From these experimental results, it is concluded that in benzotrifluoride the internal rotation is decisive for the spin relaxation of the fluorines and that the dominant relaxation mechanism is the fluctuating spin-internal-rotation interaction. The radio frequency spectrum corresponding to the reorientation of the F19 nuclear moment in flurobenzene was studied by the molecular beam magnetic resonance method.
PART II: FLUORINE SPIN-ROTATION INTERACTION AND MAGNETIC SHIELDING IN FLUOROBENZENE
PART I
NUCLEAR SPIN-INTERNAL-ROTATION COUPLING
GENERAL INTRODUCTION
With the development of molecular beam magnetic resonance spectroscopy, it was possible to accurately evaluate the much smaller, analogous interaction of nuclear moments with molecular rotation. We then derive the rotational Hamiltonian for a molecule with one internal vertex and, in the next section, the interaction of the nuclear moment at this vertex with the rotational (including internal) motions of the molecule.
NUCLEAR SPIN RELAXATION MECHANISMS AND THE CALCULATION OF RELAXATION TIMES IN MOBILE DIAMAGNETIC LIQUIDS
But this must be done only in the event that the movements of the pairs are not correlated. The traceless part, .._ (J" , I of the shielding tensor, during molecular tumbling, can produce nuclear spin relaxation.
THE SPIN-INTERNAL-ROTATION INTERACTION
However, f 1 is not the angular momentum of the internal motion, but is less than i t by the factor r. Equation (83) can be reformulated as. where j is the total angular momentum of the interior.
EXPERIMENTAL
Under these circumstances, H0 does not appear in the rotating frame, and the motion of the magnetization is determined by the magnitude of H. For a time longer than the free-induction lifetime, the spin isochromats will be uniformly distributed in x'-y'.
Ampt1!ru<it
Due to the decay of the overall magnetization in the plane it is clear that the amplifier. The transverse relaxation time, T2, is the decay constant of the integrated magnetization in the x-y plane.
LAYOUT OF PULSED NMR SPECTROMETER
I PRE-AMP
RESULTS
In addition, the results of experiments with benzyl fluoride (¢-CH2F) will be given to support the arguments that will be presented about the nature of the dominant relaxation mechanism in benzotri-. The spin-lattice relaxation curve for benzotrifluoride was precisely measured for a time period of five half-. The relaxation time for benzotrifluoride, determined either from the slope of the relaxation curve or from ln2, where 'lo is the pulse separation for.
The difference between these values is well within the reproducibility (+5%) of the experiment at a given temperature and frequency and therefore these two values can be considered equal. In order to determine to what extent the relaxation in benzotrifluoride is determined (a) by intermolecular and (b) by intramolecular interaction, T1 was measured. These results indicate that either (a) the methyl protons "replace" approximately the same contribution to intermolecular dipolar relaxation as fluorinated ones or (b) the contribution of the intermolecular fluorine-fluorine dipolar relaxation to the total relaxation time is small compared to the sum of .
Although the estimated error in an individual measurement is about +5% error in the extrapolated values for T. Spin-lattice relaxation times of benzotrifluoride and benzyl fluoride as a function of carbon disulfide concentration.
However, the solubility of ¢CF3 in durene is apparently not high enough to allow the preparation of samples with a concentration of F19 within the sensitivity of our instrument. We measured the T1 values of F19 in ortho-, meta- and para-, chloro-, bromo- and iodobenzotrifluoride. Although it would be interesting, we did not study any ring-substituted benzotrifluoride, as the pulse technique is inherently low-resolution and would not be able to distinguish between ring fluorine and upper fluorines.
The relaxation times of the pure samples for all the mono-halogen-substituted benzotrifluorides are given in Table I. F19 SPIN GRID RELAXATION OF MONO-HALO-BENZOTRIFL UORIDES ORTHO META Chlorobenzotrifluoride 5.54 2.86 Bro mobenzotrifluoridene.2zotrifluoride.2.2zotrifluoride.2.2.6.2.6.2.6.2.2.2.6.2.2.2.2.6.2.6. 52. Dilution experiments were also carried out on the three ortho-, the meta- and para- chlorine, and meta-bromo-.
Spin-lattice relaxation times of ortho-, meta-, and parachlorobenzotrifluoride as a function of concentration in carbon disulfide.
RTHO
ONH2
INTERPRETATION AND CONCLUSIONS
Green and Powles (16) concluded that the relaxation in the liquid originates mainly from the motion of -CF. These observations are attributed by Powles to the operation of the spin-rotation mechanism in the methyl group relaxation at high temperatures. For the spin-internal-rotation relaxation moment of inertia, the correlation time and the spin-rotation constants must be replaced by those applicable to the motion of the peak.
