Structural and energetic properties of cluster models of anatase-supported single late transition metal atoms: a density functional theory benchmark study

Context

Single-atom catalytic systems constitute an intriguing research topic due to their inherently different chemical behavior as compared to classic heterogeneous catalysts. In this study, cluster systems representing single late transition metal atoms adsorbed on anatase were constructed starting from previously generated periodic models and subjected to a density functional theory (DFT) benchmark study. The ability of different density functional approximations representing all rungs of the Jacob’s Ladder classification to accurately describe bond lengths and adsorption energies was assessed for these clusters with the aim of revealing the functional that allows to retain the structural characteristics of the initial periodic system, while also delivering reliable energetics. In this regard, our results indicate that optimisation of the clusters with the meta-GGA functionals TPSS or RevTPSS provides the lowest mean unsigned error and root-mean-square deviations with respect to the periodic models. Moreover, these functionals and, to a slightly lesser degree, PW91 were also found to provide adsorption energies that are statistically the least deviating from the CCSD(T) reference data. More complex hybrid functionals appear to be performing less well.

Methods

Cluster geometries were determined at the Kohn–Sham DFT level using the LANL2DZ basis set for the transition metals and the Pople 6-31G(d) basis set for O and H. The density functional approximations considered were SVWN, PBE, BP86, BLYP, PW91, TPSS, RevTPSS, M06L, M11L, B3LYP, PBE0, M06, M06-2X, MN15, ωB97X-D, CAM-B3LYP, M11, and MN12-SX. Reference adsorption energies of the metals on the support cluster were obtained at the CCSD(T)/LANL2TZ (transition metals)/6–311 +  + G(d,p)//RevTPSS/LANLD2DZ (transition metals)/6-31G*. Besides the above-mentioned functionals, energy calculations using the double-hybrid functionals, DSDPBEP86, PBE0-DH, and B2PLYP, were also performed. All adsorption energy calculations were carried out on the RevTPSS geometries.