Binding of Noble Metal Clusters with Rare Gas Atoms: Theoretical

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Binding of Noble Metal Clusters with Rare Gas Atoms: Theoretical Investigation Zahra Jamshidi, M. Fakhraei Far, and Ali Maghari J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp3106474 • Publication Date (Web): 03 Dec 2012 Downloaded from http://pubs.acs.org on December 3, 2012

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The Journal of Physical Chemistry

Binding of Noble Metal Clusters with Rare Gas Atoms: Theoretical Investigation

Zahra Jamshidi*,† Maryam Fakhraei Far‡ and Ali Maghari‡ † ‡

Chemistry and Chemical Engineering Research Center of Iran, P.O. Box 14335-186, Tehran, Iran Department of Chemistry, University of Tehran, Tehran, Iran

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Abstract Binding of noble metal clusters (Mn, M = Cu, Ag, and Au; n=2–4) with rare gas atoms (Rg = Kr, Xe, and Rn) has been investigated at the density functional (CAM-B3LYP) and ab-initio (MP2) levels of theory. The calculation shows significant affinity of neutral metal clusters for interaction with rare gas atoms. The binding energies indicate that gold clusters have the highest and silver clusters have the lowest affinity for interaction with rare gas atoms, and for the same metal clusters, there is a continuous increase in Eb from Kr to Rn. The M–Rg bonding mechanism have been 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–Rg bonds are found to be partially electrostatic and partially covalent. EDA results identify that these bonds have less than 40% covalent character and more than 60% electrostatic, and also NBO calculations predict amount of charge transfer from lone pair of rare gas to σ* and n*orbitals of metal cluster.

Keywords: DFT-D, EDA, Gold, Silver, and QTAIM.


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1. Introduction During the last few years, noble metal clusters have attracted great attention in basic science due to their unique physical and chemical properties.1,

2

These metal clusters play an

important role in several high technology fields such as nanoelectronic and nanomaterials. Determination of the structure, electronic, and optical properties of metal cluster, is still in the focus of active research. Recently, these properties for small noble metal clusters either in gas phase or embedded in rare gas matrices have been studied intensively.3-11 Rare gas matrix can provide an inert medium for preparation and characterization of small metal cluster. Rare gas layers were used in several experiments to reduce the interaction between metal clusters grown or deposited on surfaces. The noble metal clusters in neutral or charged forms show strong visible fluorescence and generally studied in the rare gas matrix that prevents photofragmentation. The geometric and electronic structure of small metal cluster seems to be hardly affected by the solvation of the rare gas atoms. In previous studies

12, 13

assumed the relatively weak van der Waals interactions between metal cluster and rare gas atoms that have nonperturbative effect on electronic structure of metal clusters. To find the effect of rare gas atoms on the electronic structure of noble metal cluster, it should be important, to investigate the interactions between noble metal clusters and different rare gas atoms. The interactions between noble metals and rare gas atoms have become of great interest in theoretical and experimental investigations due to their respective noble characters. In recent years many efforts has been expanded to prepare and characterize the systems in which a noble metal atom is bound to a noble gas atom.14-20 In 1995, Pyykkö21 predicted the existence of Au– Rg compounds based on theoretical studies on Au+–Rg (Rg = He – Xe) systems and concluded



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that Xe would form the strongest bond with closed-shell Au+ atom. Duncan22-24 and Breckenridge25-28 investigated the electronic spectroscopy of M–Rg complexes: Au–Rg (Rg = Ne, Ar, Kr and Xe), Ag–Rg (Rg = Ar, Kr, and Xe),22 and Cu–Kr23 by means of resonance enhanced multiphoton ionization (REMPI) spectroscopy. Gardner and co-workers also obtained the RCCSD(T) potential energy curves for the X2∑+ electronic states of the M–Rg (M = Cu – Au and Rg = He – Rn) complexes and derived the spectroscopic parameters and compared them with those determined experimentally.29 However, in previous investigations, there has been rarely attention on strength and nature of metal clusters interactions with rare gas atoms. Therefore, we present here a systematic study on the interactions of the coinage metal clusters (Mn, M = Cu, Ag, and Au; n=2–4) with rare gas atoms (Rg = Kr, Xe, and Rn). The nature of M–Rg 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-in-molecules (QTAIM), and energy decomposition analysis (EDA).

