Density functional estimations of Heisenberg exchange constants in oligonuclear magnetic compounds: Assessment of density functional theory versus ab initio.

Modern density functionals were assessed for the calculation of magnetic exchange constants of academic hydrogen oligomer systems. Full-configuration interaction magnetic exchange constants and wavefunctions are taken as references for several H(n) model systems with different geometrical distributions from Ciofini et al. [Chem. Phys. 309, 133 (2005)]. Regression analyses indicate that hybrid functionals (B3LYP, O3LYP, and PBE0) rank among the best ones with a slope of typically 0.5, i.e., 100% overestimation with a standard error of about 50 cm(-1). The efficiency of the highly ranked functionals for predicting the correct "exact states" (after diagonalization of the Heisenberg Hamiltonian) is validated, and a statistical standard error is assigned for each functional. The singular value decomposition approach is used for treating the overdetermination of the system of equations when the number of magnetic centers is greater than 3. Further discussions particularly about the fortuitous success of the Becke00-x-only functional for treating hydrogenic models are presented.