Optical absorption spectra of gold clusters Aun (n = 4, 6, 8,12, 20) from long-range corrected functionals with optimal tuning

Abstract

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, CAM-B3LYP∗ (where ∗ denotes a 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 Au(4) and Au(8) 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 Au(4) and 0.25 for all the larger clusters. For 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 Au(20) of ∼2.9 eV. In Au(12) this gap narrows to ∼2.1 eV. The calculated spectrum for Au(20) 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 HOMO-LUMO 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.

A Unique Au–Ag–Au Triangular Motif in a Trimetallic Halonium Dication: Silver Incorporation in a Gold(I) Catalyst

“…Improvements could be made by use of the ωB97X‐D functional, which has a long‐range corrected hybrid with atom–atom dispersion corrections 35. 36 The computationally optimized structures of 1 + – 3 + are in excellent agreement with the X‐ray data for 2⋅ 1/2H 2 O and 3⋅ CH 2 Cl 2 and in good agreement for 1⋅ CH 2 Cl 2 . Although the fit is good, all computed values are too high (they still slightly underestimate metallic interactions).…”

Local Molecular Reactivity of the Colored Dansylglycine in Water and Dioxane Studied through Conceptual DFT

“…In the past, various TDDFT studies of molecules of different sizes have used optimally tuned RSH density functionals with great success [11][12][13][14][15][16][17][18]. Table 2 provides a comparison between the results involved in the ground-state approximation derived from the HOMO-LUMO gap together with TDDFT results and the experimental value of 340 nm in water and 339 nm in dioxane.…”

“…Following the same ideas of previous works, we will consider a fixed RSH functional instead of the optimally tuned RSH density functionals that have attained great success [11][12][13][14][15][16][17][18].…”

Communication: Global minimum search of ${\rm Ag}^+_{10}$ Ag 10+ with molecular beam optical spectroscopy

“…32 The long-range corrected (LC) exchange correlation (xc) functional, LCωPBEh, 33 is used throughout our whole analysis. It has been shown to perform well for the calculation of ground and excited state properties of gold, 24,34 silver, 24 and mixed silver gold clusters, 35 where it leads to the reliable prediction of optical absorption spectra.…”

“…41 The long-range corrected xc functional LC-ωPBEh 33 is used in order to accurately recover the asymptotic behaviour of the exchange correlation potential, since this has proven to reliably reproduce vertical electronic excitation spectra. 4,6,8,24,33,34 The theoretical description of optical properties of clusters based on TDDFT calculations is easily applicable and widely used, in particular due to the low computational costs associated with the single-reference character. 42 In minimizations the BP-86 43,44 and M06-L 45 functionals are also studied for comparison purposes.…”