Determination of the chemical potential and HOMO/LUMO orbitals in density purification methods

Several density purification methods have been proposed to achieve linear scaling in Hartree–Fock and Kohn–Sham calculations. However, only the density is found, while in the traditional diagonalization method the orbitals are also obtained. This could be seen as a drawback as in many cases one would like at least the HOMO and LUMO orbitals and their orbital energies. In this letter, we show how a value for the chemical potential can be obtained as a by-product of density purification methods at negligible cost. Once the chemical potential is known, MO’s around the HOMO–LUMO gap can be calculated with the Spectral Transformation Lanczos method.