Employing the perturbation approach directly in the multiply rowing conditions are very stringent and usually cannot rotating frame, the master equation governing the spin dynamics be satisfied in biopolymer systems, in which NMR plays of scalar-coupled heteronuclear multiple-spin systems has been an important role nowadays.
derived. The resulting equation for the spin-density operator and
For the homonuclear case, Hoffman (5) proposed an alterthe matrix form of the relaxation superoperator are relatively simnative approach that is valid under the conditions of the sople under the conditions of the ''extended'' strong-narrowing limit. called strong-narrowing limit. The strong-narrowing limit is The extended strong-narrowing limit, which requires that v I i t c ΣΆ much less restrictive than the extreme-narrowing limit and 1 and 2pJ ij t c ΣΆ 1 [where I represents one of the spin types in the can be applied to most homonuclear liquid-state NMR experheteronuclear spin system, v I i is the chemical-shift range of spin iments. This approach has been used in lineshape analysis type I in radians per second, J ij is the coupling constant J between
(5) and in studying the effect of cross relaxation on the spin i and spin j (like or unlike) in hertz, and t c is the correlation apparent scalar couplings in the long-correlation-time limit time in seconds per radian], can be applied to heteronuclear spin systems of both small molecules and biopolymers in high-resolu-(6, 7). However, as pointed out by Hoffman (5), ''when tion liquid NMR. This newly developed formalism is used to invesnuclei of different gyromagnetic ratios contribute to the spectigate the effect of transverse cross relaxation on the apparent trum (the heteronuclear case), the conditions of strong narcoupling constants in a heteronuclear 1 H-1 H-13 C three-spin sysrowing . . . are essentially the same as those of extreme tem. The calculation shows that, despite the strong dipolar interacnarrowing.'' Because of this, this treatment cannot be aption between directly bonded 1 H and 13 C, this perturbation on plied to the heteronuclear spin systems of biopolymers. To the apparent couplings is trivial. This result is in contrast to the solve this problem, the spin dynamics of heteronuclear spin homonuclear proton spin system, where the scalar coupling consystems is derived in the present paper under the conditions stants between two protons are significantly modulated if one proof the ''extended'' strong-narrowing limit (which are satiston is strongly dipole coupled to another proton. The underlying fied even for biopolymers in heteronuclear high-resolution physical reasons for the different behavior of heteronuclear and liquid NMR) by employing the perturbation method directly homonuclear systems are explained.