Nature and Strength of MâS Bonds (M = Au, Ag, and Cu) in Binary

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J. Phys. Chem. A 2010, 114, 9212–9221

Nature and Strength of M-S Bonds (M ) Au, Ag, and Cu) in Binary Alloy Gold Clusters A. H. Pakiari*,† and Z. Jamshidi‡ Chemistry Department College of Sciences, Shiraz UniVersity, P.O. Box 71454, Shiraz, Iran, and Chemistry and Chemical Engineering Research Center of Iran, P.O. Box 14335-186, Tehran, Iran ReceiVed: January 15, 2010; ReVised Manuscript ReceiVed: July 22, 2010

The interactions of pure (Auk, Agk, and Cuk; k ) 1-3) and binary alloy (AunAgm and AunCum; m + n ) k e 3) metal clusters with hydrogen sulfide (H2S) have been investigated by using density functional theory (BP86, B3LYP, and CAM-B3LYP) and ab initio methods (MP2 and CCSD(T)), with a focus on the nature of metal-sulfur bonds. Binding energy calculations indicate that for pure metal clusters, the tendency of metal to interact with H2S has the order of Au > Cu > Ag. In binary alloy clusters, alloying Auk with copper and silver decreases the attraction of Au toward H2S, while alloying Agk and Cuk by gold increases the attraction of Ag and Cu toward H2S, significantly. Dissociation energy values for isolated metal clusters specify the more favorable formation of binary alloy clusters (AunAgm and AunCum) over pure ones. The nature of M-S bonds (M ) Au, Ag, and Cu) is also interpreted by means of the quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO), and energy decomposition analysis (EDA). According to these theories, the M-S bonds are found to be partially electrostatic and partially covalent. EDA results identify that these bonds have less than 35% covalent character and more than 65% electrostatic, and the covalent character increases in different metals in the order Au > Cu > Ag. 1. Introduction Bimetallic nanoclusters, which are often referred to as nanoalloys, have recently drawn considerable attention in basic studies and applications,1 due to their particular and unique structural,2-7 electronic,2,3 optical,8-10 and magnetic11-13 properties. Most of the interest and research has concentrated on nanoalloys of the late transition metals (TMs; groups 8-11), in particular, those formed between the group 11 metals (Cu, Ag and Au). Coinage metal nanoalloys, especially gold, have become an active research field lately because of their novel catalytic behavior14 and their potential applications in nanoelectronics and nanosensors.15 In the past few years, atomic and molecular chemisorptions on small coinage metal clusters, have received considerable attention.16 Although much of the experimental and theoretical work so far has been accomplished on pure coinage metal clusters, little information is available about the interactions of molecule with gold-silver and gold-copper binary clusters.17,18 Interaction of coinage metals with molecules containing sulfur atoms is extremely important in the formation of self-assembled monolayers,19 single-molecule devices,20 and markers of biological molecules, such as DNA and proteins.21 Analyzing the nature of M-S bonds is important to designing new molecular devices, and getting highly stable metal-molecule junctions (in single-molecule devices). In TM chemistry, analysis of the bonding situation is frequently discussed in terms of the familiar Dewar-Chatt-Duncanson (DCD), donor-acceptor model.22 The DCD model is based on heuristic considerations, and the analysis of the metal-ligand bond is often performed using charge partitioning schemes.23 However, accurate theoretical calculations clearly provide a good basis for the development and support of a chemical model, which is in agreement with * Corresponding author. E-mail: [email protected]. † Shiraz University. ‡ Chemistry and Chemical Engineering Research Center of Iran.

