Density Functional Study to Investigate the Ability of (ZnS)n (n = 1–12) Clusters Removing Hg0, HgCl, and HgCl2 via Electron Localization Function and Non−Covalent Interactions Analyses

In this study, the density functional theory is used to study the ability of (ZnS)n clusters to remove Hg0, HgCl, and HgCl2 and reveals that they can be absorbed on (ZnS)n clusters. According to electron localization function (ELF) and non−covalent interactions (NCI) analyses, the adsorption of Hg0 on (ZnS)n is physical adsorption and the adsorption ability of (ZnS)n for removing Hg0 is weak. When (ZnS)n adsorbs HgCl and HgCl2, two new Hg−S and Zn−Cl bonds form in the resultant clusters. An ELF analysis identifies the formation of Hg−S and Zn−Cl bonds in (ZnS)nHgCl and (ZnS)nHgCl2. A partial density of states and charge analysis confirm that as Hg0, HgCl, and HgCl2 approach (ZnS)n clusters, atomic orbitals in Hg and Zn, Hg and S, as well as Zn and Cl overlap and hybridize. Adsorption energies of HgCl and HgCl2 on (ZnS)n clusters are obviously bigger than those of Hg0, indicating that HgCl and HgCl2 adsorption on (ZnS)n clusters is much stronger than that of Hg0. By combining ELF analysis, NCI analysis, and adsorption energies, the adsorption of HgCl, and HgCl2 on (ZnS)n clusters can be classified as chemical adsorption. The adsorption ability of (ZnS)n clusters for removing HgCl and HgCl2 is higher than that of Hg0.


Introduction
Mercury can cause serious damage to the human body and ecosystems, and it is one of the most harmful pollutants in the environment [1,2]. Mercury in the atmosphere is mainly derived from flue gases released from power plants. There are three main forms of mercury in flue gas, which are divalent mercury (Hg 2+ ), particulate bound mercury (Hg P ), and elemental mercury (Hg 0 ) [2,3]. Hg 2+ and Hg P can be captured and removed by existing pollution control equipment. However, it is difficult to remove Hg 0 with existing control devices due to its low melting point, low solubility, and high volatility [4][5][6]. Therefore, how to effectively remove Hg 0 has become a major challenge to control flue gas mercury emissions. Recently, in industry, several technologies have been developed to prevent mercury emission from coal combustion, among which the most widely commercialized method is activated carbon injection before the electrostatic precipitator [7][8][9]. When the temperature of flue gas decreases, mercury is oxidized to HgCl 2 due to the large amount of chlorine in the pulverized coal. Meiji found that Hg 0 and HgCl 2 coexisted in flue gas [10]. Mercury chlorination is generally considered to be the main mercury conversion mechanism in coal−fired flue gas. According to a study by Carpi, hydrogen chloride and other contaminants can influence the distribution condition of atomic and divalent mercury [11]. The higher the concentration of chlorine, the more easily atomic mercury is oxidized to mercury chloride [12].
