Spin-rotation constants

R. Y. Dong, M. Bloom 1970, (Determination of spin-rotation constants in flu-orinated methane molecules by means of nuclear spin relaxation measurements), Can. J. Phys. 48, 793. 

The value of uw is obtained from the spin-rotation constants Cj,... 

Equations relating and the spin-rotation constants have been given by Ramsey 9, 77, 78) for linear molecules and by Flygare 24) for symmetric top, spherical top, and asymmetric molecules. A simple expression for the general case, and neglecting vibrational effects, is... 

Another interesting point is to be presented in relation to chemical shift evaluations. From the directly-measured spin-rotation constant of POF3, diamagnetic and paramagnetic contributions to phosphorus chemical shifts were estimated (ca. +1000 and —640 p.p.m.). Extended to H3P04, which is the commonly accepted reference compound, this gives about 320 p.p.m. for the absolute 31P chemical shift.a999,9)... 

Recent reports of spin-rotation constants for aluminum chloride (35) and aluminum isocyanide (36) have made possible the comparison of experimental and ab initio calculated shielding results. If one were able to measure the27A1 chemical shift of one or both these compounds, it would be possible, in principle, to establish an absolute shielding scale for aluminum however, the high reactivity of these compounds has so farprecludedsuchmeasurements. High-resolution microwave measurements have also been recently carried out on A1H (37) however, analysis of the data did not consider the 27A1 spin-rotation interaction (vide infra). 

Xdv centrifugal distortion correction to the spin spin constant. Equation (7.188). yv- electron spin-rotation constant in vibrational level v. Equation (7.189). 

YDr centrifugal distortion correction to the electron spin-rotation constant. Equation (7.189). 

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. 

The alkali halide molecules have been studied comprehensively by molecular beam electric resonance methods. Table 8.14 presents a summary with references. In most cases the electric quadrupole coupling constants have been determined, and usually also the nuclear spin-rotation constants. 

The difference in electric dipole moment (0.007 72 D) between the proton and deuteron species is discussed by Muenter and Klemperer [87] and attributed to the difference in zero-point amplitude averaged over the same dipole moment function. If the difference is purely vibrational in origin, the dipole moment of the vibrationless molecule is calculated to be 1.7965 D, which compares with a theoretical value of 1.942 D obtained from Hartree Fock calculations by Huo [94], The nuclear spin-rotation constants of non-rigid diatomic molecules have been discussed theoretically by Hindermann and Cornwell [95]. 

We now turn to the spin-rotation constants, noting first that the proton constant was determined in earlier molecular beam magnetic resonance studies by Code, Khosla, Ozier, Ramsey and Yi [106]. First there is a relativistic acceleration correction ch (acc) to the spin rotation constant,... 

The corrected value of the spin-rotation constant was then fitted to the expression... 

A similar analysis was carried out for the 35 Cl spin-rotation constants, except that an additional vibrational term was added ... 

Table 10.7. Molecular constants (in MHz) determined [116] for X2Y. CN in the v = 0 and 1 levels nuclear hyperfine and nuclear spin-rotation constants refer to 14N...

Kobayashi, Goto, Yamamoto and Saito [154] were able to determine five of the six molecular parameters listed above, only the nuclear spin rotation constant for the 14N nucleus being too small to be significant. The molecular parameters and conclusions about the spin density distribution for both the a 1A and X 3XG states are fisted in table 10.14. 

The contribution of excited electronic state mixing to the electron spin-rotation constant y is given by a second-order expression similar to those for p and q. It involves the mixing of both 2 and 2 A states with the ground state and is as follows ... 

The spin-rotation constants inequation (10.199) couldnotbe determined, butmost of the other constants were listed. The results indicate that the electron configuration 3e/24v from Ti+(4F) dominates in the ground state of TiCl. At this stage it is difficult to estimate reliably the degree of electron delocalisation, but the structure seems to be mainly ionic. 

The most interesting aspect of these constants is the much larger spin rotation constant observed for the upper state, which undoubtedly arises because of second-order mixing with other nearby electronic states. 

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