physical origin of the chemical bond.24 Therefore, we present here a systematic study on the structure and electronic properties of the pure and binary alloy coinage metal clusters complexed with H2S molecule. The nature of M-S bonds has been discussed by three quantum chemical methods, which are widely used for analyzing the chemical bonds in TM compounds: natural bond orbital (NBO), quantum theory of atoms-inmolecules (QTAIM), and energy decomposition analysis (EDA). 2. Method of Calculations The geometries of pure and binary alloy coinage metal clusters complexes with H2S molecule were fully optimized by second-order Moller-Plesset perturbation theory (MP2), and density functional theory (DFT). The DFT methods used are the gradient-corrected functional proposed by Becke and Perdew (BP86),25 Becke’s three parameter hybrid functional incorporating the correlation functional of Lee, Yang, and Parr (B3LYP),26 and new hybrid exchange-correlation functional presented by Yanai et al. who combine B3LYP at short-range with an increasing amount of exact HF exchange at long-range, which results in a functional called CAM-B3LYP.27 These calculations have been done using Gaussian 03 and 09 suite of programs.28 For coinage metals, we used pseudopotential-based augmented correlation-consistent basis sets, aug-cc-pVDZ-PP,29 based on the small core relativistic pseudopotentials (PPs) of Figgen et al.30 In these basis sets, 19 outermost electrons of metal are explicitly described by the (9s, 8p, 7d, 2f)/[5s, 5p, 4d, 2f] basis. Dunning’s aug-cc-pVDZ basis sets31 were used for hydrogen ((5s, 2p)/[3s, 2p]) and sulfur ((13s, 9p, 2d)/[5s, 4p, 2d]) atoms. The harmonic vibrational frequencies were calculated at all of the optimized geometries, and real frequencies were detected in all of the cases. The binding energy Eb of the complex Mk-SH2 is defined as the absolute value of the energy difference Eb ) EMk-SH2 - (EMk + EH2S), and all binding energies are corrected for the basis set superposition error (BSSE).32 To improve the calculated binding energies, coupled-cluster CCS-

10.1021/jp100423b  2010 American Chemical Society Published on Web 08/05/2010

M-S Bonds in Binary Alloy Au Clusters

J. Phys. Chem. A, Vol. 114, No. 34, 2010 9213

TABLE 1: Comparison of Calculated and Experimental Dissociation Energies (Do in kcal mol-1), Bond Lengths (re in Å), and Vibrational Frequencies (ωe in cm-1) for Dimer Metal Clusters Ag-Ag

Au-Ag

Au-Au

Au-Cu

Cu-Cu

method

re

ωe

Do

re

ωe

Do

re

ωe

Do

re

ωe

Do

re

ωe

Do

B3LYP CAM- B3LYP BP86 MP2 CCSD(T) expt.

