Structure and Bonding in Coinage Metal Halide Clusters MnXn, M

Article pubs.acs.org/JPCA

Structure and Bonding in Coinage Metal Halide Clusters MnXn, M = Cu, Ag, Au; X = Br, I; n = 1−6 F. Rabilloud* CNRS, UMR 5579 LASIM, Université de Lyon, F-69622 Lyon, France, and Université Lyon 1, Villeurbanne, France ABSTRACT: Ab initio calculations in the framework of density functional theory (DFT) were performed to study the lowest-energy isomers of noble metal halide clusters MnBrn and MnIn, for M = Cu, Ag, or Au and n = 1−6. For all species, the most stable structures were found to be cyclic arrangements. Calculated bond lengths and infrared frequencies were compared with the available experimental data. The nature of the ionocovalent bonding was characterized. The stability and fragmentation were also investigated. The present work confirms previous observations on the particular stability of the trimer. cyclic for neutral species.20 However, the structures of AgnFn clusters were found to be highly symmetric (Dnh) planar structures, although those of AgnBrn clusters were found to be nonplanar cycles.19 Further calculations on tetramers (MX)4 (M = Cu, Ag, or Au; X = F, Cl, Br, or I) found planar or nonplanar cyclic structures for all species.21,22 Special attention was paid to gold trihalide clusters, in which aurophilic interactions were shown to lead to relatively small Au−Au distances.23−25 In the present article, we report a systematic study of the structures and properties of both noble metal bromides, MnBrn, and noble metal iodides, MnIn, with M = Cu, Ag, and Au and n = 1−6. We compared our results, obtained within the DFT framework, with experimental data on infrared frequencies. In addition, we calculated fragmentation energies and finally investigated the ionocovalent nature of the bonding.

1. INTRODUCTION The halides of noble metals have attracted much interest in terms of both experiments and computations, particularly because of their many practical applications such as the use of silver bromide in photography1 and holography2 and the use of copper halides as catalysts.3 From a more fundamental point of view, the interactions between halide and noble metal atoms are difficult to characterize. The ionic bonding character is less marked than in alkali halide systems, and the presence of the d electrons of the noble metal makes theoretical investigations much more complicated. The nature of noble metal−halide bonding (covalent or ionic) is still controversial. Recently, a combined experimental and theoretical investigation based on photoelectron spectroscopy and ab initio calculations of cyanide halide gold complexes and noble metal diiodide complexes reported a strong ionic character in Au−F bonding and increased covalent bonding from Au−Cl to Au−I.4,5 In the gas phase, a common property of all noble metal halide compounds is the unusual abundance of trimers in the vapor.6−15 The relatively high stability of the trimer was also shown in experiments on the fragmentation of metastable clusters of silver bromide.16,17 The evaporation of a trimer was found to be the preferred dissociation channel of AgnBrn−p+ (n = 5−14, p = 1−5) clusters. Some theoretical studies18,19 investigated the electronic and structural properties of small silver bromide clusters within the framework of density functional theory (DFT) and showed that small stoichiometric clusters AgnBrn with n ≤ 6 adopt cyclic structures and not cubelike ones, as it was previously supposed. These surprising structures were found to be stabilized by a significant covalent character in the silver bromide bonding, with a substantial mixing between the s−d hybrid orbitals of silver and the p orbitals of bromine.19 The trimer was found to be particularly stable. The calculated fragmentation energies for the energetically lowest dissociation channels of AgnBrn−1+ (n = 2−6) were in complete agreement with the channels observed in experiments.19 More recently, in a joint experimental and theoretical investigation of the adiabatic electron affinities of AgnFn clusters, it was shown that the lowest-energy isomers are © 2012 American Chemical Society

