Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities

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Abstract
Hardness and softness kernels η(r,r′) and s(r,r′) are defined for the ground state of an atomic or molecular electronic system, and the previously defined local hardness and softness η(r) and s(r) and global hardness and softness η and S are obtained from them. The physical meaning of s(r), as a charge capacitance, is discussed (following Huheey and Politzer), and two alternative ‘‘hardness’’ indices are identified and briefly discussed.