2. Method of Calculations Geometries of the coinage metal clusters (Mn, M = Cu, Ag, and Au; n=2–4) interacted with rare gas atoms (Rg = Kr, Xe, and Rn) were fully optimized using the density functional theory with CAM-B3LYP functional. Although for comparison the efficiency of the method the equilibrium bond lengths (rM–Xe), binding energies (Eb) and vibrational frequencies (ωM…Xe) for the M2–Xe complexes were calculated, by ab-initio (MP2 and CCSD(T)) and DFT (M06-2X and CAM-B3LYP) methods. DFT methods that employed during this work have been used recently for weak and noncovalent interactions; CAM-B3LYP, hybrid exchange-correlation functional presented by Yanai et al.30 who combine B3LYP at short-range with an increasing amount of


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exact HF exchange at long-range and the M06-2X “Minnesota 2006 functional with double Hartree-Fock exchange” developed by Zhao and Truhlar.31,

32

The pseudopotential-based

augmented correlation-consistent basis sets, aug-cc-pVDZ-PP,33 based on the small core relativistic pseudopotentials (PPs) of Figgen et al.34 has been used for metal and rare gas atoms. In these basis sets, 19 outermost electrons of metal are explicitly described by the (9s, 8p, 7d, 2f) / [5s, 5p, 4d, 2f] basis, and 26 outermost electrons of rare gas are explicitly described by the (9s, 8p, 8d) / [5s, 4p, 3d] basis for Kr and (9s, 7p, 7d) / [5s, 4p, 3d] basis for Xe and Rn atoms. These calculations have been done using Gaussian 03 and 09 suite of programs.35 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 Mn–Rg is defined as the absolute value of the energy difference Eb = EMn-Rg – (EMn + ERg), and all the binding energies are corrected for the basis set superposition error (BSSE).36, 37 To improve the calculated binding energies, MP2 single-point calculations at the CAM-B3LYP optimized structures have been carried out with the same basis set. To reveal the nature of bonds, the NBO, QTAIM, and EDA analyses were carried out on the CAM-B3LYP optimized structures. Within the NBO analysis introduced by Weinhold and coworkers,38 in this work we paid particular attention to natural population analysis (NPA) charges39 and charge transfers. The EDA was done using the program package ADF (2010.01),4042

which is based on the EDA method of Morokuma43 and the ETS partitioning scheme of

Ziegler and Rauk.44 The bonding analysis was carried out at the B3LYP/TZ2P and B3LYPD/TZ2P levels of theory, while scalar relativistic effects have been considered using the zeroorder regular approximation (ZORA).45-47 In addition, the electron density, Laplacian,

, and its

, at bond critical points (BCPs) were computed based on Bader’s QTAIM,48 5 ACS Paragon Plus Environment


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using AIM200049 program. The NBO and QTAIM analysis were carried out at CAM-B3LYP level of theory.

3. Results and Discussion 3.1. Structures and Stability. Physical and chemical properties of coinage metal clusters depend strongly on cluster size; small clusters are more reactive than bulk materials.50 Recently many efforts has been expanded to investigate the structure and stability of small metal clusters.51-56 Pakiari and Jamshidi

57

performed ab initio (MP2 and CCSD(T)) and DFT (BP86,

B3LYP, and CAM-B3LYP) calculations for M2 (M=Cu, Ag, and Au) dimers, and compared the values with available experimental ones. They obtained that CAM-B3LYP method has a good agreement with CCSD(T) and experimental results (difference of CAM-B3LYP and CCSD(T) bond lengths and dissociation energies are less than 0.007 Å and 3.0 kcal/mol, respectively). For trimer and tetramer of coinage metal clusters determining minimum-energy structures is difficult due to low-lying isomers. The trimer coinage metal clusters have two different isomers, namely triangular (near D3h) and linear-like (C2V) structures. CAM-B3LYP calculations obtain these two isomers for gold and silver trimers with energy difference less than 1.1kcal/mol. The angles (∠ M-M-M) for triangular structure of gold and silver clusters are 67.1°, 70.6°, and for linear-like structures are 129.0°, 107.8°, respectively. These values are in agreement with the results reported in ref 58. For copper cluster only triangular structure has been obtained with angle of 68.4° (in agreement with Shen and BelBruno investigations59). For M4 clusters, we have found the minimum-energy structure to be diamond-shaped with D2h symmetry.58 There is also another isomer (which has a “dangling” M atom bonded to a M3 group) with C2V symmetry which is 1.0 kcal/mol lower in energy for gold and 2.8 and 6.2 kcal/mol higher for silver and


