Theoretical Determination of the Structural, Bonding, and

Organometallics 2010, 29, 847–859 DOI: 10.1021/om9009137

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Theoretical Determination of the Structural, Bonding, and Magnetoresponsive Properties of Square-Planar Ligand-Protected Noble Metal (Cu, Ag, Au) Clusters Efstathios E. Karagiannis and Constantinos A. Tsipis* Laboratory of Applied Quantum Chemistry, Faculty of Chemistry, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece Received October 17, 2009

Electronic structure calculations (DFT) suggest that “ligand-protected” four-membered rings of noble metals formulated as [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) are thermodynamically stable molecules with respect to their dissociation either to ML monomers or to M2L2 dimers. The M2L2 dimers are the products of the thermodynamically favored oxidative addition reactions of the L2 to M2 diatomic species. The [c-M4(μ2-L)4] (M=Cu, Ag, Au; L= H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules adopt square-planar structures involving bridging stabilizing ligands L, except [c-Au4(μ2-CH3)4]. All [c-M4(μ2-L)4] clusters are characterized by perfect planarity and equalization of all metal-metal bonds in the metallic rings, with the only exception being the [c-Cu4(μ2-Br)4] and [c-Cu4(μ2-I)4] clusters, which adopt a diamond-like core structure. In all four-membered metallic rings the intermetallic interactions are relatively weak, described as cuprophilic, argentophilic, and aurophilic interactions. The four-membered metallic rings are further stabilized by the bonding of the μ2-L bridges, which corresponds to a three-center two-electron (3c-2e) bond. Analysis of the magnetotropicity (diatropicity/paratropicity) of the [cM4(μ2-L)4] clusters based on the NICSzz-scan curves in conjunction with symmetry-based selection rules for the most significant translationally and rotationally allowed transitions revealed that all rings exhibit long-range diatropicity (aromaticity) with minima in the region of 1.8 to 4.0 A˚ above and below the ring and paratropicity (antiaromaticity) in the ring plane up to 0.7 to 2.5 A˚ above and below the ring where a nodal plane resides and having maxima at the ring center. It should be noted that the estimated NICSzzmin values are indicative of remarkable aromaticity only for the [c-M4(μ2-L)4] (M= Cu, Ag, Au; L=H, CH3) clusters; all other species should be nonaromatic or even antiaromatic.

Introduction Complexes of noble metal atoms (Cu, Ag, Au) in the þ1 oxidation state have a marked tendency to form aggregates, often with quite short metal-metal distances1 that are shorter than the sum of their van der Waals radii (Cuþ = 140 pm, Agþ =172 pm, and Auþ =166 pm).2 Such closedshell d10-d10 interactions, often termed metallophilic (cuprophilic, argentophilic, aurophilic) interactions,3,4 are responsible for unusual modes of aggregation of molecules in

the condensed phase, which affect their chemical and photophysical properties. Copper(I) 3 3 3 copper(I) bonding interactions play an important role in the photoluminescence of polynuclear Cu(I) complexes containing a variety of ligands (e.g., phosphane, pyridine, guanidine, carbene, carboxylate).5-14 In a variety of organocopper(I) compounds,15-22 such as the cyclic Cu4R4 tetramers,23 the Cu(I)

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Article

Organometallics, Vol. 29, No. 4, 2010 Scheme 1

Ag4 cluster units that are linked linearly by Ag-Ag bonds to give a stair-shaped infinite chain of silver atoms comprising two 1D zigzag chains has been reported recently.60 Theoretical calculations indicated that the Ag-Ag covalent bonds have partial ionic character with charges of þ0.35 and -0.30, and the chain has a HOMO-LUMO gap of 4.11 eV. The planar motif of noble metal clusters was very recently61 found in neutral and anionic silver fluoride clusters (AgF)n with n e 6. Schwerdtfeger et al.62 have also found similar cyclic structures for the noble metal halide tetramers (MX4) (M=Cu, Ag, or Au; X=F, Cl, Br, or I). “Bare” gold(I) clusters and “ligand-stabilized” polynuclear gold(I) complexes are particularly abundant, forming 1D, 2D, or 3D structures based on Au(I) 3 3 3 Au(I) interactions of comparable strength to that of the hydrogen bonds.63 The cyclic tetranuclear gold(I) complexes involving four-membered gold(I) rings were found in a variety of gold(I) polynuclear complexes studied so far.63 Thus, the square-planar Au4 ring consists of the core structure of [Au(Pip)Cl]4 (Pip = piperidine),64 [X(AuPh3)4]2þ (X = S, Se, Te, CH, or CR),65 and tetranuclear gold(I) alkynylcalixcrown complexes σ-coordinated by two alkynyl units, forming the linear CtC-Au-CtC bridges, while the other two Au centers were π-coordinated by the two adjacent alkynyl units in an unusual parallel η2,η2-bonding mode (Scheme 1).66 Recently, the bonding in planar MnHn (M=Cu, Ag, Au; n=3-6) clusters has been investigated, and it was claimed that the clusters were found to possess a degree of cyclic electron delocalization associated with aromaticity of the respective metallic rings.67 We have also reported on novel “ligand-stabilized” three-membered aromatic gold(I) rings and compared their aromaticity-primarily arising from both strong ns and (n - 1)d orbital contributions (σs-, σd-, (60) Moon, H. R.; Choi, C. H.; Suh, M. P. Angew. Chem., Int. Ed. 2008, 47, 1. (61) Rabilloud, F.; Bonhomme, O.; L’Hermite, J.-M.; Labastie, P. Chem. Phys. Lett. 2008, 454, 153. (62) Schwedtfeger, P.; Krawczyk, R. P.; Hammer, A.; Brown, R. Inorg. Chem. 2004, 43, 6707. (63) (a) Yam, V. W.-W.; Cheng, E. C.-C. Chem. Soc. Rev. 2008, 37, 1806. (b) Schmidbaur, H.; Schier, A. Chem. Soc. Rev. 2008, 37, 1931, and references therein. (c) Gimeno, M. C.; Laguna, A. Chem. Soc. Rev. 2008, 37, 1952. (64) Guy, J. J.; Jones, P. G.; Mays, M. J.; Seldrick, G. M. J. Chem. Soc., Dalton Trans. 1977, 80. (65) (a) Canales, F.; Gimeno, M. C.; Jones, P. G.; Laguna, A. Angew. Chem., Int. Ed. Engl. 1994, 33, 769. (b) Wang, Q. M.; Lee, Y. A.; Crespo, O.; Deaton, J.; Tang, C.; Gysling, H. J.; Gimeno, M. C.; Larraz, C.; Villacampa, M. D.; Laguna, A.; Eisenberg, R. J. Am. Chem. Soc. 2004, 126, 9488. (c) Crespo, O.; Gimeno, M. C.; Laguna, A.; Larraz, C.; Villacampa, M. D. Chem.;Eur. J. 2007, 13, 235. (d) Schmidbaur, H.; Gabbaï, F. P.; Schier, A.; Riede, J. Organometalllics 1995, 14, 4969. (e) Steigelmann, O.; Bissinger, P.; Schmidbaur, H. Z. Naturforsch. B: Chem. Sci. 1993, 48, 72. (66) Yip, S.-H.; Cheng, E. C.-C.; Yuan, L.-H.; Zhu, N.; Yam, V. W.-W. Angew. Chem., Int. Ed. 2004, 43, 4954. (67) (a) Tsipis, A. C.; Tsipis, C. A. J. Am. Chem. Soc. 2003, 125, 1136. (b) Tsipis, C. A.; Karagiannis, E. E.; Kladou, P. F.; Tsipis, A. C. J. Am. Chem. Soc. 2004, 126, 12916.

