The chemical property of hardness is extremely important in the correc
t prediction of electron transfer between reacting chemical systems. H
ardness is defined to be one-half the second derivative of the total e
nergy of a chemical system with respect to the number of electrons. Th
e 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 psudopotentials. The con
cept also clarifies the role of core density in pseudopotential applic
ation. A practical prescription is presented for generating such pseud
opotentials and their corresponding core densities, and several ab ini
tio results are compared with those of high-quality norm-conserving ps
eudopotentials. Significant improvements are found.