† Corresponding author. E-mail:
Project supported by the National Basic Research Program of China (Grant No. 2014CB643703), the National Natural Science Foundation of China (Grant Nos. 11464008 and 51401060), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant Nos. 2014GXNSFGA118001 and 2016GXNSFGA380001), and the Guangxi Provincial Key Laboratory of Information Materials (Grant Nos. 1210908-215-Z and 131022-Z).
Structural, electronic, and magnetic properties of AunGd (n = 6–15) small clusters are investigated by using first principles spin polarized calculations and combining with the ab-initio evolutionary structure simulations. The calculated binding energies indicate that after doping a Gd atom AunGd cluster is obviously more stable than a pure Aun + 1 cluster. Au6Gd with the quasiplanar structure has a largest magnetic moment of 7.421 μB. The Gd-4f electrons play an important role in determining the high magnetic moments of AunGd clusters, but in Au6Gd and Au12Gd clusters the unignorable spin polarized effects from the Au-6s and Au-5d electrons further enhance their magnetism. The HOMO–LUMO (here, HOMO and LUMO stand for the highest occupied molecular orbital, and the lowest unoccupied molecular orbital, respectively) energy gaps of AunGd clusters are smaller than those of pure Aun + 1 clusters, indicating that AunGd clusters have potential as new catalysts with enhanced reactivity.
In contrast to the pervasive inertness of bulk Au, Au nanoparticles exhibit an astonishingly high chemical activity.[1,2] A great breakthrough for excellent catalytic activities of highly dispersed gold particles on a nanoscale in participating in low temperature CO oxidation[3] has stimulated the intensive search for new Au-based nanocatalysts. Especially, the tunable magnetism can be obtained in nonmagnetic gold nanoparticles by doping transition metal (TM) or rare earth (RE) atoms.[4,5] The distinguished quantum-size effect, element synergies, and plasmonic characteristics of AunM (M = TM, RE) bimetallic clusters can be tailored through changing the size of cluster and the composition of endohedral atom,[6–9] which has exerted a tremendous fascination on designing and synthesizing highly efficient catalysts, electronic devices, imaging equipment, and many other versatile aspects.[10,11] Ultrasmall AunM clusters consisting of a few to tens of atoms have been emphatically considered as ideal candidates of catalysts due to their high specific surface area, multitudinous active sites, and high utilization efficiency of precious metal. While in the process of sample preparation, high surface energy and Ostwald ripening are generally detrimental to maintain the isolated configurations and lead ultrasmall particles to easily agglomerate together,[12,13] which adds the difficulty in obtaining ideal AunM small clusters for further investigation. Moreover, the in-situ characterizations of nanocatalysts by applying experimental methods are still underdeveloping,[14] which brings stumbling blocks to figuring out the catalytic active sites.
Currently, the state-of-the-art first principles calculations have provided an effective way to investigate and understand the structural and physicochemical properties of nanoclusters.[15–19] Some researchers have devoted a great deal of effort to theoretically designing noble metal-based bimetallic clusters doped by a TM atom like AunCu,[20] AunTi,[21] and AgnCo,[22] but a systematic study on noble metal-based small clusters doped by a RE atom is still scarce. As is well known, the relativistic effect boundary lying in the fifth and sixth period of the periodic table of elements results in significant differences in electronic configurations and elemental natures between TM and RE elements. Recently, Yadav and Kumar[23] have theoretically found a Au15Gd cluster with a cage structure and large magnetic moment of 7 μB by performing ab-initio calculations, which is desirable for cancer therapy. To the best of our knowledge, however, the investigation on the structural evolution of the Aun small cluster doped by a Gd atom (AunGd) has not been made until now. In this paper we present a systematic search for the global stable structures of AunGd (n = 6–15) clusters by employing the ab-initio evolutionary simulations, and further investigate the corresponding electronic and magnetic properties of AunGd clusters with the lowest energy based on first-principles spin polarized calculations. The ultimate goal of our study is to shed light on the explanation of correlation between electronic and geometric features when dealing with RE atom doped gold nanoclusters.