The global minimum (GM) and low−lying structures of (ZnS) n (n = 1-12) clusters are displayed in Figure 1. 1a is a linear structure in C ∞v with the Zn−S bond length being 2.05 Å. Here, the bond length of Zn−S is in the range of reported Zn−S bond lengths (2.05-2.13 Å) [22,25,26]. 2a is a rhombus D 2h structure. 2a−1 lies 1.27 eV higher than 2a, in which one S−S bond and one Zn−Zn bond are present. 3a is a triangle structure in D 3h symmetry and 3a−1 is a three−dimensional structure. 4a is composed of four S−Zn−S units, which is a rectangle structure in D 4h symmetry. 4a−1 and 4a−2 are both much higher in energy than 4a. Small size clusters (n = 1-4) have planar geometries, which is in accordance with previous studies [26][27][28]. (ZnS) n (n = 1-4) clusters adopt planar ring structures, in which Zn and S atoms alternate with the coordination number of each Zn and S being 2. 5a is a C s symmetry structure with five S−Zn−S units. 5a−1 lies 0.15 eV higher. 5a−2 lies much higher and its relative energy is 1.35 eV. 6a is in a hollow cage conformation composed of two triangular Zn 3 S 3 structures. 6a−1 has been previously predicted to be the GM structure for (ZnS) 6 [25]. Here, 6a−1 is identical to that reported in the literature using the density functional formalism and projector augmented wave method, which is a cage−like structure composed of four Zn 3 S 3 and two Zn 2 S 2 units. Our predicted GM (6a) for (ZnS) 6 is 0.63 eV lower in energy than that in the literature [25]. 6a−2 is a crown structure, and its relative energy is 1.82 eV with respect to 6a. In 1a−6a, each S atom is coordinated with two neighboring Zn atoms. 7a is a cage structure in C 3v symmetry, which includes four Zn 4 S 4 and two Zn−S edge−sharing Zn 6 S 6 units. 7a−1 and 7a−2 both lie much higher than 7a. 8a is a cage structure, and it is composed of four Zn 3 S 3 and six Zn 2 S 2 units. 8a−1 consists of two Zn 4 S 4 rings, and its energy is 1.05 eV. The energy of 8a−2 is 1.13 eV. 9a is composed of two quasi−planar Zn 3 S 3 , three triangular six−number Zn 3 S, and six Zn 2 S 2 units. 10a is a cage structure, which is composed of six Zn 3 S 3 and three Zn 2 S 2 units. The energy of 10a−1 is 0.08 eV higher, and it is composed of two pairs of Zn−S edge sharing Zn 3 S 3 cells, and each cell is composed of two Zn 3 S 3 .
Molecules 2023, 28,1214 3 of 21 symmetry structure with five S−Zn−S units. 5a−1 lies 0.15 eV higher. 5a−2 lies much higher and its relative energy is 1.35 eV. 6a is in a hollow cage conformation composed of two triangular Zn3S3 structures. 6a−1 has been previously predicted to be the GM structure for (ZnS)6 [25]. Here, 6a−1 is identical to that reported in the literature using the density functional formalism and projector augmented wave method, which is a cage−like structure composed of four Zn3S3 and two Zn2S2 units. Our predicted GM (6a) for (ZnS)6 is 0.63 eV lower in energy than that in the literature [25]. 6a−2 is a crown structure, and its relative energy is 1.82 eV with respect to 6a. In 1a−6a, each S atom is coordinated with two neighboring Zn atoms. 7a is a cage structure in C3v symmetry, which includes four Zn4S4 and two Zn−S edge−sharing Zn6S6 units. 7a−1 and 7a−2 both lie much higher than 7a. 8a is a cage structure, and it is composed of four Zn3S3 and six Zn2S2 units. 8a−1 consists of two Zn4S4 rings, and its energy is 1.05 eV. The energy of 8a−2 is 1.13 eV. 9a is composed of two quasi−planar Zn3S3, three triangular six−number Zn3S , and six Zn2S2 units. 10a is a cage structure, which is composed of six Zn3S3 and three Zn2S2 units. The energy of 10a−1 is 0.08 eV higher, and it is composed of two pairs of Zn−S edge sharing Zn3S3 cells, and each cell is composed of two Zn3S3. Two Zn5S5 ring cells constitute 10a−2 and its energy is 2.48 eV. 11a and 12a are both cage structures. 11a is composed of seven triangle Zn3S3 and four Zn3S3 units. The energy of 11a−1 is 0.68 eV. 12a in Th symmetry has eight Zn3S3 and four Zn2S2 units, which is identical to the structure in the literature [29]. 12a−1 lies much higher than 12a. 10a, 11a, and 12a are the so−called "bubble clusters", and Zn and S atoms in them connect with Two Zn 5 S 5 ring cells constitute 10a−2 and its energy is 2.48 eV. 11a and 12a are both cage structures. 11a is composed of seven triangle Zn 3 S 3 and four Zn 3 S 3 units. The energy of 11a−1 is 0.68 eV. 12a in T h symmetry has eight Zn 3 S 3 and four Zn 2 S 2 units, which is identical to the structure in the literature [29]. 12a−1 lies much higher than 12a. 10a, 11a, and 12a are the so−called "bubble clusters", and Zn and S atoms in them connect with three neighboring atoms [30]. Thus, the coordination number of S atoms increase from two to three as the cluster changes from ring structure to hollow cage structure.