2. COMPUTATIONAL DETAILS We used the DFT technique as implemented in Gaussian 0326 combined with relativistic effective core potentials (RECPs) to optimize the geometry of the clusters. Pre- and postprocessing operations were performed with the graphical interface Gabedit.27 We used the hybrid B3LYP functional involving Becke’s three-parameter exchange functional.28,29 For both Br and I, an RECP30 was applied to described the core electrons, whereas the seven active valence electrons (ns and np) were described with the decontracted basis set given in ref 30 and extended by a d-type polarization function (with exponents of 0.3 and 0.25 for Br and I, respectively). For noble metals, a small core RECP31,32 was used to describe the core electrons, whereas the 19 valence (n − 1)s, (n − 1)p, (n − 1)d, and ns electrons were described with a 8s7p6d Gaussian basis set contracted to 6s5p3d;24 an f function was found not to give significant changes and so was not used. Within this protocol, Received: January 23, 2012 Revised: March 7, 2012 Published: March 20, 2012 3474

dx.doi.org/10.1021/jp300756h | J. Phys. Chem. A 2012, 116, 3474−3480

The Journal of Physical Chemistry A

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Table 1. Equilibrium Distances (re), Vibrational Frequencies (ωe), Dissociation Energies (De), and Adiabatic Ionization Potentials (IP) of Monomersa ωe (cm−1)

re (Å)

a

De (eV)

species

calc

expt

calc

expt

calc

CuBr AgBr AuBr CuI AgI AuI Cu2 Ag2 Au2

2.22 2.44 2.41 2.39 2.67 2.58 2.25 2.59 2.58

2.17b 2.39b 2.32c 2.34b 2.55b

301 234.3 236.1 253.2 194.2 190.2 257.3 179.2 163.9

314.8b 247.7b 264.4c 264.5b 192±5g

3.06 2.60 2.32 2.74 2.36 2.18 1.87 1.52 1.85

2.22b 2.53d 2.47f

264.6b 192.4b 191f

IP (eV) expt 2.88h 2.96c

1.66e 2.29f

calc 9.69 9.57 10.02 9.19 9.05 9.47 8.21 7.86 9.26

expt 9.59b

8.8b 7.9b 7.66b 8.7−9.7b

All states are 1Σ+g or 1Σ+. bReference 33. cReference 34. dReference 35. eReference 36. fReference 37. gReference 13. hReference 15.

the ionization potentials of Cu, Ag, and Au were calculated to be 8.20, 7.97, and 9.43 eV, respectively, in comparison with experimental values of 7.73, 7.58, and 9.22 eV,33 and the electron affinities of Br and I were calculated to be 3.51 and 3.35 eV, respectively, in comparison with the experimental values of 3.36 and 3.06 eV.33 In Table 1, we have compiled several values calculated for monomers (equilibrium distances, dissociation energies, vibrational frequencies, ionization potentials). Our results compare well with experimental values when available, as well as with high-level quantum calculations [coupled-cluster CCSD(T) + spin−orbit method] by Chambaud et al.38 and the B3LYP calculations with extended basis sets by Su et al.39 The relatively short bond lengths of Au2, AuBr, and AuI with respect to those of Ag2, AgBr, and AgI are due to the relativistic effects of gold, which lead to a 6s orbital contraction, decreasing the atomic size of Au. In the optimization of the cluster geometries, a number of structures were tested for each species and each size. We initiated the geometry optimization of MnXn clusters (M = Cu, Ag, Au; X = Br, I) starting from the known structures of several small noble metal halide clusters21,22 and some silver fluoride and bromide clusters for n > 4.19,20 We tested linear, cyclic, and cubic structures. Harmonic frequency analysis was performed to confirm that the optimized structures were local minima. In the next section, we discuss only the lowest-energy stable isomers determined in our optimizations. Only singlet spin multiplicity was studied, as no spin polarization was expected. For each stable structure, the atomic charges were estimated through natural population analysis (NPA).40

