Substituent Effects on the σ ··· π Interactions Between Au6 Cluster and Substituted Benzene

The σ···π interactions in the Au 6 ···PhX (X=H, 2 ) complexes are studied using quantum chemical methods. The present study focuses on the different effects of electron-donating and -withdrawing substituent. The structure and binding strength of the complexes are examined. The interactions between Au 6 cluster and various substituted benzene become strengthened relative to the Au 6 ···benzene complex. The interaction region indicator analysis was performed, and the interaction region and interaction between the substituent and Au 6 cluster are discussed. It is found that the substituent effects on the σ···π interactions between Au 6 cluster and substituted benzene are different from π···π interactions of benzene dimer. Energy decomposition analysis was carried out to study the nature of σ···π interactions, and the substituent effects are mainly reflected on the electrostatic interaction and dispersion.

The stacking interaction between benzene (Bz) dimer is one of the most widely studied interactions in recent years [10][11][12][13]. The parallel displaced (PD) and T-shaped configurations are approximately equal in stability, which are more stronger than the parallel stacked (PS) geometry [14]. For the PD configuration, the stacking interactions come from two factors. First is the π···π interaction between the π-cloud of benzene dimer, which is electrostatically repulsive owing to the negative molecular electrostatic potential (MEP). Second is the interaction between the positively charged hydrogen atoms of one benzene and the π-cloud of the other ring. Interestingly, the σ-electron could participate stacking interactions. For example, the σ···σ interaction strength between cyclohexane dimer is -3.09 kcal·mol -1 , which is stronger than that of benzene dimer [15]. The σ···π interaction between cyclohexane and benzene (-2.91kcal·mol -1 ) is more stabilized than that of benzene dimer with PS geometry (-1.63kcal·mol -1 ) [16].
Stacking interaction can be tuned through substituent effects, and there are a great number of studies about its physical mechanism in the past two decades [17][18][19][20][21][22][23][24][25][26]. Two popular hypothesis were proposed to understand the nature of substituent effects. The viewpoint of Hunter and Sanders (HS) [17] was based on the polarization of the π-system by the substituent. Electron-withdrawing substituent can enhance the PS stacking interactions by decreasing the π-electron density of the ring, whereas introduction of electron-donating substituent should hinder the interactions through the opposite mechanism [27][28]. Wheeler and Houk (WH) proposed that the direct interaction between the substituent and the other aromatic ring determines the substituent effects on the interaction energy [16,20,23,25]. Moreover, they found that the substituent effects in the PD and PS geometries are essentially identical [23], which is in conflict with the HS view. Parrish and Sherrill [26] pointed out that both HS and WH pictures contribute to the substituent effects on stacking interactions, but the WH picture is usually dominant.
Recently, the non-covalent interactions in which coinage metal (Cu, Ag, and Au) nanoclusters involved have been received great attentions [27][28][29][30][31][32][33][34][35][36]. Regium bond [29] was introduced to represent the interaction between coinage metal nanoparticles and an electron rich moiety. MEP analysis of coinage metal clusters showed that there exists depleted electron density regions with positive MEPs [30] (also be called as σ-hole [37]) in the low-coordinated metal sites, and negative MEPs are located at bridge and hollow sites. It is well-known that benzene can absorb on coinage metals with weakly interactions [38][39][40][41][42]. The research was mainly focused on the (111) coinage metal surface, and this adsorption is a weak physisorption, which is dominated by van der Waals (vdW) interactions.
Substituent effects also exist in the interaction when aromatic ring adsorbed on the metal surface. For example, Pekӧz et al. [43] investigated the adsorption of polyhalogenated benzene on the Pt(111) surface, and they found that the relative stability of chemisorption and physisorption can be tuned by the type or the number of halogen atoms. Miller and co-workers [44] studied the adsorption of benzene functionalized with one or two substituents on Ag(111) surface, which indicates that strong electron-donating or -withdrawing substituent possessed a distinct site preference.
Given the weak absorption of benzene on the coinage metal surface, the interaction between gold cluster and benzene could be classified into σ···π interaction. Moreover, the HS and WH pictures could be applied to describe the substituent effects on the interaction. In this paper, the stacking interaction in the Au 6 ··· Bz complex was investigated using quantum chemical methods. Au 6 cluster, which has been proved to have planar geometry [45][46], has the same number of atom in the ring as benzene.