2.585 2.560 2.553 2.475 2.567 2.53

178.7 190.5 189.6 213.7 181.8 192.4

36.10 34.59 41.08 44.63 35.53 38.05 ( 0.7

2.567 2.544 2.538 2.465 2.543 2.50

179.0 188.7 185.9 217.4 188.6

43.89 42.53 49.90 58.04 45.98 47.9 ( 2.3

2.549 2.527 2.522 2.449 2.520 2.472

166.5 176.6 173.1 205.8 180.2 190.9

45.35 43.88 52.35 60.04 47.13 52.8 ( 0.2

2.380 2.361 2.351 2.283 2.358 2.330

230.5 241.5 241.7 275.8 241.2 248.3

49.72 48.34 56.58 65.41 52.66 54.05 ( 2.2

2.251 2.232 2.220 2.137 2.236 2.219

255.0 267.5 273.2 294.2 256.9 266.4

44.23 42.82 51.10 51.04 44.04 45 ( 2

D(T)33 single-point calculations at the B3LYP optimized structure have been carried out with the same basis sets, using the program package MOLPRO 2006.1.34 To reveal the nature of bonds, the NBO, QTAIM, and EDA analyses were carried out on the B3LYP optimized structures. Within the NBO analysis introduced by Weinhold and coworkers,35 in this work we paid particular attention to natural population analysis (NPA) charges36 and charge transfers. The EDA was done using the program package ADF (2008.01),37 which is based on the work by Ziegler and Rauk,38 and Morokuma.39 The bonding analysis was carried out at the BP86/ TZ2P and B3LYP/TZ2P levels of theory, while scalar relativistic effects have been considered using the zero-order regular approximation (ZORA).40 In addition, the electron density, F(r), and its Laplacian, ∇2F(r), at bond critical points (BCPs) were computed based on Bader’s QTAIM,41 using AIM200042 program. The NBO and QTAIM analysis were carried out at B3LYP level of theory. 3. Results and Discussion 3.1. Structure and Stability of Free Clusters. Physical and chemical properties of coinage metal clusters depend strongly on the cluster size; small clusters are more reactive than bulk materials.43 In this section, we have considered the structure and stability of pure and binary alloy dimers and trimers of coinage metal clusters, and investigated the effect of alloying gold cluster by Ag and Cu metals. Table 1 shows the comparison between ab initio (MP2 and CCSD(T)), DFT (BP86, B3LYP, and CAM-B3LYP) and available experimental44,45 bond lengths, vibrational frequencies and dissociation energies of dimer metal clusters. From this table, it can be realized that the DFT and CCSD(T) bond lengths are slightly longer than the experimental values (by less than 0.07 Å), while the MP2 bond distances are slightly shorter (by less than 0.05 Å). This deviation is observed for both pure and binary alloy clusters. Despite different methods, the computed bond lengths obey the same trend: rAg-Ag > rAg-Au > rAu-Au > rAu-Cu > rCu-Cu. The shorter bond length of Au-Au with respect to Ag-Ag is related to the stronger relativistic effect experienced by gold, which causes a more significant relativistic bond length contraction in gold compounds.46 For dimer metal clusters, the experimental and CCSD(T) dissociation energies (Do) are in good agreement with the B3LYP and CAM-B3LYP values, and in a reasonable agreement with the MP2 and BP86 ones. The MP2 calculations overestimate Do by 24 and 17% with respect to CCSD(T) and experimental results, respectively. Theoretical studies by Kim et al,17 (on gold-silver binary alloy clusters) have shown that MP2 method with Ermler-Christiansen (EC) and StuttgartDresden-Bonn (SDB) pseudopotential basis set, respectively underestimated and overestimated the dissociation energies. However, calculations with different methods show the same trend for dissociation energy: Do(Au-Au) > Do(Au-Ag) >

Do(Ag-Ag) and Do(Au-Cu) > Do(Au-Au) > Do(Cu-Cu). The larger dissociation energy of Au-Cu in comparison with Au2 and Cu2 suggests a high tendency of Au to bind with Cu. For Au-Ag, CCSD(T) binding energy per atom (22.99 kcal mol-1) is larger than the average value (20.66 kcal mol-1) of Au2 (23.56 kcal mol-1) and that of Ag2 (17.76 kcal mol-1). The higher stability of Au-Ag and Au-Cu bonds over Au2, Cu2, and Ag2 (as considered by Kim17 and Tsipis et al18) is related to the highest electron affinity of Au among the coinage metals (Au (2.31 eV), Ag (1.30 eV), and Cu (1.23 eV)).47 The strong electron affinity of Au is known to be related to the relativistic stabilization of its 6s and 6p orbitals, and the relativistic expansion/destabilization of the 5d shell.48 In binary alloy metal clusters, this property results in a partial charge transfer from the Cu and Ag atoms to the Au, which provides significant electrostatic stabilization, which makes the alloy formation more favorable. A similar trend is observed in the case of trimers. For the most stable structure of trimer, the binding energies per atom of Au3, Au2Ag, AuAg2, and Ag3 are predicted to be 25.8, 26.9, 24.8, and 20.1 kcal mol-1, respectively. (The highest binding energy of Au2Ag compared with Au3 is noticeable.) The corresponding values for CuAu2, Cu2Au and Cu3 are 32.9, 30.2, and 26.4 kcal mol-1, respectively, and in this case the binding energies of Cu2Au and Au2Cu are larger than those of Cu3 and Au3. Determining minimum-energy structure for trimers metal clusters is difficult due to the possible low-lying structural isomers. The pure coinage metal clusters have two different isomers, namely triangular and linear-like structures. The B3LYP angles (∠M-M-M) for triangular structure of gold, silver and copper clusters, are 68.4°, 75.7,° and 69.3°, and for linear-like structures are 133.8°, 139.1°, and 117.7°, respectively. The energy difference between triangular and linear-like structures is very small (less than 0.1 eV). For binary alloy trimers triangular structures are the most stable forms with angles of 63.7° (∠AuAgAu), 57.4° (∠AgAuAg), 53.8° (∠CuAuCu), and 70.3° (∠AuCuAu) for Au2Ag, AuAg2, AuCu2, and Au2Cu clusters, respectively, and these results confirm previous studies.17,18 3.2. Structure and Stability of Complex Clusters. In this section, the effect of alloying gold by Cu and Ag atoms on the binding energies of Au-S has been investigated by DFT (BP86, B3LYP, and CAM-B3LYP) and ab initio (MP2) methods. In order to test the performance of these computational methods, we performed the CCSD(T) optimization (with the same basis set) for H2S-M (M ) Cu, Ag, and Au) complexes and compared the results with the MP2 and DFT values. For H2S-Au, H2S-Ag and H2S-Cu, the CCSD(T) bond lengths (rM-S) [2.579, 3.014, 2.402 Å, respectively] are in good agreement with the B3LYP (and CAM-B3LYP) values [2.624 (2.574), 2.998 (2.899), 2.439 (2.393) Å, respectively] and in reasonable agreement with the MP2 values [2.382, 2.761, 2.157

