Structure and Properties of Small Aurocarbons: A Selective Study

Article pubs.acs.org/JPCA

Structure and Properties of Small Aurocarbons: A Selective Study C. N. Ramachandran and Fedor Y. Naumkin* Faculty of Science, University of Ontario Institute of Technology (UOIT), Oshawa, Ontario, Canada L1H7K4 S Supporting Information *

ABSTRACT: Gold clusters are versatile catalysts, and adding nonmetal dopants can allow tuning of their electronic properties via both shape and composition alteration. In the present work, mixed clusters of carbon and gold atoms are studied in terms of structure, stability, and the correlation between the shape and electronic properties by using a density functional theory approach. Four series of isomers (hydrocarbon analogues, carbon chains and cycles on gold surface, and carbon cores encapsulated by gold atoms) are investigated, exhibiting variation of the relative stability with the system size. Calculated vertical ionization energies, vertical electron affinities, and HOMO−LUMO energy gaps of the mixed clusters show a considerable change relative to the values for the pure gold clusters, the properties generally altering more strongly for the gold-encapsulated-carbon isomers. Also discussed are the structure, stability, and properties of larger clusters with a few such encapsulated-carbon units, with pronounced effects due to aggregation. organic reactions.2,30−32 Catalytic properties of gold clusters vary significantly with size and shape.33 It has been proposed that the roughening of the surface of gold promotes the reactivity by localizing the electrons.34 Such a surface modification could be possible via the interaction of gold with nonmetals such as carbon atoms. It is known that Au/C catalysts have found applications in selective oxidation and hydrochlorination reactions.35−37 The self-assembly of gold nanowires along carbon nanotubes is also reported.38 The above illustrates the importance of studies of the structure, stability, and reactivity for the mixed clusters of gold and carbon atoms. Some of the studies in this direction are available in the literature. In particular, Ejgierd and Pyykkö have investigated the structure and stability of CAu4, C2Aun (n = 2− 6), and C6Au6 species and pointed out that the aurophilic interaction plays an important role in stabilization of such compounds.26 A variety of carbon−gold species including core−shell systems have also been reported earlier.27−29 In the present study, we investigate the structure, stability, and properties of the systems with the general formula C4Aun, where n = 4, 6, and 8. The studies are also extended to some of the larger clusters with a few such structural units.

1. INTRODUCTION Gold has attracted human kind both in the ancient and in the modern civilizations. However, the chemistry of gold was not rich until the last decades due to its lower reactivity in the bulk metallic form.1 Advances in nanoscience and nanotechnology have accelerated the studies of gold and its compounds in their low dimensions, which find applications in the fields of catalysis, electronics, and medicine.2−5 Experimental results on gold and related compounds have stimulated many theoretical studies,6−28 and development of effective core potentials (ECPs) for gold has added momentum to this research. Among those studies, the aggregation of gold atoms has been given special attention, and it was shown that small clusters of gold atoms form two-dimensional planar structures, whereas the larger clusters form three-dimensional cage structures. The turnover point between the 2D and 3D gold clusters (Aun) has been found to vary between n = 6 and 12 depending on the methods and basis sets used for calculations.6−11 The corresponding 2D-to-3D turnover points for the anionic and cationic clusters of gold have also been discussed recently.12 Apart from the self-aggregation, studies on the aggregations of gold atoms with silver, copper, and many other transitionmetal atoms are available in the literature as well.13−17 Mixed clusters of gold with nonmetals emphasizing the covalent nature of the bond between gold and nonmetal atoms have also been investigated.18−29 In particular, using photoelectron spectroscopy and ab initio methods, Wang has pointed out that gold atoms behave like hydrogen atoms, forming aurosilicon and auroboron clusters with strong covalent bonding.18 The interactions of gold with carbon atoms have received special attention due to the role of gold as a catalyst in many © 2013 American Chemical Society

2. COMPUTATIONAL METHODOLOGY All calculations have been carried out using the computational chemistry package NWChem 6.0.39 Electronic energies have been computed using density functional theory with the M06-L functional in conjunction with the basis set aug-cc-pVTZ for carbon atoms and the LANL2DZ ECP and the associated basis Received: April 11, 2013 Revised: June 26, 2013 Published: July 29, 2013 6803

dx.doi.org/10.1021/jp4035858 | J. Phys. Chem. A 2013, 117, 6803−6808

The Journal of Physical Chemistry A

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Table 1. Calculated Values of the Stabilization Energy, VIE, VEA, and HOMO−LUMO Energy Gaps for the Optimized Systems

a

system

stabilization energy/atom (eV)