3. RESULTS AND DISCUSSION 3.1. Optimized Structures and Infrared Spectra. The calculated ground-state structures of noble metal bromide clusters MnBrn (M = Cu, Ag, Au) are shown in Figure 1. The bond distances are listed in Table 2. For dimers, the D2h rhombus is the lowest-energy isomer for Cu2Br2, with Cu−Br and Cu−Cu bond lengths of 2.40 and 2.42 Å, respectively (and a Cu−Br−Cu angle of about 60°). Similarly, the most stable structure for Ag2Br2 is the D2h rhombus, with Ag−Br and Ag− Ag distances of 2.65 and 2.86 Å, respectively (and a Ag−Br−Ag angle of 65°). For Au2Br2, the rhombus (with Au−Br and Au− Au bond lengths of 2.66 and 2.81 Å, respectively) is stable but lies 0.15 eV above a Cs-symmetry structure in which one Au−Br bond is broken to lead a quasilinear BrAuBr substructure. At the same time, the other three Au−Br bonds are strengthened because the Au−Br distances are shortened from 2.66 Å (in D2h symmetry) to 2.42, 2.57, and 2.55 Å. For n > 2, all of the

Figure 1. Optimized structures of MnBrn and MnIn clusters, M = Cu, Ag, Au. Bromine and iodine atoms are represented by large spheres. Relative energies are given in eV, where a dash indicates that the structure is not a minimum. The spatial symmetry is also given.

lowest-energy isomers of MnBrn clusters are planar or nonplanar cycles composed of linear BrMBr subelements. The trimer has a quasitriangular shape with strong M−M interactions favored by relatively short distances (2.69, 3.10, and 3.08 Å for Cu−Cu, Ag−Ag, and Au−Au bond lengths, respectively). The Cu−Br, Ag−Br and Au−Br distances are 2.33, 2.55, and 2.54 Å, respectively. For tetramers, a planar D4h ring competes with a nonplanar D2d cycle. Cu4Br4 favors the former, whereas Ag4Br4 and Au4Br4 favor the latter. In the D2dsymmetry structure of Cu4Br4, the Cu−Br and Cu−Cu bond lengths are 2.31 and 2.93 Å, respectively, and the CuBrCu angle is 79°. The dihedral angle is about 115°. In the D4h-symmetry 3475



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Table 2. M−X/M−M Bond Lengths (in Å) for Cyclic Structures of MnXn Clusters (M = Cu, Ag, Au; X = Br, I) CunBrn AgnBrn AunBrn CunIn AgnIn AunIn

n=2

n=3

n=4

n = 5a

n = 6b

2.40/2.42 2.65/2.86 2.66/2.81 2.57/2.43 2.80/2.86 2.81/2.82

2.33/2.69 2.55/3.10 2.54/3.08 2.51/2.73 2.71/3.16 2.69/3.17

2.31/2.93 2.53/3.57 2.49/3.51 2.49/2.87 2.69/3.77 2.66/3.76

2.31/3.05 2.53/3.69 2.49/3.62 2.49/3.14 2.69/3.83 2.66/3.87

2.31/2.98 2.53/3.66 2.49/3.59 2.49/2.92 2.69/3.81 2.66/3.87

a For pentamers, we give the average M−M distances in the cyclic structure. bFor hexamers, we give the M−M distance of the D3d-symmetry structure.

