Core excitation spectra in the Static Exchange approximation¶
A well known limitation of the time dependent Hartree-Fock approximation is that electronic relaxation is not accounted for in the calculation of excitation energies. This relaxation can be understood as a correlation effect, since it is due to the simultaneous excitation of an electron and the relaxation of the remaining N-1 electrons (or rather orbitals) due to the “hole” left behind by the excited electron. On the other hand the relaxation is well described already at the Hartree-Fock level when the excited states are optimized separately, in the so-called ΔSCF approach.
The Static Exchange (STEX) approximation is a cheap way to incorporate relaxation effects into the calculation of core excitation spectra, where it is particularly important for excitation energies and transition probabilities. The method works by making a configuration interaction singles expansion of the excited states with a reference determinant optimized for core holes in a particular set of orbitals. The excited states are then not orthogonal to the Hartree-Fock ground state, and wavefunction overlaps have to be explicitly taken into account.
A STEX calculation typically proceeds in the following way:
- The Hartree-Fock groundstate is calculated with Dirac, and the wavefunction saved in the DFCOEF file.
- The groundstate output is examined and the indices of the core orbital of interest are noted. If the core orbitals are not well localized to individual atoms it may be necessary to add a small fractional charge to break a symmetry of the molecule. This change can then be removed in the final calculation.
- An average-of-configuration open shell Hartree-Fock calculation is performed to get an approximate wavefunction of the core ionized molecule. This wavefunction should then be saved to a file DFCOEF.ION. In order for the core ionized state to converge it is necessary to use overlap selection and possibly orbital freezing.
- The STEX calculation is run with the specified hole orbitals, starting from the previously calculated DFCOEF and DFCOEF.ION files.
- please provide an
- example !
Indicate (singly occupied) hole orbitals. Example:
.HOLES ! Expects format like (NFSYM=2) 2 ! nr of holes in fermion symmetry 1. 5 9 ! holes in fs 1 1 ! nr of holes in fermion symmetry 2. 1 ! holes in fs 2
Print level. Default: 0
Number of simultaneous Fock matrices to build. Default: 4
Set default cutoff in eV. Default: 100 eV