Transforms of the Electronic Energy and Their Derivatives

LEGENDRE TRANSFORMS OF THE ELECTRONIC ENERGY AND THEIR DERIVATIVES 

It has been discussed elsewhere [5,7,8,12,13,93,137,138] that there are four alternative Legendre-transformed representations of a molecular (single component) 

Such an ensemble generalized ground-state energy functional, E = E[N, v] = E[p[N. i l- represents the thermodynamic potential of the N, v -representation, with the corresponding generalized Hellmann-Feynman expression for its differential (see equations (17), (22) and (27))  

The corresponding potentials for the three remaining specifications of the system equilibrium state are given by the relevant Legendre transforms of the 

The energy functional defines the second derivatives of equations (23)-(26), called the principal charge sensitivities, which determine the associated second differential of the Taylor expansion of equation (27)  

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Legendre transforms of the electronic energy and their derivatives 141... 

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