The global minimum structures (GMs) at the PBE0−D3BJ/def2−TZVP level of theory for (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 are shown in Figure 2. From the figure, the structure of 1b is an almost a linear structure, and the Hg atom is bound to the Zn atom. The formed Zn−Hg bond in 1b is 2.63 Å. In 2b, the Zn−Hg bond is 2.68 Å and Hg connects to the Zn atom. In 3b, three Zn atoms are located in the middle of three S−Zn−S units. The Hg atom connects to one of the three Zn atoms in the (ZnS) 3 cluster and the Zn−Hg bond is 2.84 Å. The Zn−Hg bond in 4b is 3.01 Å. It is worth mentioning that Hg adsorbed on (ZnS) 4 cluster has been studied recently and it was found that the Hg atom also bound to the Zn atom [21]. However, the global minimum structure of the (ZnS) 4 cluster in the literature lies 0.27 eV higher relative to the GM structure reported here. In 5b, the Hg atom is located above the (ZnS) 5 cluster, forming three Zn−Hg bonds, and the lengths of them are 3.41, 3.41 and 3.42 Å, respectively. The Hg atom in 6b is on the top of one Zn 3 S 3 unit, forming three Zn−Hg bonds, which are all 4.03 Å. The Hg 0 position in 6b is similar to Hg 0 adsorbed on the CuS(001)−Cu/S surface [31]. In 5b and 6b, there are also Hg−S bonds present beside Zn−Hg bonds. In other words, Hg 0 is stabilized by multi−interactions with neighboring Zn and S atoms. In 7b, the Hg atom connects to the (ZnS) 7 cluster by the Hg atom and the Zn atom in one of (ZnS) 3  three neighboring atoms [30]. Thus, the coordination number of S atoms increase from two to three as the cluster changes from ring structure to hollow cage structure.
The global minimum structures (GMs) at the PBE0−D3BJ/def2−TZVP level of theory for (ZnS)nHg, (ZnS)nHgCl, and (ZnS)nHgCl2 are shown in Figure 2. From the figure, the structure of 1b is an almost a linear structure, and the Hg atom is bound to the Zn atom. The formed Zn−Hg bond in 1b is 2.63 Å . In 2b, the Zn−Hg bond is 2.68 Å and Hg connects to the Zn atom. In 3b, three Zn atoms are located in the middle of three S−Zn−S units. The Hg atom connects to one of the three Zn atoms in the (ZnS)3 cluster and the Zn−Hg bond is 2.84 Å. The Zn−Hg bond in 4b is 3.01 Å . It is worth mentioning that Hg adsorbed on (ZnS)4 cluster has been studied recently and it was found that the Hg atom also bound to the Zn atom [21]. However, the global minimum structure of the (ZnS)4 cluster in the literature lies 0.27 eV higher relative to the GM structure reported here. In 5b, the Hg atom is located above the (ZnS)5 cluster, forming three Zn−Hg bonds, and the lengths of them are 3.41, 3.41 and 3.42 Å , respectively. The Hg atom in 6b is on the top of one Zn3S3 unit, forming three Zn−Hg bonds, which are all 4.03 Å . The Hg 0 position in 6b is similar to Hg 0 adsorbed on the CuS(001)−Cu/S surface [31]. In 5b and 