mSASS part 3 - Continuous symmetry parametrization of multielectronic configurations

2-electron basis functions Eigenvalues
The mSASS Hamiltonian
The tutorial shows the construction of the mSASS-Hamiltonian for a p4 configuration with spin-orbit interaction. We discuss the splitting of two electrons occupying a j=3/2 state in an octahedral field. It is a continuation of part 1 - d1 configuration in an octahedral field and part 2 - d1 configuration in an octahedral field with spin-orbit interaction. More information can be found in the following reference:
R. M. Geilhufe, J. D. Rineart, arXiv:2209.03123
GTInstallGroup
Installs point and space groups
GTAngularMomentumRep
Computes representation matrices for the irreducible representations of O(3) or SU(2)
GTClebschGordanSum
Constructs the Clebsch-Gordan sum of two representations
Install the point group O.
2-electron basis functions
The alternating square of the D3/2 representation gives : A(D3/2⊗D3/2)=D0⊕D2.
Generate 2-electron basis functions using Clebsch-Gordan coefficients.
The mSASS Hamiltonian
Compute SO(3) representation matrices for J=0 and J=2.
Construct the super representation from the Clebsch-Gordan sum of D0 and D2.
Generate a generic 6x6 Hamiltonian matrix.
Calculate the symmetry projection.
Solve for the symmetry invariant terms.
Calculate the final Hermitian Hamiltonian.
Eigenvalues
Compute the eigensystem of the mSASS Hamiltonian.
Construct the eigenfunctions from the eigenvectors.