Article pubs.acs.org/JPCA
Dual Bonding between H2O/H2S and AgCl/CuCl: Cu/Ag Bond, Sister Bond to Au Bond Guiqiu Zhang,* Xingjuan Zhao, and Dezhan Chen College of Chemistry, Chemical Engineering and Materials Science, Shandong Normal University, Wenhua East Road 88, Jinan, Shandong 250014, P. R. China S Supporting Information *
ABSTRACT: Recently, Legon et al. reported the first generation and characterization of H2O/H2S···AgCl complexes by rotational spectroscopy and proposed whether there is a silver bond analogous to the more familiar hydrogen and halogen bonds. In this study, a theoretical investigation was performed to answer this question and to deepen the nature of intermolecular interactions for H2O/H2S···M−Cl (M = Cu, Ag, and Au) complexes. NBO analyses reveal that two types of delocalization interactions coexist in these complexes. Apart from the expected σ-donation interaction, the hyperconjugation interaction between H2O/H2S and M−Cl also takes part in the bonding. On the basis of such a dual-bonding mechanism, one class of bond, termed Cu/Ag bond, was defined in this study. In addition, the topological properties at a bond critical point, binding energies, and stretching frequency shifts studied here support that Cu/Ag bond is a sister bond to Au bond put forward previously by Sadlej et al. The Cu/Ag/Au bond is partially covalent and partially electrostatic in nature. Finally, the dual-bonding mechanism of Cu/Ag/Au bond was further discussed. This dual-bonding scheme may be considered a new synergistic bonding model for coordination compounds. these bound adducts,15 although they used to be classified as van der Waals (vdW) complexes. In short, more and more evidence from many theoretical and experimental lines provides support for the general conclusion that the hyperconjugation concept can explain satisfactorily the formation of numerous intermolecular interactions. Recently, Legon et al.16 reported the first generation and characterization of two simple compounds formed by the interaction of either H2O or H2S with AgCl, namely, H2O··· AgCl and H2S···AgCl complexes. The heavy atoms are collinear, while the local C2 axis of the water molecule intersects the axis defined by the heavy atoms at a different angle ϕ. The geometries of H2O···AgCl and H2S···AgCl are isomorphic with those of their hydrogen- and halogen-bonded counterparts. They proposed whether there is a silver bond analogous to the more familiar hydrogen and halogen bonds. Soon after, their group reported the generation and characterization of analogous CuCl-containing complexes. They observed pure the rotational spectra of the ground vibrational state of H2O···CuCl17 and H2S···CuCl.18 They also found that the collinear geometries of the corresponding complexes H2O··· CuCl and H2S···CuCl are similar to those of H2Y···HCl and H2Y···ClF (Y = O or S). This naturally raises one question:
1. INTRODUCTION Intermolecular interactions have been an active field of research in chemistry and physics owing to their importance in a multitude of chemical and biological phenomena. Among intermolecular interactions, hydrogen bond A−H···D (A−H denotes the electron acceptor and D denotes the electron donor)1−5 was carefully analyzed. It shows directional preference; that is, its A−H···D angle is usually 180° or close to 180°. According to one latest definition4 proposed by Weinhold and Klein, hydrogen bond commonly originates in the nD → σ*A−H donor−acceptor interaction between the lone pair nD of the Lewis base and the antibond σ*A−H of the Lewis acid. Another intermolecular interaction, which has been a hot topic of research in the recent years, is halogen bond.6−8 Halogen bond prefers linear or close-to-linear A−X···D interactions, where X represents halogen atom. It was found that the charge transfer via hyperconjugation interaction plays an important role in the formation of halogen bonds.9 Two recent studies10,11 about chalcogen and pnicogen bonds extended intermolecular interactions. The A−P···D angle of the pnicogen bond prefers 180°. A possible bonding mechanism for the A−P···D bonding interaction is the hyperconjugation between the lone pair of the electron-donor atom and the antibond orbital σ*A−P. Also, there are several relevant theoretical studies12−14 about He···MX, Ne···MX, and Ar···MX (M = Cu, Ag, and Au; X = F and Cl) complexes. The NBO analyses revealed that hyperconjugation is important in © 2013 American Chemical Society