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πd-, and δd-aromaticity)-to the traditional organic aromaticity due to 2p orbital contributions (πp-aromaticity).68 Li et al.69 using DFT computational methods predicted that the aromatic [c-Cu4(μ-H)4] and [c-Cu5(μ-H)5] hydrometals can host planar tetracoordinated and pentacoordinated nonmetals at the center of the rings, forming perfect squareplanar and pentagonal Cu4H4X and Cu5H5X (X=B, C, N, O) complexes. Tsipis and Stalikas70 using electronic structure calculation methods (DFT) investigated the structural, energetic, spectroscopic (IR, NMR, UV-vis), and electronic properties of a novel series of hydrido-bridged binary coinage metal clusters with general formulas [c-CunAg3-n(μ2H)n] (n=1-3), [c-CunAg4-n(μ2-H)n] (n=1-4), and [c-CunAg5-n(μ2-H)n] (n = 1-5). More recently we addressed a number of points related to the ligand effects on the stability, conformational preference, and diatropic response of the aromatic [c-Cu3(μ-H)3Ln] (L = N2, CO, CN-, H2O, NH3, and PH3; n=1-3) compounds.71 The novel [c-Cu3(μ-H)3Ln] molecules are predicted71 to adopt planar structures, which are characterized by perfect equalization of all metal-metal bonds in the aromatic metallic rings for the fully substituted derivatives. Successive nucleophilic attack of the parent aromatic [c-Cu4(μ-H)4] molecules by a series of nucleophiles Nuc (Nuc = N2, CO, H2O, NH3, and PH3) affords the [cCu4(μ-H)4Nucn] clusters, which, depending on the nature of Nuc and the degree of substitution, adopt planar, bent, or 3D tetrahedral geometries.72 The 3D structures are obtained for the higher degrees of substitution, that is, in the [c-Cu4(μ-H)4Nuc3] and [c-Cu4(μ-H)4Nuc4] clusters. Continuing our interest in unveiling thermodynamically stable planar ring architectures in noble metal “ligandstabilized” polynuclear compounds we address herein the structural, bonding, and magnetoresponsive properties of “ligand-stabilized” tetranuclear noble metal clusters formulated as [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I). The effect of the bridging ligands on the magnetotropicity (aromaticity/ antiaromaticity) of the four-membered M4 rings is also a main concern of the present work.

Theoretical Methods In view of the good performance of density functional theory (DFT), we performed DFT calculations with the BP86 functional73,74 and energy-consistent accurate relativistic small-core pseudopotentials (cc-pVDZ-PP) on the noble metal75 and the heavy halide (Br, I) atoms76 and the correlation-consistent polarized valence (cc-pVDZ) basis sets77 on all other elements E (E=H, C, N, P, Si, Ge, O, F, Cl) of the compounds we studied using the GAUSSIAN03 program suite.78 We will denote the (68) Tsipis, A. C.; Tsipis, C. A. J. Am. Chem. Soc. 2005, 127, 10623. (69) (a) Li, S.-D.; Miao, C.-Q.; Ren, G.-M. Eur. J. Inorg. Chem. 2004, 2232. (b) Li, S.-D.; Ren, G.-M.; Miao, C.-Q.; Jin, Z.-H. Angew. Chem., Int. Ed. 2004, 43, 1371. (70) Tsipis, A. C.; Stalikas, A. V. New J. Chem. 2007, 31, 852. (71) Tsipis, C. A.; Kefalidis, C. E.; Charistos, N. D. In Coordination Chemistry Research Progress; Cartere, T. W.; Verley, K. S., Eds.; Nova Science Publishers: New York, 2007; pp 201-215. (72) Tsipis, C. A.; Charistos, N. D. Open Mech. Eng. J. 2008, 2, 12. (73) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (74) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (75) Peterson, K. A.; Puzzarini, C. Theor. Chem. Acc. 2005, 114, 283. (76) Peterson, K. A.; Figgen, D.; Goll, E.; Stoll, H.; Dolg, M. J. Chem. Phys. 2003, 119, 11113. (77) (a) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (b) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 98, 1358. (78) Frisch, M. J.; et al. et al. Gaussian 03, Revision B.03; Gaussian, Inc.: Pittsburgh, PA, 2003. See Supporting Information for the full reference.

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computational approach used as BP86/cc-pVDZ-PP(Cu,Ag, Au,Br,I)∪cc-pVDZ(E). Full geometry optimization was performed for each structure using Schlegel’s analytical gradient method,79 and the attainment of the energy minimum was verified by calculating the vibrational frequencies that result in absence of imaginary eigenvalues. All the stationary points have been identified for minima (number of imaginary frequencies NIMAG=0) or transition states (NIMAG=1). The vibrational modes and the corresponding frequencies are based on a harmonic force field. This was achieved with the SCF convergence on the density matrix of at least 10-9 and a rms force less than 10-4 au. All bond lengths and bond angles were optimized to better than 0.001 A˚ and 0.1°, respectively. The computed electronic energies, the enthalpies of reactions, ΔRH298, and the free energies, ΔG298, were corrected to constant pressure and 298 K, for zero-point energy (ZPE) differences, and for the contributions of the translational, rotational, and vibrational partition functions. The natural bond orbital (NBO) population analysis was performed using Weinhold’s methodology.80 Magnetic shielding tensors have been computed with the GIAO (gauge-including atomic orbitals) DFT method81,82 as implemented in the GAUSSIAN03 series of programs78 employing the BP86 level of theory. Nucleus-independent chemical shift (NICS) values were computed at the BP86/cc-pVDZ-PP(Cu,Ag, Au,Br,I))∪cc-pVDZ(E) level according to the procedure described by Schleyer et al.83 The magnetic shielding tensor element was calculated for a ghost atom located at the center of the ring. Negative (diatropic) NICS values indicate aromaticity, while positive (paratropic) values imply antiaromaticity. Timedependent density functional theory (TD-DFT)84 calculations were performed on the equilibrium ground-state geometries employing the same density functionals and basis sets used in geometry optimization. The Davidson algorithm was used, in which the error tolerance in the square of the excitation energies and trial-vector orthonormality criterion were set to 10-8 and 10-10, respectively. The success of the TD-DFT method in calculating excitation energies of transition metal complexes has been demonstrated in several recent studies.85

