Energy derivatives in density-functional theory

Abstract

For an N-electron system characterised by an external potential v(r), the curvature theorem expressed as the inequality ∂²E/∂λ²≤∝ drρ r)/∂² (r)/∂λ²where 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/∂N²are obtained in terms of the electron density ρ (r) and various interconnections and implications of related local quantities are discussed.