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copper, respectively. During these studied the triangular and diamond-shaped structures were chosen as model for trimer and tetramer clusters. In this section, the interactions of neutral metal cluster (Mn; M = Cu, Ag, and Au, and n = 2–4) with rare gas atoms have been investigated at the MP2/aug-cc-pVDZ-PP//CAMB3LYP/aug-cc-pVDZ-PP level of theory. In order to test the performance of the computational methods, the CCSD(T) optimization (with the same basis set) for M2–Xe (M = Cu, Ag, and Au) complexes has been performed and compared with the MP2 and DFT (CAM-B3LYP and M062X) results. The values in Table 1 and Figure 1 show that for the Au2–Xe, Ag2–Xe, and Cu2–Xe complex, CAM-B3LYP bond lengths (rM–Xe) [2.868, 3.130, 2.761 Å, respectively] are in good agreement with CCSD(T) values [2.810, 3.080, 2.728Å, respectively], and MP2 (and M06-2X) values [2.730 (3.025), 2.991 (3.216), 2.620 (2.932) Å, respectively] are in reasonable agreement with CCSD(T). MP2 bond lengths are smaller than those of CCSD(T) (by less than 0.1 Å). The CCSD(T) binding energies (Eb) for Au2–Xe, Ag2–Xe, and Cu2–Xe complexes are 4.66, -0.96, and -1.14 kcal/mol; the MP2 values are -7.22, -1.90, and -2.51 kcal/mol; the CAMB3LYP values are -5.52, -1.68, and -3.05 kcal/mol; the M06-2X values are -5.56, -2.86, and 3.41 kcal/mol. The Eb (MP2), overestimated comparing with Eb (CCSD(T)), however, they have the same trend as CCSD(T) values (Eb (MP2) and Eb (CCSD(T) decrease about 16% and 24% by going from Cu2–Xe to Ag2–Xe and increase about 74% and 79% by going from Ag2–Xe to Au2– Xe, respectively). Therefore, for Mn–Rg complexes Eb obtained based on MP2 method, on the optimized CAM-B3LYP structures. To determine the minimum orientation of metal cluster rare gas complexes, the potential energy curves for different orientations of Aun–Xe complexes has been obtained (based on



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CAM-B3LYP/aug-cc-pVDZ-PP) and reported in supporting information (Figure S1). For all of the complexes, the Rg atom is bonded to a single metal atom. Geometrical parameters and binding energies, for most stable Mn–Rg, are collected in Table 2 and Figure 2. For all of the complexes, the geometries of the metal clusters do not change significantly after interaction. Clearly in Table 2, the hardly any deviation observed for M–M bond lengths of cluster in the complexes from isolated ones. For M2-Rg complexes the M–M bond lengths increase less than 0.006 Å and for M3-Rg and M4-Rg increase less than 0.025 Å. For the same metal cluster, the absolute value of Eb increases through Kr to Rn (in agreement with previous studies for M–Rg complexes).29 In tetramer metal cluster, Eb (MP2) for Au4–Rn (-11.46 kcal/mol) is about 13% higher than Au4–Xe (-9.96 kcal/mol), and Au4–Xe is about 42% higher than Au4–Kr (-5.78 kcal/mol). Increasing Eb through Mn– Kr to Mn– Rn, can be explained in term of the increase in polarizability of the Rg atoms by increasing the atomic number (Kr (17.07 a.u.), Xe (27.81 a.u.), and Rn (34.33 a.u.)).60 Obviously, for the different metals interacted with the same rare gas atoms, the affinity of the silver cluster toward Rg atoms 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 cluster. For example, for M4–Xe complexes the absolute values of Eb have the order of Eb

Au4–Xe

(9.96

kcal/mol) > Eb Cu4–Xe (6.06 kcal/mol) > Eb Ag4–Xe (4.55 kcal/mol). The difference between the binding

energies can be explained by relativistic effects and also in the case of Au, lanthanide contraction that tends to contract and stabilize the s and p shells and expand and destabilize the d and f shells.61 The relativistic bond length contraction also exists and able to pull in the Aun–Rg bond lengths near similar or less than those of the corresponding Agn–Rg bonds.