the lowest-energy isomer is still a cyclic arrangement. It can be described as a nonplanar distorted pentagon with Br apexes and IMI sides having different M−I−M angles (ranging from 70° to 98°) around the cycle. All 10 M−I bond lengths are strictly identical (2.49, 2.69, and 2.66 Å for Cu−I, Ag−I, and Au−I, respectively). For the hexamers, two nonplanar cycles compete for the ground state: D3d- and D2-symmetry structures. At the present level of theory, we are not able to predict which of the two configurations is the most stable because the energy difference is only 0.01 eV and the potential energy surfaces are nearly flat. The structures are distinguishable only by their dihedral angles, as both the M−M and M−Cl distances are identical for all structures. The M−I bond lengths were found to be 2.49, 2.69, and 2.66 Å for copper, silver, and gold iodides, respectively, in the two configurations, and the metal−metal distances were found to be about 2.92, 3.81, and 3.87 Å for Cu−Cu, Ag−Ag, and Au−Au, respectively. Our calculations clearly show the strong tendency of noble metal halide clusters to adopt cyclic arrangements at least up to the hexamer. Our current results are in global agreement with previous ones concerning the structural arrangement of tetramers.21,22 At the B3LYP/LanL2DZ level, Schwerdtfeger and co-workers21 found a trend for copper halide to form D2h structures but found D2h- and D4h-symmetry structures to be quasidegenerate for Ag4I4 and Au4I4. In all cases, the potential energy surface describing the D4h/D2d distortion was quite shallow. The present results are also in line with previous works on AgnBrn clusters.18,19 Interestingly, in previous work20 on silver fluoride clusters AgnFn, we found a strong tendency to form planar (Dnh) rings up to at least the hexamer. Compared with the present results, one can conclude that the planar character is mainly due to the halide, as the planar/nonplanar distortion occurs earlier (generally at n = 4) for noble metal bromides and iodides than for noble metal fluorides. In experiments, indirect information about the structure can be obtained from infrared (IR) spectroscopy. Calculated absorption frequencies are reported in Tables 3 and 4 for MnBrn and MnIn, respectively. These values could help to distinguish among some isomers that compete for the most stable structure. For example, the IR spectra of Cs- and D2hsymmetry arrangements for Au2Br2 and Au2I2 are very different. However, for the hexamers, the spectra of the two quasidegenerate structures (D2- and D3d-symmetry) are roughly similar. Martin and co-workers9 reported infrared absorption spectra for matrix-isolated (MX)n clusters with M = Cu and Ag and X = Cl and Br. The experimental absorption frequencies for CuBr, (CuBr)2, and (CuBr)3 are reported in Table 3, together with the present calculated values. The very good agreement between our calculated values and the experimental ones is a validation of the reliability of the present calculations. For the tetramer (CuBr)4, our calculations give a strong

structures, the Ag−Br and Ag−Ag distances in Ag4Br4 are 2.53 and 3.57 Å, respectively, and the Au−Br and Au−Au distances in Au4Br4 are 2.49 and 3.51 Å, respectively. For n = 5, the lowest-energy isomer is still a cyclic arrangement. It can be described as a nonplanar distorted pentagon with Br apexes and BrMBr sides having different M−Br−M angles (ranging from 76° to 100°) around the cycle. All 10 M−Br bond lengths are strictly identical (2.31, 2.53, and 2.49 Å for Cu−Br, Ag−Br, and Au−Br, respectively). For hexamers, two nonplanar cycles were found to compete for the ground state. They are represented in Figure 1 and labeled with their symmetries: D3d and D2. At the present level of theory, we are not able to predict which of the two configurations is the most stable because the energy difference is only 0.01 eV and the potential energy surfaces are nearly flat. The structures are distinguishable only by their dihedral angles, as both M−M and M−Br distances are identical for all structures. The M−Br bond lengths were found to be 2.31, 2.53, and 2.49 Å for copper, silver, and gold bromides, respectively, in both configurations, and the metal− metal distances were found to be about 2.98, 3.66, and 3.59 Å for Cu−Cu, Ag−Ag, and Au−Au, respectively. Also note that the metal−bromine bond distances are constant (2.31, 2.53, and 2.49 Å for Cu−Br, Ag−Br, and Au−Br bond distances, respectively) for n = 4, 5, and 6. The most stable structures of noble metal iodides were found to be somewhat similar to those of noble metal bromides but with some differences. For dimers, the D2h-symmetry structure is the lowest-energy isomers for the three metal iodides (see Figure 1). The metal−iodine and metal−metal bond lengths are 2.57, 2.80, and 2.81 Å and 2.43, 2.86, and 2.82 Å for Cu2I2, Ag2I2, and Au2I2, respectively (Table 2). However, for Au2I2, a Cs-symmetry structure was found to lie only 0.03 eV above the rhombus. In this structure, three Au−I bonds are strengthened (the Au−I distances are shortened from 2.81 to 2.60, 2.76, and 2.69 Å), but the fourth is broken. The trimers have a quasitriangular shape with strong M−M interactions favored by relatively short distances (2.73, 3.16, and 3.17 Å for Cu−Cu, Ag−Ag, and Au−Au bonds, respectively), somewhat similar to those in the M3Br3 trimers. The Cu−Br, Ag−Br, and Au−Br distances are 2.51, 2.71, and 2.69 Å, respectively. For tetramers, a planar D4h ring competes with a nonplanar D2d cycle. Cu4I4 and Ag4I4 favor the nonplanar D2d cycle. However, their structures are somewhat different because the M−I−M angle and the dihedral angle are much smaller for Cu4I4 (70° and 94°, respectively) than for Ag4I4 (89° and 159°, respectively), resulting in a much shorter metal−metal distance in the former (2.87 Å for Cu−Cu versus 3.77 Å for Ag−Ag). Hence, the D2dsymmetry structure of Ag4I4 can be seen as a slight deformation of the D4h ring, whereas the structure of Cu4I4 is much farther from this ring. Au4I4 favors the D4h-symmetry ring, with Au−I and I−I distances of 2.66 and 3.76 Å, respectively. For n = 5, 3476



