Proton spin relaxation in methyl substituted aromatic radical ions. A formula for the CH3 proton NMR linewidth

Abstract

The proton relaxation has been studied in methyl substituted aromatic radical ions in solution. The linewidth parameter T 2 of the protons in such radicals is goveméd by two intramolecular interactions, namely, the Fermi contact interaction and the anisotropic dipolar interaction. For the methyl protons the interactions are modulated in time by both intemal rotation and tumbling of the whole molecule in solution. Equations have been derived to account for the effect of these motions on the CH3 proton linewidth. The resulting formulas are used to analyze the NMR proton linewidths for the anion of 3, 3'-dimethylbiphenyl.

Electron spin distribution and molecular dynamics of aromatic hydrocarbon radical anions studied by1H and2D N.M.R.

“…The Fermi contact interaction (and also the anisotropic dipolar interaction) can then be written as [3,20,43] WFo(t) = E F(q)(t)I(q), q= -1, 0, + 1,…”

“…x (F2(t)F2(t + r)*} + ~ exp (ioaer)(Fo(t)Fo(t + r)*}}JThe functions Fh(t ) are the irreducible components of the T-tensor defined in the laboratory reference frame. When the anisotropic dipolar interaction is modulated only by Brownian rotational motion, then the following relation can be derived[43] :(Fh(t)Fh(t+r)*}= 2 (a~Jk~(h)(t)}(Ckm(r)Cz~(r)}T~jTm~"(B 2) i,],h,I,m,n…”

“…Anisotropic dipolar relaxationFollowing the treatment of de Boer et al[43] T2, Dip -1 is given by equation (A 2). The correlation functions associated with the spectral densities Jo(~o) and Jl(oJ) are given by[43] go(r) = 89+ 1) exp ( -]rl/re){(Fo(t)Fo(t + -r)*} I + 2 exp ( -i~Oer)(Fl(t)Fl(t + r)*} + 2 exp (iwer) x (F~(t)*F~(t+'r)}}, r) = 89 + 1) exp ( -[r [/re){(Fl(t)Fa(t + r)*} + 2 exp ( -iCOer ) [ ! x (F2(t)F2(t + r)*} + ~ exp (ioaer)(Fo(t)Fo(t + r)*}}JThe functions Fh(t ) are the irreducible components of the T-tensor defined in the laboratory reference frame.…”

Nuclear magnetic resonance spectroscopy

“…NMR investigations of organic radical species include studies of: DPPH (885), aromatic radical ions (886), cation radicals from halides of some jV.jV'-disubstituted 4,4'-dipyridylium derivatives (887), -hydrogen bonding involving stable hydrocarbon radicals (888), l,4-bis(2,2,6,6-tetramethyl-l-oxyl-4-hydroxy-4-piperidyl)butane (889), di-tertbutyliminoxy and di(l-adamantyl)iminoxy (890), TMPO (891), and a number of other nitroxides (892,893). GENERAL…”