Spin rotation tensor

We now turn to the nuclear spin-rotation tensor c/ for the Mi nucleus in equation (8.155). This contains a purely nuclear contribution, arising from the third term of the first-order expression (8.153), and a purely electronic contribution coming from the third term of the second-order expression (8.154). To be specific ... 

If x, y and z are the principal axes of the molecule, the shielding and nuclear spin rotation tensors for the Mi nucleus are diagonal. The xx components, for example, are... 

A microwave study of the spin-rotation tensor of GaF in the gas phase has been reported by Wasylishen et al This provides spin-rotation constants for both the F and the Ga nucleus. A value of (an — aj ) = 945 35 ppm for Ga is derived from the experimental spin-rotation constant. The absolute Ga isotropic shielding obtained from the experimental spin-rotation constant at the ground vibrational state of GaF is... 

Note that authors sometimes use the notation A instead of C for the spin-rotation tensor. It is appropriate to refer these quantities to the molecular principal-axis system (a, b, c). In this way, the tensor components C, D., and cr. become uniquely defined molecular properties (g, g = a, b,... 

The summation should be taken over all nuclei n except N. Analogous expressions connect the other a and M tensor components. Thus, if the molecular structure is known and all the spin rotation tensor components, M, M and M can be determined from microwave spectroscopic... 

The following spin-rotation tensor elements are obtained by least-squares fitting earlier [65K1,67K1,68K1,70K2] BMS data ... 

Nuclear spin-rotation tensor (f Second derivative of energy with respect to rotational angular momentum and nuclear spin... 

The nuclear spin-rotation tensors are second-order properties and can be obtained by means of either analytic derivative theory or linear response theory [38]. Without going into detail, we refer interested readers to the literature [e.g., 38, 39]. We only briefly note that the electronic part of the nuclear spin-rotation tensor can be computed as a second derivative with respect to the nuclear spin and the rotational angular momentum as perturbations,... 

Spin-Rotation Interaction As explained above, the nuclear spin-rotation tensor consists of an electronic and a nuclear part, with the former computed as the second derivative of the electronic energy with respect to the rotational angular momentum and the appropriate nuclear spin as perturbations [38]. This is efficiently done using analytic second-derivative techniques [65], but, while calculations carried out using standard basis functions suffer from a slow basis set convergence, the use of perturbation-dependent basis functions significantly accelerates the basis set convergence [38]. 

Table 6.3 Comparison of Experimental and Computed Diagonal Elements of Spin-Rotation Tensors (kHz) of CF2 and CCI2 [90]...

Despite the importance of the nuclear quadrupole coupling in affecting the rotational spectra, the literature concerning the theoretical predictions of its related constants is rather limited. A significant example is provided by the recent investigation performed on the hyperfine structure in the rotational spectra of bromofluoromethane [75]. The experimental determination was supported by quantum chemical calculations of the nuclear quadrupole-coupling and spin-rotation tensors of Br and Br, performed at the CCSD(T) level in conjunction with core-valence correlation-consistent bases. Zero-point vibrational (ZPV) corrections were computed at the MP2 level in conjunction with the cc-pCVTZ basis set, whereas relativistic effects on the electric field gradient at the bromine... 

Table 6.9 E uilibrinni Values and Vibrational Corrections for Oxygen Spin-Rotation Tensor (kHz) of [80]...

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