Small clusters of aluminum and tin: Highly correlated calculations and validation of density functional procedures

Abstract

We present results of molecular electronic structure treatments of multireference configuration interaction (MRCI) type for clusters Al(n) and Sn(n) in the range up to n = 4, and of coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) type in the range up to n = 10. Basis sets of quadruple zeta size are employed, computed energy differences, such as cohesive energies, E(coh), or dissociation energies for the removal of a single atom, D(e), differ from the complete basis set limit by only a few 0.01 eV. MRCI and CCSD(T) results are then compared to those obtained from density functional theory (DFT) treatments, which show that all computational procedures agree with the general features of D(e) and E(coh). The best agreement of DFT with CCSD(T) is found for the meta-GGA (generalized gradient approximation) TPSS (Tao, Perdew, Staroverov, Scuseria) for which D(e) differs from CCSD(T) by at most 0.15 eV for Al(n) and 0.21 eV for Sn(n). The GGA PBE (Perdew, Burke, Ernzerhof) is slightly poorer with maximum deviations of 0.23 and 0.24 eV, whereas hybrid functionals are not competitive with GGA and meta-GGA functionals. A general conclusion is that errors of D(e) and/or energy differences of isomers computed with DFT procedures may easily reach 0.2 eV and errors for cohesive energies E(coh) 0.1 eV.

Structural evolution of small ruthenium cluster anions

“…This quite satisfactory performance of TPSS is in line with a recent validation of DFT functionals for the metal clusters Al n and Sn n for n up to 8. 40 In comparison with MR-CISD, MR-ACPF, and CCSD(T) treatments, it was found that TPSS is slightly more accurate than PBE, which is better than BP86 and in turn much better than the hybrid functional B3LYP.…”

Density Functional Theory Assessment of Molecular Structures and Energies of Neutral and Anionic Aln (n = 2–10) Clusters

“…The reliability of the def2-TZVPP basis set ((14s 9p 3d 1f)/[5s 5p 3d 1f]) was tested in an earlier study on Al clusters. 23 One of the main purposes of the present study is to identify a suitable DFT functional for further investigations of large Al clusters. For this, the segment contraction basis set in the DFT calculations is more appropriate than a general contraction one, such as the correlation-consistent (CC) basis set.…”

“…The latter two parameters in a previous study were considered to assess the DFT functionals. 23 Two energetic parameters (vIE and vEDE) are also included, making an assessment of the DFT performance more reasonable. The present study examined DFT performance by calculating the four energetic parameters of Al clusters.…”

Assessment of DFT Functionals in Predicting Bond Length and Atomization Energy of Catalytically Important Metal Dimers

“…Present calculations have shown that, the Ti-Ti bond length of Ti2 dimer predicted by Minnesota M06-L functional is in close agreement with the experimental value. [46] The difference in the Ti-Ti bond length between calculated and experimental results is 0.04 Å. The other DFT functionals that are taken for this study are found to underestimate the Ti-Ti bond length.…”

“…Due to these discrepancies, large structural and energetical values for Cr2 dimer have been obtained. In 2.701 [44] 1.943 ± 0.001 [46] 1.770 [50] 1.679 [52] ≤ 3.4 [57] 2.020 ± 0.020 [59] -2.310 [62] -2.155 ± 0.001 [14] 2.219 [67] 2.350 ± 0.080 [69] summary, the lower level basis set is not suitable for the calculation of structural and energetical parameters in this dimer. From the earlier studies, it is clear that even using higher level ab initio calculations also, one could not produce accurate results in this dimer.…”