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Clearly by changing the size of metal cluster from dimer to tetramer (as Figure 2 shows), the absolute values of binding energy increase and the bond lengths decrease and this trend is the same for different metals and Rg atoms. 3.2. Natural Bond Orbital Analysis. NPA was calculated by the NBO method at the CAM-B3LYP level of theory. Charge distributions of the active sites are summarized (for selected structure) in Table 3. In all of the complexes, the Rg atom carries a positive charge, and the interacting metal atom is electronegative. The positive charge of Rg atoms in the same metal complexes increases through Kr to Rn. As an example, for Au2–Rg complexes; qKr(0.068) < qXe (0.128) < qRn (0.146). For the different metal complexes with same rare gas atom, qRg have the order of

. Table 3 also shows, the difference of charges of metal

clusters (∆qMn = qMn(complexed) - qMn(isolated)) before and after interaction. In all of the complexes ∆qMn is negative, and this indicates a substantial amount of charge transfer from Rg to Mn cluster. The Wiberg bond indices62 are helpful in evaluating the bond orders. The values of Wiberg bond indices for M–Rg bonds (bM-Rg) have been obtained and shown in Table 3. For the selected complexes the bM-Rg values have the same order as binding energies and bond lengths; bAu–Rg > bCu–Rg > bAg–Rg and bM–Rn > bM–Xe > bM–Kr. 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 3, the perturbative stabilization energies ΔECT for M–Rg bonds are listed. In these complexes, charge is transferred from the lone pair of Rg atoms to the σ* and n* orbitals of coinage metal atoms. ΔECT values have the same trend as binding energies, for gold dimer, (21.8 kcal/mol) >

(22.0 kcal/mol) >

(12.4 kcal/mol). Therefore, as already known charge transfer can be 9 ACS Paragon Plus Environment


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the source of interaction between clusters and Rg atoms. On the other hands, the increase of M– M bond lengths (Table 2) conforming the electron donation from lone pair of rare gas to σ* orbital of M2. 3.3. Energy Decomposition Analysis. The Mn–Rg interactions have been considered by means of energy decomposition analysis (EDA).43, between two fragments,

44

In this method, the interaction energy

, is split up into three and also four physical meaningful

components: (1) 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.

gives

the repulsive four-electron interactions between occupied orbitals. The stabilizing orbital interaction term,

, is calculated in the final step of the analysis when the Kohn-Sham

orbitals relax to their optimal form. The associated orbital term

accounts for charge

transfer, polarization, and electron-pair bonding. In addition,

has been calculated when the dispersion corrected density functional

has been used, this term basically is the difference between total energy based on DFT-D and DFT methods.63 Therefore, by going from DFT to DFT-D methods the and

,

,

values remain unchanged and the dispersion correction appears as an extra term. The result of EDA calculations for Au2–Xe and Au4–Xe complexes by different DFT

functionals, including recent dispersion corrected Grimme’s density functional for heavy


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elements (DFT-D and DFT-D3)64 and some common and well-established order ones are collected in Table S1 and compared with super-molecular interaction energies. According to these values; B3LYP-D for dimer and B3LYP for tetramer have been selected for EDA calculations. Table 4 shows the energy decomposition for the closed-shell M2–Rg and M4–Rg complexes the interaction energies ( and

and also

) that come from the summation of

,

(for dimer complexes) are in the same order as Eb; . The absolute values of

and ,

,

, and

for the gold complexes are much larger than those of the copper and

silver homologues. These values for the same metal complexes with different Rg atoms do not change significantly (less than 3%). ΔEelstat has been used to estimate the strength of the electrostatic or ionic bonding and ΔEorb for the covalent bonding. As one can find in Table 4, the Mn –Rg interactions are little more electrostatic or ionic in nature, because the contribution of the electrostatic term into attractive term is always larger (

than that of the orbital (

) term.