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Pakiari and Jamshidi

TABLE 2: Selected Features of H2S-Monomer Complexes

a M is Au, Ag, and Cu atoms. b The length of M-S bonds, in Å. c Vibratinal frequency of M-S bonds in the complexed, in cm-1. d The binding energy Eb (including zero-point energy and BSSE correction), in kcal mol-1. e The bond length and binding energy values are obtained from ref 47.

Å, respectively]. The MP2 values are smaller than CCSD(T) values (by less than 0.25 Å). The CCSD(T) binding energies (Eb) for H2S-Au, H2S-Ag, and H2S-Cu complexes are -6.79, -2.22, and -5.53 kcal mol-1; the B3LYP values are -6.24, -1.39, and -4.49 kcal mol-1; the CAM-B3LYP values are -6.43, -1.77, and -5.03 kcal mol-1; the MP2 values are -8.44, -1.10, and -4.39 kcal mol-1. The B3LYP (and CAM-B3LYP) binding energies show good agreement with CCSD(T) values. In the case of BP86 calculation, binding energies overestimated and bond lengths underestimated (compared to CCSD(T) values). It seems that with the corresponding basis set, B3LYP (and CAM-B3LYP) yields results that are near the CCSD(T) values. Geometrical parameters and binding energies, for pure and binary alloy metal cluster complexes with H2S molecules, are collected in Tables 3, 4, and 5, and Figure 1. In all of the complexes, the S atom is bonded to a single metal atom, and the geometries of the metal clusters and H2S molecule do not change significantly after interaction. Most of the optimized structures were found to have a Cs point symmetry group (where H2S-AuM2 and H2S-Au2M (M ) Ag and Cu) for triangular, and H2S-CuAu2 and H2S-Cu3 for linear-like trimer are asymmetric complexes). For pure metal clusters, in agreement with previous studies,49 the affinity of the silver clusters toward H2S is significantly lower than that of the copper and gold clusters, and the corresponding binding energy of the gold cluster is higher than that of the copper clusters. It can be realized based on Tables 3, 4, and 5, that by going from dimer to trimer, Eb increases and rM-S decreases; for instance, for a Aun cluster, Eb and rM-S (B3LYP) are -19.98 and -22.48 kcal mol-1, and 2.394 and 2.372 Å for dimer and trimer, respectively. Alloying gold clusters by copper and silver affects the attraction of Au toward H2S notably. Figure 1 shows clearly that, for the trimer binary alloy cluster, the binding energy of