Results and Discussion Equilibrium Geometries of the [c-M4(μ2-L)4] (M=H, Cu, Ag, Au; L=CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) Compounds. Stationary point geometries of the [c-Cu4(μ2L)4], [c-Ag4(μ2-L)4], and [c-Au4(μ2-L)4] (L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules computed at the BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(E) level of theory are shown in Figures 1, 2, and 3, respectively. All [c-M4(μ2-L)4] (M =Cu, Ag, Au; L = CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) compounds, except [c-Au4(μ2-CH3)4], (79) Schlegel, H. B. J. Comput. Chem. 1982, 3, 214. (80) (a) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899–926. (b) Weinhold, F. In The Encyclopedia of Computational Chemistry; Schleyer, P. v. R., Ed.; John Wiley & Sons: Chichester, 1998; pp 1792-1811. (81) Ditchfield, R. Mol. Phys. 1974, 27, 789. (82) Gauss, J. J. Chem. Phys. 1993, 99, 3629. (83) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Hommes, N. J. R. v. R. J. Am. Chem. Soc. 1996, 118, 6317. (84) (a) van Gisbergen, S. J. A.; Kootstra, F.; Schipper, P. R. T.; Gritsenko, O. V.; Snijders, J. G.; Baerends, E. J. Phys. Rev. A 1998, 57, 1556. (b) Jamorski, C.; Casida, M. E.; Salahud, D. R. J. Chem. Phys. 1996, 104, 5134. (c) Bauernschmitt, R.; Ahlrichs, R. Chem. Phys. Lett. 1996, 256, 454. (85) (a) van Gisbergen, S. J. A.; Groeneveld, J. A.; Rosa, A.; Snijders, J. G.; Baerends, E. J. J. Phys. Chem. A 1999, 103, 6835. (b) Rosa, A.; Baerends, E. J.; van Gisbergen, S. J. A.; van Lenthe, E.; Groeneveld, J. A.; Snijders, J. G. J. Am. Chem. Soc. 1999, 121, 10356. (c) Boulet, P.; Chermette, H.; Daul, C.; Gilardoni, F.; Rogemond, F.; Weber, J.; Zuber, G. J. Phys. Chem. A 2001, 105, 885.


24, adopt a planar M4 ring core structure stabilized by the ligands L, which form μ2-bridges between neighboring metal atoms of the four-membered rings. The Au4 core structure of complex 24 is bent with a Au-Au-Au-Au dihedral angle of 38.6°, while the methyl groups are terminal without forming Au(μ2-CH3)Au bridges. The structures and electronic and bonding properties of the hydrido [c-M4(μ2-H)4] (M = Cu, Ag, Au) complexes have been reported previously67 and will not be discussed further. In all [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = CH3, SiH3, GeH3) molecules, except [c-Au4(μ2-CH3)4], 24, the C, Si, and Ge donor atoms are coplanar with the M4 ring plane. Noteworthy are the “in-plane” agostic interactions in the [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = CH3, SiH3, GeH3) molecules, where the H atom of the CH3, SiH3, or GeH3 groups participating in the agostic interactions is coplanar with the M4 plane, while the other two H atoms being perpendicular to the M4 plane are oriented above and below the plane. The strength of the agostic interactions increases along the series methyl- < silyl- < germyl-protected fourmembered rings (compare the M 3 3 3 H distances shown in Figures 1-3). The ring radius, Rav, evaluated as Rav = 1 P4 /4 i=1Ri, where Ri is the distance from the ring center to the nucleus i in the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=CH3, SiH3, GeH3) molecules, follows the trend methyl- < silyl- < germyl-protected four-membered rings (Rav[c-Cu4(μ2-L)4]: 1.671, 1.745, 1.754 A˚; Rav[c-Ag4(μ2-L)4]: 1.902, 1.979, 1.995 A˚; Rav[c-Au4(μ2-L)4]: -, 1.975, 1.979 A˚ for the methyl, silyl, and germyl derivatives respectively). In the amido-bridged [c-Cu4(μ2-NH2)4], 5, and [c-Ag4(μ2NH2)4], 16, the amido-bridges are not coplanar with the M4 (M=Cu, Ag) ring plane. One pair of the amido bridges in trans position is oriented above the ring plane and the other below the plane (the M-M-M-N dihedral angles are 19.6° and 6.5° for the copper and silver clusters, respectively). In the amido-bridged [c-Au4(μ2-NH2)4], 27, cluster the nitrogen donor atoms of the amido bridges are coplanar with the Au4 ring plane, with the amide hydrogen atoms being perpendicular to the plane found above and the other below the ring plane. The estimated ring radius of the M4 rings of the amido-bridged complexes are 1.897, 2.205, and 2.218 A˚ for the Cu, Ag, and Au clusters, respectively. The analogous phosphido-bridged [c-M4(μ2-PH2)4] (M=Cu, 6; Ag, 17; and Au, 28) complexes adopt a perfect planar geometry, forming heterocyclic eight-membered rings. The M 3 3 3 M distances being higher than the sum of the respective van der Waals radii are indicative for the absence of intermetallic interactions in these clusters. The estimated ring radii of the M4 rings of the phosphido-bridged complexes are 2.791, 3.036, and 2.965 A˚ for the Cu, Ag, and Au clusters, respectively. The geometry of the hydroxo-bridged [c-M4(μ2-OH)4] (M=Cu, 7; Ag, 18; and Au, 29) complexes corresponds to a perfect planar M4 ring core structure with the O donor atoms of the hydroxo bridges being coplanar with the ring plane. The H atoms of one pair of trans hydroxo bridges are found above and the other below the ring plane. The estimated ring radii of the M4 rings of the hydroxo-bridged complexes are 1.849, 2.129, and 2.152 A˚ for the Cu, Ag, and Au clusters, respectively. Finally, all halide-bridged [c-M4(μ2-X)4] (M=Cu, Ag, Au; X=F, Cl, Br, I) complexes contain a perfect square-planar M4 ring core structure, except the [c-Cu4(μ2-Br)4], 10, and [cCu4(μ2-I)4], 11, clusters, which exhibit a “diamond-like” rhombic M4 ring core structure. In the [c-Cu4(μ2-I)4], 11,

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Figure 1. Equilibrium geometries (bond lengths in A˚, angles in deg) of the [c-Cu4( μ2-L)4] (L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules corresponding to global minima in the PES computed at the BP86/cc-pVDZ-PP(Cu,Br,I)∪cc-pVDZ(E) level of theory.

cluster Cu 3 3 3 Cu interactions across the small diameter of the rhombus also exist (Cu-Cu=2.694 A˚). With the exception of the fluoride-bridged clusters the halide bridges are found out of the M4 ring plane, one pair of trans halide bridges above and the other below the plane. The M-M-M-X tortional angles are 37.0°, 57.9°, and 70.1° for the chloro-, bromo-, and iodo-bridged copper clusters, 24.6°, 37.9°, and 43.6° for the chloro-, bromo-, and iodo-bridged silver clusters, and 22.5°, 32.9°, and 42.8° for the chloro-, bromo-, and iodo-bridged gold clusters, respectively. The estimated ring radii of the M4 rings of the halide-bridged complexes are 1.817, 1.814, 1.758, and 1.733 A˚ for the fluoro-, chloro-, bromo-, and iodo-bridged copper clusters, 2.129, 2.195, 2.139, and 2.131 A˚ for the fluoro-, chloro-, bromo-, and iodo-bridged silver clusters, and 2.216, 2.249, 2.215, and 2.152 A˚ for the fluoro-, chloro-, bromo-, and iodo-bridged gold clusters, respectively. Stability of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) Compounds. The stability of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules is investigated using their fragmentation either to ML monomers or M2L2 dimers. The calculated binding energies are compiled in Table 1. It can be seen that all [c-M4(μ2-L)4] molecules are predicted to be bound with respect to their dissociation to either