The ionic character of the bonds can be interpreted by means of NPA charges, as you can find in Table 3, the two fragments have opposite charge. The covalent character of the M–Rg bond increases in the order of Au > Cu > Ag. As the dispersion term is the difference between interaction energy of DFT and DFT-D method, the contribution of this term to interaction energies is differed between 15% to 54% for M2-Rg Complexes. Decomposition of

based on the orbitals belonging to different irreducible

representations has been considered for Au2–Xe and Au4–Xe complexes. For Au2–Xe complex 11 ACS Paragon Plus Environment


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with C point group contribution from the orbitals with σ, π, φ, and δ symmetry are almost 80.9, 18.9, 0.2, and 0.0%, respectively. Therefore, the orbital with σ symmetry has the highest contribution to the orbital interaction, and Figure 3 shows the highest lying MOs HOMO-13 (35 σ), possessing main contribution to the stabilization energy of the Au–Xe bond. This orbital comes from the bonding combination of the σg orbital of Au2 with the pz lone pair of Xe with contributions almost 30% and 64%, respectively. Figure 3 also shows HOMO-11 (20πy) and HOMO-12 (20πx) with π symmetry, which come from the 90% lone pair of Xe (px and py) and 7% πu orbital of Au2. For Au4–Xe complexes with C2v point group contribution from the orbitals with a1, a2, b1, and b2 symmetry are about 72.1, 2.4, 14.5, and 11.0%, respectively. Figure 4 shows the highest lying MOs, HOMO-24 (66 a1) with σ symmetry, possessing main contribution to the stabilization energy of the Au–Xe bond. This orbital comes from the bonding combination of the Ag orbital of Au4 and the pz lone pair of Xe with contributions almost 46% and 48%, respectively. Figure 4 also shows HOMO-24 (45 b1) and HOMO-23 (33 b2) with π symmetry, which come from the 17% px and 83% py lone pair of Xe, and 81% b3u and 13% b2u orbitals of Au4, respectively. 3.4. Atoms in Molecules Analysis. In Bader’s topological QTAIM analysis,65 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, 2 (r) , is related to the bond interaction energy by local expression of virial theorem:48 (2)

1 2   (r )  2G(r )  V (r ) 4

where G(r) is the electronic kinetic energy density, which is always positive and V(r) is the


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electronic potential energy density and must be always negative.66 The sign of 2 (r) at a BCP is determined by which energy is in excess over the viral average of 2:1 of kinetics to potential energy. In covalent interactions, the charge density at the BCP is tightly bound and compressed over its average distribution. Therefore for covalent bonds, a negative value of 2 (r) is expected, because V(r) dominates in equation 2. On the other hand, in electrostatic interactions the electronic charge is expanded relative to its average distribution. The kinetic energy density is dominant and 2 (r) is positive at the BCP. 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 CAM-B3LYP density. The computed electron density (  (r ) ), Laplacian ( 2 (r) ), and the electronic energy density (H(r)) at the BCPs of selected M–Rg bonds are presented in Table 5. 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 2 (r) at the BCPs of various M–Rg bonds, listed in Table 5, 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–Rg bonds imply the covalent nature of the corresponding bonds. Comparing the values of  (r ) and H(r) for M–Xe have been shown that Ag–Xe bond has the lowest values of  (r ) and H(r) compared with Au–Xe and Cu–Xe bonds, in agreement with



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the lowest binding energy of this bond. Considering the positive values of 2 (r) and negative values of H(r) at the BCP of M–Rg bonds indicated that these bonds must be considered as partially covalent and partially electrostatic, in agreement with EDA results.

4. Conclusion In summary, we have studied the interaction of noble metal clusters (Mn, M = Cu, Ag, and Au; n=2–4) with rare gas atoms (Rg = Kr, Xe, and Rn) to investigate the nature of M–Rg bonds. Geometrical structures, binding energies, and vibrational frequencies of the complexes were calculated at the MP2/aug-cc-pVDZ-PP//CAM-B3LYP/aug-cc-pVDZ-PP level of theory. In all of the complexes, the geometries of the metal clusters do not change significantly after interaction. The values of binding energies for the same metal clusters show the continuous increase from Kr to Rn, and for the same rare gas atoms interacted with different metal clusters, Eb increases in order Au > Cu > Ag. NBO analysis points to the amount of stabilization energies during the charge transfer from the rare gas atom to the metal cluster, and NPA revealed the negative charge of metal cluster after interaction with rare gas atoms (|∆qMn| > 0.1). The QTAIM analysis, based on the bond critical point properties, revealed that M–Rg bonds had both electrostatic ( 2 (r )  0 ) and covalent (H(r) < 0) characters, simultaneously. Decomposing of binding energy into its components (ΔEPauli, ΔEelstat, ΔEorb, and ΔEdisp), show the large Pauli repulsion contribution to the M–Rg bonds that due to the lone pair electrons of metal and rare gas atoms. The attractive interaction of these bonds comes from ΔEorb (< 40%) and ΔEelstat (> 60%), and also decomposition of orbital interaction shows that orbital with σ symmetry possess the main contribution to ΔEorb. These results are in confirmation with QTAIM and NBO calculations. 14 ACS Paragon Plus Environment

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Author Information Corresponding Author *Email: [email protected], [email protected] Acknowledgments The authors are grateful to thank the reviewers for the valuable comments. This investigation was supported by Iran National Science Foundation. We appreciate the computing resources of the Department of Chemistry University of Basel.