Au4 Au6 Au8 C4Au4-a C4Au4-b C4Au4-c C4Au4-d C4Au6-a C4Au6-b C4Au6-c C4Au6-d C4Au6-e C4Au8-a C4Au8-b C4Au8-c C4Au8-d C8Au8 C16Au12 C16Au16

−1.46 −1.84 −1.95 −3.79 −3.72 −3.60 −3.59 −3.47 −3.41 −3.41 −3.32 −3.31 −3.36 −3.26 −3.04 −3.00 −3.80 −4.11 −3.90

stabilization energy wrt 3Cn + 1Aum (eV)

−4.31 −3.77 −2.82 −2.69 −3.47 −2.92 −2.89 −1.98 −1.90 −4.56 −3.34 −0.75 −0.28 +1.82a, −2.73b

VIE (eV)

VEA (eV)

EHOMO−LUMO (eV)

7.62 8.11 7.67 6.73 7.69 6.74 6.20 7.22 7.38 7.64 6.57 6.56 7.43 7.34 6.22 6.11 7.00 5.26 5.98

2.36 1.93 1.94 1.85 2.69 2.00 1.80 3.02 2.20 3.00 1.90 2.01 2.57 3.02 2.35 2.81 2.54 2.40 3.40

1.27 2.62 2.23 1.82 1.00 1.37 1.14 0.61 1.73 1.00 1.66 1.40 1.41 1.01 0.81 0.25 1.34 0.55 0.14

With respect to linear C8 (triplet). bWith respect to C8-cube (singlet).

set for gold atoms. The main goal is thus a systematic study of a variety of systems at a (tested) uniform level of theory rather than a comparison of the performance of various methods for a single system or a few. The choice of the density functional and basis set has been based on the comparison of predicted parameters for constituent diatoms with experimental and high-level theoretical results. The results of the calculations carried out for CAu and Au2 using different density functionals and basis sets are given in the Supporting Information along with some earlier references. The bond length and dissociation energy of Au2 obtained at the indicated preferred level are 2.55 Å and 2.13 eV, respectively, comparable to the corresponding experimental values40 of 2.47 Å and 2.29 ± 0.01 eV. The bond length of 1.89 Å and the dissociation energy of 3.00 eV obtained for CAu at this level match very well the corresponding values of 1.83 Å and 3.03 eV predicted41 at a CCSD(T) level. In addition, the calculated ionization energy of 8.8 eV and electron affinity of 2.0 eV for the Au atom are in good agreement with the experimental values42 of 9.2 and 2.3 ± 0.1 eV. The M06-L functional has also been reported to be suitable in the studies of organometallic compounds43 and the ionic clusters of gold.12 The all-atom geometry optimizations have been carried out without any symmetry constraints from multiple initial geometries. Four groups of isomers have been selected based on the distribution of carbon atoms in the system. These include hydrocarbon analogues (in view of the previous discussion about such a similarity), carbon chains and cycles on the gold cluster surface (essentially compounds built from separate components), and carbon cores encapsulated by gold atoms (a tribute to stable cage isomers of gold). In all cases, a nonfragmented carbon core is considered because breaking strong C−C bonds is associated with high-energy barriers and would lead to higher-energy species, as discussed in the next section. Frequency calculations have been performed for the optimized geometries in order to distinguish minima and saddle points. The predicted structures are analyzed using the visualization software Jmol.44

The stabilization energy of each system has been calculated relative to the separated atomic species in their respective ground states and relative to the corresponding pure carbon and gold components, both values being listed in Table 1. The vertical ionization energy (VIE) and vertical electron affinity (VEA) of the clusters have been calculated from the energy of the neutral, anionic, and cationic species in the geometry of the neutral species as follows VIE = Ecation − Eneutral

(1)

VEA = Eneutral − Eanion

(2)

3. RESULTS AND DISCUSSION The optimized geometries of the C4Aun (n = 4, 6, and 8) clusters are given in Figure 1. Among the systems with a given number of gold atoms, the most stable one is designated as C4Aun-a. Thus, among the C4Au4 clusters, C4Au4-a corre-