The global structure searches of AunGd (n = 6–15) clusters were performed using the evolutionary algorithm implemented in the USPEX code.[24,25] The population size was set to be 30 and the initial population was randomly produced by applying the possible point group symmetries. The succeeding generations were obtained by applying heredity, mutation operators with probabilities of 50% and 30%, respectively. Currently, the USPEX code has a great number of successful applications in the structure determination of various materials including bulk solids,[26,27] surfaces,[28] and isolated clusters.[29] The underlying total energy calculations were performed within the spin-polarized density functional theory by using the all-electron projector augmented wave (PAW) method[30] as implemented in the Vienna Ab-initio Simulation Package (VASP).[31] The exchange–correlation functional was dealt with the Perdew–Burke–Ernzerhof (PBE) form of generalized gradient approximation.[32] The energy cutoff for the plane-wave basis set was set to be 380 eV, which guarantees good convergence. All the obtained clusters were optimized in a 15 Å × 15 Å × 15 Å cubic cell, large enough to neglect the interaction between the cluster and its replicas in neighboring cells. The Brillouin zone was sampled using a single Γ point for the geometry optimization. The atomic coordinates of clusters were relaxed until the self-consistent total energy was less than 0.01 meV, and the ionic forces on each atom were less than 0.005 eV/Å.
For comparison, the lowest-energy structures of pure Aun + 1 (n = 6–15) clusters are first predicated from our evolutionary simulations and presented in Fig.
To verify whether it is favorable to dope/substitute a Gd atom in Aun clusters, we calculate the substitution energy (Es) which is defined as
In order to further investigate the size-dependent thermodynamic stability of AunGd clusters, the average binding energy (Eb) changing with cluster size is calculated. The values of Eb of AunGd and pure Aun + 1 clusters are defined as follows:
The total magnetic moment of a cluster is a combination of the spin and orbital magnetic moments. However, the magnetic moment of a cluster is mainly dominated by the spin magnetic moment since the contribution from the orbital magnetic moment of an electron can be neglected. The total magnetic moments of AunGd clusters obtained from the spin-polarized calculations are presented in Table
It can be seen that the calculated magnetic moment shows an odd–even oscillation with the increase of cluster size. The calculated magnetic moment of Au15Gd is 7 μB, and consistent with a previously reported value.[23] When n = 7, 9, 11, 13, the total magnetic moments of AunGd clusters are also almost close to 7 μB. However, the calculated magnetic moments of AunGd clusters with even n are larger than 7 μB. Especially, Au6Gd atomic cluster possesses the largest magnetic moment of 7.421 μB. It is not surprising if one considers the fact that atomic clusters with the reduced coordination number and higher symmetry would exhibit enhanced magnetization.[34] In all of AunGd atomic clusters considered here, as discussed above, Au6Gd with C6v symmetry has the lowest coordination number of 6. Although Au12Gd has a relatively high coordination number, its symmetry with D6d is the highest in AunGd clusters. Hence, the calculated magnetic moment of Au12Gd with 7.226 μB is also significantly larger than those of other AunGd clusters except Au6Gd. Additionally, our calculations indicate that the additional magnetic moments beyond 7 μB for AunGd clusters with even n are fully from Au atoms. For Au6Gd, the local magnetic moment on each Au atom is about 0.07 μB. In fact, Au bulk solid is known to be weakly diamagnetic, but a great variety of magnetic phenomena have been found in polymer-capped Au nanoparticles due to the strong chemical affinity of Au atoms to the capping molecules.[38] Moreover, recent experiments have confirmed the existence of spontaneous magnetic moments in bare Au nanoparticles.[39]
To gain an insight into the origin of magnetism in AunGd clusters, the electronic density of states (DOS) is further investigated. For comparison, the calculated total DOS and partial DOS (PDOS) on Au and Gd atoms of Au6Gd, Au12Gd, and Au15Gd clusters are presented in Fig.
The calculated charge density difference between Au6Gd and Au7Gd is displayed in Fig.
The calculated energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of AunGd and Aun + 1 (n = 6–15) clusters are presented in Fig.
In this paper, we have systematically investigated the structural, electronic, and magnetic properties of AunGd (n = 6–15) small clusters by performing first-principles calculations and evolutionary simulations. Our results indicate that the 2D-3D crossover for AunGd occurs in advance in comparison with pure Aun + 1 clusters and the structural stability of AunGd is significantly enhanced due to the stronger interaction between Gd and Au atoms. In all of the AunGd clusters considered here, Au6Gd has the largest magnetic moment with 7.421 μB due to its reduced coordination number and higher symmetry. The calculated DOS shows that the Gd-4f electrons are mainly responsible for the high magnetic moments of AunGd clusters, and in Au6Gd and Au12Gd clusters the spin polarized effects from the Au-6s and Au-5d electrons are not ignored and further enhance their magnetism. In comparison with pure Aun + 1 clusters, the chemical stability of AunGd clusters with the narrower HOMO–LUMO energy gaps decreases, which indicates that AunGd small clusters have promise to be used as catalysts with the enhanced reactivity.
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