Evaluation of hardness in Kohn-Sham theory with local density and generalized gradient approximations

Abstract

By making use of Janak’s interpolation in the Kohn-Sham method, together with an explicit and differentiable functional of the density for the exchange-correlation energy, like LDA or GGA, the second derivative of the energy with respect to the number of electrons, <i>N</i>, is evaluated from the derivative of the highest occupied molecular orbital (HOMO) with respect to <i>N</i> (left derivative), or from the derivative of the lowest unoccupied molecular orbital (LUMO) with respect to <i>N</i> (right derivative). Both cases lead to expressions that may be evaluated from a single post-SCF calculation that avoids the use of the frontier orbitals eigenvalues. The results obtained for two test sets of molecules and for several atoms indicate that both provide a better description than the LUMO-HOMO eigenvalue difference and that the left derivative seems to lead to more confident results than the right derivative.