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Table 3. Calculated Infrared Absorption Spectra (in cm−1) of MnBrn (M = Cu, Ag, Au) Clustersa,b Cu2Br2 Cu3Br3 Cu4Br4 Cu5Br5 Cu6Br6 Ag2Br2 Ag3Br3 Ag4Br4 Ag5Br5 Ag6Br6 Au2Br2 Au3Br3 Au4Br4 Au5Br5 Au6Br6

calc

exptc

66, 122, 237 78, 83, 142, 301 72, 302, 316 74, 300, 307, 315 D3d: 74, 177, 294, 317 D2: 72, 75, 165, 293, 296, 312, 315 47, 105, 185 54, 60, 124, 232 51, 60, 148, 234 54, 58, 225, 231, 233, 238 D3d: 54, 59, 231, 236 D2: 56, 58, 231, 236 Cs: 87, 121, 195, 247 D2h: 47, 76, 162 51, 69, 134, 218 72, 171, 224 171, 216, 221, 225, 228 D3d: 176, 222, 226 D2: 176, 223, 224, 226

123, 239 83, 93, 154, 319

experimental infrared absorption spectrum of matrix-isolated clusters extracted from the vapor composed of (CuBr)6, (CuBr)7, and (CuBr)8 clusters. This spectrum shows some strong lines at around 300 cm−1 that fit our calculated lines well for both the D3d and D2 structures. In the case of silver bromide clusters, our calculated values of 105 and 185 cm−1 for the dimer and 124 and 232 cm−1 for the trimer fit well the experimental values of 101 and 195 cm−1 for the Ag2Br2 and 133 and 251 cm−1 for Ag3Br3. Table 4 presents the calculated IR frequencies of metal iodides. To our knowledge, the IR spectrum of Ag3I3 measured in the gas phase by Kovacs and Konings13 represents the only available experimental data. The experimental value of 205 cm−1 is in very good agreement with our calculated value of 203 cm−1. 3.2. Characterization of the Ionocovalent Bonding. Our study found that cyclic arrangements are favored by noble metal halides at least up to the hexamer. The structures are characterized by a strong XMX alignment and M−X−M angles in the range of 80−100° (where M and X are the noble metal and the halide, respectively). To understand the origin of these peculiar geometries, we show in Figure 2 some selected

101, 195 133, 251

a

When several structures compete for the ground state, data for all quasidegenerate isomers are given. bTransitions with highest intensities are in bold. cValues from ref 9.

Table 4. Calculated Infrared Absorption Spectra (in cm−1) of MnIn (M = Cu, Ag, Au) Clustersa,b calc Cu2I2 Cu3I3 Cu4I4 Cu5I5 Cu6I6 Ag2I2 Ag3I3 Ag4I4 Ag5I5 Ag6I6 Au2I2 Au3I3 Au4I4 Au5I5 Au6I6

55, 103, 211 62, 67, 103, 263 65, 101, 171 60, 243, 256, 259, 266, 273 D3d: 58, 130, 252, 275 D2: 61, 249, 257, 271, 272 40, 84, 160 45, 95, 203 48, 112, 202, 206 45, 194, 201, 203, 207 D3d: 45, 115, 200, 206 D2: 46, 200, 205 D2h: 38, 66, 140 Cs: 29, 80, 144, 160, 201 106, 186 187 182, 185, 187, 189 D3d: 186, 188 D2: 186, 188

exptc

205 ± 10

a

When several structures compete for the ground state, data for all quasidegenerate isomers are given. bTransitions with highest intensities are in bold. cValues from ref 13.