ML monomers or M2L2 dimers in their ground states. The estimated binding energies per ML monomer are in the ranges 33.7-58.9, 21.6-47.1, and 18.5-50.5 kcal for the [cCu4(μ2-L)4], [c-Ag4(μ2-L)4], and [c-Au4(μ2-L)4] clusters, respectively. For all clusters the amido-bridged clusters have the higher binding energies per ML monomer, while the methyl-, silyl-, and germyl-bridged ones the lower. This observation indicates that the μ2-L bridges are weaker for the methyl, silyl, and germyl bridges and stronger for the amido bridges. Moreover, with the exception of the methyl-, silyl- and germyl-bridged clusters, the binding energies follow the trend [c-Cu4(μ2-L)4] > [c-Au4(μ2-L)4] > [cAg4(μ2-L)4]. For the methyl-, silyl-, and germyl-bridged clusters the binding energies per ML monomer decrease along the series [c-Cu4(μ2-L)4] > [c-Ag4(μ2-L)4] > [c-Au4(μ2-L)4]. Exactly the same trends are followed by the binding energies per M2L2 dimer, which are in the ranges 22.2-66.7, 26.5-56.1, and 18.2-58.0 kcal for the [cCu4(μ2-L)4], [c-Ag4(μ2-L)4], and [c-Au4(μ2-L)4] clusters, respectively. We have also computed the heat of formation of the M2L2 species from M2(g) and L2(g) according to the chemical equation:

M2 ðgÞ þ L-LðgÞ f M2 L2 ðgÞ

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Figure 2. Equilibrium geometries (bond lengths in A˚, angles in deg) of the [c-Ag4( μ2-L)4] (L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules corresponding to global minima in the PES computed at the BP86/cc-pVDZ-PP(Ag,Br,I)∪cc-pVDZ(E) level of theory.

where M=Cu, Ag, Au; L-L=H-H, H3CCH3, H3SiSiH3, H3GeGeH3, H2NNH2, H2PPH2, HO-OH, F-F, Cl-Cl, Br-Br, I-I. The estimated ΔH298 and ΔG298 values of the above oxidative addition reactions computed at the BP86/ cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) level are compiled in Table 2. Perusal of Table 2 illustrates that all oxidative addition reactions, except the oxidative addition of H2 and H3CCH3 to Ag2 diatomic, are exothermic with exothermicities ranging from -7.4 to -146.3, -10.6 to -104.6, and -4.0 to -89.1 kcal/mol for the L-L activation processes by the Cu2, Ag2, and Au2 diatomics respectively. The oxidative addition of H2 and H3CCH3 to Ag2 diatomic is predicted to be endothermic, the estimated endothermicities found to be 6.6 and 24.1 kcal/mol, respectively. The most exothermic processes are the oxidative addition of fluorine to Cu2, Ag2, and Au2 diatomics. The exothermicities of the oxidative addition reactions of halides decrease on going down groups 17 (F>Cl > Br>I) and 11 (Cu>Ag > Au). For the oxidative addition reaction of hydrogen peroxide (H2O2) the exothermicities decrease also going down group 11, while the exothermicities of the remaining oxidative addition reactions follow the trend Cu > Au > Ag. It can be concluded that the activation of the L-L bonds by the Cu2, Ag2, and Au2 diatomics is thermodynamically most favored in the case of the Cu2 diatomic. The equilibrium geometries of the M2L2 dimers are shown in Figure 4.

It can be seen that all dimers, except the [Cu2(μ2-SiH3)2], [Cu2(μ2-GeH3)2], [Cu2(μ2-Br)2], [Cu2(μ2-I)2], [Ag2(μ2-Br)2], [Ag2(μ2-I)2], [(CH3)AuAu(CH3)], and [AuAuF2] dimers, keep the structural integrity adopted in the tetramers, that is, involve one μ2-L bridge and one terminal L ligand. In all dimers, except the phospido-bridged ones, there are strong metal-metal interactions, reflected in the M-M bond lengths shown in Figure 4. The [Cu2(μ2-SiH3)2], [Cu2(μ2GeH3)2], [Cu2(μ2-Br)2], [Cu2(μ2-I)2], [Ag2(μ2-Br)2], and [Ag2(μ2-I)2] dimers adopt a diamond-like structure with strong intermetallic interactions and two symmetrical μ2-L bridges. Noteworthy are the remarkable agostic interactions in all methyl-, silyl-, and germyl-bridged dimers, being stronger in the germyl-bridged dimers. Surprisingly the [(CH3)AuAu(CH3)] dimer involves two terminal methyl groups in anti position, while in the [AuAuF2] dimer both fluoride ligands are coordinated to one of the Au atoms. Electronic and Bonding Properties of the [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) Molecules. Selected electronic parameters of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl; Br, I) molecules have been collected in Table 3. The high stability of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl; Br, I) rings is reflected in the high εLUMO - εHOMO energy gap, the socalled global hardness η. According to the computed

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Figure 3. Equilibrium geometries (bond lengths in A˚, angles in deg) of the [c-Au4( μ2-L)4] (L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules corresponding to global minima in the PES computed at the BP86/cc-pVDZ-PP(Au,Br,I)∪cc-pVDZ(E) level of theory. Table 1. Binding Energies ΔE1 and ΔE2 (in kcal mol-1) of the [c-M4( μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) Compounds Computed at the BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) Level cluster

ΔE1a

ΔE2b

cluster

ΔE1

ΔE2

cluster

ΔE1

ΔE2

[c-Cu4( μ2-H)4] (D4h), 1 [c-Cu4( μ2-CH3)4] (S4), 2 [c-Cu4( μ2-SiH3)4] (C4h), 3 [c-Cu4( μ2-GeH3)4] (C4h), 4 [c-Cu4( μ2-NH2)4] (D2d), 5 [c-Cu4( μ2-PH2)4] (D4h), 6 [c-Cu4( μ2-OH)4] (D2d), 7 [c-Cu4( μ2-F)4] (D4h), 8 [c-Cu4( μ2-Cl)4] (D2d), 9 [c-Cu4( μ2-Br)4] (D2), 10 [c-Cu4( μ2-I)4] (D2), 11

163.4 135.4 134.8 136.2 235.7 160.3 221.5 205.9 183.2 177.7 172.2

98.5 83.5 50.8 44.3 133.4 100.4 118.8 105.0 93.7 74.0 62.8

[c-Ag4( μ2-H)4] (D4h), 12 [c-Ag4( μ2-CH3)4] (S4), 13 [c-Ag4( μ2-SiH3)4] (C4h), 14 [c-Ag4( μ2-GeH3)4] (C4h), 15 [c-Ag4( μ2-NH2)4] (D2d), 16 [c-Ag4( μ2-PH2)4] (D4h), 17 [c-Ag4( μ2-OH)4] (D2d), 18 [c-Ag4( μ2-F)4] (D4h), 19 [c-Ag4( μ2-Cl)4] (D2d), 20 [c-Ag4( μ2-Br)4] (D2d), 21 [c-Ag4( μ2-I)4] (D2d), 22

