A comment on powder averaging in wide line NMR.
Computer calculations of wide line NMR spectra of powders usually involve numerical evaluation of double integrals over two Euler angles. Practice confirms intuition-based expectations that the integration results should be independent from the choice of the crystal-fixed (or molecule-fixed) coordinate system used in the calculations. However, a closer inspection of the relevant integration formulas may make one wonder why this is so. The present paper provides a rigorous mathematical proof of the validity of these intuitive predictions, by formulating the problem in terms of surface integrals on a sphere, which has presumably no precedence in the NMR literature.
Department of Mathematics, Syracuse University, 900 South Crouse Ave, Syracuse, NY 13244, USA.
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Iwaniec
Department of Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland.
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Kopiecki
Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland. Electronic address: sszym@icho.edu.pl.
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Szymanski
Euler angles; Numerical line shape calculations; Powder averaging; Wide line NMR