Analysis of Carrmdash;Purcell Spinhyphen;Echo NMR Experiments on Multiplehyphen;Spin Systems. I. The Effect of Homonuclear Coupling

摘要

The effect of homonuclear coupling in a molecule on Carrmdash;Purcell spinhyphen;echo (CPSE) nuclear magnetic resonance experiments is investigated. A densityhyphen;matrix approach is used to derive a general equation for the CPSE train of multiplehyphen;spin molecules in the liquid state. This general equation predicts a CPSE train modulated with one or more frequencies, whose relative amplitudes are, in general, not equal. Unmodulated contributions may also arise. It is shown that the modulation frequencies and their relative amplitudes are functions not only of the relative chemical shifts and coupling constants, but are strongly dependent on the separation between the 180deg; pulses,tcp.In addition, the modulation can always be eliminated by making the pulse repetition rate, 1/tcp,large with respect to all the relative chemical shifts and coupling constants. It is also shown that, for weak coupling, it is possible to derive simplified equations by neglecting the nonsecular part of the coupling Hamiltonian, but this approximation is valid only when 1/tcpis of the order of, or smaller than the relative chemical shifts.Procedures for solving the general equation to obtain closed formulas for the CPSE train of a specific system are discussed. Solutions for spinhyphen;frac12; nuclei are treated in detail. Closed equations are derived for the AB, A2B, and A3B systems, and they are used in some numerical calculations. Simplified weakhyphen;coupling formulas are also derived for these systems, and their range of validity is discussed.A very brief discussion of heteronuclear coupling is presented.