New Effective Core Method (Effective Core Potential and Valence Basis Set) for Al Clusters and Nanoparticles and Heteronuclear Al-Containing Molecules

In previous work we have shown that the PBE0 hybrid density functional method with the MG3 all-electron basis set is an accurate method for calculating the atomization energies of small aluminum clusters (Al2-Al7). However, the MG3 basis set is very expensive for molecules much larger than Al13; therefore, we have developed a new effective core potential (ECP) method for aluminum to reduce the cost of obtaining accurate results for nanoparticles. Our method involves a hybrid of the Stuttgart semiempirical effective core potential and the compact effective potential (CEP) potential, and it uses a newly optimized polarized valence triple-ζ basis set. The combination of the new ECP and the new polarized valence triple-ζ basis set for Al is called the Minnesota effective core (MEC) method for Al. The method was optimized with a training set of atomization energies and geometries for AlH, AlC, AlO, AlCCH, Al2H, Al2C, Al2O, and Al3 and atomization energies of three Al13 structures, and we tested it on six test sets composed of 20 atomization energies for systems as large as Al13. We also present an improved all-electron polarized triple split basis set for oxygen, called 6-311+G(d*,p). For the test sets, the mean unsigned error (MUE) of the new method with respect to PBE0/MG3 is 0.06 eV for atomization energies and 0.007 Å for bond lengths, which constitutes a very significant improvement over the quality of the results that can be obtained with effective core potentials and valence basis sets in the literature (of the eight methods in the literature, the best previous method had average errors of 0.63 eV and 0.036 Å). We have also tested the MEC method with a variety of hybrid density functional theory, hybrid meta density functional theory, and pure GGA and meta GGA functionals and found that the average MUE, relative to each functional with all-electron basis sets, is 0.04 eV for atomization energies and 0.009 Å for bond lengths for the new effective core method and 0.16-0.20 eV and 0.013-0.033 Å for effective core potential and valence basis sets in the literature.