On the performance of local, semilocal, and nonlocal exchange-correlation functionals on transition metal molecules.

The lowest singlet-triplet transition (X (1)Sigma+-(3)Sigma+) of AgI has been used to study systematically the performance of local [local density approximation (LDA)], semilocal [generalized gradient approximation (GGA)], and nonlocal (semiempiric hybrid and meta)-type exchange-correlation functionals on a transition metal molecule where dynamic electronic correlation effects are essential. Previous benchmark ab initio calculations showed that the triplet ground state possesses a shallow well in the Franck-Condon region before becoming repulsive at longer internuclear distance [A. Ramirez-Solis, J. Chem. Phys. 118, 104 (2003)]. Several density functional theory (DFT) descriptions are compared with the benchmark complete active space self-consistent-field+averaged coupled pair functional results, using the same relativistic effective core potentials and optimized Gaussian basis sets. A rather unreliable performance of exchange-correlation functionals was found when ascending the various rungs in DFT Jacob's ladder for this complex molecule. While some of the simpler (LDA and GGA) functionals correctly predict the presence of a short-distance maximum for the (3)Sigma+ state, more sophisticated hybrid and meta-functionals lead to totally repulsive or oscillating curves for the ground triplet state. A thorough discussion addressing the local versus nonlocal character of the exchange and correlation effects on the triplet potential curve is presented. The author concludes that any new efforts directed at producing more accurate exchange-correlation functionals must take into account the more complex electronic structure arising in transition metal molecules, whether these efforts follow the dominant pragmatic semiempiric trend or the more philosophically correct nonempiric pathway to develop better exchange-correlation functionals; only then will the Kohn-Sham version of DFT make the necessary improvements to correctly describe the electronic structure of complex transition metal systems.