Contains research objectives and reports on three research projects

Bitter, F.

Melissinos, A. C.

Waugh, J. S.

DSpace@MIT

V. NUCLEAR MAGNETIC RESONANCE AND HYPERFINE STRUCTUREProf. F. Bitter Dr. P. L. Sagalyn R. F. LaceyProf. L. C. Bradley III B. B. Aubrey E. LustigProf. J. S. Waugh R. W. Fessenden A. C. MelissinosDr. S. P. Davis R. H. Kohler S. T. Wray, Jr.RESEARCH OBJECTIVES1. Nuclear Magnetic Resonance(a) Nuclear Spin Interactions in Molecules. It has become clear that high-resolution nuclear-resonance experiments can give a great deal of information relativeto the geometrical and electronic structures of molecules. It is believed that allobserved spectral structures can be accounted for on the basis of the Hamiltonian-_ = h H ~yi ( I - i) + J.. I. I.i i j>iwhere H is the applied magnetic field, yi is the gyromagnetic ratio of nucleus i, Iiis its spin operator, and 6 and Jij are coupling constants characteristic of the elec-tronic wavefunctions of the molecule. We are attempting to justify the form of thisHamiltonian in intermediate coupling cases, and to correlate the coupling constantswith simple descriptions of the molecular wavefunctions. Standard radiofrequencytechniques are being used, with particular attention to the magnetic field uniformityand stability which will permit resolution of lines separated by approximately 1part in 108 of the total field.(b) Molecular Motion in Solids. Large-scale motion in solids can have importanteffects on the macroscopic properties of substances in which they occur. This fact isparticularly evident in solid-state diffusion and chain twisting in polymers such asrubber. Nuclear-resonance linewidth measurements can give rather direct infor-mation on the types of motion that are present and on their activation energies. Weare applying this method to cases that are not practicably accessible by other methods,with special reference to ion and terminal group reorientation. Results which have beenobtained deal with Co(NH+++ and MF ions and -CH 3 and -CF 3 groups in variouscrystal lattices.J. S. Waugh2. Hyperfine StructureThe purpose of this work is to learn about nuclear structure from detailed inves-tigations of atomic energy levels. Atomic electrons actually penetrate the nucleus inthe course of their orbital motion, and the position of the various possible energy levelsis influenced by the electron-nuclear interaction.The investigations of this group are concerned with changes in the energy levelsproduced by reorientation of the nucleus with respect to the atomic angular momentum,and with accurate comparison of energy levels of isotopes, both stable and unstable.A combination of radiofrequency or microwave and optical techniques is being used.Previously reported investigations of the isotopes of mercury are being extended,and new work on cadmium and calcium is being undertaken.F. Bitter(V. NUCLEAR MAGNETIC RESONANCE)A. SOME INTERRELATIONS OF THE MAGNETIC SUBLEVELS OFHYPERFINE -STRUCTURE LINESIn the double-resonance experiment performed on natural mercury (described inprevious reports), microwave resonance was established between the m-sublevels ofa certain F-level belonging to one of the odd isotopes (Hg 1 9 9 or Hg201). The energyof these sublevels depends upon the following parameters:B , the magnetic fieldg , the atomic g-factor for the electronic configurationa, the magnetic dipole interaction energyb, the electric quadripole interaction energy (for Hg 2 0 1 only)and it is given by the roots of secular equations which are easily obtained from anelementary quantum-mechanical calculation (1).The value of gJ is accurately known from measurements on the even isotopes;in establishing a resonance we accurately determine the energy difference betweentwo such m-sublevels, so that, if we also know the magnetic field, we have a relationbetween the remaining constants. For Hgl 9 9 , one resonance suffices to obtain a; forHg , each resonance gives a relation between a and b. Consequently, from two201resonances in Hg , we can obtain both a and b.The determination of a and b has been achieved in various ways; for example,2 7by Kusch, Millman, and Rabi (2) on the S/ state of Li . But their technique wasdifferent from ours. In their apparatus the frequency could be varied, and the fieldcould be kept constant, so that they were able to eliminate B from their equations.ZWe did not have the advantage of a variable frequency and were forced to use B inour calculations. Consequently, our equations take a different form.If we setAy = energy difference between sublevels in cm-H = B gz J B in cm- 1199the value of a for Hg 9 , as obtained from transitions in the F = 3/2 level, is2y - AyH 1 3a = for m =---m - -2 (1)3andAy - AyH 1 3a = for m =--m=32 2- y - H(V. NUCLEAR MAGNETIC RESONANCE)201For Hg we were not able to find a closed form for the expression for a and b, andhad to use a computational method. (The root of a third-order equation is included inthis expression.) However, from a transition in the F = 5/2 level. (m = 3/2 - m = 5/2),we obtain the following relation between a and b:5 AyZ - AyH-a+ 10b = (2)Z H -Ay5It is interesting that5- a + 10b2is exactly the splitting between the F = 5/2 and F = 3/2 levels of Hg 2 0 1 (at zero field),as predicted by the interval rule. Furthermore, Eqs. 1 can also be transformed togive3 Ay - AyH- a = + (3)-H - Aywhere (3/2)a is, again, the exact splitting of the F = 3/2 and F = 1/2 levels of Hg1 9 9 .Equations 2 and 3 are obtained from rather lengthy expressions which containradicals, and so forth, so that the possibility of a reduction to simple forms isinteresting. Moreover, the symmetry between Eqs. 2 and 3 and the fact that theyare related to the zero-field splitting of the F-levels raises the suspicion that theymight be consequences of a more general quantum-mechanical rule. If this is true,a knowledge of the underlying general rule should permit the formulation of closed-form results for any arbitrary combination of J and I. This will be extremely helpful,especially in cases in which our straightforward calculations present impossible alge-braic difficulties.A. C. MelissinosReferences1. See, for example, Th. Schmidt, Z. Physik 111, 332 (1938-39).2. P. Kusch, S. Millman, and I. I. Rabi, Phys. Rev. 57, 765 (1940).B. INTERMEDIATE COUPLING IN NUCLEAR RESONANCE SPECTRAWe define an intermediate coupling case as one in which, in the molecular nuclearspin Hamiltonian, J.ij H(yi6i - y. 6 .) for one or more nuclear pairs (i, j). In thesecases the energy level schemes and selection rules are complicated, and lead to(V. NUCLEAR MAGNETIC RESONANCE)PPMI PIA B CFig. V-1. Proton resonance spectrum of styrene. Parametersused for predicting spectrum:B - SA = 0.55 PPM JAB = 1.6 cps6C - A = 1. 6 7 PPM JAC = 12 cpsJBC = 20 cpscomplex spectra that provide a stringent test of the Hamiltonian. We have attemptedto find consistent sets of J's and 6's from which observed spectra can be calculated,with the sort of success illustrated in Fig. V-1, which applies to the three-spinethylenic system of styrene. The intense line on the right is attributable to theprotons ignored in this calculation. Five adjustable parameters are able to repro-duce 12 line positions and 12 intensities within experimental error.These calculations are now being extended to more complex systems, with someattention to the information obtainable from incompletely resolved spectra.J. S. WaughC. THE FREE ELECTRON MODEL FOR CHEMICAL SHIFTSThe problem of calculating S's (chemical shifts) and J's (spin-spin interaction con-stants) from molecular theory is a very difficult one. In the comparatively simple caseof aromatic molecules, we have extended a suggestion of Pople (1) to calculate chemicalshifts on the basis of a free electron model. The chemical shifts are regarded as beingcaused by the magnetic fields arising from precession of the Tr electron systems of thesemolecules in the applied field. A complete description of this work will appear soon (2).J. S. WaughReferences1. J. A. Pople, J. Chem. Phys. 24, 1111 (1956).2. J. S. Waugh and R. W. Fessenden, J. Am. Chem. Soc. (in press).

Nuclear Magnetic Resonance and Hyperfine Structure

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Nuclear Magnetic Resonance and Hyperfine Structure

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