Hohenberg-Kohn theorem energy surfaces

An extension of the Hohenberg-Kohn theorems to an arbitrary excited electronic state has not been possible till date. It has been possible only for the lowest state of a given symmetry [45] and for the ensemble of states [46], It may be anticipated from the principles of maximum hardness and minimum polarizability that a system would become softer and more polarizable on electronic excitation since it is generally more reactive in its excited state than in the ground state. Global softness, polarizability, and several local reactivity parameters p(r, t), Vp, —V2p,/(r), electrostatic potential, and quantum potential have been calculated [25] for different atoms, ions, and molecules for the lowest energy state of a particular symmetry and various complexions of a two-state ensemble. It has been observed that a system is harder and less polarizable in its ground state than in its excited states, and an increase in the excited state contribution in a two-state ensemble makes the system softer and more polarizable. Surface plots of different local quantities reveal an increase in reactivity with electronic excitation. 

The most convenient criterion is offered by the energy or its density functionals. But which energy - the one of the atom in the molecule or of the molecule as a whole Hence there appears the need for nuances in the Hohenberg-Kohn Theorem on the analytical domains and subdomains. It follows that the atom properties transferability from one molecule to another is natural and the atom bordered in molecule by an area SQ satisfies the stationary eondition of the density flow on the surface bordering the field... 

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