Theoretical methods
Geometry optimizations were implemented using PBE0 exchange-correlation functional [47][48] in conjunction with def2-TZVP [49] basis set. Previous studies have proved that PBE0 is able to describe the non-covalent interactions including transition metals [50][51][52]. Frequency analyses were carried out at the same level and all geometries are characterized to minima on the potential energy surface. Grimme's DFT-D3(BJ) empirical dispersion correction [53] was used in the geometry optimizations. The above calculations were performed using Gaussian 09 software (revision D.01) [54].
In order to obtain accurate binding energy of the stacking interaction, single point calculations were performed at the PWRB95-D3(BJ)/def2-QZVPP level. The combination between double hybrid functional PWRB95 [55] and larger basis set def2-QZVPP [49] can give improved binding energy for weakly interaction systems.
Binding energies were calculated as the energy of the complex and E Au6 and E PhX refer to the energies of Au 6 and Bz or substituted benzene in the complex, respectively. The Counterpoise correction was adapted using Boys and Bernardi's method [56] to evaluate the basis set superposition error (BSSE). The ORCA 4.2.1 program [57] was employed for this part of calculation. The RI and RIJCOSX [56] technique were used to accelerate the calculation. SAPT analysis [59] using the scaled SAPT0 method with def2-SVP basis set was carried out with the help of PSI4 1.3.2 code [60]. The total interaction energy of this level is in consistent with the result of PBE0/def2-TZVP calculation.
The MEP mapped vdW surface on the 0.001 a.u. contours of the electronic density was generated at the PBE0-D3(BJ)/def2-TZVP level. To intuitively show the stacking interaction in real space, IRI method [61] was applied. The above analysis were performed with the Multiwfn code [62]. Molecular graphs of MEP and IRI maps are rendered by means of Visual Molecular Dynamics (VMD) software [63]. Since the main focus is stacking interaction, the other types of interaction are not included in this paper.

