Corrections for Orbital Energy Gaps in Solids

Auxiliary basis functions for expanding exchange-correlation potentials are used in the Wu-Yang (WY) constrained search method. Excerpt from Teale et al. (2008) 

Let us examine the self-energy correction based on the GW approximation as an approach in band calculations for reproducing accurate orbital energies. The self-energy, E, is defined as 

The LDA+U method (Liechtenstein et al. 1995) is one of the most frequently used corrections for orbital energy gaps in band calculations. In the LDA+U method, the difference of the Coulomb-exchange interactions from their averaged value is added 

What should be noted is that, since the corrections in the band calculations of solids are usually specialized to make the orbital energy gaps close to the band gaps, these are not available to improve the orbital energy calculations of molecules. 

---