Figure 2. Selected molecular orbitals of Au4I4, Cu4I4, Au3Cl3, and Cu6I6 (D3h-symmetry structure). Orbital energies (in au) and symmetries are given in italics. The isovalue is 0.02 au.

absorption line at 302 cm−1 for the cyclic D2d structure, whereas the cubelike isomer (which lies 1.33 eV above the D2d structure) has two main lines at 112 and 194 cm−1. The IR absorption frequencies would be a good way to distinguish the isomers. Unfortunately, however, no experimental data are available for the tetramer. For the pentamer, three strong lines were found around 300 cm−1. For (CuBr)6, the IR spectra of the two quasidegenerate isomers are roughly similar, with two strong lines at 294 and 317 cm−1 for the D3d structure and at 293 and 312 cm−1 for the D2 isomer. In ref 9, Martin gives an

molecular orbitals that illustrate mixing between pX and dM orbitals. The XMX alignment is due to pXdMpX interactions, whereas the roughly acute M−X−M angles are favored by strong dMpXdM interactions (see, for example, the orbitals of the D4h-symmetry ring Au4I4 in Figure 2). In the nonplanar cycles, the noble metal atoms tend to shorten their interatomic separations with respect to what they would be in planar cycles. Some metal−metal covalent interactions clearly appear in the orbitals of Cu4I4 (see Figure 2). For example, HOMO − 31, 3477



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HOMO − 22, HOMO − 20, and HOMO − 19 show sd−sd overlap. In particular, HOMO − 31 (symmetry A1) provides significant stability. It originates from an A1g-symmetry orbital in a planar D4h ring (similar to HOMO − 28 of Au4I4) and is characterized by the mixing of three-center molecular orbitals dMpXdM. Thanks to the covalent metal−metal interactions and dMpXdM interactions, the metal−metal distances are roughly constant for n = 4−6 for each species: about 2.9 Å for the Cu− Cu bond lengths in both CunBrn and CunIn, about 3.6 Å for both Ag−Ag and Au−Au distances in AgnBrn and AunBrn, and about 3.8 Å for both Ag−Ag and Au−Au distances in AgnIn and AunIn. The three-body interactions (dMpXdM and pXdMpX) are still present in the hexamer (for example, see HOMO − 47, HOMO − 42, and HOMO − 41 of Cu6I6 in Figure 2). In addition to this covalent character, the M−X bonding is expected to present a partial ionic character because of the partial transfer of the ns electron from the noble metal to the bromine or iodine atom. We estimated this partial transfer using natural population analysis.40 The charge transfer in MnXn was found to be roughly independent of n (see Figure 3). The

Figure 4. Dissociation energies of MnXn clusters as a function n.

Figure 4 and Table 5, the dissociation energies of MnXn, defined as En = [nE(M) + nE(X) − E(M nX n)]/n

