Validation of Theoretical Methods for the Structure and Energy of Aluminum Clusters

Abstract

We calculated the atomization energy of aluminum clusters (Al 2 -Al 7 ) with several multilevel methods, including MCG3/3 and G3X, that have been previously shown to provide high accuracy for atomization energies. We used the results to test a number of hybrid density functional theory (HDFT) methods and found that the PBE0 method is in best agreement with the accurate methods. We then used the PBE0/MG3 method to develop a more extensive data set for the energies of small aluminum clusters (Al 2 -Al 13 ), and this was used to test a number of semiempirical methods, in particular Austin model 1 (AM1), modified neglect of differential overlap (MNDO), modified symmetric-orthogonalized intermediate neglect of differential overlap (MSINDO) with and without d-functions, parametrized model 3 (PM3), and the tight-binding total energy (TBTE) method, for geometries, energies, and multiplicities of Al clusters. The AM1 model and MSINDO model are the most accurate of the semiempirical methods for energetics, and PM3 is the most accurate method for geometries.

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

“…Overall, the PBE0 and mPW1PW91 functionals are recommended for calculating all the molecular properties of neutral and anionic Al clusters. This study is consistent with earlier studies by Schultz et al 22 and Miller et al, 57 who suggested that PBE0 performed well in a study of Al clusters. They found small absolute error differences from the results of the PBE0 functional compared to the available experimental results.…”

Large-scale first principles configuration interaction calculations of optical absorption in aluminum clusters

“…Among them, rhombus structure is the most stable with 3 14 We note that bond lengths are in good agreement but bond angles appear to vary a bit.…”

“…9,10 Shell structure and s-p hybridization in anionic aluminum clusters were probed using photoelectron spectroscopy by Ganteför and Eberhardt, 11 and Li et al 7 Evolution of electronic structure and other properties of aluminum clusters has been studied in many reports. [7][8][9][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] Structural properties of aluminum clusters were studied using density functional theory by Rao and Jena. 8 An all electron and model core potential study of various Al clusters was carried out by Martinez et al 22 Upton performed chemisorption calculations on aluminum clusters and reported that Al 6 is the smallest cluster that will absorb H 2 .…”

Growth Pattern of Truncated Octahedra in AlN (N ≤ 310) Clusters

“…14 Especially in the prediction of structural evolution, more recently, Al clusters above Al 23 were found to have a fragment of bulk motif, which is face-centered-cubic (fcc) for aluminum. 18,19 However, a study of Al clusters suggested that fcc atomic packing that is dominant in bulk aluminum obtained from small cluster sizes is inadequate because there exists a strong competition among decahedral structures, fragments of fcc crystalline lattice, and hexagonal-like structures for Al [23][24][25][26][27][28][29][30][31][32][33][34] clusters. 20 Therefore, structural evolution or transition in aluminum clusters needs more investigation in the range of medium or large sizes.…”