With increasing barrier height (j") decreases and the effect of internal rotation as a relaxation mechanism diminishes, remaining. For the low-barrier case, inspection of the matrix elements in (ASa,b) predicts that the wavefunctions will take the form The matrix elements of the spin-rotation interaction Hamiltonians in the coupled and uncoupled cases were
The spin-rotation Hamiltonian derived in the previous section can be written as a tensor coupling of the nuclear spin and molecular rotational angular momentum. In the event that two of the three spins are more strongly coupled to the rotation, then we use the third.
PART II
INTRODUCTION
In molecular beam magnetic resonance spectroscopy, the nuclear resonance of a magnetic nucleus often exhibits fine structure or is broadened due to the interaction of the magnetic nucleus with the magnetic field produced by end-over-end rotation of the molecule. The importance of these spin-rotation constants lies in their intimate relationship with the high-frequency part of the nuclear magnetic shielding constant. The absolute shielding constant, 0; , for a nucleus N is related to the diagonal components of the spin-rotation tensor in the principal inertial axis system by (1).
I«A are the principal moments of inertia of the molecule and c~«s are the diagonal components of the spin-rotation tensor about these principal axes. The sum of the remaining two terms then usually refers to the high-frequency or paramagnetic contribution to shielding. Consequently, magnetic shielding constants, along with other molecular properties, are of essential fundamental importance for understanding the electronic structures of molecules.
In this paper, we would like to report on the experimental determination of the diagonal components of the fluorine spin-rotation tensor in fluorobenzene using the molecular beam magnetic resonance method. From these data and the known structure of the molecule, the high-frequency part of the fluorine nuclear shielding, the absolute fluorine shielding and the anisotrophy of the magnetic shielding tensor are determined.
EXPERIMENTAL
SPECTRA
The spectrum corresponding to the reorientation of the H1 nuclear moment is shown in Fig. lb. However, unlike the width of the fluorine resonance, the proton resonance is only 20 kc/s wide.
INTERPRETATION
We now show that spin-spin interaction cannot take into account the linewidth of the fluorine resonance spectrum. Based on the above, we can therefore conclude that the spin-spin interaction cannot contribute significantly to the overall width of the fluorine resonance spectrum. In fact, the large difference between the widths of the fluorine and proton spectra is strong evidence that the main source of broadening is the fluorine resonance.
On the other hand, large differences in the fluorine and proton spin-rotation interactions within the same molecule are not unknown and should be expected. In the next section we will attempt to analyze the observed fluorine resonance spectrum in terms of the following greatly simplified Eamiltonian. Since more than 100 J levels of the fluorobenzene molecule are populated at room temperature (Figure 2), we see that the full width of the fluorine resonance can be as much as 400 kc/s if the C~g's are approx. 1 - 2 kc/s.
The proton resonance spectrum is not only a composite spectrum over many rotational states, but also includes contributions from three sets of nonequivalent protons. Furthermore, since the proton resonance spectrum is not much wider than the width of a single resonance transition, the method we have used for the analysis of the fluorine resonance spectrum is not.
SPECTRAL ANALYSIS
If we further assume that the rotational energy levels are essentially independent of the vibration. It is only strictly valid in the limit where the width of the resonance spectrum is much larger than the width of . To establish the equivalence of the method of moments and the approach just described, it is sufficient to show.
Our preferred values of spin-rotation constants for the fluorine core in fluorobenzene are. Whenever possible, the spin-rotation constants obtained by the moment analysis method should therefore be checked by direct calculation of the shape of the composite resonance spectrum. Two methods are known for the direct calculation of the band shape of molecular beam nuclear resonance broadened by spin-rotational interaction.
One of the calculated spectra (curve A) in Figure 5 was compiled using the spin-rotation constants obtained. In light of the quality of the experimental data, we feel that further refinement is not warranted.
DISCUSSION
The sum of the first two terms in equation (2) is proportional to the total electrostatic potential at the core below. A calculation of the diamagnetic part of the fluorine shielding (Lamterm) in fluorobenzene was not done. However, it is possible to make an extremely good estimate of the total fluorine shielding in fluorobenzene in the following way.
478.3 ppm for the diamagnetic scan of the fluorine atom and 480.3 ppm for the fluorine ion. To be as conservative as possible, we will assign a value of +470 +10 ppm to the sum of the first two terms in the shielding expression for fluorine. We now turn our attention to a discussion of the anisotropy of fluorine shielding in fluorobenzene.
However, we obtained a quite different value for the magnitude of the shielding anisotropy from the measured rotation of our spin. Here, s denotes the degree of sp hybridization of fluorine (the J' bond orbital in the C-F bond and I is its
