Long-Range Corrected DFT Calculations of First Hyperpolarizabilities and Excitation Energies of Metal Alkynyl Complexes

The performance of the CAM-B3LYP, ωB97X and LC-BLYP long-range corrected density functional theory methods in the calculation of molecular first hyperpolarizabilities (β) and low-lying charge transfer (CT) excitation energies of the metal alkynyl complexes M(C≡C-4-C₆ H₄ -1-NO₂ )(κ² -dppe)(η⁵ -C₅ H₅ ) [M=Fe (1), Ru (2), Os (3)] and trans-[Ru{C≡C-(1,4-C₆ H₄ C≡C)_n -4-C₆ H₄ -1-NO₂ }Cl(κ² -dppm)₂ ] [n=0 (4), 1 (5), 2 (6)] was assessed. The BLYP, B3LYP and PBE0 standard exchange-correlation functionals and the Hartree-Fock method were also examined. The BLYP functional was shown to perform poorly in the calculation of β and low-energy CT transitions. The hybrid functionals (B3LYP and PBE0) showed significant improvement over the pure functional BLYP, but overestimated the hyperpolarizability ratios and the wavelengths of the lowest energy metal-to-ligand CT transitions for 5 and 6. The effect of long-range corrections is noteworthy, particularly for the larger complexes, improving the calculation of β ratios for 4-6. However, CAM-B3LYP, ωB97X, and LC-BLYP considerably overestimated the low-lying CT energies. PBE0 was found to give the best transition energy match for 4. The influence of the phenylene ring orientation in the alkynyl ligand on the calculated properties is substantial, particularly for the larger complexes. For these types of calculations, a basis set with diffuse functions (at least 6-31+G(d)) for the heavy elements is recommended.