Geometries and binding energies
The optimized structures of the Au 6 ··· Bz complex and benzene dimer are displayed in Figure 2. Three geometrical parameters (R, θ 1 , and θ 2 ) are defined. R denotes the distance between the molecular plane of Au 6 cluster and benzene, and θ 1 and θ 2 is misalignment angle and the included angle of the two planes, respectively. The geometrical parameter and binding energy are collected in Table 1. One can see that the structure of the Au 6 ··· Bz complex is similar to that of Bz· ·· Bz, for which the PD geometry is the most stable configuration. The value of R in the Au 6 ···Bz complex is 3.783Å, which is smaller than that of benzene dimer. This indicates that the Au 6 and Bz molecular plane get closer from the direction perpendicular to the ring in the former complex. Misalignment angle θ 1 reflects the overlap degree along the ring. It is seen that this value in the Au 6 ··· Bz complex is slightly larger than that of benzene dimer, which indicates that the molecular plane overlap of σ···π interaction is a little smaller than π···π interaction. Moreover, the two aromatic rings in the benzene dimer is almost flat, and the plane of Au 6 cluster presents small deviation with the included angle of 3.29°. The binding energy of benzene dimer at the PWRB95-D3(BJ)/def2-QZVPP level is -2.93kcal·mol -1 , which is in accord with the S66 database [64], where interaction strength of π···π interaction is -2.82kcal·mol -1 .
This demonstrates that the result in this study should be reliable. The binding energy of the Au 6 ···Bz complex is -10.57kcal·mol -1 , which is even more than three times than that of PD benzene dimer. This indicates that the σ···π interaction in the Au 6 ···Bz complex is far more strengthened than that of π···π interaction of benzene dimer. It is interesting to note that the experimental adsorption energy of benzene on Au(111) is 0.64 eV(about 14.78kcal·mol -1 ) [65], which is comparable to the binding energy of Au 6 ···Bz complex.  To investigate the substituent effects of the stacking interaction between Au 6 cluster and benzene, the Au 6 ···PhX (X=-CH 3  The optimized structures of the Au 6 ···PhX complexes are displayed in Figure 3. One can see that there has been no apparent change on the structures of Au 6 ···PhCH 3 , Au 6 ···PhOH, Au 6 ···PhNH 2 , Au 6 ···PhOCH 3 , Au 6 ···PhF compared to the Au 6 ···Bz complex. In the Au 6 ···PhCl, Au 6 ···PhBr, Au···PhCN, and Au···PhNO 2 complexes, the overlap between Au 6 cluster and substituted benzene becomes more prominent, which induced a trend of change from PD to PS configuration. Table 2  . This is similar to the study of absorption of PhF on Ag(111) [44], in which the binding strength is weaker than that of benzene. The binding energy of the σ···π interaction is different from the results of PD and PS benzene dimer. Theoretical study [18] has suggest that the introduction of any substituent should increase the strength of π−stacking interaction of benzene dimer. Moreover, the electron-withdrawing substituent makes the π-stacking interaction more stronger than the electron-donating substituent. This can be easily explained by the π-polarization model because electron-withdrawing substituent decreases the repulsion between π-cloud and increases the acidity of hydrogen atoms.
In the Au 6 ···PhX complexes, the σ···π interactions have been strengthened through the substituent effects except for the Au 6 ···PhF complex. Overall, the influence of electron-withdrawing substituent is more pronounced than the electron-donating substituent. There is a correlation between interaction energy and the Hammett sigma meta constants (σ m ) for the PS dimer of substituted benzene, but there is not distinct relationship between binding energy and σ m in the Au 6 ···PhX complexes. For example, the binding energies of the Au 6 ···PhCH 3 and Au 6 ···PhCN complexes are -12.18 and -11.95kcal·mol -1 , respectively. This could not reflect the difference between electron-donating substituent -CH 3 and electron-withdrawing substituent -CN. From the above discussion, it is seen that the σ···π interactions between Au 6 cluster and substituent benzene can not fully understood in terms of the character of the substituent. There exists correlation between dispersion energy and the π components of the polarizability of substituted benzene [18]. From this, the polarizability (P ZZ ) in the direction perpendicular to the molecular plane of substituted benzene was calculated at the PBE0-D3(BJ)/def2-TZVP level. The P ZZ values of Au 6 cluster and benzene are 118.86 and 38.37a.u., respectively, which can account for the strong σ···π interaction in the Au 6 ···BZ complex. It is also found that the P ZZ values of PhF and PhOH are relative small compared to other substituted benzene, which is in accord with the binding energy of the corresponding complexes. Figure 4 displays the scatter diagram between binding energy and the value of P ZZ . One can see that except for the -OCH 3 and -NO 2 substituent, E b presents a good correlation with P ZZ . PhOCH 3 has the largest P ZZ value (51.02a.u.), which is not consistent with the medium binding energy (-12.10kcal·mol -1 ). The P ZZ value of PhNO 2 is 43.09 a.u., but the σ···π interaction in the Au 6 ···PhNO 2 is very strong (-12.82kcal·mol -1 ). This contradiction can be understood by the geometries of the corresponding complexes. It is seen from Figure   2 that the Au 6 ···PhOCH 3 complex has a PD configuration, but the structure of the Au 6 ···PhNO 2 complex is almost a PS geometry. It is obvious that the -NO 2 substituent has a direct interaction with Au 6 cluster, but for the Au 6 ···PhOCH 3 complex, there is no direct interaction between the -OCH 3 substituent and Au 6 cluster.

