Spin-rotation constants, nuclear magnetic

Lichten [3 5] studied the magnetic resonance spectrum of the para-H2, N = 2 level, and was able to determine the zero-field spin-spin and spin-orbit parameters we will describe how this was done below. Before we come to that we note, from table 8.6, that in TV = 2 it is not possible to separate Xo and X2. Measurements of the relative energies of the J spin components in TV = 2 give values of Xo + fo(iX2, and the spin-orbit constant A the spin rotation constant y is too small to be determined. In figure 8.18 we show a diagram of the lower rotational levels for both para- and ortho-H2 in its c3 nu state, which illustrates the difference between the two forms of H2. This diagram does not show any details of the nuclear hyperfine splitting, which we will come to in due course. 

Figure 6.10. Flowchart for the derivation of nuclear magnetic shielding constants from experimental spin-rotation constants.

Calculated Rovibrational Contributions, Temperature Corrections, and Nuclear Magnetic Shielding Constants at 300 K [<7(300 K)] in Comparison with Corresponding Shielding Constants Derived from Experimental Spin-Rotation Constants" ... 

Stephens showed that, by including also nonadiabatic effects, a vibrationally induced magnetic moment can arise that will lead to a nonvanishing rotational strength [250]. Vibrational circular dichroism is thus an example of a nonadiabatic effect, in a similar manner as properties such as the nuclear spin-rotation constant or the rotational g tensor [251, 252]. 

Cl, C2, C3, C4 iS) 2S> 1Tj 2T Cl, Cj spin-rotation constants of molecule AB for nucleus A and B, respectively C3 tensorial part of the nuclear spin-spin interaction C4 scalar part of the nuclear spin-spin interaction scalar and tensorial parts of the magnetic shielding of the magnetic moment of nucleus A and B, respectively... 

Hindermann, D. K. and Cornwell, C. D. (1968). Vibrational corrections to the nuclear-magnetic shielding and spin-rotation constants for hydrogen fluoride shielding scale for F. J. Chem. Phys., 48, 4148-4154. 

Sundholm, D., 8c Gauss, J. (1997). Isotope and temperature effects on nuclear magnetic shieldings and spin-rotation constants calculated at the coupled-cluster level. Molecular Physics, 92,1007. 

With the gauge origin at the nucleus in question, o in Ramsey s expression is related to another molecular property, the nuclear spin-rotation constant. The nuclear spin-rotation constant arises from the coupling of the magnetic moment of a nucleus with the magnetic field generated by the molecular rotation at that nucleus. Ramsey and Flygare have shown that... 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

In the external constant magnetic field H0 the nuclear magnetic moments of hydrogens p./ (associated with the nuclear spin / = 1/2), and that of metallic atoms Ps (associated with the nuclear spin S), rotate with the Larmor frequencies oo/= gj H0 and (os = gs H0, where g/ and gs are the giromagnetic ratios of corresponding nuclei. 

One of the most interesting and important results of the study was to show how the molecular constants change as the vibrational quantum number v increases. This behaviour is presented in table 8.10. The electron spin-spin and rotational constant values came, initially, from the analysis of the optical electronic spectrum [47], although the values of the spin-spin constants for different vibrational levels were refined by the analysis of the radiofrequency spectrum. The nuclear hyperfine parameters are obtained solely from the magnetic resonance experiments. We will discuss the significance of these constants in the following subsection. 

The magnetic resonance spectrum of HF was studied some nine years earlier than the electric resonance spectrum by Baker, Nelson, Leavitt and Ramsey [93] in this case the transitions studied were magnetic dipole, corresponding to reorientation of the proton and fluorine nuclear spins. Values of the nuclear spin rotation and dipolar constants were essentially confirmed by the later electric resonance measurements. We now describe measurements of the electric resonance spectrum in the additional presence of a strong magnetic field, carried out by de Leeuw and Dymanus [89]. 

In order to assign the Zeeman patterns for the three lowest rotational levels quantitatively, one must determine the spacings between the rotational levels, and the values of g/and gr-In the simplest model which neglects centrifugal distortion, the rotation spacings are simply B0. /(./ + 1) this approximation was used by Brown and Uehara [10], who used the rotational constant B0 = 21295 MHz obtained by Saito [12] from pure microwave rotational spectroscopy (see later in the next chapter). The values of the g-factors were found to be g L = 0.999 82, gr = —(1.35) x 10-4. Note that because of the off-diagonal matrix elements (9.6), the Zeeman matrices (one for each value of Mj) are actually infinite in size and must be truncated at some point to achieve the desired level of accuracy. In subsequent work Miller [14] observed the spectrum of A33 SO in natural abundance 33 S has a nuclear spin of 3/2 and from the hyperfine structure Miller was able to determine the magnetic hyperfine constant a (see below for the definition of this constant). 

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