Michał Hapka

Computational and experimental modeling of intermolecular structures
and interactions relevant for intelligent and functionalized materials

Michał Hapka , UW
Supervisor: prof. Grzegorz Chałasiński (UW), dr hab. Janusz Zachara (WUT)

Absorption UV spectra of gold clusters Au_n (n = 4, 6, 8, 12, 20) are investigated using the time - dependent density functional theory (TDDFT). The calculations employ several long-range corrected xc functionals: ωB97X, LC-ωPBEh, CAMB3LYP* (where * denotes variant with corrected asymptote of CAM-B3LYP), and LC-ωPBE. The latter two are subject to first-principle tuning according to a prescription of Stein et al. (Phys. Rev. Lett., 105, 266802 (2010)) by varying the range separation parameter. TDDFT results are validated for Au₄ and Au₈ against the equation-of-motion coupled cluster singles and doubles results and the experiment. Both long-range correction and the inclusion of a fixed portion of the exact exchange in the short-range are essential for the proper description of the optical spectra of gold. The ωB97X functional performs well across all studied cluster sizes. LC-ωPBEh, with parameters recommended by Rohrdanz et al. (J. Chem.Phys. 130, 054112 (2009)), affords the best performance for clusters of n≥4. The optimally tuned CAM-B3LYP* features the range separation parameter of 0.33 for Au₄ and 0.25 for all the larger clusters. LC-ωPBE the tuning procedure resulted in incorrect transition energies and oscillator strengths despite the fact that the optimized functional showed the accurate linear dependence on fractional electron numbers. Au_n (n=4, 6, 8) feature optical gaps above of 3 eV and Au₂₀ of ca. 2.9 eV. In Au₁₂ this gap narrows to ca. 2.1 eV. The calculated spectrum for Au₂₀ involves intensity being concentrated in only a few transitions with the absorption maximum at 3.5 eV. The intense 3.5 eV absorption is present in all cluster sizes of n≥4. The calculated Kohn-Sham gaps for all cluster sizes are within 0.5 eV of the difference between the vertical ionization potential and electron affinity. The reasons for this and for the failure of conventional xc functionals for optical spectra of gold are discussed.

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