Construction of the adiabatic connection

Two models for the change in the λ-dependent exchange-correlation energy upon atomization ΔExc,λ = Excλatoms − Excλmolecule are proposed, where Exc,λ = 〈ψλ|V̂ee|λλ〉 - ʃ d3r d3r′ p(r)p(r′)/2|r − r′|. The wavefunction ψλ yields the ground-state density ϱ adn mininizes T̂ + λV̂ee. These models (ΔExc,λmodel) make use of the exact Ex and generalized gradient approximations (GGAs) to Exc. The construction of the simplest model is verified by calculating the exact dΔExc,λ/dλ|λ=0 from density functional pertubation theory and comparing it to dΔExc, λmodel/dλ|λ=0. For systems with strong static correlations, explicit inclusion of dΔExc,λ/dλ|λ=0 further improves the approximation to ΔExc, λ. Atomization energies calculated from ΔExc,λmodel show a significant improvement over GGA.