Nonorthogonal quasi-degenerate perturbation theory for L-edge X-ray spectroscopy and beyond

Quantum mechanical calculations of core electron ionizations and excitations are relevant to interpreting X-ray spectroscopy. State-specific optimization approaches like Δ-SCF or orbital-optimized density functional theory (OO-DFT) accurately predicts K-edge ionization energies but is challenged by the presence of significant spin–orbit coupling (SOC) at L- and higher edges involving inner-shell orbitals with nonzero angular momentum. To extend these to L-edges and higher, our method utilizes scalar-relativistic, spin-restricted open-shell determinants to construct a minimal, quasi-degenerate basis of core-hole states corresponding to a chosen inner-shell. Nonorthogonal configuration interaction (NOCI) is then used to obtain the matrix elements of the full Hamiltonian including SOC in this quasi-degenerate model space of determinants. For excitations, NOCI with singles excitations is applied to span each determinant's full virtual space. The cost of computing non-orthogonal matrix elements can be significantly reduced by imposing constrained orthogonality on the holes. The resulting NOCI eigenvalues are shifted by the average of the (scalar) OO-DFT ionization energies to correct for dynamic correlation. Our approach yields ~0.2 eV error for L-edge ionization energies of molecules containing third row atoms when using the SCAN functional and the screened 1-electron SOC operator. Preliminary results for X-ray absorption spectroscopy will also be presented.