122.9 86.2 87.3 88.6 188.3 129.0 173.6 159.3 139.6 136.3 133.5

79.7 57.4 55.6 52.3 112.2 84.0 94.2 83.5 76.8 59.1 51.7

[c-Au4( μ2-H)4] (D4h), 23 [c-Au4( μ-CH3)4] (S4), 24 [c-Au4( μ2-SiH3)4] (C4h), 25 [c-Au4( μ2-GeH3)4] (C4h), 26 [c-Au4( μ2-NH2)4] (D4h), 27 [c-Au4( μ2-PH2)4] (D4h), 28 [c-Au4( μ2-OH)4] (D2d), 29 [c-Au4( μ2-F)4] (D4h), 30 [c-Au4( μ2-Cl)4] (D2d), 31 [c-Au4( μ2-Br)4] (D2d), 32 [c-Au4( μ2-I)4] (D2d), 33

95.7 78.1 74.0 78.0 201.8 147.1 179.0 158.9 152.4 150.6 148.3

53.6 36.3 49.0 49.8 116.0 90.7 101.4 66.8 83.7 83.5 82.5

a

ΔE1 = 4E(ML) - E[c-M4( μ2-L)4]. b ΔE1 = 2E(M2L2) - E[c-M4( μ2-L)4].

Table 2. Estimated ΔH and ΔG Values (in kcal/mol) of the Oxidative Addition Reactions of L2 (L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) on Cu2, Ag2, and Au2 Diatomics Computed at the BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) Level L2

product

ΔH

ΔG

product

ΔH

ΔG

product

ΔH

ΔG

H2 C2H6 Si2H6 Ge2H6 N2H4 P2H4 O2H2 F2 Cl2 Br2 I2

Cu-Cu Cu( μ2-H)CuH Cu( μ2-CH3)Cu(CH3) Cu( μ2-SiH3)Cu(SiH3) Cu( μ2-GeH3)Cu(GeH3) Cu( μ2-NH2)Cu(NH2) Cu( μ2-PH2)Cu(PH2) Cu( μ2-OH)Cu(OH) Cu( μ2-F)CuF Cu( μ2-Cl)CuCl Cu( μ2-Br)CuBr Cu( μ2-I)CuI

-11.6 -7.4 -49.0 -52.0 -64.1 -42.0 -102.2 -146.3 -107.5 -103.7 -97.1

-5.4 -0.1 -38.2 -41.0 -55.6 -34.1 -88.3 -137.9 -99.6 -95.5 -88.8

Ag-Ag Ag( μ2-H)AgH Ag( μ2-CH3)Ag(CH3) Ag( μ2-SiH3)Ag(SiH3) Ag( μ2-GeH3)Ag(GeH3) Ag( μ2-NH2)Ag(NH2) Ag( μ2-PH2)Ag(PH2) Ag( μ2-OH)Ag(OH) Ag( μ2-F)AgF Ag( μ2-Cl)AgCl Ag( μ2-Br)AgBr Ag( μ2-I)AgI

6.6 24.1 -13.7 -10.6 -23.0 -22.4 -54.9 -104.6 -74.6 -75.3 -72.1

12.7 30.1 -5.7 -4.5 -15.5 -14.4 -45.7 -96.6 -67.1 -67.7 -64.2

Au-Au Au( μ2-H)AuH Au( μ2-CH3)Au(CH3) Au( μ2-SiH3)Au(SiH3) Au( μ2-GeH3)Au(GeH3) Au( μ2-NH2)Au(NH2) Au( μ2-PH2)Au(PH2) Au( μ2-OH)Au(OH) Au( μ2-F)AuF Au( μ2-Cl)AuCl Au( μ2-Br)AuBr Au( μ2-I)AuI

-13.8 -4.0 -36.7 -32.8 -35.2 -43.2 -46.5 -89.1 -58.0 -53.4 -51.0

-7.3 2.3 -28.8 -24.5 -25.6 -34.2 -36.9 -81.2 -50.1 -45.6 -43.4

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Figure 4. Equilibrium geometries (bond lengths in A˚, angles in deg) of the M2L2 (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) dimers corresponding to global minima in the PES computed at the BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪ccpVDZ(L) level of theory.

η values, the stability of the H-, CH3-, and F-bridged fourmembered rings follows the trend Ag > Cu > Au, that of the SiH3- and GeH3-bridged four-membered rings follow the trend Ag > Au > Cu, and that of the NH2-, PH2-, OH-, Cl-, Br-, and I-bridged four-membered rings follow the trend Ag > Au > Cu. In general the NH2- and PH2-bridged M4 rings have the highest η values and the F-bridged ones the lowest. It should be noticed that, with the exception of the Hand CH3-bridged M4 rings, fluoride forms the weakest μ2-F bridges (WBOs of 0.604, 0.579, and 0.587 for the copper,

silver, and gold rings, respectively), while the amido and phosphido groups form the strongest μ2-NH2 (WBOs of 0.681, 0.646, and 0.660 for the copper, silver, and gold rings, respectively) and μ2-PH2 bridges (WBOs of 0.810, 0.736, and 0.812 for the cooper, silver, and gold ring, respectively). Noteworthy is the absence of intermetallic interactions in the PH2-bridged M4 rings (WBOs of 0.079, 0.048, and 0.049 for the copper, silver, and gold rings, respectively); thereby these species adopt a planar eight-membered metallacyclic ring structure.

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Table 3. Selected Electronic Parameters of the [c-M4( μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl; Br, I) Molecules Computed at the BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) Level WBO (M 3 3 3 L 3 3 3 M)

Q(M)

Q(L)

0.456 0.358 0.405 0.412 0.199 0.079 0.160 0.171 0.295 0.299

0.455; 0.455 0.572; 0.553 0.681; 0.526 0.657; 0.522 0.681; 0.681 0.810; 0.810 0.677; 0.677 0.604; 0.604 0.694; 0.694 0.741; 0.632

0.419 0.443 0.152 0.155 0.510 0.447 0.559 0.633 0.541 0.523 (0.571)

-0.419 -1.228 0.138 0.084 -1.315 -0.594 -1.048 -0.633 -0.541 -0.497

2.40

0.308 (0.282)

0.767;0.632

0.452 (0.381)

-0.416

3.58 4.18 3.20 3.08 3.82 4.00 3.08 2.74 3.64 3.44 3.22 2.60 2.70 2.92 2.70 4.10 4.02 3.12 2.30 3.72 3.50 3.24

0.376 0.247 0.265 0.262 0.081 0.048 0.061 0.050 0.126 0.157 0.173 0.445 0.406 0.297 0.298 0.091 0.049 0.075 0.080 0.117 0.147 0.190

