A new hybrid DFT approach to electronic excitation and first hyperpolarizabilities of transition metal complexes

The electronic excitations and the static first hyperpolarizability of three typical transition metal (TM) aromatic carbonyl complexes, two tungsten pentacarbonyl derivatives (W(CO)5L, L = Py and PyCHO) and one chromium tricarbonyl arene derivative (Cr(CO)3Bz, Bz = benzene), have been theoretically studied by a variety of density functional methods. The assessments reveal that most of the conventional DFT methods including local density approximation, generalized gradient approximation (GGA), and the various kinds of hybrid exchange-correlation (xc) methods present the first hyperpolarizabilities of these TM-containing molecules with large deviations from the experiments. A one-parameter hybrid xc functional is introduced by using the Perdew-Wang 1991 gradient-corrected correlation functional (PW91) and the Barone's-modified PW91 exchange functional (mPW). The ratio between the exact and the density functional exchange is determined to be 0.40 by the adiabatic connection method. The application of the new hybrid functional to the three organometallic carbonyl molecules results in the satisfactory agreement between the calculated first hyperpolarizabilities and the experimental ones. The second-order nonlinear optical properties of the three organometallic complexes are addressed to the metal-to-ligand charge transfers, and the extended pi-delocalization ligands benefit the enhancement of the first hyperpolarizability.