Akm parameters for D3 (or other unusual) point group

Dear Maximilian Kusch,

Indeed the function PotentialExpandedOnClm is only implemented for a few high symmetry groups in standard orientations. While implementing the lower symmetries I noticed that one does not only need functions for the 32 some point groups, but for each point group also in different orientations. For groups where the d or f orbitals have several states belonging to the same irreducible representation the input became quite arbitrary and non-intuitive.

The alternative you can find here: https://www.quanty.org/physics_chemistry/point_groups You first need to select a point group For example https://www.quanty.org/physics_chemistry/point_groups/d3d For a given group you then need to select an orientation / setting. The website shows in pictures what the symmetry axis in x, y, and z coordinates are For example the D3d group with the C3 axis in the z direction and one of the C2 axis in the x direction https://www.quanty.org/physics_chemistry/point_groups/d3d/orientation_zx When you scroll down you find a section potentials for d orbitals (or potentials for f orbitals). If you expand this you find the input you can use in Quanty For the d orbitals

Akm = {{0, 0, (1/5)*(Ea1g + (2)*(Eeg1 + Eeg2))} , 
       {2, 0, Ea1g + Eeg1 + (-2)*(Eeg2)} , 
       {4, 0, (3/5)*((3)*(Ea1g) + (-4)*(Eeg1) + Eeg2)} , 
       {4,-3, (3*I)*((sqrt(7/5))*(Meg))} , 
       {4, 3, (3*I)*((sqrt(7/5))*(Meg))} }

The definitions of the parameters you can find on the website where you also find the expansion.

Hope this helps. Best wishes, Maurits