ENERGY DERIVATIVES IN DENSITY-FUNCTIONAL THEORY

For an N-electron system characterised by an external potential v(r), the curvature theorem expressed as the inequality ∂2E/∂λ2 ≤ ∝ dr ρ{variant}(r)/∂2v(r)/∂λ2, where λ is a parameter defining v(r), is dervied through a functional Taylor expansion of the energy E using density-functional theory. New expressions for the hardness parameter ∂2E/∂N2 are obtained in terms of the electron density ρ(r) and various interconnections and implications of related local quantities are discussed. © 1990.