An Introduction to the Analysis of Spin-Spin Splitting in High-Resolution Nuclear Magnetic Resonance Spectra

Abstract

From the preface: To learn to apply the methods of wave mechanics in a practical way seems to involve a quantum-like transition with a relatively low transition probability. Chemistry students by the thousands are exposed to the principles and jargon of wave mechanics and are able to talk in a most knowing way about orbitals, overlap, spin, etc. But very few of these students can set about to make any sort of an actual calculation of resonance energies of conjugated systems or the energy levels of nuclear spin systems, and this despite the fact that the mathematics involved, although perhaps tedious, usually does not require more than college algebra. I lay the blame for this situation just as much on the writers in the field and the students themselves as on the intrinsic difficulties of the subject. Many writers seem sincerely anxious to impart their knowledge to novices but may have forgotten, or never really knew, how difficult it is for the average chemist to make the transition between knowing and not knowing. Certainly, it is a long and tedious job to try to make clear in writing step by step what is involved, particularly when exciting prospects of discussing applications and new developments beckon. Students in their turn make things hard for themselves by their failure to work problems or to work through even simple derivations. Although it may seem presumptuous to some readers for a synthetic organic chemist to write an introduction to the quantum mechanical formulation of nuclear spin states and transitions, I have pointed out elsewhere [J. Am. Chem. Soc., 82, 5767 (1960)] that I believe all chemists can use nuclear magnetic resonance spectroscopy with greater interest, skill, and understanding by having at least a rudimentary knowledge of the quantitative theory of spin-spin splitting. The purpose of this book is to show that the path to making practical calculations of spin-spin splittings is not really difficult. No prior knowledge of quantum mechanics or the mathematics thereof will be assumed. Familiarity with the elements of nuclear magnetic resonance spectroscopy at the level of Roberts, "Nuclear Magnetic Resonance," McGraw-Hill Book Company, Inc., New York, 1959, and Jackman, "Applications of Nuclear Magnetic Resonance Spectroscopy in Organic Chemistry," Pergamon Press, New York, 1959, will be particularly important. Since in my opinion it is very difficult to gain mastery of the material presented without a great deal of practice, exercises have been interspersed at appropriate places in the text. It is strongly recommended that these be worked through as encountered. The coverage throughout is intended to be illustrative rather than comprehensive. The AX and AB cases are discussed in considerable detail to show how the nuclear spin states are formulated, their energies computed, and the probabilities of transitions between them calculated. Then AX2 and AB2 are compared in sufficient detail to make clear how more lines can appear than would be expected from a simple counting of the number of interactions involved. Some discussion is presented of ABX to illustrate the important point that a nucleus such as X can often appear to be coupled to A even when J AX is zero. The effect of changing the relative signs of coupling constants is also considered in connection with ABX. Finally the A2X2 systems with JAX [does not equal] J'AX are covered to show that it is possible to have spectra influenced by JAA and JXX even when (v A - v X ) >> JAA or JXX. No discussion will be presented of the many advantages of applying group theory to the problem of simplifying the formulation of complex spin states having some degree of symmetry. There are several reasons for this: First, many less-familiar mathematical operations would have had to be introduced and explained. Second, the use of group theory is most important as a mathematical shortcut and does not contribute in itself in an important way to an understanding of the principles of spin-spin splitting. Finally, the need for mathematical shortcuts has been much reduced by the availability of computer programs for calculation of transition energies and intensities for even quite complex spin systems. I am deeply indebted to Professor Harden M. McConnell for helping me through his very important contribution to the field [H. M. McConnell, A. D. McLean, and C. A. Reilly, J. Chern. Phys., 23, 1152 (1955)]; this book is very largely based on an impromptu private lecture that Professor McConnell delivered on July 4, 1956. I am also much indebted to Dr. V. Schomaker for many hours of patient explanation of quantum mechanical principles. The success (if any) of the treatment is largely due to these gentlemen; the shortcomings and errors are all my own. Many helpful suggestions regarding the manuscript were received from Dr. Marjorie C. Caserio, Professor Max T. Rogers, and Dr. Thomas H. Regan. The NMR spectra were obtained with skill and patience by Mr. Donald R. Davis, and the manuscript was prepared by Mrs. Allene Luke and Miss Joy Matsumoto. The heretofore unpublished research described in this book was supported by the Office of Naval Research. JOHN D. ROBERTS

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