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

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.