Modern Techniques in High-Resolution FT-NMR pp 226-259 | Cite as

# Multiple-Quantum Spectroscopy

Chapter

## Abstract

Multiple-quantum transitions (MQT’s), which are the subject of this chapter, involve a change in magnetic quantum number (
These functions are given for systems of upto eight spins in Table 5.1. (When equivalences are involved, the number of transitions is reduced for all orders except the highest.) The counting procedure also includes the combination lines for each order, which are

*M*) of*p*units (i.e., Δ*M*= ±*p*) and occur by the simultaneous absorption of*p*equal quanta. The number of*p*-quantum transitions (*p*= 0, 1, 2, …,*N*) in a system of*N*inequivalent spin-1/2 nuclei is given by:$$ \begin{gathered} p = 0:\frac{1}{2}\left[ {\left( {_N^{2N} } \right) - 2^N } \right] \hfill \\ p \ne 0:\left( {_{N - p}^{2N} } \right) \hfill \\ \end{gathered} $$

(1)

*M*-spin*p*-quantum transitions (*M*>*p*) that are of vanishing intensity even for*p*= 1, in a conventional one-dimensional (ID) spectrum. It is clear from the table that single-quantum transitions (SQT’s) are the most numerous single group, but beyond*N*= 3, the total number of MQT’s is higher than that of SQT’s. At the same time, the number of MQT’s drops very rapidly for higher values of*p*in each case. It is often the case that the single-quantum spectrum is too crowded for analysis and assignment; in such situations, it may be of value to study the high-order MQ spectra of the system, which exhibit fewer transitions and yet contain all the desired information on the spin system.### Keywords

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## Copyright information

© Springer-Verlag New York Inc. 1987