0.476; 0.476 0.558; 0.502 0.690; 0.430 0.659; 0.426 0.646; 0.646 0.736; 0.736 0.639; 0.639 0.579; 0.579 0.644; 0.644 0.665; 0.665 0.697; 0.697 0.475; 0.475 0.974; 0.045 0.842; 0.379 0.777; 0.375 0.660; 0.660 0.812; 0.812 0.643; 0.643 0.587; 0.587 0.670; 0.670 0.709; 0.709 0.737; 0.737

0.412 0.500 0.218 0.227 0.465 0.398 0.532 0.629 0.554 0.558 0.425 0.293 0.241 0.046 0.039 0.347 0.217 0.415 0.531 0.388 0.327 0.239

-0.412 -1.258 0.055 -0.014 -1.262 -0.560 -1.011 -0.629 -0.554 -0.558 -0.425 -0.293 -0.940 0.226 0.169 -1.165 -0.376 -0.912 -0.531 -0.388 -0.327 -0.239

cluster

η (eV)

[c-Cu4(μ2-H)4] [c-Cu4(μ2-CH3)4] [c-Cu4(μ2-SiH3)4] [c-Cu4(μ2-GeH3)4] [c-Cu4(μ2-NH2)4] [c-Cu4(μ2-PH2)4] [c-Cu4(μ2-OH)4] [c-Cu4(μ2-F)4] [c-Cu4(μ2-Cl)4] [c-Cu4(μ2-Br)4]

3.10 3.22 2.56 2.36 3.48 3.36 2.94 2.44 3.02 1.29

[c-Cu4(μ2-I)4] [c-Ag4(μ2-H)4] [c-Ag4(μ2-CH3)4] [c-Ag4(μ2-SiH3)4] [c-Ag4(μ2-GeH3)4] [c-Ag4(μ2-NH2)4] [c-Ag4(μ2-PH2)4] [c-Ag4(μ2-OH)4] [c-Ag4(μ2-F)4] [c-Ag4(μ2-Cl)4] [c-Ag4(μ2-Br)4] [c-Ag4(μ2-I)4] [c-Au4(μ2-H)4] [c-Au4(μ2-CH3)4] [c-Au4(μ2-SiH3)4] [c-Au4(μ2-GeH3)4] [c-Au4(μ2-NH2)4] [c-Au4(μ2-PH2)4] [c-Au4(μ2-OH)4] [c-Au4(μ2-F)4] [c-Au4(μ2-Cl)4] [c-Au4(μ2-Br)4] [c-Au4(μ2-I)4

WBO (M-M)

According to the natural bond orbital and Mulliken population analysis (Table 3), the Cu, Ag, and Au ring atoms acquire positive natural charge of about 0.15-0.63 |e|, 0.22-0.63 |e|, and 0.04-0.53 |e|, respectively. As expected, the highest positive natural charges on the metal ring atoms occur in the F-bridged molecules and the lowest in the SiH3- and GeH3-bridged ones. The transferred electronic density from the metal ring atoms to the bridging ligands originates primarily from the ns electrons and to a lesser extent from the (n - 1)d electrons Moreover, the natural electron configurations (Table 3) indicate that there is also promotion of a relatively small amount of electron density from the (n - 1)d10 to the ns orbitals amounting to 0.08-0.40 |e|. Inspection of the estimated WBOs reveals remarkable metal-metal interactions corresponding roughly to one electron bond for the H-, CH3-, SiH3-, and GeH3-bridged M4 rings (WBOs in the range 0.247-0.456), which can be described as cuprophilic, argentophilic, and aurophilic interactions. Weaker cuprophilic, argentophilic, and aurophilic interactions occur in the NH2-, OH-, Cl-, Br-, and I-bridged M4 clusters (WBOs in the range 0.061-0.308). Such interactions can be ascribed to orbital interactions resulting in the formation of molecular orbitals (MOs) localized on the M4 framework. Representative MOs describing the intermetallic interactions are shown in Figure 5. On the other hand, the bonding of the μ2-L bridges corresponds to a three-center two-electron (3c-2e) bond, which contributes significantly to the stability of the M4 rings.

nec(M) ns/np/(n - 1)d 0.68/0.04/9.85 0.52/0.26/9.77 0.60/0.44/9.80 0.59/0.46/9.80 0.74/0.03/9.71 0.70/0.01/9.83 0.69/0.02/9.69 0.60/0.03/9.70 0.59/0.05/9.81 0.60/0.02/9.81 (0.62/0.05/9.84) 0.63/0.03/9.83 (0.67/0.07/9.86) 0.67/0.01/9.90 0.64/0.01/9.84 0.63/0.27/9.88 0.62/0.28/9.88 0.74/0.01/9.76 0.72/0.01/9.87 0.64/0.02/9.78 0.50/0.02/9.81 0.54/0.03/9.87 0.56/0.03/9.90 0.62/0.04/9.92 0.84/0.02/9.84 1.09/0.01/9.65 0.85/0.30/9.80 0.84/0.31/9.80 1.03/0.01/9.60 0.99/0.01/9.78 0.94/0.04/9.60 0.77/0.03/9.65 0.82/0.02/9.76 0.83/0.03/9.81 0.87/0.04/9.85

Magnetotropicity of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L= H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) Molecules. Planarity, high stability, bond length equalization, and hardness are conventionally good indicators of aromaticity, but this is restrictive in many examples. In order to verify the magnetotropicity (diatropicity/paratropicity) of the [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules, we analyzed the NICSzz-scan curves in conjunction with symmetry-based selection rules for the most significant translationally and rotationally allowed transitions of the molecules. The NICSzz-scan profiles of selected [c-M4(μ2-L)4] clusters are visualized in Figure 6, while the most salient features of the NICSzz-scan curves along with the Rav values of the rings are compiled in Table 4. The NICSzz-scan patterns of the [c-Cu4(μ2-L)4] (L = H, CH3, SiH3, GeH3, NH2, PH2, Cl) clusters are typical for long-range weak diatropicity (aromaticity) with minima in the region 1.8 to 3.6 A˚ above and below the ring and paratropicity (antiaromaticity) in the ring plane up to 0.7 to 2.1 A˚ above and below the ring where a nodal plane resides and having maxima at the ring center. In other words, [cCu4(μ2-L)4] (L=H, CH3, SiH3, GeH3, NH2, PH2, Cl) rings exhibit successive aromatic and antiaromatic zones separated by a nodal plane. It is important to note that the isotropic NICS(R) (R=0 or 1) does not work well as a probe of the aromaticity/antiaromaticity of the Cu4 rings, since it predicts weak aromaticity, practically nonaromaticity, in many cases. Thus, according to the NICS(R) (R = 0 or 1) values, only the Cu4 rings of the [c-Cu4(μ2-L)4] (L=H, CH3,

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Figure 5. The most relevant valence molecular orbitals of the [c-Cu4( μ2-CH3)4], [c-Ag4( μ2-NH2)4], and [c-Au4( μ2-Cl)4] molecules.

Figure 6. NICSzz-scan profiles (NICSzz in ppm, R in A˚) of the[c-M4( μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) clusters computed at the GIAO-BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) level.

