Francesca
Baletto
*a and
Riccardo
Ferrando
b
aPhysics Department, King's College London, Strand, WC2R 2LS, London, UK. E-mail: francesca.baletto@kcl.ac.uk
bPhysics Department, Univ. of Genova, Italy
First published on 15th April 2015
A first-principles investigation of the effect of the doping of golden cages of 32 atoms is proposed. It is shown that Ag and Cu doping affects the geometrical stability of the icosahedral fullerene Au32 cage, where Ag-doping leads to a new, low symmetric, and prolate motif while Cu-doping leads to a lump, incomplete decahedral shape. Most significantly, the HOMO–LUMO gap depends strongly on the cluster geometry while its dependence on the cluster chemical composition seems to be weaker.
The surge of interest in hollow nanostructures, together with the wide range of possibilities offered by nanoalloys with respect to elemental clusters,17 has led recently to the study of bimetallic cages.18–21 However, these studies are often limited to the investigation of a single metal atom encapsulated into a golden cage,22–27 whereas a systematic study of the stability of golden cages after doping with other metallic species is still missing.
In this paper, we perform density functional theory (DFT) calculations to systematically study the effects of changes in composition on the Au32 fullerene, by doping it with silver or copper atoms. We observe that Ag-doping leads to the formation of a new low symmetry motif, always in very close competition with the fullerene – within 0.1–0.2 eV – for all compositions. On the other hand, doping by 50 at% of Cu leads to the preferential formation of compact shapes with decahedral symmetry. The dependence of the HOMO–LUMO (HL) gap on the geometry and on the doping is also discussed. On that regard, we have shown that the gap depends little on the chemical composition, while there is a huge difference between lump/compact and hollow/open geometries, with the latter having a gap at least 0.6 eV wider.
AuAg and AuCu have been chosen because they may be expected to show different behaviours, as follows from examining their bulk phase diagrams. In bulk crystals, AuAg forms solid solutions in the full composition range, while in AuCu three ordered phases are formed (Au0.5Cu0.5 (fcc, L10), Au0.25Cu0.75, and Au0.75Cu0.25 (fcc, L12)).28 In AuAg, Ag segregation is expected in bulk crystal surfaces, due to the lower surface energy of Ag. However, this trend can somewhat change in small clusters because charge transfer effects can lead Au atoms to occupy low-coordination sites, such as vertexes.29,30 In AuCu, some preference for Au surface segregation follows already both from the size effect – which drives the larger atom to the cluster surface – and from surface energy considerations. Recently, atomistic calculations confirm this trend.31,32 In both AuAg and AuCu, a high degree of intermixing is expected in the interior of nanoparticles.
In order to estimate the HOMO–LUMO band gap (HL gap) a ΔSCF method has been used. This technique allows us to calculate the ionization potential (IP) and the electron affinity (EA) as the difference of two ground state configurations, one corresponding to the neutral system and the other obtained eliminating one electron from, or adding one to it (for IP and EA, respectively). For the treatment of the charged systems, where a positive uniform background is added, a Markov–Payne correction36 has been applied in order to improve the convergence with the cubic box size. The ΔSCF method has been shown to be particularly accurate for small and finite systems as the correlation effects on quasi-particle energy levels are generally captured by charge relaxation following the addition or the removal of an electron.37 Very recently, Baroni and coworkers38 have used the ΔSCF method within the Quantum Espresso distribution to calculate the IP and EA values of pure Au clusters in the size range between 2 and 32 atoms and the same authors have shown that the approach gives a similar trend with respect to the most accurate GW calculations and experiments. Here, our calculations are aimed at determining whether there is any clear effect of the doping on the HL gap.
