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.
- Euler angles
- Numerical line shape calculations
- Powder averaging
- Wide line NMR
ASJC Scopus subject areas
- Nuclear and High Energy Physics