Au-S decreases by increasing the number of Ag and Cu atoms in the cluster. In dimer metal clusters, Eb (B3LYP) for H2S-Au2 (-19.98 kcal mol-1) is about 47 and 45% higher than that for H2S-AuAg (-10.49 kcal mol-1) and H2S-AuCu (-10.89 kcal mol-1) complexes, respectively. On the other hand, in pure Agn and Cun metal clusters (in which H2S interacts through Ag and Cu atom), substitution of Ag and Cu atoms by Au increases the binding energies. For example, replacing one Ag or Cu atom in Ag2 or Cu2 clusters by Au atom enhanced the affinity toward H2S, increasing the binding energy of H2S-AgAu (-13.76 kcal mol-1) and H2S-CuAu (-20.86 kcal mol-1) by 42% and 35% with respect to H2S-Ag2 (-7.94 kcal mol-1) and H2S-Cu2 (-13.48 kcal mol-1). For trimers, the order of Ag(Cu)-S binding energies is as follows: MAu2 > M2Au > M3, where M ) Ag or Cu. It means that Eb increases with increasing the number of Au atoms in the binary alloy metal clusters. This observation can be attributed to the higher electron affinity of gold compared to Ag and Cu. In the binary alloy clusters, Au atom attracts electron density from Ag and Cu, and consequently these atoms behave as good acceptors for the lone pair electrons of sulfur. On the other hand, this electron-rich Au atom (compared with Au atoms in pure cluster) cannot serve as a good electron acceptor. 3.3. Natural Bond Orbital Analysis. NPA was calculated by the NBO method at the B3LYP level of theory. Charge distributions of the active sites are summarized in Table 6. In all of the complexes, the S atom carries a negative charge, and the metal atom is electropositive in most of the cases. In isolated dimer metal clusters, AuAg and AuCu, the charge of Au atom is -0.312 and -0.268, respectively. The high negative charge of Au in binary alloys indicates that this site can not behave as a good acceptor, while the Ag and Cu atoms with large positive charges are good accepting sites for the lone pair of sulfur. Table 6 also shows the difference of charges of the sulfur atom (∆qS ) qS(complex) - qS(isolated)) and metal clusters (∆qcluster



TABLE 3: Selected Features of H2S Molecules Complexed with Dimer Metal Clusters

a M is Au, Ag, and Cu atoms. b The length of M-S bonds, in Å. c Vibratinal frequency of M-S bonds in the complexed, in cm-1. d The binding energy Eb (including zero-point energy and BSSE correction), in kcal mol-1.

) qMn(complexed) - qMn(isolated)) before and after interaction. In all of the complexes ∆qS is positive and ∆qcluster is negative, and charge is transferred from the lone pair of S atoms to the coinage metal atoms. Comparison of the absolute values of ∆qS and ∆qcluster with binding energies, indicates that for the similar M-S bonds, these values increase by increasing the binding energies. A second-order perturbation theory analysis of the Fock matrix was also carried out to evaluate the donor-acceptor interaction on the NBO basis. In the Table 6, the perturbative stabilization energies ∆ECT for M-S bonds are listed. In these complexes, charge is transferred from the lone pair of sulfur to the σ* and n* orbitals of coinage metal atoms. ∆ECT values have the same trend as binding energies, for trimers (triangular structure), ∆ECT (H2S-Au3) > ∆ECT (H2S-Au2M) > ∆ECT (H2S-AuM2) and ∆ECT (H2S-MAu2) > ∆ECT (H2S-M2Au) > ∆ECT (H2S-M3) (M ) Ag and Cu). Therefore, as already known charge transfer is the source of interaction between clusters and H2S molecule.

3.4. Energy Decomposition Analysis. The M-S bonding situation in complexes has been investigated by means of EDA.38,39 In this method, the interaction energy between two fragments, ∆Eint, is split up into three physically meaningful components:

∆Eint ) ∆Eelstat + ∆EPauli + ∆Eorb

(1)

∆Eelstat gives the electrostatic interaction energy between the fragments, which is calculated with a frozen electron density distribution in the geometry of the complex. It can be considered as an estimate of the electrostatic contribution to the binding energy. ∆EPauli gives the repulsive four-electron interactions between occupied orbitals. In addition, the stabilizing orbital interaction term ∆Eorb is calculated in the final step of the analysis when the Kohn-Sham orbitals relax to their optimal

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TABLE 4: Selected Features of H2S Molecules Complexed with Trimer (Triangular) Metal Clusters


form. The orbital term ∆Eorb can be considered as an estimate of the covalent contributions to the attractive interactions. The latter term can be partitioned further into contributions by the orbitals that belong to different irreducible representations of the point group of the interacting system.