Supporting Information Full citation of ref 35. Figure S1: Potential energy curves calculated at the CAM-B3LYP/aug-ccpVDZ-PP level of theory for different orientations of Au2–Xe, Au3–Xe, and Au4–Xe complexes. Table S1: EDA calculations for Au2–Xe and Au4–Xe complexes by different DFT methods. This information is available free of charge via the Internet at http://pubs.acs.org.

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Table 1. Comparison Calculated Binding Energies (in kcal/mol), Bond Lengths (in Å), and Vibrational Frequencies (in cm-1) for M2 – Xe Complexes.

Complex Cu2–Xe

Ag2–Xe

Au2–Xe

Method

r(M-Rg)

ω(M-Rg)

Eb

CCSD(T) MP2 CAM-B3LYP M06-2X

2.728 2.620 2.761 2.932

76.7 92.3 71.9 48.5

-1.14 -2.51 -3.05 -3.41


3.080 2.991 3.130 3.216

50.7 39.1 45.0 45.5

-0.96 -2.17 -1.90 -2.86


2.810 2.730 2.868 3.025

81.1 80.0 75.2 62.8

-4.66 -7.22 -5.52 -5.56


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Table 2. Selected Features of Rare Gas Atoms Complexed with Metal Clusters

r(M-Rg)a

∆rM-Mb

ω(M-Rg)c

Cu2-Kr Cu2-Xe Cu2-Rn Ag2-Kr Ag2-Xe Ag2-Rn Au2-Kr Au2-Xe Au2-Rn

2.678 2.761 2.840 3.125 3.130 3.155 2.838 2.868 2.928

0.002 0.005 0.006 0.000 0.000 0.001 0.004 0.002 0.001

65.7 71.9 63.2 39.7 45.0 43.1 69.1 75.2 65.1

-1.86 -3.05 -3.51 -0.89 -1.68 -2.22 -3.10 -5.52 -6.44

-1.27 -2.14 -3.09 -0.80 -2.12 -2.33 -3.61 -7.23 -8.45


2.581 2.676 2.756 2.983 3.025 3.075 2.824 2.849 2.910

0.012 0.018 0.018 0.007 0.011 0.013 0.014 0.022 0.024

84.2 83.7 72.1 53.0 53.7 49.8 68.1 72.2 63.8

-3.60 -5.35 -5.75 -1.66 -2.89 -3.49 -3.47 -6.40 -7.44

-3.52 -6.00 -6.52 -2.29 -4.04 -4.83 -4.88 -9.30 -10.75


2.629 2.714 2.791 2.990 3.027 3.075 2.888 2.884 2.940

0.021 0.024 0.025 0.011 0.016 0.018 0.004 0.020 0.023

71.9 71.3 62.1 49.4 50.3 44.7 47.2 32.4 46.2

-3.09 -4.78 -5.18 -1.80 -3.06 -3.63 -2.65 -5.29 -6.32

-3.41 -6.06 -6.63 -2.64 -4.55 -5.38 -5.78 -9.96 -11.46

Mn– Rg

d

a

The length of M-Rg bonds, in Å. bThe difference between bond lengths of M-M in the complexed and isolated fragment, in Å. cVibratinal frequency of M-Rg bonds, in cm-1. dThe binding energy Eb (including BSSE correction), in kcal/mol.



