Additional condition for transferability in pseudopotentials

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Abstract
The chemical property of hardness is extremely important in the correct prediction of electron transfer between reacting chemical systems. Hardness is defined to be one-half the second derivative of the total energy of a chemical system with respect to the number of electrons. The requirement that the total energies of atom and pseudoatom match to second order with arbitrary changes in valence-state occupancy yields major decreases in the errors made when using pseudopotentials. The concept also clarifies the role of core density in pseudopotential application. A practical prescription is presented for generating such pseudopotentials and their corresponding core densities, and several ab initio results are compared with those of high-quality norm-conserving pseudopotentials. Significant improvements are found.