are given as a function of n. They increase rather quickly up to n = 3 and then exhibit a plateau at about 1.5 eV above the dissociation energy of the monomer. The plateau seems to be a characteristic of the cyclic structures and might exist until the cluster size becomes large enough to lead to three-dimensional structures. For both bromides and iodides, copper has the highest dissociation energy, followed by silver and gold. For all noble metals, the metal bromides have higher dissociation energies than the metal iodides. As mentioned in the Introduction, in experiments, a high abundance of trimers was measured in the vapor of noble metal halide compounds at high temperature (typically 1000 K in the experiments of Martin and Schaber9). To explain this unusual abundance, one should consider the Gibbs free energy including both thermal and entropic effects. In Table 5, we give the Gibbs free energies of dissociation at 1000 K and constant pressure (1 atm) including the contributions of translational, rotational, and vibrational partition functions, entropic effects, and zero-point vibrational energy corrections. For all species, the size n = 3 (along with the size n = 4 for gold bromide) appears to be particularly stable. Thus, thermal and entropic effects favor the trimer. 3.3. Fragmentation Energies. From the calculated data, one can consider fragmentation into a number of channels implying smaller stoichiometric clusters. The corresponding fragmentation energies of MnBrn and MnIn (M = Cu, Ag, Au) are given in Table 6. Fragmentation of MnBrn and MnIn clusters into MBr and MI monomers is the lowest channel up to size n = 4 for M = Cu or Ag and up to n = 5 for M = Au. Then, for larger clusters, the channel leading to a trimer is the lowest. For all species, the trimer is the most stable cluster. It was found to be much more stable with respect to one monomer + one dimer than was the dimer with respect to two monomers and almost as stable as the monomer MX with respect to M + X. In particular, the symmetric dissociation of hexamers into two trimers occurs with a low fragmentation energy (in the 0.15− 0.87 eV range). This is in line with previous experiments on the fragmentation of metastable silver bromide clusters16,17,41 in which the evaporation of a trimer was found to be the preferred dissociation channel of AgnBrn−p+ (n = 5−14, p = 1−5) clusters. Although the energies of the heptamers M7X7 are not known, we can conclude from the present calculations that their dissociation into a trimer + a tetramer is the lowest channel for all species.

Figure 3. Average atomic charges (in au) on noble metal atoms from NPA for monomers (n = 1) and cyclic structures (n > 1).

transferred charge is stronger on bromine (in the range of 0.40−0.61 au) than on iodine (in the range of 0.29−0.50 au). This is in line with recent results on cyanide halide gold complexes, which revealed increased covalent bonding from Au−Cl to Au−I.5 The atomic charges on gold atoms are systematically 0.1 au lower than those on cuprous and silver atoms. For all species, the relatively small charge transfer (in the range of 0.3−0.6 au) indicates a slight ionic character of the bonding. Hence, the M−X bonds are rather covalent. The least ionic compound is gold iodide, for which the charge transfer is lower than 0.3 au, whereas the most ionic is silver bromide, with a charge transfer of about 0.6 au. The electronic density transferred from the metal to the halide atoms originates primarily from the ns electrons and to a lesser extend from the (n − 1)d electrons. As an illustration, the natural electron configurations in Au4I4 were found to be 6s0.805d9.876p0.01 on Ag and 5s1.935p5.34 on I, whereas those in Ag4Br4 were found to be 5s0.454d9.925p0.01 on Ag and 4s1.954p5.634d0.01 on Br. From our present analysis, we can conclude that the cyclic structures are stabilized by ionocovalent interactions with a dominant covalent character in all species, the latter being particularly strong in gold halide clusters. The interactions between the dM and pX orbitals favor halide−metal−halide alignment and bent metal−halide−metal substructures. In 3478



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Table 5. Dissociation Energies (in eV) of MnXn Clusters, Defined as [nE(M) + nE(X) − E(MnXn)]/n, along with Gibbs Free Energies of Dissociation at 1000 K Including Thermal and Entropic Effects and Zero-Point Vibrational Energy Correction in Parentheses n=1 CunBrn AgnBrn AunBrn CunIn AgnIn AunIn

3.06 2.60 2.32 2.74 2.36 2.18

n=2

(2.15) (1.71) (1.42) (1.84) (1.49) (1.29)

4.01 3.39 2.85 3.68 3.15 2.77

n=3

(2.40) (1.84) (1.43) (2.09) (1.61) (1.23)

4.60 3.90 3.69 4.17 3.61 3.52

n=4

(2.76) (2.11) (1.85) (2.37) (1.85) (1.72)

