ORCA 6.1.1 tensor-direction postprocessing

Own actual fixed methyl-radical PBE0 EPR-II/III response tensors from the cluster.
No new SCF or EPR response calculation. The two original electronic calculations
are supplied as inputs with their own scientific output/property text.

Fresh complete workflow: bash run.sh
Existing supplied reference only: bash analyze.sh
New own output: bash analyze.sh work

Module orca/6.1.1 contains official precompiled CPU executables; supporting
OpenMPI 4.1.8 was built with GCC 13.3. Python uses the existing ase-3.29.0
environment with NumPy, SciPy and Matplotlib. No binaries are included.

The six native executions cover ZYZ, ZXZ and reference order 3 2 1 for two bases.
Results: work/euler-iii/native.log and case.N.A.xyz / case.N.g.xyz; N starts at 0.
He is an auxiliary origin, Ne/Ar/Kr are x/y/z auxiliary axis endpoints, not new
chemical atoms. Axis lengths are display lengths, not the tensor magnitudes.
The g reference is sorted min/mid/max by default; A is reordered/signed to
minimize its relative rotation. Retain the corresponding Ax/Ay/Az columns.

Figures: figures/*.png. Tables: tables/angles-principals.csv and axis-directions.csv.
The independent analysis reconstructs tensor axes and physical rotation matrices
within native XYZ rounding; angles are compared at their actual 0.1 degree
printed precision. Nearly degenerate principal planes and gimbal-lock choices
make individual Euler angle triplets nonunique. The same physical rotation
can have multiple valid angle descriptions. No higher-spin D or quadrupole
example is claimed, and this package does not contain a paramagnetic NMR workflow.