Received: August 7, 2013 Revised: September 25, 2013 Published: September 26, 2013 10944
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3. RESULTS AND DISCUSSION 3.1. Geometry, Frequency, and Binding Energy. The optimized geometry structures of all the MCl-containing (M = Cu, Ag, and Au) complexes are of Cs symmetry with a linear O(S)···Cu(Ag/Au)−Cl bridge shown in Figure 1. In the case of
does the hyperconjugation effect exist in the CuCl/AgClcontaining complexes? Despite the similarities to the hydrogenand halogen-bonded complexes in geometry, the measured centrifugal distortion constants and nuclear quadruple coupling constants imply much stronger binding in these CuCl/AgClcontaining species. Prior to this work, computational evidence about Au bond was first given by Sadlej et al.19 in their paper “Strong interactions through the X···Au−Y bridge: the Au bond?” Note that the term Au bond was introduced and was used by them for describing the X···Au−Y interaction. The X··· Au−Y bridge is almost collinear. Although they are structurally similar to the analogous H-bonded complexes,19,20 HF···Au− OH and H2O···Au−OH have significantly large dissociation energies relative to their analogous hydrogen-bonded complexes. In light of the similar electronic structures between the Cu, Ag, and Au atom, this naturally raises the second question: is the Cu/Ag bond a sister bond to Au bond? In this article, we want to find out (1) whether the hyperconjugation effect exists in the CuCl/AgCl-containing complexes and (2) whether there is a Cu/Ag bond analogous to the more familiar hydrogen and halogen bonds or analogous to Au bond. A theoretical study on the interactions of H2O··· AgCl, H2S···AgCl, H2O···CuCl, and H2S···CuCl was performed. For comparison, hydrogen-, halogen-, and Au-bonded analogues, H2O···HCl, H2S···HCl, H2O···ClF, H2S···ClF, H2O··· AuCl, and H2S···AuCl were added to this study. We tried, in this article, to study the bonding mechanism of the intermolecular interactions by using natural bond orbital (NBO) method. At last, we analyzed the topological properties at the bond critical point of hydrogen/halogen and Cu/Ag/Au bonds.
Figure 1. Optimized geometry of all the MCl-containing (M = Cu, Ag, and Au) complexes.
analogous hydrogen- and halogen-bonded complexes, both the O/S···H−Cl bridge and the O/S···F−Cl bridge are found to be linear. From Figure 1, we can see that the halogen, hydrogen, and metal atom bridge approaches along the direction in which it is hoped to find a lone pair of the O/S atom of the Lewis base, defining in this way, the angular geometry. Moreover, in all of the complexes, the oxygen and sulfur atoms are pyramidal, and the axis of the CuCl/AgCl/HCl/HF molecule lies along the axis of one nonbonding electron pair on the oxygen or the sulfur atom in each case. The local C2 axis of the water molecule intersects the axis defined by the heavy atoms at an angle ϕ. Also, the calculated and experimental values of the defined ϕ are listed in the Table 1. From this table, we can see the theoretical calculation results almost agree well with the experiment results. It is clear that the geometries of the studied Cu/Ag/Au-bonded complexes are isomorphic with those of their hydrogen- and halogen-bonded complexes. Here, the analogy between hydrogen/halogen- and Cu/Ag/Au-bonded systems appears to end. Yet, more similarities between Au bond and Cu/Ag bond will be discussed below. First, the stretching frequency analysis reveals the blueshifting characteristic of the Au bond. In the case of the CuCl/ AgCl-containing complexes, our results show a large increase of the Cu/Ag−Cl stretching frequency upon the interaction with the electron donors. The blue-shifting characteristic of the Cu/ Ag−Cl bond is