Letter pubs.acs.org/JPCL
Au102+: A Tetrahedral Cluster Exhibiting Spherical Aromaticity Petronela M. Petrar,†,§ Menyhárt B. Sárosi,†,§ and R. Bruce King‡,* †
Faculty of Chemistry and Chemical Engineering, Babeş-Bolyai University, M. Kogălniceanu 1, RO-400084 Cluj-Napoca, Romania Department of Chemistry, University of Georgia, Athens, Georgia, 30602, United States
‡
S Supporting Information *
ABSTRACT: We propose that the global minimum structure of the Au102+ system has a highly symmetrical tetrahedral geometry and is clearly separated from the other isomers by a high relative energy gap. The large highest occupied molecular orbital-to-lowest unoccupied molecular orbital (HOMO− LUMO) gap as well as the superatom and spherical aromatic characters account for the high stability of this Td Au102+ geometry.
SECTION: Molecular Structure, Quantum Chemistry, and General Theory
S
pherical aromaticity is a property inherent not only to three-dimensional (3D) main group element polyhedral clusters but also to gold clusters.1 Perhaps the best example of a gold cluster exhibiting spherical aromaticity is the neutral gold cluster Au20, discovered by means of laser vaporization of a pure gold target with a helium carrier gas.2 Besides the relativistic effect, aromaticity is one important factor in stabilizing the spherical structure of Au20.3 Herein we present a theoretical 10vertex dicationic gold cluster with similar spherical aromatic properties. Density functional calculations using the B3PW91 functional4−8 in combination with an augmented triple-ζ quality and fully relativistic effective core potential basis set9,10 revealed the structure 1 with Td symmetry as the global minimum of the Au102+ system from a series of ten clusters of different symmetry taken into consideration. B3PW91 is known to give results in agreement with more precise coupled-cluster calculations.11−13 All calculations were carried out with the Gaussian 09 program package.14 Starting structures were chosen based on analogy with proposed geometries of 10vertex high-symmetry germanium clusters (which are isolobal with boranes and metallaboranes).15 Figure 1 shows the four lowest relative energy optimized Au102+ structures. The remaining isomers with even higher relative energy are shown in the Supporting Information (SI). The previously reported Au102+ structure with D4d symmetry is now found to lie at a significantly higher relative energy value (structure 9, SI).16 It has been proposed that stable 3D gold clusters can be built starting from small tetrahedral units in which the atoms form a four-center two-electron bond.17,18 Ten-vertex gold clusters constructed in this manner lead to the same Td structure as 1, and it has been confirmed as the global minimum structure for © 2012 American Chemical Society
Figure 1. The four lowest relative energy optimized Au102+ structures.
the Au102+ system.18 The global minimum 1, shows a symmetric tetrahedral structure pattern similar to Au20 and consist of six “inner” gold atoms (Aui) forming an octahedral central cavity capped by four additional “outer” gold atoms (Auo). Thus, the structure of 1 can be deconstructed into four equivalent AuoAui3 tetrahedral cavities (Figure 1). This picture corresponds with the chemical bonding in Td Au102+ proposed by Boldyrev and co-workers.18 Received: October 3, 2012 Accepted: October 26, 2012 Published: October 26, 2012 3335
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presented system is a dicationic one, the probability of an electrophilic attack is negligible. The charge distribution of 1 leads to the same conclusions for the preferred sites of nucleophilic attack as found above. The natural charges obtained from natural population analysis24 for the two types of gold atoms in 1 are +0.041 (Aui) and +0.438 (Auo), respectively. Thus, the positive charge is concentrated on the gold atoms at the vertices of 1, while the six atoms in the central octahedron carry a significantly less positive charge. This natural atomic charge distribution is opposite to the one determined for Au20.3 Our computations indicate that the ground state of the Au102+ system is a stable tetrahedral structure with high symmetry showing similarities to the experimentally known tetrahedral Au20.2,3 The large HOMO−LUMO gap as well as the superatom and spherical aromatic characters account for the high stability of the Td Au102+ geometry 1 (Table 1). Our findings also suggest that the 2D → 3D transition in dicationic gold clusters occurs at atom numbers lower than 10.
