### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 25-30 |

Number of pages | 6 |

Journal | Solid State Nuclear Magnetic Resonance |

Volume | 68 |

DOIs | |

State | Published - Jun 1 2015 |

### Keywords

- Euler angles
- Numerical line shape calculations
- Powder averaging
- Wide line NMR

### ASJC Scopus subject areas

- Radiation
- Chemistry(all)
- Nuclear and High Energy Physics
- Instrumentation

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## Cite this

*Solid State Nuclear Magnetic Resonance*,

*68*, 25-30. https://doi.org/10.1016/j.ssnmr.2015.04.004