The first is a fragment of the Marks decahedron of 75 atoms (half-Dh, hDh), whereas the second is a poly-icosahedral arrangement. Hollow structures of pure clusters have been obtained by eliminating inner atoms from compact structures at larger sizes extracted from our structural database.15 This has allowed us to single out three significant cage motifs which are reported in the mid panel of Fig. 1. From left to right, we report the cage obtained by emptying a poly-icosahedral (polyIh) structure of 38 atoms, the cage obtained by emptying a truncated octahedron of 38 atoms, and the cage corresponding to the external shell of the anti-Mackay icosahedron of 45 atoms. The latter cage has icosahedral symmetry and it is usually called golden fullerene. In the bottom row of Fig. 1 we report the last open geometry. This is a new, low-symmetry shape, referred to as worm shape in the following, which has been obtained by the ionic relaxation of an empty decahedral shape. As Ag, Au and Cu worms have shown slightly different relaxations, thus they are all reported in the bottom row of Fig. 1. The longest length is about 13.1 Å, 13.2 Å, and 11.3 Å in Ag, Au and Cu, respectively. The empty region has a diameter of about 4.5 Å, 5 Å, and 5.5 Å in Ag, Cu, and Au, respectively. The number of nearest neighbour (NN) pairs varies depending on the metal, from 100 in Ag, to 97 in Cu, and to 92 in Au. This should be compared with the number of nearest neighbour pairs in a fullerene cage, which is 90, and in a compact poly-icosahedral shape, which is 114. The coordinates of the new worm shape for the pure metals are reported in the ESI.†
We have analysed the worm structure by the common-neighbour analysis.40 The CNA analysis gives a signature of three integer numbers (r,s,t) for each NN pair: r is the number of common nearest neighbors of the atoms of the pair, s is the number of nearest-neighbour bonds among these common nearest neighbours, and t is the length of the longest chain which can be formed with these common bonds. The CNA reveals that the worm structure has only surface signatures (in prevalence (200) and (300) signatures, which characterize (100) and (111) facets, respectively). In the case of silver, there is one atom that cannot be classified as a surface atom, leading to a small percentage of (433) CNA signatures. Anyway, there is still an empty region in the Ag worm, which thus preserves its hollow and elongated nature. In addition, this is the only silver isomer with a maximum pair distance longer than 10 Å and a minimum distance of 4.5 Å between atoms at the opposite sites with respect to the central axis. This is highlighted in Fig. 2 where the pair distribution function is plotted for four Ag isomers.
Fig. 2 Pair distribution function of four Ag32 isomers. The worm shape is hollow and elongated in one direction. |
In agreement with other DFT studies, the best Au isomer is the icosahedral fullerene cage. This structure corresponds to the external shell of the anti-Mackay icosahedron of 45 atoms.41 The second isomer is the tubular worm at 0.6 eV above. All the other geometries – including the empty truncated octahedron and the empty pancake – are at least at 0.8 eV above. The two lump shapes result to be slightly distorted after the ionic relaxation, loosing their symmetry and they are considerably higher in energy above 1.8 eV. It should be noted that the relative stability of the ionic forms is slightly different compared to the neutral case, where the cationic worm is almost degenerate to the fullerene Au32+. But the anionic fullerene is still 0.2 eV better than the negatively charged worm. It should be noted that the third isomer for Au32− is the empty pancake being higher by 0.4 eV. Further, all but the incomplete Dh are within 0.9 eV.
Not surprisingly, the lowest energy isomer for Cu32 is found to have a compact decahedral shape, obtained cutting asymmetrically a larger Marks decahedron of 75 atoms in such a way that the 5-fold symmetry axis is displaced towards the surface. This isomer is in close competition with another lump poly-icosahedral configuration, just a few hundredths of eV above. On the other hand, any hollow geometry is lying at least 2 eV above – for the fullerene, while the empty TO and the empty pancake are at 3.5 and 3.3 eV, respectively. Charging the system does not change the overall picture, where hollow geometries remain very unfavourable. On the other hand, one should notice that Cu32− prefers to adopt a polyIh shape instead of an incomplete Dh, but the Cu32+ hDh gain is more stable than the polyIh by roughly 0.4 eV.
Ag32 shows a very interesting behaviour, indeed. First of all, all the considered structural motifs are within 1.46 eV. Four shapes are so close in energy as less as 0.25 eV. Among them, the new low symmetry tubular shape, named worm, has been identified. The worm and the incomplete Dh are isoenergetic within a few meV. The third isomer is the poly-icosahedral geometry at just 0.04 eV and the fullerene cage is at 0.24 eV. The worst two isomers, lying at 1.46 and 1.33 eV, are the empty pancake and the empty truncated octahedron, respectively.
It should be noted that Ag32+ has a different energy ladder, where the positively charged worm is now at 0.55 eV while the polyIh is at 0.4 eV above the incomplete Dh. The fullerene Ag32+ becomes really unfavorable being higher 1 eV than the best isomer. As observed for copper, Ag32− as a preference for the polyIh, followed by the worm-Ag32−. The incomplete Dh negatively charged is the third isomer at 0.35 eV above and followed by the fullerene at 0.6 eV. The charged empty cages are truly unfavourable from an energetic point of view.
