The use of interference terms to separate dipolar and chemical-shift anisotropy contributions to nuclear spin relaxation

Abstract

For numerous spin-4 nuclear isotopes such as 15N, r9F, and 3’P incorporated in bulky molecular frameworks, chemical-shift anisotropy and intramolecular dipolar interactions often provide competitive mechanisms for a&cting nuclear spin relaxation. In the past few years, there has been widespread interest in rationalizing-and exploiting-the synergistic nature of these two relaxation mechanisms. A novel investigation recently described how one could utilize this synergism to individually quantify the dipolar and chemical-shift anisotropy contributions without the need for supplemental Overhauser or variation-in-field studies (1). In the following note, we would like to clarify certain features of this proposed methodology and add some cautionary comment. For our treatment, we will consider the same system as discussed in (I): two unlike spin-4 nuclei, 19F and 31P, relaxed by dipolar and chemical-shift anisotropy interactions outside the extreme narrowing limit. The two components of the phosphorus doublet have linewidths equal to Au& + AU&A + ~CP(AV~~AV&~)~‘~ and AvEn + AU&A 2cp( Av~&&,) ‘I’, whereas the two components of the fluorine doublet have linewidths equal to AZ& + AI& + 2CF(Av~nAv&~)“’ and Agn + AU&A 2C,~(Av~nAv&~) . ‘I2 (For the special case of isotropic molecular reorientation, the correlation factor, CP(~, is defined as (3 cos2Q 1) where Q is the angle between the F-P internuclear vector and the principal axis of the phosphorus (fluorine) chemicalshift tensor.) Thus, the summed width of either doublet is independent of the interference term, 2Ci(A&A&A)“‘, whereas the differential width of either doublet depends solely upon this interference. In a study of the type outlined in (I), there are four observable.linewidths and five unknown parameters, A$&, A V&A, AU&A, Cr, and Cr. Thus, without an additional assumption or independent measurement, one cannot deduce the dipolar and chemicalshift anisotropy contributions individually. In (I), it was assumed that Cr = Cr = 1. Although it was stated, “for clarity of explanation only,” it is seen that this assumption was an integral ingredient in the subsequent development. Only in the unlikely situation where all interactions share a common principal axis or highly anisotropic motions prevail (2), will this completely correlated limit obtain. A more general interpretation of the data given in (I) is displayed in Fig. 1. This figure summarizes all possible, internally self-consistent, sets of A&, AI$~, , Au&, C,, and Cr compatible with the observed linewidths. The pertinent relationships are