Fitting alignment tensor components to experimental RDCs,CSAs and RQCs

Residual dipolar couplings, chemical shift anisotropies and quadrupolar couplings provide information about the orientation of inter-spin vectors and the anisotropic contribution of the local environment to the chemical shifts of nuclei, respectively. Structural interpretation of these observables requires parameterization of their angular dependence in terms of an alignment tensor. We compare and evaluate two algorithms for generating the optimal alignment tensor for a given molecular structure and set of experimental data, namely SVD (Losonczi et al. in J Magn Reson 138(2):334–342, 1999), which scales as \({{\mathcal {O}}(n^2)}\), and the linear least squares algorithm (Press et al. in Numerical recipes in C. The art of scientific computing, 2nd edn. Cambridge University Press, Cambridge, 1997), which scales as \({{\mathcal {O}}(n)}\).