6b, there are also Hg−S bonds present beside Zn−Hg bonds. In other words, Hg 0 is stabilized by multi−interactions with neighboring Zn and S atoms. In 7b, the Hg atom connects to the (ZnS)7 cluster by the Hg atom and the Zn atom in one of (ZnS)3 units, and the forming Zn−Hg bond is 2.75 Å . The Hg atom in 8b links to the Zn atom at the edge of the (ZnS)8 cluster and the forming Zn−Hg bond is 2.80 Å . The forming Zn−Hg bonds in 9b, 10b, 11b, and 12b are 2.80, 2.85, 2.88, and 2.94 Å , respectively. From the above analysis, it is clear that the Hg atom interacts with the Zn atom in the (ZnS)n cluster forming a Zn−Hg bond. The Zn−Hg bond lengths in 1b−3b and 7b−12b are comparable to that in the Hg 0 binding on the ZnS(110) system (2.97 Å ) [8]. In 1c, Hg connects to S, while Cl bonds to Zn, and Hg−S is 2.50 Å and Zn−Cl is 2.10 Å. In 2c, the Cl atom links to the Zn atom through the Zn−Cl bond, whereas Hg interacts with S through the Hg−S bond. In 2c, the rectangle Zn 2 S 2 conformation is damaged when HgCl goes near the (ZnS) 2 cluster. It should be noted that Hg and Cl are parted with each other in 1c and 2c. When the HgCl molecule moves to the (ZnS) 3 cluster, one of the Zn−S bonds break to form 3c. In 3c, the Zn−Cl and Hg−S bonds are 2.24 and 2.58 Å, respectively. Hg and Cl interact with S and Zn in 4a, respectively, to form 4c. As compared with 5a, the structure of (ZnS) 5 unit in 5c changes. One S−Zn−S angle in 5c is as small as 124.3 • . As compared with 6a, (ZnS) 6 in 6c is similar to 6a. 6c forms from the Hg and Cl atoms interacting with the S and Zn atoms in different (ZnS) 3 units of 6a. In 6c, Hg−S is 2.60 Å and Zn−Cl is 2.24 Å. When adding the HgCl molecule to 7a, the resultant molecule is 7c. The (ZnS) 7 unit in 7c is similar to 7a. The Hg and Cl atoms interact with the S and Cl atoms in 7c, respectively. The Hg and Cl atoms form two six−number structures in 7c, and both of the six−number structures are Zn 2 S 2 HgCl. In 8c, the HgCl molecule and the neighboring Zn and S atoms form one eight−number unit and one six−number unit. When the HgCl molecule approaches 9a, one of the Zn−S bonds on the edge breaks to form Hg−S and Zn−Cl bonds. Two six−number Hg−S−Zn−S−Zn−Cl units form in 9c. In 10c and 11c, the Hg and Cl atoms of HgCl form two six−number ring structures, which are Hg−Cl−Zn−S−Zn−S units. When adding the HgCl molecule to 12a, two eight−number ring structures form in 12c. From the above analysis, it can be seen that when HgCl is adsorbed on (ZnS) n clusters, Hg in HgCl interacts with one S atom, and Cl in HgCl interacts with one Zn atom in the (ZnS) n cluster. The adsorption of HgCl on (ZnS) n clusters is different from that of HgCl on the ZnS(110) surface [8]. When adsorbing HgCl on the ZnS(100) surface, the Hg and Cl atoms of HgCl bind to two Zn atoms of the ZnS(100) surface [8].