The calculated energy of 1 differs significantly from that of the other structures (Table 1). This considerable relative Table 1. Relative Energies (rel. E, kcal mol−1), Shortest and Longest Bonding Au−Au Distances (dmin and dmax, in Å), HOMO−LUMO Energy Gaps (ΔEHL, in eV) and NICS(0) Values of the Optimized Au102+ Structures 1 2 3 4
rel. E
dmin
dmax
ΔEHL
NICS(0)
0.0 24.6 29.2 30.9
2.702 2.620 2.673 2.636
2.868 2.950 2.943 2.838
3.88 2.03 2.67 2.96
−17.1 −21.8 −34.6 −18.0
energy gap is the first indication for the high stability of the global minimum tetrahedral structure 1. A large diatropic NICS(0) value19 calculated in the center of the cluster cage indicates the spherical aromatic character of 1 and could also contribute to the high stability of the Td geometry. Thus, there is little doubt that the ground state of the Au102+ system is structure 1. We propose that the Au102+ ions generated during collision-induced dissociation experiments20 have the same structure as 1, because of the predicted high stability of this tetrahedral geometry (Table 1). The high-symmetry minimum identified for the Au102+ clusters also has a magic number of electrons, corresponding to a closed S2P6 shell for superatoms.21 This is supported by the fact that the highest occupied molecular orbital (HOMO) state of 1 is triply degenerate (Figure 2). Furthermore, from all of the optimized Au102+ geometries, 1 has the largest energy gap between the HOMO and the lowest unoccupied molecular orbital (LUMO) (Table 1).
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ASSOCIATED CONTENT
S Supporting Information *
All optimized Au102+ structures, total energies (au), zero-point corrected energies (au), relative total and zero-point corrected energies (kcal mol−1), HOMO−LUMO gaps of all the optimized Au102+ structures (eV), number of imaginary frequencies, and optimized Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions §
These authors contributed equally.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by CNCSIS-UEFISCDI, projects PNII−ID_PCCE_129/2008 and the U.S. National Science Foundation (Grant CHE-1057466).
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REFERENCES
(1) Chen, Z.; King, R. B. Spherical Aromaticity: Recent Work on Fullerenes, Polyhedral Boranes, and Related Structures. Chem. Rev. 2005, 105, 3613−3642. (2) Li, J.; Li, X.; Zhai, H.-J.; Wang, L.-S. Au20: A Tetrahedral Cluster. Science 2003, 299, 864−867. (3) King, R. B.; Chen, Z.; Schleyer, P. v. R. Structure and Bonding in the Omnicapped Truncated Tetrahedral Au20 Cluster: Analogies between Gold and Carbon Cluster Chemistry. Inorg. Chem. 2004, 43, 4564−4566. (4) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (5) Perdew, J. P. In Electronic Structure of Solids; Ziesche, P., Eschrig, H. I., Eds.; Akademie: Berlin, 1991. (6) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Phys. Rev. B 1992, 46, 6671−6687. (7) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Erratum: Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient
Figure 2. Frontier molecular orbitals of 1 (isovalue = 0.05).
It should not be surprising that the ground state of the Au102+ system is a 3D cluster. It has been shown that the twodimensional (2D) → 3D transition occurs at lower atom numbers in cationic than in neutral gold clusters.22 Planar 2D structures are preferred up to n = 10 for the neutral Aun0 system and an n of 7 for cationic Aun+1 clusters.23 The current findings suggest that the 2D → 3D transition in dicationic gold clusters occurs in clusters with fewer than 10 gold atoms. The closed electron configuration of 1, along with a large HOMO−LUMO gap, supports the chemical stability of this tetrahedral cluster.2 The HOMO of 1 is composed of s and d orbitals of the Aui gold atoms, and the main contributions to the LUMO of 1 come from the atomic orbitals of the Auo gold atoms (Figure 2). This suggests that nucleophiles will prefer to attack the gold atoms at the vertices (Auo) of 1. Since the 3336
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