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Table 4. NICS Values (in ppm) Calculated at the Ring Center, NICS(0), and 1.0 A˚ above the Ring Center, NICS(1), the zz-Component of the Shielding Tensor Elements, NICSzz(0) and NICSzz(1), and Rav (in A˚) of the [c-M4( μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl; Br, I) Clusters Computed at the GIAO-BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) Level cluster

NICS(0)

NICS(1)

NICSzz(0)

NICSzz(1)

NICSzzmin

Rmin

[c-Cu4( μ2-H)4] [c-Cu4( μ2-CH3)4] [c-Cu4( μ2-SiH3)4] [c-Cu4( μ2-GeH3)4] [c-Cu4( μ2-NH2)4] [c-Cu4( μ2-PH2)4] [c-Cu4( μ2-OH)4] [c-Cu4( μ2-F)4] [c-Cu4( μ2-Cl)4] [c-Cu4( μ2-Br)4] [c-Cu4( μ2-I)4] [c-Ag4( μ2-H)4] [c-Ag4( μ2-CH3)4] [c-Ag4( μ2-SiH3)4] [c-Ag4( μ2-GeH3)4] [c-Ag4( μ2-NH2)4] [c-Ag4( μ2-PH2)4] [c-Ag4( μ2-OH)4] [c-Ag4( μ2-F)4] [c-Ag4( μ2-Cl)4] [c-Ag4( μ2-Br)4] [c-Ag4( μ2-I)4] [c-Au4( μ2-H)4] [c-Au4( μ-CH3)4] [c-Au4( μ2-SiH3)4] [c-Au4( μ2-GeH3)4] [c-Au4( μ2-NH2)4] [c-Au4( μ2-PH2)4] [c-Au4( μ2-OH)4] [c-Au4( μ2-F)4] [c-Au4( μ2-Cl)4] [c-Au4( μ2-Br)4] [c-Au4( μ2-I)4]

-10.6 -5.0 -2.9 -3.0 -1.7 0.7 -3.3 -8.1 -8.7 -15.4 -19.5 -7.1 -3.4 -2.4 -2.2 -0.7 0.8 -2.6 -4.3 -3.6 -4.3 -3.9 -9.7 -11.3 -1.0 -0.5 1.0 2.0 0.0 -2.6 -2.1 -2.9 -3.5

-4.4 -1.2 -0.8 -0.9 -0.2 0.6 -0.3 -2.0 -3.6 -6.4 -8.1 -3.7 -1.1 -0.7 -0.6 0.1 0.6 -0.7 -1.5 -1.7 -2.3 -2.2 -5.3 -5.7 0.1 0.5 1.4 1.8 1.2 0.2 -0.7 -1.4 -2.0

7.2 13.5 20.6 23.5 9.9 14.4 -0.4 -13.8 7.1 -0.6 -2.0 17.7 26.3 26.9 28.9 19.0 16.8 15.0 10.8 18.3 20.5 22.7 19.4 15.3 36.4 40.1 24.2 23.3 19.4 12.2 22.4 24.6 27.7

-3.6 2.6 5.4 6.8 3.8 8.3 -0.3 -5.9 1.6 -2.9 -4.1 2.0 8.3 9.7 11.2 8.7 10.2 5.9 3.4 7.9 9.1 10.8 0.4 5.1 14.1 16.5 12.1 14.6 9.5 6.0 10.9 11.8 13.3

-7.6 -4.6 -4.9 -5.1 -3.1 -2.2 -2.5 -13.8 -4.3 -5.0 -4.8 -7.8 -5.9 -5.4 -5.3 -3.8 -2.6 -4.0 -4.0 -4.5 -4.9 -4.7 -10.6 -7.1 -5.8 -5.6 -3.4 -2.2 -3.0 -2.2 -4.2 -4.8 -5.0

1.8 2.3 2.4 2.6 2.7 3.6 2.5

F, Cl, Br, I) clusters should be remarkably aromatic rings (Table 4). The NICSzz-scan curve of the [c-Cu4(μ2-F)4] cluster is typical for aromatic syatems, while those of the [c-Cu4(μ2-L)4] (L = OH, Br, I) clusters are indicative for practically nonaromatic systems. The NICSzz-scan patterns of the [c-M4(μ2-L)4] (M=Ag, Au; L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) clusters are also typical for long-range weak diatropicity (aromaticity) with minima in the region 2.2 to 3.8 A˚ (2.1 to 4.0 A˚) above and below the ring and paratropicity (antiaromaticity) in the ring plane up to 1.1 to 2.2 A˚ (1.0 to 2.5 A˚) above and below the ring where a nodal plane resides and having maxima at the ring center for the silver and (gold) clusters, respectively. It should be noted that the estimated NICSzzmin values are indicative of remarkable aromaticity only for the [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3) clusters; all other species should be nonaromatic. The magnitude and type (σ-, π-, δ-) of induced diatropic and paratropic ring currents are determined by the excitation energies of the most significant Tx,y- and Rz-allowed occupied f unoccupied and occupied f singly occupied molecular orbital transitions86 given in Table 5. In the [c-M4(μ2-H)4] (M = Cu, Ag, Au) rings with D4h symmetry the chief contribution to diatropic ring current arises from the eu f b1g excitation, which correspond to Tx,yallowed transitions. On the other hand, the chief contribution to paratropic ring current arises from the a2g f a1g excitation, which corresponds to Rz-allowed transitions. In (86) Tsipis, A. C.; Depastas, I. G.; Karagiannis, E. E.; Tsipis, C. A. J. Comput. Chem. 2010, 31, 431, and references therein.

2.8 2.8 3.5 2.2 2.6 2.7 2.9 3.0 3.8 2.8 2.6 3.0 3.3 3.7 2.1 2.4 2.8 2.9 3.2 4.0 3.1 3.0 3.2 3.3 3.5

all cases the excitation energies of the Tx,y-allowed transitions are lower than the excitation energies of the Rz-allowed transitions; thereby the induced diatropic ring current exceeds the paratropic one and the [c-M4(μ2-H)4] (M=Cu, Ag, Au) rings exhibit aromatic character, as established previously.67 Considering the nature of the MOs involved in the diatropic transitions it is easy to diagnose the double (σþπ)-aromaticity of the [c-M4(μ2-H)4] (M = Cu, Ag, Au) rings. In the [c-M4(μ2-CH3)4] (M=Cu, Ag, Au) rings with S4 symmetry the chief contribution to diatropic ring current arises from the e f a excitation, which correspond to Tx,y-allowed transitions, while the chief contribution to paratropic ring current arises from the a f a excitation, which corresponds to Rz-allowed transitions. In the [c-Cu4(μ2-CH3)4] ring the excitation energies of the Tx,y-allowed transitions are higher than the excitation energies of the Rz-allowed transitions; thereby the induced paratropic ring current exceeds the diatropic one and the [c-Cu4(μ2-CH3)4] ring exhibits negligible aromatic character (NICSzzmin=-4.6 ppm), being practically a nonaromatic ring. In contrast for the [c-Ag4(μ2-CH3)4] and [c-Au4(μ2-CH3)4] rings the excitation energies of the Tx,y-allowed transitions are lower than the excitation energies of the Rz-allowed transitions, and therefore the [c-Ag4(μ2-CH3)4] and [c-Au4(μ2-CH3)4] rings exhibit higher aromatic character with NICSzzmin values of -5.9 and -7.1 ppm, respectively. In the [c-M4(μ2-SiH3)4] and [c-M4(μ2-GeH3)4] (M = Cu, Ag, Au) rings with C4h symmetry the chief contribution to diatropic ring current arises from the eu f ag excitation,

