption spectrum) the vibration-rotation interaction constant a and, more importantly, B may be obtained, from Equation (7.92), for that electronic state. From B the value of for that state easily follows. 

Hubbard P. S. Theory of nuclear magnetic relaxation by spin-rotational interactions in liquids. Phys. Rev. 131, 1155-65 (1963). 

Courtney J. A., Armstrong R. L. A nuclear spin relaxation study of the spin-rotation interaction in spherical top molecules. Can. J. Phys. 50, 1252-61 (1972). 

The probability that J has a wave vector K relative to I in HD + is given by the momentum transform of the wave function for the vibrational and rotational interactions in HD +. The probability that I is captured by X with a wave vector k is given by the momentum transform of the wave function for the rotational and vibrational interactions in XI+. 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

When other relaxation mechanisms are involved, such as chemical-shift anisotropy or spin-rotation interactions, they cannot be separated by application of the foregoing relaxation theory. Then, the full density-matrix formalism should be employed. 

A model which takes into account the spin-rotation interaction has been found to satisfactorily explain the 0 rotation band of PHg. The millimetre-wave spectra of HCP and DCP have been compared with those of HCN and DCN. A method of estimating frequencies of bands in this region due to processes such as pseudorotation has been suggested. This new approach involves calculation of the rovibronic energy levels from the effects of quantum-mechanical tunnelling. ... 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

In Equation (15), R others encompasses all secondary interactions which are not included in the first two terms (for instance the interaction with an unpaired electron, the spin-rotation interaction,...). By contrast, the expression of the cross-relaxation rate is simply... 

Since these terms are proportional to tr, they increase with decreasing temperature.1 There are several line-width contributions, included in oc0, which do not depend on m,-. These include magnetic field inhomogeneity and the spin rotation interaction, the latter increasing with 1/tr and thus with increasing temperature. These and other line-width effects have been studied in some detail and are discussed elsewhere.13... 

C. R. Quade, A note on internal rotation rotation interactions in ethyl alcohol. J. Mol. Spectrosc. 203, 200 202 (2000). 

Herman, R., and Wallis, R. F. (1955), Influence of Vibration-Rotation Interaction on Line Intensities in Vibration-Rotation Bands of Diatomic Molecules, 7. Chem. Phys. 23, 637. 

In Equation 12.8 Be is the rotational constant, Be = h/(8jt2I), (I is the moment of inertia), coe is the vibrational frequency, 27T(oe = (k/ix)1, (k the vibrational force constant and x the reduced mass), re the equilibrium bond length (isotope independent to reasonable approximation), and ae is the vibration-rotation interaction constant... 

Recent microwave data for the potential interstellar molecule Sis is used together with high-level coupled-cluster calculations to extract an accurate equilibrium structure. Observed rotational constants for several isotopomers have been corrected for effects of vibration-rotation interaction subsequent least-squares refinements of structural parameters provide the equilibrium structure. This combined experimental-theoretical approach yields the following parameters for this C2v molecule re(SiSi) = 2.173 0.002A and 0e(SiSiSi) = 78.1 O.2 ... 

The purpose of this report is to demonstrate the ease with which highly accurate equilibrium structures can be determined by combining laboratory microwave data with the results of ab initio calculations. In this procedure, the effects of vibration-rotation interaction are calculated and removed from the observed rotational constants, Aq, Bq and Cq. The resulting values correspond to approximate rigid-rotor constants and and are thus inversely... 

Five isotopomers of Sia were studied in Ref (20), and are labeled as follows Si- Si- Si (I) Si- Si- Si (II) Si- Si- Si (III) Si- "Si- Si (IV) Si- Si- °Si (V). Rotational constants for each (both corrected and uncorrected for vibration-rotation interaction) can be found towards the bottom of Table I. Structures obtained by various refinement procedures are collected in Table II. Two distinct fitting procedures were used. In the first, the structures were refined against all three rotational constants A, B and C while only A and C were used in the second procedure. Since truly planar nuclear configurations have only two independent moments of inertia (A = / - 4 - 7. = 0), use of B (or C) involves a redundancy if the other is included. In practice, however, vibration-rotation effects spoil the exact proportionality between rotational constants and reciprocal moments of inertia and values of A calculated from effective moments of inertia determined from the Aq, Bq and Co constants do not vanish. Hence refining effective (ro) structures against all three is not without merit. Ao is called the inertial defect and amounts to ca. 0.4 amu for all five isotopomers. After correcting by the calculated vibration-rotation interactions, the inertial defect is reduced by an order of magnitude in all cases. 

In a previous study of cyclic SiCs, a residual inertial defect of only slightly smaller magnitude was found, despite the fact that an extremely high level of calculation (surpassing that in the present study) was used to determine the vibration-rotation interaction contributions to the rotational constants. This was subsequently traced to the so-called electronic contribution, which arises from a breakdown of the assumption that the atoms can be treated as point masses at the nuclear positions. Corrections for this somewhat exotic effect were carried out in that work and reduced the inertial defect from about 0.20 to less than 0.003 amu A. However, the associated change in the rotational constants had an entirely negligible effect on the inferred structural parameters. Hence, this issue is not considered further in this work. 

This phenomenon of antiparamagnetic paramagnetic terms clearly needs a name and is called here the Cornwell effect (ideally the Cornwell-Santry effect). Positive contributions to op (which may or may not be positive overall) are expected in heteronuclear diatomics if they have a IT state this excludes, e.g., HF, InF, and TIF. In homonuclear diatomics, the IT -> a excitation is symmetry-forbidden. The possibility has been mentioned for XeF (34), although, from the chemical shift and calculated values of aa, the resultant Op ( F) is negative in XeFg and KrFj (cf. Fig. 7). Another candidate is FC DH, from the evidence of the fluorine chemical shift and spin-rotation interaction (96). According to this interpretation there should be a substantial upheld shift of the... 

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