Computer Analysis of NMR Spectra: Magnetic Equivalence Factoring

Abstract

An extension of the NMR analysis method of Swalen and Reilly is described. The Hamiltonian matrix is factored to reduce it to minimal dimension by taking advantage of magnetic equivalence. Significant improvements are obtained in computation speed, computer program capacity, and convenience of use. Other extensions of the method provide a thorough statistical assessment of the resulting parameter estimates, and permit a solution even when some of the energy levels do not participate in any of the assigned transitions. The method has been tested by analyzing the 60-Mc/sec proton resonance spectra of propane (A6B2) and isobutane (A9B). The chemical shifts, downfield from internal tetramethylsilane, and the coupling constants are: CH3CH2CH3; δ(CH3) = 0.912±0.005 ppm, δ(CH2) = 1.350±0.005 ppm, J = 7.35±0.02 cps: (CH3)3CH; δ(CH3) = 0.900±0.005 ppm, δ(CH) = 1.738±0.005 ppm, J = 6.73±0.05 cps.