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Table 5. Excitation Energies (in eV) of the Most Significant Tx,y- and Rz-Allowed Transitions of the [c-M4( μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) Clusters Computed at the BP86/cc-pVDZ-PP(Cu,Ag,Au,Br,I)∪cc-pVDZ(L) Level

which correspond to Tx,y-allowed transitions, while the chief contribution to paratropic ring current arises from the ag f ag excitation, which corresponds to Rz-allowed transitions. The low excitation energies of the Rz-allowed transitions are indicative for the higher paratropicity (antiaromaticity) of the rings and the weaker long-range diatropicity (aromaticity), with NICSzzmin values ranging from -4.9 to -5.8 ppm. In the [c-M4(μ2-PH2)4] (M=Cu, Ag, Au) and [c-Au4(μ2NH2)4] rings with D4h symmetry the chief contribution to diatropic ring current arises from the eu f a2u and eu f a1g excitations, which correspond to Tx,y-allowed transitions, while the chief contribution to paratropic ring current arises from the a2g f a1g excitation, which corresponds to Rz-allowed transitions. The relatively high excitation energies (around 4.0-5.0 eV) of both the Tx,y-allowed and Rz-allowed transitions are in support of nonaromatic systems with NICSzzmin values around -2.0 to -3.0 ppm. In the [c-M4(μ2-F)4] (M=Cu, Ag, Au) rings having also D4h symmetry the chief contribution to diatropic ring current arises from the eu f a1g excitations (Tx,y-allowed transitions), while the chief contribution to paratropic ring current arises from the a2g f a1g excitation (Rz-allowed transitions). The relatively low excitation energies (around 2.3-3.4 eV) of both the Tx,y-allowed and Rz-allowed transitions are suggestive of comparable contributions to the induced diatropic and paratropic ring currents. Therefore

the [c-M4(μ2-F)4] (M=Cu, Ag, Au) rings could be considered as nonaromatic rings. Finally, in the [c-M4(μ2-X)4] (M=Cu, Ag, Au; X=Cl, Br, I) rings with D2d symmetry, except the [c-Cu4(μ2-Br)4] and [c-Cu4(μ2-I)4] clusters, having a diamond-like structure of D2 symmetry, the chief contribution to diatropic ring current arises from the e f a1 excitation (Tx,y-allowed transitions), while the chief contribution to paratropic ring current arises from the a2 f a1 excitation (Rz-allowed transitions). The estimated excitation energies of both the Tx,y-allowed and Rz-allowed transitions are suggestive for comparable contributions to the induced diatropic and paratropic ring currents, and therefore the [c-M4(μ2-X)4] (M = Cu, Ag, Au; X = Cl, Br, I) rings could also be considered as nonaromatic or roughly antiaromatic rings. The same holds true for the [c-Cu4(μ2-Br)4] and [c-Cu4(μ2-I)4] clusters with D2 symmetry, where the b3 f a and b2 f a excitations (Tx,y-allowed transitions) and the b1 f a excitation (Rz-allowed transition) contribute equally to the induced diatropic and paratropic ring current.

Concluding Remarks In this paper we have demonstrated for the first time, using electronic structure calculation methods (DFT), that “ligand-protected” four-membered rings of noble metals formulated as [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) are thermo-

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dynamically stable molecules with respect to their dissociation either to ML monomers or to M2L2 dimers. The latter are the products of the thermodynamically favored oxidative addition reactions of the L2 to M2 diatomic species. The results can be summarized as follows: The [c-M4(μ2-L)4] (M = Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules are predicted to adopt square-planar structures analogous to those of the corresponding organic counterparts, which are characterized by perfect planarity and equalization of all metal-metal bonds in the metallic rings with the exception of the [cCu4(μ2-Br)4] and [c-Cu4(μ2-I)4] clusters, which adopt a diamond-like core structure. A thorough search of the potential energy surfaces (PES) revealed that the global minima of all [c-M4(μ2-L)4] (M=Cu, Ag, Au; L = H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) clusters, except [c-Au4(μ2-CH3)4], correspond to the structures involving bridging stabilizing ligands L. Inspection of the estimated WBOs reveals remarkable metal-metal interactions corresponding roughly to one electron bond for the H-, CH3-, SiH3-, and GeH3-bridged M4 rings (WBOs in the range 0.247-0.456), which can be described as cuprophilic, argentophilic, and aurophilic interactions. Weaker cuprophilic, argentophilic, and aurophilic interactions occur in the NH2-, OH-, Cl-, Br-, and I-bridged M4 clusters (WBOs in the range 0.061-0.308). Such interactions can be ascribed to orbital interactions resulting in the formation of molecular orbitals (MOs) localized on the M4 framework. Notice that such intermetallic interactions are absent in the phosphido-bridged M4 rings (WBOs of 0.079, 0.048, and 0.049 for the copper, silver, and gold rings, respectively); thereby these species adopt a planar eightmembered metallacyclic ring structure. Furthermore, the bonding of the μ2-L bridges corresponds to a three-center two-electron (3c-2e) bond, which contributes significantly to


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the stability of the M4 rings. Noteworthy are the “in-plane” agostic interactions in the [c-M4(μ2-L)4] (M = Cu, Ag, Au; L=CH3, SiH3, GeH3) molecules, where the H atom of the CH3, SiH3, or GeH3 groups participating in the agostic interactions is coplanar with the M4 plane, while the other two H atoms, which are perpendicular to the M4 plane, are oriented above and below the plane. The strength of the agostic interactions increases along the series methyl- < silyl- < germyl-protected four-membered rings. The magnetotropicity (diatropicity/paratropicity) of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) molecules was analyzed in terms of the NICSzz-scan curves in conjunction with symmetry-based selection rules for the most significant translationally and rotationally allowed transitions of the molecules. The NICSzz-scan patterns of the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=H, CH3, SiH3, GeH3, NH2, PH2, OH, F, Cl, Br, I) clusters are typical for long-range diatropicity (aromaticity) with minima in the region 1.8 to 4.0 A˚ above and below the ring and paratropicity (antiaromaticity) in the ring plane up to 0.7 to 2.5 A˚ above and below the ring where a nodal plane resides and having maxima at the ring center. In other words, the M4 (M = Cu, Ag, Au) rings exhibit successive aromatic and antiaromatic zones separated by a nodal plane. It should be noted that the estimated NICSzzmin values are indicative of remarkable aromaticity only for the [c-M4(μ2-L)4] (M=Cu, Ag, Au; L=H, CH3) clusters; all other species should be nonaromatic or even antiaromatic. Supporting Information Available: Complete author list for ref 78. The Cartesian coordinates, NICS-scan values, and energies of all stationary points are compiled in Table S1. This information is available free of charge via the Internet at http:// pubs.acs.org.

Theoretical Determination of the Structural, Bonding, and

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