Figure 1. The optimized geometries of C4Aun (n = 4, 6, and 8) clusters. The relative energies of the isomers are given in parentheses. 6804



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sponds to the lowest-energy isomer, stabilized by −30.32 eV with respect to the separated carbon and gold atoms in their ground atomic states. The energy change associated with the formation of C4Au4-a from the clusters C4 and Au4 has been found to be −4.31 eV. This system can be considered as a gold analogue of butatriene (CH2CCCH2). The next isomer C4Au4-b, which is 0.54 eV higher in energy compared to C4Au4-a, is obtained by attaching a linear C4 unit to planar Au4, forming two C−Au bonds. In C4Au4-c, which is ∼1 eV above C4Au4-b in energy, the carbon unit is arranged in a puckered shape, and each carbon atom is connected to a gold atom. Three of these C−Au bonds are pointed downward and one upward. Unlike for C4Au4-c, both carbon and gold atoms are arranged nearly planar in C4Au4-d, thereby forming a partial (2D) core−shell structure analogous to another C4H4 isomer, cyclobutadiene, and only 0.13 eV higher in energy relative to C4Au4-c. Additional calculations have been carried out for the case of C4Au4 with a fragmented carbon component, the geometries and relative energies being given in the Supporting Information. One such isomer is effectively a dimer of two distorted acetylene-like C2Au2 units (thus with two C−C bonds remaining) cross-linked by C−Au bonds, and the other one is a distorted cube with alternating C and Au atoms in its corners (hence with no C−C bonds). The acetylene dimer isomer is higher in energy relative to the linear-C4-based counterparts but lower than the cyclic-C4-based ones, while the cube-like isomer is least stable among all C4Au4 species studied here. The latter “cubic” systems have been investigated previously as well.45 Both of these isomers as well as their larger analogues are believed to be less likely products of Cn + Aum interactions due to high barriers for breaking the strong C−C σ bonds, while, for instance, formation of the C4 cycle would break weaker π bonds only. Hence, we do not consider analogous isomers for larger sizes. Among the C4Au6 clusters, C4Au6-a is the lowest-energy isomer stabilized by −34.69 eV. It can be considered as an extension of C4Au4-b by adding two gold atoms and forming six additional Au−Au bonds. In the next isomer C4Au6-b, the carbon atoms are arranged in a puckered manner as in C4Au4-c but with all of the C−Au bonds pointed downward and the gold atoms held together by an additional Au2 unit. Like C4Au6-a, the isomer C4Au6-c can be considered as an extension of C4Au4-b by adding two gold atoms at different positions. However, unlike in C4Au6-a, only four additional Au−Au bonds are formed in C4Au6-c, which therefore becomes the higherenergy isomer. The isomer C4Au6-c can also be considered as formed by attaching linear C4 to planar Au6, with a binding energy 0.9 eV smaller than that for the C4Au4-b counterpart. In C4Au6-d, the carbon atoms are arranged linearly, leading to a gold analogue of 2-butyne (CH3−CC−CH3). The gold analogue of 1,3 butadiene (CH2CH−CHCH2) was found to be 1.61 eV higher in energy compared to C4Au6-d. The complex C4Au6-e can be considered as an extension of C4Au4-d by adding two gold atoms, with the carbon atoms partially encapsulated by the gold atoms. Among the C4Au8 clusters, C4Au8-a has the lowest energy and is stabilized by −40.33 eV. Even though it can be thought of as formed from C4Au6-a, the extra gold atoms are added in such a way that the linear C4 unit is attached to the gold moiety formed by the combination of two trigonal bipyramidal units with a shared edge. Addition of two gold atoms across the two Au−Au bonds on the opposite sides of C4Au6-b results in the

