Construction of the adiabatic connection

Two models for the change in the lambda-dependent exchange-correlation energy upon atomization Delta E(xc,lambda) = E(xc,lambda)(atoms) - E(xc,lambda)(molecule) are proposed, where E(sc,lambda) = [psi(lambda)\<(V)over cap (ee)>)\psi(lambda)] - integral d(3)r d(3)r' rho(r)rho(r')/2\r - r'\. The wavefunction psi(lambda) yields the ground-state density rho and minimizes (T) over cap + <lambda(V)over cap (ee)>. These models (Delta E(xc,lambda)(model)) make use of the exact E(x) and generalized gradient approximations (GGAs) to E(xc). The construction of the simplest model is verified by calculating the exact d Delta E(xc,lambda)/d lambda\(lambda=0) from density functional perturbation theory and comparing it to d Delta E(xc,lambda)(model)/d lambda\(lambda=0). For systems with strong static correlation, explicit inclusion of d Delta E(xc,lambda)/d lambda\(lambda=0) further improves the approximation to Delta E(xc,lambda). Atomization energies calculated from Delta E(xc,lambda)(model) show a significant improvement over GGA.