Ab‐initio studies of magnetic properties of small‐sized and cuboctahedral aluminum nanoclusters

Abstract

Magnetic properties of Al n clusters are investigated using ab initio density functional calculations based on plane-wave and the all electron projector augmented-wave (PAW) method. We present stable structures of small-sized Al n (n = 2−17) clusters obtained from optimization with binding energy, magnetization, and compared our results with experiment data. The size dependence of binding energy and magnetization are clarified. For large clusters, we discuss the stability of cuboctahedral Al n clusters with up to 923 atoms based on the size dependent binding energy. The coefficients corresponding to surface and edge energies for cuboctahedral Al n clusters have been estimated. We have obtained the cohesive energy of the bulk system to be E c = 3.418 eV, close to the experimental value (3.39 eV) through the fitting function of size dependent binding energy. We discuss the magnetization of cuboctahedral Al n clusters in relation to shell structure. When the size of the cluster is enlarged, the distribution of magnetization shows that the spin density is largest at the outmost shell. From Al 309 to Al 923 clusters, electron and spin density in the center and innermost shell behave similar to the bulk.

Theoretical Study of the Spin Competition in Small-Sized Al Clusters

“…When the triple-ζ and higher basis sets are employed in DFT computations, the bond lengths found for the 3 Π u state range between 2.74 and 2.77 Å (Table SI-V), in agreement with previous reports. − ,, In the case of the 3 Σ g – state the BL ranged between 2.48 and 2.51 Å, also consistent with previous reports ,,,,, depending on the functional and the basis set. The BL obtained with small basis set D95 or SDecp pseudopotential were systematically larger, both in good agreement with previous reports employing similar treatments. , …”

“…An excited state 3 Σ g – is also consistently reported by DFT computations − , and CCSD­(T); ,, also, multireference singles–doubles configuration-interaction (MRSDCI) calculations have been performed by Shinde and Shukla obtaining the excited 3 Σ g – state. We found that for DFT computations employing the double-ζ: DGDZVP, triple-ζ: DGTZVP, TZVP, def2-TZVPP, and aug-cc-pV x Z ( x = D, T, Q) basis sets, the 3 Σ g – state appears to be the ground state, consistent with previous reports. , In particular for the TPSS/aug-cc-pVDZ level, both the 3 Π u and the 3 Σ g – states appear degenerate.…”

“…Al 4 cluster exhibits a rhomboidal structure in a triplet spin state with D 2 h symmetry, ,, in a 3 B 2g , a 3 B 3g , and a 1 A g ground state. ,, Distortion of planarity has been obtained within DFT theory using PBE0/aug-cc-pVTZ, M06-2X/aug-cc-pVTZ, and CCSD­(T)/aug-cc-pVQZ . In this work we have obtained a D 2 h planar rhomboidal structure in a 3 B 3g ground state (Figure ), in agreement with previous reports. ,, The 1 A g ground state was obtained for the meta-GGA TPSS and revTPSS when the DGDZVP and DGTZVP basis sets are used and revTPSS/aug-cc-pVDZ, in agreement with previous reports ,, (Tables SI-XIII and SI-XIV) . The BL found range from 2.63 and 2.73 Å for D95 and SDecp.…”

“…During the past decades Al 2 clusters have been extensively investigated both experimentally and theoretically. − Resonant two-photon ionization spectroscopy report a 3 Π u ground state . For this state the bond length (BL) is 2.7011 ± 0.0015 Å, the dissociation energy ( D e ) is 1.34 ± 0.06 eV, and the vibrational frequency is 285.8 cm –1 .…”

Magnetism in Simple Metal and 4d Transition Metal Clusters

“…Upton [45], in his model calculation, predicted Al 2 and Al 6 to have nearly degenerate singlet and triplet states, but found Al 4 to be a singlet, and the odd-sized clusters Al 3 and Al 5 to be doublets. Phung et al [46] found Al 2 , Al 4 , Al 6 , Al 10 , Al 12 and Al 16 to have triplet ground states in their DFT calculations. However, Al 8 was found to be a singlet, contrary to the conclusions of Cox et al Al 14 also turned out to be a singlet.…”