similar to that of the corresponding bond in Aubonded complexes,29 but both the hydrogen- and halogenbonded complexes perform different extent of red shifts. Although the Cu/Ag-bonded complexes are structurally similar to its corresponding hydrogen- and halogen-bonded complexes, they offer quite a different pattern of changes. For example, the corresponding stretching vibration of M−Cl bond in the Mbonded complexes displays similar frequency shifts (blue shifts). Here, there seems to be a contradiction between the blue shift and the hyperconjugation effect existed in Cu/Ag/Au bonding. In the NBO section, the reason will be discussed in detail. Second, Table 2 shows the calculated counterpoise-corrected interaction energies (Ecp) of the Cu/Ag/Au-bonded complexes H2O···CuCl, H2O···AgCl, H2O···AuCl, H2S···CuCl, H2S··· AgCl, and H2S···AuCl are 15.81, 10.38, 16.12, 11.88, 9.03, and 21.64 kcal/mol, respectively. They are much more strongly bound than the hydrogen- and halogen-bonded complexes. The interaction energies of the Cu/Ag/Au-bonded complexes are well above the characteristic values for what is called the van der Waals complexes and approach the observed values for strong hydrogen bonds in ionic hydrogen-bonded species.19 According to the intermolecular stretching force constant kσ, H2O···CuCl, H2O···AgCl, H2O···AuCl, H2S···CuCl, H2S···
2. COMPUTATIONAL DETAILS The present study is not aimed at the highly accurate determination of the structure and energy of the studied complexes. The main objective of our calculations is rather to provide firm theoretical evidence for strong interactions in the CuCl/AgCl-containing complexes and to compare their features with the analogous X···H−Y structures. For this reason, we employed routine, well-established, and inexpensive computational methods. All the complexes were fully optimized and characterized with the Gaussian09 program package21 at second-order Møller−Plesset (MP2) level of theory.22 The augcc-pVDZ-PP basis set23,24 was used for Cu, Ag, and Au atoms, whereas the aug-cc-pVTZ basis set was adopted for other atoms. Harmonic frequency calculations were then performed at the MP2 level to identify that these structures are local minima on the energy surfaces. We corrected the interaction energies for the basis set superposition error (BSSE) by using the Boys−Bernardi counterpoise scheme.25 We analyzed the topology properties of hydrogen/halogen and Cu/Ag/Au bonds by using Bader’s “atoms in molecules” (AIM) theory.26 Identification and quantification of the closed-shell and sharedshell characteristics of interactions was analyzed in the present work. AIM analyses were performed with the software Multiwfn27 in our work. Here, the natural bond orbital (NBO)28 method implemented within the Gaussion09 set of codes was applied. The MP2-optimized structures and the Hartree−Fock (HF) densities were used during the NBO analyses. 10945
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Table 1. Optimized Geometries (Angstroms and Degrees) and Shift of Stretching Frequency (Inverse Centimeters) of the Complexesa E···F−Xb,c H2O···CuCl H2S···CuCl H2O···AgCl H2S···AgCl H2O···AuCl H2S···AuCl H2O···HCl H2S···HCl H2O···ClF H2S···ClF
rF‑Xd 2.02(2.06) 2.04(2.06) 2.26(2.27) 2.27(2.27) 2.18(-) 2.22(-) 1.29(1.28) 1.29(1.27) 1.66(1.63) 1.68(1.63)
rE···F
ΔrF−X
1.87(1.92) 2.09(2.15) 2.18(2.20) 2.36(2.38) 2.07(-) 2.22(-) 1.86(1.94) 2.42(2.53) 2.52(2.61) 2.72(2.85)
−0.0066 0.00788 −0.0227 −0.0186 0.0043 0.0370 0.01820 0.01368 0.01741 0.04299
ϕe f
44.8(40.9 ) 71.8(74.5g) 45.6(37.4f) 80.0(78.0g) 53.78(-) 71.67(-) 45.5(34.7h) 85.7(93.8i) 56.1(58.9j) 89.9(98.4k)
νF−Xa
ΔνF_X
504.69(428.84) 462.73(428.84) 377.25(344.36) 369.46(344.36) 415.22(409.61) 404.55(409.61) 2791.4(3045.0) 2847.0(3045.0) 757.49(799.62) 674.19(799.62)
75.85 33.89 32.89 25.10 5.61 −5.06 −253.6 −198.0 −42.62 −125.4
a Numbers in bold are those of the corresponding monomers. bE = H2O, H2S. cF = Cu, Ag, Au, H, and Cl. dX = Cl, F. eNumbers in bold are those of the experimental results. fReference 17. gReference 18. hReference 30. iReference 31. jReference 32. kReference 33.