Table 7 collects the results of the EDA calculations at the B3LYP/TZ2P and BP86/TZ2P levels for the dimer metal complexes. The M-S interactions arise mainly from the repulsive term, ∆EPauli, which can be explained by the number of lone pair electrons of the metal atom. Figure 2 represents



TABLE 5: Selected Features of H2S Molecules Complexed with Trimer (Linear-like) Metal Clusters


Figure 1. Binding energy (in kcal mol-1) for trimer metal complexes, as a function of M.

the orbital correlation diagram for the donor-acceptor interactions between a H2S molecule and a Au2 metal cluster. In this figure, σ highest occupied molecular orbitals (HOMOs) of the dimer metal cluster, which are mainly Au lone-pair orbitals, have a relatively large extension toward the sulfur atom, and yield large Pauli repulsion.

Table 7 also shows the percentage values of ∆Eelstat and ∆Eorb for M-S bonds in the complexes; these values change very little for different metal clusters. The M-S bonds are more electrostatic in nature because the contribution of the electrostatic term (∆Eelstat) to the binding energy is always larger than that of the covalent term (∆Eorb). The BP86 calculations revealed

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TABLE 6: Calculated NPA Charges and Charge Transfer Feature Based on NBO Theorya complexes

charge transfer

∆ECTb

qMc

qS

∆qSd

∆qclustere

H2S-Au2 H2S-Ag2 H2S-AuAg H2S-AgAu H2S-Cu2 H2S-AuCu H2S-CuAu H2S-Au3

nS4fσ*Au1-Au2 nS4fσ*Ag1-Ag2 nS4fσ*Au1-Ag2 nS4fσ*Ag2-Au1 nS1fσ*Cu4-Cu5 nS3fσ*Au1-Cu2 nS3fσ*Au1-Cu2 R nS4fn*Au1 β nS4fn*Au1 R nS5fσ*Ag1-Au3 β nS5fσ*Au2-Au3 R nS4fσ*Ag1-Au3 β nS4fσ*Ag1-Au3 R nS5fσ*Cu1-Au2 β nS5fσ*Au2-Au3 R nS4fσ*Cu2-Au3 β nS4fσ*Cu2-Au3 R nS4fσ*Ag1-Ag3 β nS4fn*Ag1 R nS3fσ*Ag5-Ag6 β nS3fσ*Au1-Ag5 R nS5fn*Ag1 β nS5fn*Ag1 R nS4fσ*Cu1-Cu2 R nS4fσ*Cu1-Cu3 β nS4fn*Cu1 R nS5fσ*Cu1-Cu2 β nS5fn*Cu2 R nS5fn*Cu1 β nS5fn*Cu1

74.64 26.10 27.55 39.07 40.10 49.04 51.82 50.27 47.48 31.77 29.41 27.11 18.23 25.40 20.74 29.72 21.41 14.90 16.38 16.67 15.50 22.74 21.86 11.91 12.13 27.04 23.78 29.44 31.60 30.25