formation of C4Au8-b. This isomer is 1.2 eV higher in energy. The carbon atoms of C4Au8-b are pushed toward the surface as in the case of C4Au6-b. The isomer C4Au8-c corresponds to the gold-substituted analogue of 2-butene (CH3−CHCH− CH3), although two CAu3 units at the ends are eclipsed to each other. The analogue of this isomer with staggered CAu3 units is 0.20 eV higher in energy. It is also found that the relative energy of the gold-substituted analogue of 1-butene (CH3−CH2−CHCH2) is 0.38 eV higher in energy than C4Au8-c. Addition of two gold atoms to C4Au6-e yields another, higher-energy (by ∼0.5 eV) isomer C4Au8-d, in which the carbon cyclic unit is trapped between two Au4 square units. Among the studied C4Aun systems, those with the near-linear carbon unit at the surface are the most stable isomers for n = 6 and 8, whereas for n = 4, the linear chain hydrocarbon analogue is the most stable one. Both cases are consistent with the linear chain as the lowest-energy isomer of C4. The extra stability of C4Au4-a relative to C4Au4-b can be attributed to two additional C−Au bonds in the former being stronger than two extra Au− Au bonds in the latter. The next two isomers involve less stable cyclic C4, with more distant (hence interacting more weakly) Au−Au pairs in the higher-energy C4Au4-d. The higher stability of C4Au6,8-a, C4Au6-c,d, and C4Au8-c as compared to C4Au6,8b, C4Au6-e, and C4Au8-d, respectively, could again be correlated to the lower-energy near-linear C4 unit in the former. On the other hand, even though C4Au6-d and C4Au8-c have linear or near-linear carbon chains as well, their higher energies (even relative to C4Au6,8-b with C4 cycles) can be due to weaker stabilizing contributions from the less compact or even fragmented (as in C4Au6-d) gold components. In particular, C4Au6-b and -c are almost degenerate, the higherenergy carbon component being compensated for by additional C−Au bonds. In other words, the relative stabilities of the isomers result from the interplay of contributions from the carbon and the gold components as well as the interaction between the components. This analysis is quantitatively supported by single-point energy calculations for the separate carbon and gold components in their geometries within the optimized systems. In particular, the results also indicate that the gold components contribute to the higher stability of C4Au4-b, C4Au6-a, and C4Au8-a as compared to C4Au4-c, C4Au6-b, and C4Au8-b, respectively. The examination of the various bond lengths of the optimized geometries of the C4Aun clusters indicates that their values vary significantly and are increased relative to those for CAu and Au2. For example, the C−Au bond lengths vary in the range of 1.94−2.53 Å as compared to 1.89 Å for the dimer CAu. Similarly, the Au−Au bond lengths are in the range of 2.62−3.40 Å, in comparison with 2.55 Å for Au2. The C−C bond lengths of the complexes lie in the range from that for a triple bond (1.23 Å) to that for an extended C−C single bond (1.71 Å). Mulliken charges can give an idea about how electrons are distributed between atoms. For the optimized geometries, the carbon atoms are negatively charged, and the Au atoms are positively charged. This indicates that the electrons are transferred from gold to carbon atoms. It is also found that the negative charge on the carbon atom increases with the number of gold atoms attached to it, consistent with more electron donors. The VIEs of the pure and carbon-doped gold clusters are calculated as described above and listed in Table 1, as well as being illustrated in the Supporting Information. We can see that 6805