In 1d, the Zn−Cl, Hg−S, and Hg−Cl bond lengths are 2.09, 2.30, and 2.28 Å, respectively. 2d is a strange structure. When the HgCl 2 molecule approaches 1a, the HgCl 2 molecule disintegrates to Hg, Cl, and Cl atoms. One Zn−Hg bond is present in 2d. The S−Cl bond length is 2.05 Å. 3d is similar to 3c. 3d can be regarded as one Cl atom adding to 3c. One Hg−Cl bond elongates to 3.02 Å, much bigger than the other Hg−Cl bond (2.27 Å). In 4d, one Cl atom is located above the Zn 4 S 4 unit forming two Zn−Cl bonds. The Hg atom in the HgCl 2 molecule interacts with the S atom through the Hg−S bond, which is 2.32 Å. The two Hg−Cl bonds in 4d are 3.66 and 2.27 Å, respectively. 5d is a cage structure, in which Hg, Cl, and Cl atoms in HgCl 2 participate in forming a ring structure with neighboring Zn and S atoms. When the HgCl 2 molecule approaches 6a, the Cl atom and one Zn atom in the Zn 3 S 3 unit form a Zn−Cl bond, while the Hg atom and one S atom in another Zn 3 S 3 unit forms an Hg−S bond. The Zn−Cl and Hg−S bonds are 2.21 and 2.36 Å, respectively. In 7d, Hg−S is 2.35 Å and Zn−Cl is 2.18 Å. In 8d, one Zn−S bond cracks to form Zn−Cl and Hg−S bonds when the HgCl 2 molecule appears. Similarly, one Zn−S bond breaks to form Zn−Cl and Hg−S bonds, which are 2.17 and 2.34 Å, respectively. In 9d, one Zn−S bond breaks to form Zn−Cl and Hg−S bonds with the HgCl 2 molecule. In 9d, the newly formed Zn−Cl bond is 2.20 Å and Hg−S is 2.35 Å. In 10d, the Zn−Cl and Hg−S bonds are also 2.20 and 2.35 Å, respectively. The main conformation of the (ZnS) 11 unit in 11d does not change much as compared with 11a. The new formed bond lengths of Hg−S and Zn−Cl are identical in 10d and 11d. In 12d, the broken Zn−S bond is elongated to 3.98 Å, and the newly formed Zn−Cl and Hg−S bonds are 2.22 and 2.36 Å, respectively. The binding conformation of HgCl 2 adsorbed by (ZnS) n clusters is similar to HgCl 2 on the Fe 3 O 4 (111) surface [32]. When the HgCl 2 molecule is adsorbed on the (ZnS) n cluster, HgCl 2 decomposes into HgCl and Cl, then Hg in HgCl parts, and the separate Cl atoms bind with S and Zn atoms, respectively. However, when HgCl 2 is adsorbed on the ZnS(110) surface, the Hg atom binds with the S atoms, and two Cl atoms bind with two Zn atoms. Here, when HgCl 2 is adsorbed on the (ZnS) n cluster, only one Cl atom is bound to the Zn atom.
Based on the above analysis, when Hg 0 approaches the (ZnS) n cluster, one Zn−Hg bond forms and the main frame of the (ZnS) n cluster remains. Hg 0 prefers the Zn−Hg bond to the Hg−S bond. When the (ZnS) n cluster adsorb the HgCl molecule, one Zn−S bond in (ZnS) n cracks, and then Hg−S and Zn−Cl bonds form. When the HgCl 2 molecule is absorbed by the (ZnS) n cluster, one Zn−S bond breaks, meanwhile Hg−S and Zn−Cl bonds form.