Table 2. Some Significant Donor−Acceptor Orbital Interactions, Wiberg Bond Index (WIB), Interaction Energies (kilocalories per mole), and Second-Order Perturbation Stabilization Energies (ΔEi‑j*(2), kilocalories per mole) of the Complexes complex
WIB
Ecp
donor
acceptor
H2O···CuCl
0.1636
15.81
H2S···CuCl
0.3920
11.88
H2O···AgCl
0.0997
10.38
H2S···AgCl
0.3202
9.031
H2O···AuCl
0.2115
16.12
H2S···AuCl
0.6377
21.64
H2O···HCl H2S···HCl H2O···ClF H2S···ClF
0.0321 0.0431 0.1058 0.1575
3.398 0.745 2.635 0.835
LP(O) LP(O) LP(S) LP(S) LP(O) LP(O) LP(S) LP(S) LP(O) LP(O) LP(S) LP(S) LP(O) LP(S) LP(O) LP(S)
BD*Cu−Cl LP*Cu BD*Cu−Cl LP*Cu BD*Ag−Cl LP*Ag BD*Ag−Cl LP*Ag BD*Au−Cl LP*Au BD*Au−Cl LP*Au BD*H−Cl BD*H−Cl BD*Cl−F BD*Cl−F
interactiona n n n n n n n n n n n n n n n n
→ → → → → → → → → → → → → → → →
σ* LP* σ* LP* σ* LP* σ* LP* σ* LP* σ* LP* σ* σ* σ* σ*
ΔEi‑j*(2) 21.07 90.39 30.49 224.83 5.94 15.42 11.19 108.33 36.27 37.58 42.18 194.60 15.15 13.14 10.07 28.13
σ*denotes the formally empty antibond orbital; LP* denotes the unoccupied orbital of Cu/Ag/Au atom; n denotes the lone pair on the O/S atom in H2O/H2S. a
pattern of changes such as the stretching frequency shifts and interaction energies. The blue-shifting characteristic and strong bonding interaction energies indicate the similarities between Cu/Ag bond and Au bond. 3.2. Natural Bond Orbital Analyses. The NBO method is very useful for analyzing the binding mechanism of intermolecular interactions when the electron delocalization takes place. The energy decrease caused by the electron delocalization is generally estimated by the second-order perturbation energy ΔEi‑j*(2). To investigate the formation mechanism of Cu/Ag/Au bonds, we carried out NBO analyses for the studied complexes. Table 2 lists the significant donor− acceptor orbital interaction and the corresponding secondorder perturbation energy ΔEi‑j*(2). For the Cu/Ag/Au-bonded complexes, the delocalization interactions take place between the lone pair of the O/S atom and σ*M−Cl antibond orbital, and between the lone pair of the donor O/S atom and the empty ns (n = 4, 5, and 6) orbital of the coinage metal atoms. Apart from the expected σ-donation interaction, the hyperconjugation interaction between H2O/H2S and Cu/Ag/Au−Cl also takes part in the binding. However, in the case of hydrogen and halogen bonds, the delocalization interaction occurs only between the lone pair of the donor O/S atom and σX(H)‑Cl*
AgCl, and H2S···AuCl are much more strongly bound than the hydrogen- and halogen-bonded analogues. Thus, the above calculated counterpoise-corrected interaction energies are in accordance with intermolecular stretching force constant kσ obtained from the experiment. As we know, the Wiberg bond index34 (WIB) is helpful in evaluating the binding energy. NBO analyses (see next section) gave the Wiberg bond index listed in Table 2. For the selected complexes, the WIB values have the same ordering as binding energies, for example, WIBAu−O > WIBCu−O > WIBAg−O, and WIBM−S > WIBM−O. Obviously, for the different metals interacted with the same electron donor, the affinity of the silver complexes toward chalcogen atoms is significantly lower than that of the copper and gold complexes, and the corresponding binding energies of the gold complexes are higher than those of the copper complexes. For example, the absolute value of Ecp has the ordering of Ecp(AuCl···H2O) 16.12 kcal/mol > E cp(CuCl···H 2 O) 15.81 kcal/mol > Ecp(AgCl···H2O) 10.38 kcal/mol. The difference among the binding energies of the Cu/Ag/Au-bonded complexes can be explained by using relativistic effects and lanthanide contraction.15,35 To sum up, although the Cu/Ag bond is structurally similar to the hydrogen and halogen bonds, it offers quite a different 10946
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antibond orbital. Obviously, the Cu/Ag/Au bond has a dualbonding mechanism, significantly different from that of the hydrogen and halogen bonds. The distinguishing feature of Cu/ Ag/Au bonds is their binding in terms of the hyperconjugation interaction, apart from the expected σ-donation interaction. On the basis of such a new dual-bonding mechanism, we define a new kind of bond, termed Cu/Ag bond. In addition to the analyses on ΔEi‑j*(2), we also analyzed the binding mechanism of Cu/Ag/Au bond from charge transfer (CT). As reported in Sadlej’s paper, the Au-bonded interaction between AuOH and the lone donors (HF, H2O) was found to involve significant charge transfer (CT). Table 3 shows the