IRI analysis
To visually exhibit the region of σ···π interactions in the Au 6 ···BZ and Au 6 ···PhX complexes, IRI analysis was performed using the PBE0-D3(BJ)/def2-TZVP wave functions. IRI is a a new real space function, which is a slight modification on reduced density gradient (RDG) [61]. IRI is defined as , where ρ is electron density and r is coordinate vector. The parameter a is an adjustable parameter, and a=1.1 is adopted for standard definition of IRI. In this method, isosurfaces of IRI is employed to exhibit chemical bonding and non-covalent interaction regions. By mapping the sign(λ 2 )ρ function onto IRI isosurfaces with different colors, the nature of the interactions can be vividly displayed. Figure 5 shows the IRI isosurface maps of the Au 6 ···Bz and Au 6 ···PhX complexes, and the map of PD benzene dimer is also collected. It is seen that there are green isosurface in the π-stacking regions in the benzene dimer, which indicates that the main driving force of the π···π interaction is vdW interaction. For the Au 6 ···Bz complex, the color of isosurface darkened and the area of the interaction region enlarged. This suggests that the σ···π interaction is stronger than the π···π interaction, which is consistent with the result of binding energy. In the Au 6 ···PhX complexes, the

SAPT analysis
The inherent nature of the σ···π interactions between Au 6 cluster and substituted benzene can be understood using the SAPT approach. The SAPT energy can be expressed as . The E elst , E ind and E dis terms reflect the electrostatic interaction, induction and dispersion contribution, respectively. The values of three terms are negative, and they are attractive forces when the complexes formed. The E exch term is the exchange-repulsion contribution with positive value, which behaves as a repulsive force. The energy components from SAPT calculations are extracted and plotted in Figure 6. As can be seen, dispersion dominates the σ···π interactions in the Au 6 ···Bz and Au 6 ···PhX complexes. This is consistent with the π···π interaction in the PD and PS benzene dimer. The electrostatic interaction is also important, which accounts for more than half of the dispersion term. The induction contribution, which is only -1~-3kcal·mol -1 , is very weak relative to electrostatic interaction and dispersion contribution.
The electrostatic interaction in the Au 6 ··· Bz complex is -13.12kcal·mol -1 , which is less negative than that of the complexes with -CH 3 , -OCH 3 , -NH 2 , and -Br substituent.
This is very interesting because the electron-donating substituent can increase the π density in the ring and decrease the acidic of hydrogen atom. It is worth noting that the exchange-repulsion contribution in the corresponding complexes becomes more positive compared to Au 6 ···Bz. In a sense, -Br behaves like an electron-donating substituent in the Au 6 ···PhBr complex. In the Au 6 ···PhOH complex, the electrostatic interaction is less strong and the E exch term is smaller than those of Au 6 ···Bz, which indicates that the -OH can be deemed as an electron-withdrawing substituent. The dispersion contribution increases in the Au 6 ···PhX complexes except for the Au 6 ···PhF complex. For the Au 6 ···PhCH 3 , Au 6 ···PhNH 2 , Au 6 ···PhOCH 3 , Au 6 ···PhBr, and Au 6 ···PhNO 2 complexes, the E dis term spans in a range from -20.73 to -25.28kcal·mol -1 , which becomes more negative relative to Au 6 ···Bz. This can attributed to the larger number of atoms and electrons in the substitute. Moreover, increment of the interaction region in the Au 6 ···PhBr and Au 6 ···PhNO 2 complexes also play important role.

Conclusion
The substituent effects on the σ···π interactions between Au 6 cluster and substituted benzene have been explored using quantum chemical methods. The σ···π interaction in the Au 6 ···Bz complex is more strengthened than the π···π interaction of benzene dimer. Investigation on the Au 6 ···PhX (X=CH 3 , OH, OCH 3 , NH 2 , F, Cl, Br, CN, NO 2 ) complexes reveals that influence of electron-withdrawing substituent on the σ···π interactions is more pronounced than the electron-donating substituent. Substituent -F have little influence on the binding strength of σ···π interactions, which is different from the substituent effect in the benzene dimer. IRI analysis indicates that the substituent effects usually associated with the variation of vdW interaction strength region. The interaction between the substituent and the aromatic ring is more prominent for the electron-withdrawing substituent than the electron-donating substituent. SAPT calculation suggests that dispersion dominates the σ···π interaction and electrostatic interaction has very important contribution. Substituent effect on the components of SAPT energy did not depend on the characteristic of the substituent.
This study can enrich the knowledge of noncovalent interaction related to coinage metals, and also provide a different way to investigate the absorption of organic molecules on metal surfaces.