The problem of core-hole localization has been broadly debated since the work of Bagus and Schaefer about the core ionization of molecular oxygen. They showed that the localization of core hole orbitals lowers the binding energy of the O2+ (1s-1) ion at the Hartree-Fock level, obtaining a better agreement with the experiment. The lowering of the energy obtained in the localized basis is misleading related to an electronic correlation effect since this is a compensating effect due to the inadequacy of the applied orbitals.
We present an alternative approach, analyzing the effects of using the localized and delocalized core orbitals basis. In both cases, the molecular orbitals are simultaneously optimized in an approach developed to treat core-shell states, called inner-shell multiconfigurational self-consistent field (IS-MCSCF). This approach shows some advantages once it can lead to reliable transition energies by using a concise wave function, avoiding large CI calculations, and allows the potential energy surfaces of the excited states to be computed reliably even at the dissociation limit. Dynamic correlation effects were also considered by using the multiconfigurational perturbation theory (GMCPT).
We found that the localized basis underestimates the value of the energy transition, which indicates that the excited states are better described than the ground state at this level of approximation. The use of perturbation theory to recover correlation of both ground and inner-shell state provides a solution to this, adjusting this effect in both localization basis. The results obtained at the IS-GMCPT level are in fairly good agreement with experimental results. The analysis of the potential energy curves of inner-shell states of CO2 along ground state normal modes of vibration shows that they are bent as predicted by the Renner-Teller effect.
Rocha, A., de Moura, C. (2011). The problem of hole localization in inner-shell states of N2 and CO2 revisited with complete active space self-consistent field approach The Journal of Chemical Physics 135(22), 224112. https://dx.doi.org/10.1063/1.3666016
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