Table 4. Calculated Charges (natural charge from NBO) at Metal Atom, q(M) and the Change of s Character (ΔsCl %) in the Cl Hybrid Orbital of the M-Cl Bond (%) qM (e) CuCl AgCl AuCl H2O···CuCl H2S···CuCl H2O···AgCl H2S···AgCl H2O···AuCl H2S···AuCl
Table 3. Charge Transfer (Δn) between Electron Donor (H2O/H2S) and Electron Acceptor (CuCl, AgCl, AuCl, HCl, and ClF) complexes
donor
acceptor
H2O···CuCl
LP(O) LP(O) LP(S) LP(S) LP(O) LP(O) LP(S) LP(S) LP(O) LP(O) LP(S) LP(S) LP(O) LP(S) LP(O) LP(S)
BD*Cu−Cl LP*Cu BD*Cu−Cl LP*Cu BD*Ag−Cl LP*Ag BD*Ag−Cl LP*Ag BD*Au−Cl LP*Au BD*Au−Cl LP*Au BD*H−Cl BD*H−Cl BD*Cl−F BD*Cl−F
H2S···CuCl H2O···AgCl H2S···AgCl H2O···AuCl H2S···AuCl H2O···HCl H2S···HCl H2O···ClF H2S···ClF
interaction n n n n n n n n n n n n n n n n
→ → → → → → → → → → → → → → → →
σ* LP* σ* LP* σ* LP* σ* LP* σ* LP* σ* LP* σ* σ* σ* σ*
0.7899 0.8215 0.6333 0.6461 0.5099 0.7326 0.5916 0.4917 0.3428
Δ qM (e)
sCl %
ΔsCl %
−0.1438 −0.2800 −0.0889 −0.2299 −0.1416 −0.2905
9.75 14.57 6.44 28.62 33.68 20.96 25.45 18.91 22.00
18.87 23.93 6.39 10.88 12.47 15.56
hyperconjugation effect. Such a result is responsible for the blue-shifting stretching vibration of Cu−Cl/Ag−Cl bond in Cu/Ag-bonded complexes. Thus, there is no contradiction between the blue shift and hyperconjugation effect for studied complexes. 3.3. Atoms in Molecules Analyses. Bader’s AIM theory, based on a topological analysis of the electron density (ρb) and its Laplacian (∇2ρb), has been widely applied in the study of intermolecular interactions.8,38 For example, Caroll and Bader39 and Koch and Popelier40 proposed some criteria indicative of hydrogen bonds. The criteria are composed of a set of local topological properties of the electron density. The electron density (ρb) at the bond critical point (BCP) should range from 0.002 to 0.035 au and the Laplacian of the electron density should range from 0.024 to 0.139 au. Of course, the most important evidence of hydrogen bond is the existence of a bond path and a bond critical point between hydrogen and the electron donor atom. Figure 2 listed the structures and molecular graphs for the studied complexes. Obviously, the bond paths and the bond critical points exit in all the Mbonded complexes. Furthermore, the ∇2ρb values of the Cu/ Ag/Au bond in the six M-bonded complexes are positive. They are 0.3768, 0.3071, 0.3762, 0.2316, 0.5105, and 0.2499 au, respectively. Clearly, the Laplacian of the electron density for the Cu/Ag/Au bond falls out of the proposed range of 0.002 to 0.035 au for the hydrogen bonds, and they are much larger than the values in hydrogen- and halogen-bonded complexes. From the Table 5, we can also see that the complex of H2S···AuCl has the largest value of the electron density and that the electron density at the critical point of the Cu/Ag/Au bond is larger than these of the hydrogen and halogen bonds. These results are in accordance with the results based on the interaction energy analyzed in the section 3.1. Additionally, the Laplacian (∇2ρb) of the electron density, which is defined as the sum of the three eigenvalues of the Hessian, λ1, λ2, and λ3, provides information about either the charge concentration (∇2ρb < 0) or the charge depletion (∇2ρb > 0) of the electron distribution. When the Laplacian is negative, the electronic charge is concentrated and the potential energy dominates both the local total electronic energy H (ρb) and the local virial relationship. Additionally, when the Laplacian is positive, the electronic charge is locally depleted and the kinetic energy is in local excess.39 According to Bader and Essen,41 the former situation occurs in shared interactions, whereas the latter situation is characteristic of closed-shell interactions. Typical properties of closed-shell interactions: the value of electron density, ρb, is relatively low; the ratio of the perpendicular contractions of ρb to its parallel expansion |λ1|/λ3