0.114 0.076 -0.189 0.300 0.136 -0.124 0.346 0.231

-0.177 -0.245 -0.217 -0.233 -0.238 -0.206 -0.233 -0.174

0.104 0.036 0.064 0.048 0.043 0.075 0.048 0.107

-0.155 -0.079 -0.106 -0.098 -0.086 -0.113 -0.102 -0.159

0.111

-0.184

0.097

-0.151

-0.029

-0.208

0.073

-0.125

0.042

-0.198

0.083

-0.132

0.018

-0.203

0.078

-0.122

0.228

-0.242

0.039

-0.085

0.339

-0.235

0.046

-0.098

0.454

-0.225

0.056

-0.115

0.277

-0.250

0.031

-0.077

0.361

-0.244

0.037

-0.086

0.430

-0.238

0.043

-0.099

H2S-Au2Ag H2S-AuAg2 H2S-Au2Cu H2S-AuCu2 H2S-Ag3 H2S-Ag2Au H2S-AgAu2 H2S-Cu3 H2S-Cu2Au H2S-CuAu2

a For triangular structure of trimers. b ∆ECT in kcal mol-1. c Charges, q, in |e-|. d ∆qS ) qS(complexed) - qS(isolated). e ∆qcluster ) qMn(complexed) qMn(isolated).

that ∆Eelstat accounts for 66.1% to 69.4% of the attractive interactions of the M-S bonds. The covalent character of the M-S bond increases in the order of Au > Cu > Ag. In pure metal complexes, one can observe that the absolute values of ∆EPauli, ∆Eelstat, and ∆Eorb for the gold complexes are much larger than the copper and silver homologues. Decomposition of ∆Eorb based on the orbitals belonging to different irreducible representations of the Cs point group shows that the contribution from the orbitals with A′ symmetry is much larger (>85%) than those with the A′′ symmetry. Figure 2 shows the two highest lying MOs (HOMO-12(17 A′) and HOMO13(16 A′)) with A′ symmetry, possessing main contribution to the stabilization energy of the M-S bond. These orbitals have a near σ symmetry in the metal cluster region, and come from the bonding combination of the σg orbital of Au2 with the 1b2 and 2a1 lone pair orbitals of H2S. Figure 2 also shows HOMO11(10A′′) of H2S-Au2 with πu symmetry character, which contributes to the ∆EA′′. 3.5. Atoms in Molecules Analysis. In Bader’s topological QTAIM analysis,50 the nature of bonding is analyzed in terms of the properties of electron density and its derivatives. The Laplacian of electron density at the BCP, ∇2F(r), is related to the bond interaction energy by local expression of virial theorem:41

p 2 ∇ F(r) ) 2G(r) + V(r) 4m

(2)

where G(r) is the electronic kinetic energy density, which is always positive and V(r) is the electronic potential energy density and must be always negative.51 The sign of ∇2F(r) at a

BCP is determined by which energy is in excess over the viral average of 2:1 of kinetics to potential energy. A negative ∇2F(r), shows the excess potential energy at BCP. It means that electronic charge is concentrated in the internuclear region and therefore shared by two nuclei. This is the case in all shared electron (covalent) interactions.52 A positive ∇2F(r) at the BCP reveals a local excess in kinetic energy and indicates depletion of electronic charge along the bond path. This is the case in a closed-shell electrostatic interaction. Apart from this, the electronic energy density, H(r), as H(r) ) G(r) +V(r), evaluated at a BCP, can be used to compare the kinetic and potential energy densities on an equal footing. For all interactions with significant sharing of electrons, H(r) is negative, and its absolute value reflects covalent character of the interaction. The QTAIM analysis was performed using the calculation results at the B3LYP density. The computed electron density (F(r)), Laplacian (∇2F(r)), and the electronic energy density (H(r)) at the BCPs of M-S bonds are presented in Table 8. Calculated values of electron density indicate that for the same bond (in different complexes), the order of electron densities is in line with the binding energies, which means that, as expected, a strong bond is usually associated with a high electron density at the BCP. A positive value of ∇2F(r) at the BCPs of various M-S bonds, listed in Table 8, indicates that this interaction should be classified as a closed-shell (electrostatic) type of bonding. On the other hand, negative values of H(r) for all the M-S bonds imply the covalent nature of the corresponding bonds. In dimer metal complexes, alloying Au2 by Ag and Cu decreases F(r) and the absolute values of H(r) at BCPs, as well as the binding energies, meaning that covalent character of the

TABLE 7: EDA of M-S Bonds for Dimer Metal Clusters (in kcal mol-1)



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Figure 2. Orbital correlation diagram for the donor-acceptor interactions between a H2S molecule and Au2 metal cluster.