4.65 3.96 3.83 4.20 3.65 3.62

(2.70) (2.08) (1.86) (2.29) (1.83) (1.70)

n=5 4.65 3.96 3.83 4.20 3.65 3.62

(2.70) (1.98) (1.76) (2.28) (1.70) (1.58)

n=6 4.65 3.96 3.83 4.20 3.65 3.62

(2.65) (2.03) (1.81) (2.25) (1.76) (1.63)

Table 6. Fragmentation Energies (in eV) X = Br parent

fragments

MX M2X2 M3X3

M+X 2 × MX M2X2 + MX M3X3 + MX 2 × M2X2 M3X3 + M2X2 M4X4 + MX 2 × M3X3 M4X4 + M2X2 M5X5 + MX M4X4 + M3X3 M5X5 + M2X2 M6X6 + MX

M4X4

M5X5

M6X6

M7X7a

M= Cu

M= Ag

X=I M= Au

M= Cu

M= Ag

M= Au

3.06 1.88 2.73

2.60 1.57 2.31

2.32 1.23 2.87

2.74 1.89 2.42

2.36 1.57 2.18

2.18 1.19 2.86

1.76

1.56

1.92

1.54

1.42

1.72

2.60 1.44

2.29 1.35

3.56 2.22

2.07 1.09

2.02 1.15

3.39 2.00

1.58

1.37

1.53

1.44

1.30

1.46

0.30 1.32

0.42 1.17

0.87 1.83

0.15 1.04

0.28 1.04

0.61 1.74

1.62

1.38

1.53

1.48

1.31

1.47

Δ1

Δ2

Δ3

Δ4

Δ5

Δ6

Δ1 + 1.15 Δ1 + 1.42

Δ2 + 0.94 Δ2 + 1.14

Δ3 + 1.35 Δ3 + 1.05

Δ4 + 0.98 Δ4 + 1.38

Δ5 + 0.88 Δ5 + 1.14

Δ6 + 1.40 Δ6 + 1.12

Figure 5. Selected molecular orbitals of Au3I3. Orbital energies (in au) and symmetries are given in italics. The isovalue is 0.02 au.

metal−metal distance and increase the mixing between dmetal and phalide orbitals. The cyclic structures are stabilized by ionocovalent interactions, with a strong covalent character. For all species, the trimer was found to be particularly stable because of both strong interactions between metal and halide atoms and also metal−metal interactions that strengthen the aggregation of noble metal atoms. The transition to a threedimensional solid-state-like structure does not yet occur for the hexamer; further studies will investigate larger clusters to characterize the two-dimensional−three-dimensional transition.

a

Although the energies of the heptamers M7X7 are not known, we were able to calculate their fragmentation energies to a constant Δ.

To further understand the large relative stability of the trimer M3X3 with respect to the neighboring sizes (dimer and tetramer), one can note the important role of metal−metal bonds due to both the sharing of valence s electrons and the strong overlaps of d atomic orbitals. Some bonding orbitals of Au3I3 are shown in Figure 5. HOMO − 21, HOMO − 16, and HOMO − 14 illustrate metal−metal interactions with strong overlap between hybrid sd atomic orbitals. These metal−metal interactions are more stabilizing in the trimer than in the dimer because there are three metal−metal bonds instead of two. They are less strong in the tetramer because the metal atoms are more distant in that case. Moreover, the three-body interactions dMpXdM are also strong in the trimer because of the small M−X−M angles. Thus, the trimer is particularly stable with respect to the neighboring sizes thanks to both metal− metal interactions and strong mixing between dM and pX orbitals leading to three-center molecular dMpXdM orbitals.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 33 4 72 43 29 31. Fax: 33 4 72 43 15 07. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author thanks the Pôle Scientifique de Modélisation Numérique (PSMN) at Lyon, France, for generous allocation of computation time.

4. CONCLUSIONS We have presented the first systematic study of the lowestenergy isomers of coinage metal bromide and iodide clusters. Our calculations clearly show the strong tendency of noble metal halide clusters to adopt cyclic arrangements. The latter become nonplanar for tetramers and pentamers to decrease the

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Structure and Bonding in Coinage Metal Halide Clusters MnXn, M

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