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.

Quadratic and cubic hyperpolarizabilities of nitro-phenyl/-naphthalenyl/-anthracenyl alkynyl complexes

1-Nitronaphthalenyl-4-alkynyl and 9-nitroanthracenyl-10-alkynyl complexes [M](C[triple bond, length as m-dash]C-4-C10H6-1-NO2) ([M] = trans-[RuCl(dppe)2] (6b), trans-[RuCl(dppm)2] (7b), Ru(PPh3)2(η5-C5H5) (8b), Ni(PPh3)(η5-C5H5) (9b), Au(PPh3) (10b)) and [M](C[triple bond, length as m-dash]C-10-C14H8-9-NO2) ([M] = trans-[RuCl(dppe)2] (6c), trans-[RuCl(dppm)2] (7c), Ru(PPh3)2(η5-C5H5) (8c), Ni(PPh3)(η5-C5H5) (9c), Au(PPh3) (10c)) were synthesized and their identities were confirmed by single-crystal X-ray diffraction studies. Electrochemical studies and a comparison to the 1-nitrophenyl-4-alkynyl analogues [M](C[triple bond, length as m-dash]C-4-C6H4-1-NO2) ([M] = trans-[RuCl(dppe)2] (6a), trans-[RuCl(dppm)2] (7a), Ru(PPh3)2(η5-C5H5) (8a), Ni(PPh3)(η5-C5H5) (9a), Au(PPh3) (10a)) reveal a decrease in oxidation potential for ruthenium and nickel complexes on proceeding from the phenyl- to naphthalenyl- and then anthracenyl-containing bridge. HOMO → LUMO transitions characteristic of MC[triple bond, length as m-dash]C-1-C6H4 to 4-C6H4-1-NO2 charge transfer red-shift and gain in intensity on proceeding to the ruthenium complexes; the low-energy transitions have increasing ILCT character on proceeding from the phenyl- to naphthalenyl- and then anthracenyl-containing bridge. Spectroelectrochemical studies of the Ru-containing complexes reveal the appearance of low-energy bands corresponding to chloro-to-RuIII charge transfer that red-shift on proceeding from the phenyl- to naphthalenyl- and then anthracenyl-containing bridge. Second-order nonlinear optical (NLO) studies at 1064 nm employing ns pulses and the hyper-Rayleigh scattering technique reveal an increase in quadratic optical nonlinearity upon introduction of metal to the precursor alkyne to afford alkynyl complexes and on proceeding from ligated-gold to -nickel and then to -ruthenium for a fixed alkynyl ligand. Quadratic NLO data of the gold complexes optically transparent at the second-harmonic wavelength reveal an increase in βHRS on proceeding from the phenyl- to the naphthalenyl-containing complex. Broad spectral range third-order nonlinear optical studies employing fs pulses and the Z-scan technique reveal an increase in two-photon absorption cross-section on replacing ligated-gold by -nickel and then -ruthenium for a fixed alkynyl ligand. Computational studies undertaken using time-dependent density functional theory have been employed to assign the nature of the key optical transitions and suggest that the significant optical nonlinearities observed for the ruthenium-containing complexes correlate with the low-energy formally Ru → NO2 band which possesses strong MLCT character, while the more moderate nonlinearities of the gold complexes correlate with a band higher in energy that is primarily ILCT in character.