The structural relaxation of AuAg and AuCu cages has been summarised in Fig. 3 where the atomic binding energy,
(1) |
Fig. 3 Binding energy per atom (eV) of Au-based nanocages at 32 atoms for Ag (top) and Cu (bottom) doping. Empty symbols stand for hollow geometries, while full symbols represent compact shapes. |
On the other hand, the specific chemical ordering pattern makes a difference for AuAg clusters. The BE shows a clear linear dependence on the Au-concentration. Ag-doped fullerene cages prefer to adopt the worm shape, with the exception of very high Au concentrations, as 80% and above. Anyway, at all concentrations, the fullerene cage and the worm shape are in very close competition and, thus, different chemical ordering patterns determine the lowest energy isomer corresponding to the different compositions. The best chemical ordering in AuAg is the one that maximizes the number of mixed pairs, as already suggested by Lopez and coworkers in ref. 43 for clusters of 13 atoms. Whenever it is possible, the best isomer is characterised by a complete intermixing while all segregated patterns, such as the Janus-like, are strongly unfavorable. At very low Au concentration, gold atoms prefer to occupy vertex positions while at low Ag concentration, silver atoms prefer to form only one Ag–Ag bond and to lie on the same facet. In hollow shapes, this tendency to intermixing often leads to an Au-line decoration pattern. For example, the best chemical pattern in the Au12Ag20 fullerene cage is the one where Au atoms formed a zig-zag line – resulting in only 48 mixed nearest neighbour pairs – depicted in Fig. 4, while the full mixing – characterised by 60 mixed pairs – lies 0.27 eV above.
Fig. 4 Golden line decoration on silver cages, worm (left) and fullerene (right). Silver are in grey and gold in yellow. |
The linear decoration pattern of Au seems however to be present only in cages that have a real empty space inside, see Fig. 4. This follows from considering the Ag tetrahedron of 20 atoms, which is a structure with no internal atoms, but without a notable empty inner space. In this Ag20 tetrahedron, we have substituted 4 Ag atoms with Au atoms, finding that placing the Au atoms at vertices is more favourable than placing them on a line on the same edge, by 0.27 eV. About the anionic and cationic AuAg32, we should notice that the Au24Ag8 icosahedral cage becomes unfavorable with respect to the worm or the polyIh by 0.3 eV.
In the golden fullerene, a large band gap should be expected due to its spherical aromaticity (2(N + 1)2) as discussed in ref. 44. A low symmetry cage as the “worm” shows a HL-gap of 3.1–3.3 eV, while lump, compact shapes the gap is from 2.6 to 2.9 eV. In the case of nanoalloys, we have limited our analysis to AuCu and AuAg clusters with an Au concentration of 25%, 50% and 75% and we have considered only the best chemical pattern for each geometrical motifs. We should notice that doping has a very little effect on the gap, while it depends strongly on the geometry, where open motifs have a consistently wider gap than the decahedral or poly-icosahedral ones. A doped Au–fullerene cage shows a gap between 3.6–3.8 eV for both AuCu and AuAg. The worm gap is slightly more affected by the doping and the gap is between 3.1 and 3.7 eV. On the other hand, incomplete Dh has a 2.7–3.1 eV gap.
Further, we would like to discuss the values of the first ionization potential, as reported in Table 1 for the elemental noble metal clusters and in Fig. 6 for the binary cases. The bulk values are 7.7 eV, 7.6 eV and 9.2 eV, respectively, for Cu, Ag and Au. In the case of pure metals, it is clear that the IP is dramatically lower than the corresponding bulk value. The ionization potential depends little on the geometrical shape, with a minimum for the hDh, 5.2 for Ag, 5.4 eV for Cu and 6.5 for Au, and a peak for the truncated octahedral cage, 6.1 for Ag, 6.4 for Cu 7.3 eV for Au. For the nanoalloys, the first IP increases as the gold concentration increases, with a maximum for the fullerenic cage – between 6.4–6.7 eV – and a minimum for the incomplete decahedron at 5.6 eV for both Au8Cu24 and Au8Ag24. As far as we can see, the specific chemical ordering pattern should affect little the optical properties of these small nanoalloys, in qualitative agreement with time-dependent DFT calculations.45
Worm | Fullerene | hDh | polyIh | |
---|---|---|---|---|
Pure Au | ||||
IP | 6.48 | 7.02 | 6.52 | 6.80 |
EA | 3.37 | 2.98 | 3.58 | 3.89 |
Pure Cu | ||||
IP | 5.74 | 6.30 | 5.43 | 5.77 |
EA | 2.65 | 2.45 | 2.54 | 2.97 |
Pure Ag | ||||
IP | 5.74 | 6.03 | 5.19 | 5.54 |
EA | 2.41 | 2.15 | 2.53 | 2.91 |
Fig. 6 First ionization potential in eV for pure and mixed clusters, colour scheme as in Fig. 5. |
We have shown that the HL gap seems to depend prevalently on the geometry more than on the chemical composition. These results are somehow expected taking into account the Jellium model. Recently, it has been shown that this should be independent of the chemical composition.46 We hope that our work stimulate further theoretical investigations and experiments, because those hollow bimetallic isomers with a large gap might be considered as a new state of matter, and classified as super-cages.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5cp01061f |
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