Δn 0.01018 0.07562 0.01956 0.18259 0.03430 0.14906 0.02471 0.15691 0.04639 0.19293 0.08324 0.27860 0.02272 0.02945 0.02380 0.08987
charge transfer between the donor and the acceptor in our studied complexes. The significant CT shown in Table 3 is in agreement with Sadlej’s results on Au bond. Furthermore, we found that the large charge transfer (0.075−0.278 e) occurs mainly between the lone pair of the donor chalcogen atom and the empty ns (n = 4, 5, and 6) orbital of the coinage metal atoms. Less charge transfer (0.01−0.08 e) occurs between the donor chalcogen atom and the antibond Cu/Ag/Au−Cl orbital. From the above discussion, we know that two types of interaction coexist in the MCl-containing (M = Cu, Ag, and Au) complexes, including the interaction L(ligand) → TM(transition metal) from the lone pair of the donor chalcogen atom to the empty ns (n = 4 and 5) orbital and the hyperconjugation interaction L → σ*M−Cl from the lone pair of the donor chalcogen atom to the M−Cl (M = Cu, Ag) antibond σ* orbital. For Cu/Ag/Au bonds, the primary interaction is L → TM, and the second interaction is L → σ*M−Cl. Both interactions (L → TM and L → σ*M−Cl) work together to enhance the donor−acceptor bond in these coordination compounds. Owing to this result, the dualbonding mechanism found here may be considered as a new synergistic bonding model for coordination compounds. Besides the above analyses from the donor−acceptor viewpoint, we also analyzed the hybridization effect. From Table 4, the complexation leads to the decrease of the charge of the metal atom and the concomitant increase of the s-character of the M−Cl in the most complexes except H2S···AuCl. Here, the rehybridization effect36,37 is relatively large to the 10947
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In addition to Caroll and Bader’s and Koch and Popelier’s criteria, it is also interesting to consider the interaction classification proposed by other authors. Cremer and Kraka,42 for instance, suggested the use of the electronic energy density, H(b), to characterize hydrogen bonds. According to these authors, when |V(b)| > G(b) and H(b) is therefore negative, the interaction is indicative of being shared, but when G(b) > | V(b)| and H(b) is positive, the interaction is indicative of being closed-shell. Thus, they suggested that the larger the value of | V(b)| and the more negative the value of H(b), the more shared the bonded interaction and the greater the stabilization of the structure. From the Table 6, for all the complexes, the value of |V(b)| is larger than G(b), and H(b) is therefore negative. Thus, the Table 6. Densities of Kinetic Energy G(b), Potential Energy V(b), |V(b)|/G(b) Ratio, and the Total Energy H2O···CuCl H2S···CuCl H2O···AgCl H2S···AgCl H2O···AuCl H2S···AuCl H2O···HCl H2S···HCl H2O···ClF H2S···ClF
V(b)
G(b)
H(b)
|V(b)|/G(b)
−0.2217 −0.1674 −0.1083 −0.1037 −0.1851 −0.1770 −0.02615 −0.01060 −0.02346 −0.02747
0.1903 0.1221 0.1012 0.08079 0.1563 0.1197 0.02499 0.01033 0.02650 0.02465
−0.03737 −0.0502 −0.00711 −0.02288 −0.02871 −0.05726 −0.00116 −0.00027 0.002517 −0.00282
1.1650 1.3710 1.0703 1.2832 1.1836 1.4785 1.0464 1.0261 0.8852 1.1141
interaction is indicative of being shared. Espinoza et al.43 stated that bonded interactions can be classified on the basis of the | V(b)|/G(b) ratio where a bonded interaction is defined as closed-shell when the ratio |V(b)|/G(b) < 1, as shared when | V(b)|/G(b) > 2, and as intermediate when the ratio falls between 1 and 2. Here, the values of |V(b)|/G(b) of the Mbonded (M = Cu, Ag, and Au) bonds are 1.1650, 1.3710, 1.0703, 1.2832, 1.1836, and 1.4785, respectively. Hence, it is between closed-shell and shared. The topological properties of the Cu/Ag bond are similar to those of Au bond. Cu, Ag, and Au bonds are all partially covalent and partially electrostatic in nature.
Figure 2. Structures and molecular graphs for the studied complexes (magenta and orange spheres correspond to (3, −3) and (3, −1) critical points; brown lines denote bond paths).
was