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Table 3. Calculated NPA Charges and Charge Transfer Feature Based on NBO Theory

Complex Cu2-Xe Ag2-Xe Au2-Kr Au2-Xe Au2-Rn Au3-Xe Au4-Xe a

Charge Transfer nKr nKr nXe nXe nKr nKr nXe nXe nRn nRn nXe nXe nXe nXe b

*

n Cu(1) * σ Cu(1)-Cu(2) * n Ag(1) * σ Ag(1)-Ag(2) * n Au(1) * σ Au(1)-Au(2) * n Au(1) * σ Ag(1)-Ag(2) * n Au(1) * σ Au(1)-Au(2) * n Au(1) * n Au(1)

∆ECTa 29.70 11.15 13.16 6.51 10.55 9.01 20.94 11.37 21.07 11.42 25.89 25.43 76.98 25.15

Au(1) * n Au(1) c

bM-Rgb

qRgc

qM

∆qMnd

0.186

0.110

-0.083

-0.110

0.105

0.066

-0.062

-0.066

0.120

0.077

-0.046

-0.077

0.211

0.135

-0.083

-0.135

0.227

0.150

-0.094

-0.150

0.292

0.169

-0.040

-0.169

0.333

0.190

-0.134

-0.190

d

ΔECT in kcal/mol. Wiberg bond index. Charges, q, in |e-|. ΔqMn=qMn(complexed) – qMn(isolated).


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Table 4. The EDA of M– Rg Bond forM2 – Rg and M4 – Rg Complexes. (in kcal/mol)

Complex

∆EPauli

∆Eelstat

∆Eorb

∆Edisp

∆Eint

Eb

Au2-Kr

25.26

-16.97

-10.71

-0.63

-3.05

-3.10

Au2-Xe

43.23

-30.28

-17.58

-0.79

-5.42

-5.52

Au2-Rn

45.82

-33.38

-18.37

-1.04

-6.97

-6.44

Cu2-Xe

32.15

-23.08

-11.47

-0.47

-2.87

-3.05

Ag2-Xe

19.39

-13.79

-6.27

-0.79

-1.46

-1.68

Au4-Kr

19.40

-12.97

-8.64

-2.21

-2.65

Au4-Xe

35.91

-25.29

-15.45

-4.83

-5.29

Au4-Rn

38.40

-28.03

-16.44

-6.07

-6.32

Cu4-Xe

28.61

-20.50

-12.35

-4.24

-4.78

Ag4-Xe

17.45

-12.44

-7.22

-2.23

-3.06



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Table 5. Bond Critical Point Data (in au) from QTAIM Analysis.

Complex

BCP

ρ(r)

Au2–Kr Au2–Xe

Au–Kr

0.032

0.011

ρ(r)

-0.001

Au–Xe

0.041

0.111

-0.005

Au2–Rn

Au–Rn

0.040

0.098

-0.005

Cu2–Xe Ag2–Xe

Cu–Xe

0.033

0.101

-0.003

Ag–Xe

0.021

0.061

0.000

Au3–Xe Au4–Xe

Au–Xe

0.043

0.115

-0.005

Au–Xe

0.040

0.107

-0.005


H(r)

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Cu2-Xe

Au2-Xe Ag2-Xe Cu2-Xe

Eb (kcal/mol)

Au2-Xe

-7.22 -5.52 -4.66

-2.51

-3.05

-1.14 -2.17

-0.96 CCSD(T)

rM-Xe (Å)

Ag2-Xe

MP2

-5.56

2.991 2.868

2.810

-3.41

3.216 3.025 2.932

2.730 2.728

-2.86 -1.90 CAM-B3LYP

3.130

3.080

M06-2X

CCSD(T)

2.761 2.620 MP2

CAM-B3LYP

M06-2X

Figure1. Plot of computed dissociation energies and bond lengths for M2–Xe (M = Cu, Ag, and Au) complexes with various theoretical methods.



-12

3.2

-10

Aun- Xe

-8 -6

Cun- Xe

-4

Agn- Xe

3.1

rM _ Xe (Å)

Eb (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

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3

Agn- Xe

2.9

Aun- Xe

2.8 Cun- Xe

2.7

-2

2.6

0 M2

M3

M2

M4

M3

M4

Figure 2. Binding energy (kcal/mol) and M – Xe bond length (Å) curves as a function of different size Mn clusters (M = Cu, Ag, and Au; n = 2–4).


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Figure 3. Orbital correlation diagram for the interaction between a Au2 metal cluster and Xe atom.



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Figure 4. Orbital correlation diagram for the interaction between a Au4 metal cluster and Xe atom.


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-12 -10

Eb (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Aun- Xe

-8 Cun- Xe

-6

Agn- Xe

-4 -2 0 M2

M3

M4

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