Spin-rotation parameters

In a similar manner, there is a second-order contribution to the spin-rotation parameter which arises from the cross-term between the spin orbit coupling and the... 

In other words, each of the parameters is the sum of a first-order and a second-order contribution. We have met equation (7.126) for the effective rotational constant operator before, in an earlier section, where we pointed out that the second-order contribution Ba> is very much smaller than BiV) and that these two contributions have a different reducedmass dependence. It is importantto realise thatthis is not generally true. Indeed, except for molecules with very light atoms such as H2, the second-order contribution to the spin-rotation parameter is usually very much larger in magnitude than the first-order contribution. The same is also often true for the spin-spin coupling parameter /.. The reduced mass dependences of the two contributions to the spin-rotation parameter y are different from each other and quite complicated. However, Brown and Watson [17] were able to show the rather remarkable result that when one takes the first- and second-order contributions together as in equation (7.127), the reduced mass dependence of the resultant parameter y(R) is simply /u-1. 

A very similar treatment can be applied to the spin-rotation parameter y. Once again there is a first- and second-order contribution with the second-order contribution dominating in all but the lightest molecules. Full expressions for yn> and ya> are given in equations (7.110) and (7.122). 

By this stage, it will be apparent that even the sign of the spin-rotation parameter contains valuable information on the electronic structure of the molecule. To appreciate this point fully, let us consider a3 state which arises from a 2 electron configuration. The effective spin rotation interaction arises from second-order mixing with3 n states. Let us assume that there is only one such state which lies higher in energy so that the... 

These qualitative predictions are clearly too simple but they provide a useful zeroth-order model of the electronic structure. For example, the model predicts values for the spin-rotation parameters in the A, B, and C states of CaNH2 that are in reasonable agreement with experiment [53]. The qualitative predictions of molecular properties can also be compared with the results of ab initio calculations. The first calculations on CaNH2 [54] and related molecules such as CaBH4 were made by Ortiz... 

The most interesting aspect of the rotational analyses of the A X, B-X and C X transitions are the values for the complete set of nine spin rotation parameters of the A, B, and C states (i aa, sbb, and f.cc for each state). If the orbitals containing the unpaired electron in these three states (Fig. 7) are approximate by a set of p orbitals (px, py, pz) then all nine spin-rotation constants can be easily estimated by pure precession relationships. 

TABLE 6 CaNH Spin-Rotation Parameters for the A2B2, B2Bl, and C2/ , States of... 

Ruorine nuclear spin-rotation parameter, compare subvolume Il/I9c, p. 264 (replace by N). 

At the end of the 1970s proposals were made [G179] to measure a third, independent proton-nucleus elastic scattering observable, specifically the spin rotation parameter, which is referred to as 0. 

All values in kHz. Spin-spin interactions are ignored in [80K1]. In [80J1], they have been partly determined from the spectral fit while the Br spin-rotation parameters were indirectly concluded and held fixed. 

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