TABLE 8: BCP Data (in au) from QTAIM Analysisa

4. Conclusion

Complexes

BCP

F(r)

∇2F(r)

H(r)

H2S-Au2 H2S-Ag2 H2S-AuAg H2S-AgAu H2S-Cu2 H2S-AuCu H2S-CuAu H2S-Au3 H2S-Au2Ag H2S-AuAg2 H2S-Au2Cu H2S-AuCu2 H2S-Ag3 H2S-Ag2Au H2S-AgAu2 H2S-Cu3 H2S-Cu2Au H2S-CuAu2

Au · · · S Ag · · · S Au · · · S Ag · · · S Cu · · · S Au · · · S Cu · · · S Au · · · S Au · · · S Au · · · S Au · · · S Au · · · S Ag · · · S Ag · · · S Ag · · · S Cu · · · S Cu · · · S Cu · · · S

0.069 0.041 0.041 0.060 0.056 0.056 0.082 0.068 0.067 0.062 0.063 0.080 0.048 0.060 0.063 0.079 0.081 0.083

0.340 0.164 0.160 0.153 0.276 0.244 0.204 0.366 0.328 0.288 0.288 0.176 0.192 0.150 0.157 0.200 0.203 0.204

-0.020 -0.007 -0.008 -0.013 -0.015 -0.013 -0.029 -0.018 -0.017 -0.014 -0.014 -0.022 -0.009 -0.013 -0.014 -0.026 -0.028 -0.030

a

For the triangular structure of trimers.

bond is decreased by alloying. However, in the case of Ag2 and Cu2, alloying by gold increases F(r) and the absolute values of H(r); therefore, for these clusters, alloying by Au strengthens the covalent interaction. In pure metal clusters, Ag-S bond has the lowest values of F(r) and H(r) compared with Au-S and Cu-S bonds, in agreement with the lowest binding energy of this bond. Considering the positive values of ∇2F(r) and negative values of H(r) at the BCP of M-S bonds indicated that these bonds must be considered as partially covalent and partially electrostatic, in agreement with EDA results.

In summary, we have studied pure and binary-alloy coinage metal clusters as well as their interactions with H2S, and investigated the strength and nature of M-S bonds (M ) Au, Ag, Cu) in different clusters. Geometrical structures, binding energies, and vibrational frequencies of the complexes were calculated using DFT (BP86, B3LYP, and CAM-B3LYP) and MP2 methods. CCSD(T) single-point calculations were also carried out to test the validity of the DFT results. In isolated metal clusters, partial charge transfer in the binary system results in electrostatic energy gain for the binary cluster (AumAgn and AumCun) over pure ones, which is responsible for the favorable formation of alloys. This fact is explained by comparing calculated dissociation energies of pure and binary alloy metal clusters. Alloying of gold clusters affects the attraction of Au toward H2S notably. In binary alloy clusters, Eb for Au-S is decreased by increasing the number of Ag and Cu atoms in the clusters. On the other hand, the attraction of Ag and Cu toward H2S is increased by substitution of Ag and Cu atoms with Au. In trimers, Eb (for Cu-S and Ag-S bonds) shows the order of MAu2 > M2Au > M3, where M ) Ag or Cu. NPA revealed a large negative charge of Au atom in binary alloys, therefore this atom cannot behave as a good acceptor; however, Ag and Cu atoms with positive charge worked as good accepting sites for the lone pair of sulfur. QTAIM analysis was performed to extract the BCP properties. It is shown that ∇2F(r) and H(r) for M-S bonds are positive and negative, respectively, revealing that these bonds are partially electrostatic and partially covalent. EDA decomposed the binding energy into three major components (∆EPauli, ∆Eelstat, and ∆Eorb). This calculation

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Nature and Strength of MâS Bonds (M = Au, Ag, and Cu) in Binary

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Nature and Strength of MâS Bonds (M = Au, Ag, and Cu) in Binary