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the ionization energies of the gold clusters are reduced by adding carbon components, more strongly for smaller systems. For example, the VIE is decreased by 0.9 eV for C4Au4-a as compared to Au4 and for C4Au6-a relative to Au6 and by 0.2 eV for C4Au8-a with respect to Au8. With increasing number of Au atoms in the most stable isomers, the VIE values increase by 0.5 and 0.2 eV from n = 4 to 6 and from n = 6 to 8, respectively. It is interesting to note that for the systems with a given number of gold atoms, the ionization energy is lowest for the isomers in which the carbon atoms are encapsulated by the gold atoms. For example, the VIE of C4Au4-d is 0.5 eV lower as compared to C4Au4-a. For C4Au6 and C4Au8, the difference in the VIE between the encapsulated-carbon isomer and that with the carbon atoms at the surface increases further to about 0.7 eV. Table 1 also lists the calculated values of the VEA for all of the clusters. It can be seen that the VEA of Au4 is reduced by 0.5 eV upon adding C4 and thereby forming C4Au4-a. However, a reverse trend was observed for Au6 and Au8, with the VEA increasing by 1.1 eV from Au6 to C4Au6-a and by 0.6 eV from Au8 to C4Au8-a. Among the most stable C4Aun isomers, the electron affinities are found to increase in the order C4Au4-a < C4Au8-a < C4Au6-a, different from Aun. We can also note that among the C4Aun clusters with the same number of gold atoms, the electron affinity is generally less for the isomers in which the carbon atoms are surrounded by gold atoms as compared to that for the isomers in which the carbon atoms are at the surface. The values of the energy gap between the HOMOs and LUMOs (EHOMO−LUMO) of various systems, as given in Table 1 and depicted in the Supporting Information, do not show any apparent trend upon addition of either carbon or gold atoms. While adding C4 to Au4 can either increase or decrease the gap for different isomers of C4Au4, it is decreased for all aurocarbon isomers when C4 is added to larger gold units. Among these systems, the HOMO−LUMO energy gap is the lowest (0.25 eV) for C4Au8-d where the carbon atoms are encapsulated by the gold atoms. The above discussion clearly illustrates that the addition of carbon atoms to the gold clusters alters their properties more significantly than the addition of gold atoms. Moreover, it is found that the properties change more strongly for the systems in which the carbon atoms are encapsulated by the gold atoms, potentially enabling a higher flexibility in designing gold-based nanocatalysts. Further, the latter systems have more symmetric structures as compared to the other isomers and are thus more interesting as potential building blocks for larger aggregates. We therefore extend our study to larger clusters with a carbon core inside of a gold shell. The optimized geometries of some such clusters are depicted in Figure 2. The larger clusters can be thought of as formed from the carbon and gold atoms. Also, the larger species with parts resembling smaller clusters can also be thought of as formed from those. Thus, the stabilization energies of the larger clusters are also calculated relative to the smaller structural units and are discussed below. The cluster C8Au8, a gold-substituted analogue of cubane, can be viewed as a 3D analogue of C4Au4-d and is stabilized by −60.78 eV with respect to the isolated atomic species. This system is stable by ∼3 eV with respect to cubic-C8 (in its singlet ground state) and Au8, likely kinetic products of the dissociation, but is higher in energy by ∼2 eV than linear-C8 (triplet ground state) and Au8. The formation of C8Au8 is possible by the attachment of two Au4 units to the opposite

Figure 2. The optimized geometries of C8, C8Au8, C16Au12, and C16Au16 clusters.

sides of C8, with a binding energy of 6.64 eV. The fusion of two C4Au4-d units can also lead to the formation of C8Au8, which dimerization leads to an additional stabilization by −3.39 eV. Furthermore, the resulting system is more stable per atom than any smaller species considered here (Table 1). The VIE of C8Au8 is 0.7 eV less than that of Au8 and 0.8−0.9 eV higher than the VIE values of the other two encapsulatedcarbon species C4Au4-d and C4Au8-d. In contrast, the VEA of C8Au8 is higher than that of Au8 by 0.6 eV and is also higher compared to the corresponding value of C4Au4-d, the encapsulated-carbon species that could be thought of as a structural motif of C8Au8. However, the VEA of C8Au8 is ∼0.3 eV less relative to that of another encapsulated-carbon species C4Au8-d. The HOMO−LUMO energy gap of C8Au8 is comparable to that for its structural motif C4Au4-d and is decreased by 0.9 eV relative to that for Au8 while exceeding the value for C4Au8-d by 1.1 eV. The cluster C16Au12 is an extension of C8Au8 with two such units merged via a shared Au4 face. The stabilization energy of C16Au12 with respect to the isolated atomic species is −115.18 eV, corresponding to the highest value per atom among all species studied in this work. The C16Au12 cluster may also be formed by the combination of two C8 units and three Au4 units, with a binding energy of 12.74 eV. However, the fusion of two molecules of C8Au8 to form C16Au12 and Au4 according to the reaction 2C8Au8 → C16Au12 + Au4

(3)

is energetically unfavorable, the energy increasing from the products to the reactants by 0.54 eV. The ionization energy of C16Au12 (∼5 eV) is the lowest among the carbon−gold clusters studied here, including the C8Au8 predecessor. The HOMO−LUMO energy gap is also very small (∼0.5 eV), less than half of that for C8Au8 and lower than that for all smaller systems above except C4Au8-d, another system with the carbon atoms encapsulated by the gold atoms. The electron affinity of C16Au12 is close to that for C8Au8 and comparable to those for most of the other carbon−gold species discussed above (Table 1). The dimerization of C8Au8 leads to the formation of an extended system C16Au16 in which two C8Au8 units preserve their integrity, are rotated relative to one another by 45°, and are fused via staggered Au4 faces (Figure 2). The dimer is stabilized by −3.15 eV with respect to the monomers. The dimerization of C8Au8 is accompanied by a dramatic (10-fold) reduction of the HOMO−LUMO energy gap (Table 1). The VIE is decreased by 1 eV, and the VEA is increased by 0.9 eV, reaching the value largest of those found in this work. 6806



