Lawrence G. Werbelow

Carbon‐13 relaxation in multispin systems of the type AXn

The equations of time evolution which describe various aspects of longitudinal relaxation in methylene and methyl groups are derived on the basis of the Redfield–Bloch density operator theory of relaxation. It is assumed that the relaxation is dominated by intramolecular dipole–dipole interactions. The (cross‐) correlation between the various internuclear vectors is explicitly taken into account; it is not assumed that the various pairwise interactions are additive. Although such correlation effects have long been dismissed, the present calculations demonstrate quite vividly such effects may be much more influential than is commonly thought, especially in the relaxation of carbon. Multiplet relaxation in the four‐spin 13CH3 system is discussed in some detail with numerical calculations included to provide some compelling arguments against continued complacency regarding the need to consider multispin correlations. More general applications of the present theory await many inviting experimental studies.

Proton‐decoupled carbon‐13 relaxation in 13CH2 and 13CH3 spin systems

The transient behavior of the carbon magnetization in proton decoupled spectra is discussed in detail for 13CH2 and 13CH3 spin systems. The influence of multispin dipolar cross correlation effects is shown to influence the decoupled inversion‐recovery experiment and lead to a predicted biexponential recovery of the carbon magnetization. It is rationalized that for methyl relaxation, the interference effects will play an inconsequential role. However, in the methylene case, it is demonstrated that there may arise many possible instances when it will become necessary to consider these correlation effects in much greater detail. It is also shown that if (1) extreme narrowing arguments are invalid or (2) other relaxation mechanisms compete with dipolar interactions, then the NOE enhancement factors deviate from those predicted from conventional treatments. For many conceivable situations, the inferred relaxation rate will underestimate the sum of the dipolar and nondipolar contributions whereas the usage of O...

Magnetization modes and evolution matrices for some simple spin systems in anisotropic media

The time evolution of complete sets of coupled magnetization mode variables for the AX2, AX3, and X3 spin one‐half systems are presented. The chosen modes prove to be the natural kinetic variables for free and partially constrained nuclear magnetic relaxation studies in both spacially isotropic and spacially anisotropic environments. The relationship between spacial anisotropy, the concomitant failure of time reversal symmetry, and the appearence of complex valued angular correlation time constants is also discussed. It is rationalized that the absence of time reversal symmetry necessitates the introduction of certain zero frequency phase coherence variables which linearly couple into the magnetization (population) mode variables. Thus, relaxation studies may indeed distinguishbetween degenerate irreducible multiplicities.

Transverse relaxation of three identical Spin-12 nuclei subject to shift anisotropy interactions

The transverse relaxation of three identical Spin-12 nuclei subject to intramolecular dipolar, chemical shift anisotropy, and fully correlated random field spin-lattice couplings is derived from the semiclassical density operator formalism. Retention of dipolar-dipolar and dipolar-shift anisotropy cross-correlation terms significantly alters the calculation compared with simplified intuitive approaches. It is shown that the transverse magnetization is described by four coupled equations, whereas previous calculations have shown that the longitudinal relaxation is governed by five time constants. This anomaly, which can be viewed as a generalization of the “76 effect,” arises since the shift anisotropy interaction is not rotationally invariant. The spectral densities of the lattice correlation functions, which quantitatively describe the time evolution of the density operator, are calculated for both immobilized and internally rotating triads attached to isotropically reorienting molecular frameworks characterized in size by rotational diffusion correlation times that span a complete range of ω0τc. It is demonstrated that the transverse relaxation reflects dipolar-shift anisotropy interference only if (1) γhr−3 ⋍ B0 Δσ, (2) the motion is quite isotropic, or (3) the overall correlation time is relatively long (ω0τc, > 1). However, the primary concern in such multispin systems is the influence of dipolar-dipolar interference terms. The practical consequences of this investigation may be of central importance to the interpretation of CF3 “reporter group” relaxation as employed in various biophysical NMR studies.

Multiplet relaxation studies in anisotropic media

Abstract Equations describing the magnetization recovery rate of the three identical spins one-half system are presented. The equations are tailored for nuclear spin relaxation studies performed in anisotropic fluids. The ramifications of these expressions are briefly discussed.