18.4 Principal Axis System and Euler Angles

The principal axis system (PAS) and the respective Euler angles for the g-tensor can be obtained with mpshift and the flag $epr. The orientation of the PAS of the HFC and EFG is further calculated relative to the g-tensor frame. Note that mpshift with $epr calculates the g-tensor, the HFC, the EFG, and the NQI. Note that one-component approaches use the symmetric method, i.e. the tensors are symmetrized and then diagonalized. Two-component calculations can use the symmetric method and the product method. The latter diagonalizes the product of the real tensor and the transposed tensor.

For two-component runs, the post-processing script epreuler.py is needed. Like the scripts calcgtens.py and calchfc.py, this script accumulates the g-tensor and HFC results from the three non-collinear calculations. By default, the EFG needs to be stored in ‘ridft.efg’ with the z-spin orientation. Make sure to use picture-change correction for the proper run of ridft.

Note that the Euler angles are not unique, for instance, when flipping the sign of the \(\beta\) angle, we have to add or subtract \(\pi\) to the \(\alpha\) and \(\gamma\) angles to get the same rotation matrix.