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Previously, a similar dimerization has been studied for “cubic” Si4Au4 isomers.45 One further point to be noted is the variation of stabilization energy per atom for the species mentioned above. Among the C4Aun (n = 4, 6, and 8) series, this energy is decreased with the addition of gold atoms. For example, for the most stable isomers, the value drops by ∼0.3 eV from C4Au4-a to C4Au6-a and then further by ∼0.1 eV for C4Au8-a. The same applies to larger species, with the reduction by ∼0.2 eV for C16Au16 as compared to C16Au12. On the other hand, the stabilization energy per atom increases with the number of carbon atoms, such as by ∼0.4 eV for C8Au8 relative to C4Au8. These variations can be explained in terms of the relative strength of bonds in the order of C−C > C−Au > Au−Au. Thus, with the increase in the number of carbon atoms, more C−C and C−Au bonds are formed and results in the higher stabilization energy per atom.

stabilization energy per atom, accompanied by the highest electron affinity (reaching that for halogen atoms) and lowest HOMO−LUMO energy gap (∼0.1 eV), in particular indicating a possibility of high conductivity of extended (C8Au8)n nanowires.

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ASSOCIATED CONTENT

S Supporting Information *

Table of equilibrium parameters of Au2 and CAu obtained using different density functional methods; optimized geometries and stabilization energies of the acetylene dimer and cube-like isomers of C4Au4; and plots of the VIE, the VEA, and the HOMO−LUMO gaps for various CnAum clusters. This material is available free of charge via the Internet at http:// pubs.acs.org.

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4. CONCLUSIONS The structure and stability of a series of aurocarbons with the general formula C4Aun, where n = 4, 6, and 8, and of some larger clusters are investigated using a DFT approach. Four groups of isomers have been characterized based on the distribution of carbon atoms in the system. These include hydrocarbon analogues, carbon chains and cycles on gold cluster surfaces, and carbon cores encapsulated by gold atoms. The hydrocarbon analogue C4Au4, with a linear chain of carbon atoms, correlates to the most stable system for C4Au4. However, such isomers become less stable as the number of gold atoms is increased. For C4Au6 and C4Au8, the carbon atoms preferentially adhere together over the gold moieties. For different isomers of the aurocarbons, the relative stabilities can be correlated to those of their carbon and gold components. These results can be useful in developing stable gold−organic molecular interfaces and carbon−gold nanocomposites. Although the isomers with the carbon atoms encapsulated by gold atoms are relatively less stable, their formation, at least as of kinetic products, should not be ruled out as is evident from their stabilization energy with respect to the isolated atomic species as well as with respect to the carbon and gold components. Once formed, they could be sufficiently longliving species due to potential energy barriers separating them from the lower-energy isomers and resulting from a major bond-breaking required for the associated geometry change (in particular, those involved in the cyclic-to-linear-C4 rearrangement, similar to the hydrocarbon analogues) as well as from the directionality of the stronger C−Au bonds imposing a higher rigidity on the gold component. The latter aspect can be illustrated with a cubane-like C8Au8 preserving its integrity in a dimer. Interestingly, such encapsulated-carbon isomers can exhibit the largest changes in properties from the pure gold clusters as compared to other isomers of a given formula, for instance, in the ionization energy (for all C4Aun), in the electron affinity (as for C4Au4), or in the HOMO−LUMO gap (as for C4Au8). This suggests possible applications in goldbased nanocatalyst design, in particular, property tuning. These species can merge together to form larger clusters and stabilize further, as shown for C8Au8 built via dimerization of C4Au4-d and further dimerized to C16Au16. Among the systems studied, C16Au12 with a carbon core surrounded by gold atoms exhibits the highest stabilization energy per atom and the lowest ionization energy (close to that of alkali metals). Another encapsulated-carbon species, C16Au16, has a high

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1-905-7218668 x2942. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support of the NSERC of Canada (Discovery Grant to F.Y.N.) and the technical support of the staff of the high-performance computing facilities in the UOIT Faculty of Science and the SHARCnet distributed academic network of Ontario. Gurpaul Kochhar is thanked for preliminary calculations on cube-like C4Au4 and related species.

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Structure and Properties of Small Aurocarbons: A Selective Study

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