Adsorption Energy
The interactions among Hg 0 , HgCl, HgCl 2 , and (ZnS) n clusters are investigated to obtain the removal ability of (ZnS) n clusters. If E ad is negative, the adsorption reaction is exothermic. The more negative E ad is, the stronger the interaction between adsorbate and substrate. Generally, if E ad is less than −29.8 kJ/mol, it is physical adsorption; if E ad is higher than −50.0 kJ/mol, it is chemical adsorption [33]. The E ad values of Hg 0 , HgCl, and HgCl 2 with (ZnS) n (n = 1-12) clusters are calculated. E ad values versus cluster sizes n are given in Figure 3. From Figure 3a, the E ad values of Hg 0 on (ZnS) n (n = 1-12) clusters range from −13.34 to −4.04 kcal/mol. From the adsorption energy point of view, the adsorption of Hg 0 on (ZnS) n clusters is physical and weak chemical adsorption. From Figure 3a, the E ad of Hg 0 decreases with an increase in n. At n = 1 and 4, the adsorption energies are the maximum and minimum of all sizes, which are −13.33 and −4.04 kcal/mol, respectively. At n = 5 and 7, n is larger than that of the adjacent sizes, which are −9.62 and −9.04 kcal/mol, respectively. A previous study has revealed that n for Hg 0 on the ZnS(110) surface is −21.00 kcal/mol [8]. Thus, it is obvious that the adsorption of Hg 0 over (ZnS) n (n = 1-12) clusters is much weaker than Hg 0 over the ZnS(110) surface. The reason may be that when Hg 0 is adsorbed by (ZnS) n clusters, Hg 0 only binds and interacts with the Zn atom in the (ZnS) n clusters; when Hg 0 is adsorbed by ZnS(110), Hg 0 binds and interacts with Zn and also binds with S on the ZnS(110) surface [8].
In order to study the reasons for the low adsorption energy of Hg 0 on (ZnS) n (n = 1-12) clusters, we analyzed the Zn-Hg bond lengths in (ZnS) n (n = 1-12) clusters. Based on the geometry discussion section, the Zn-Hg bond lengths in (ZnS) n Hg range from 2.84-4.03 Å for (ZnS) n Hg (n = 3-12), while those for (ZnS) n Hg (n = 1-2) are 2.63 and 2.68 Å, respectively. The sum of the radius of Hg and Zn atoms is 2.94 Å according to the van der Waals radii by Bondi [34]. The Zn-Hg bond lengths in (ZnS) n Hg (n = 3-12) are near or bigger than the sum of the radius of Hg and Zn atoms, which indicates that interactions between Zn and Hg in the forming Zn-Hg bond are probably weak. The big steric hindrance in (ZnS) n may result in big bond lengths of Zn-Hg bonds in (ZnS) n Hg, particularly for n = 7-12. For n = 5 and 6, the very big Zn−Hg bonds are due to their particular structures of (ZnS) 5 Hg and (ZnS) 6 Hg. However, the bond lengths of Zn-Hg in (ZnS) n Hg (n = 1-2) are smaller than the sum of the radius of Hg and Zn atoms (2.94 Å) probably due to its small sizes of ZnS and (ZnS) 2 .
It can be seen from Figure 3b,c that when (ZnS) n clusters adsorb HgCl and HgCl 2 , the changing trends of E ad with n are similar. For HgCl and HgCl 2 , when n increases from 1 to 12, E ad tends to decrease. Overall, E ad of HgCl adsorbed on (ZnS) n cluster is smaller than that of HgCl 2 . The adsorption energies of HgCl on (ZnS) n clusters range from −137.02 to −34.31 kcal/mol, while those of HgCl 2 range from −233.11 to −117.27 kcal/mol with an exothermic process. Thus, the adsorption strength of HgCl 2 over (ZnS) n clusters is much stronger than that of HgCl over (ZnS) n clusters. When n = 5 and 7, the adsorption energies are larger than that of the adjacent size. E ad for (ZnS) 5 HgCl cluster is −106.54 kcal/mol, while (ZnS) 5 HgCl 2 is −179.79 kcal/mol. E ad values of HgCl and HgCl 2 on (ZnS) 7 cluster are −81.00 and −140.11 kcal/mol. When (ZnS) n (n = 1-12) clusters adsorb HgCl, HgCl decomposes into Hg and Cl atoms. This result can be interpreted as Hg and Cl atoms forming chemical bonds with S and Zn atoms in (ZnS) n clusters, respectively. When (ZnS) n (n = 1-12) clusters adsorb HgCl 2 , HgCl 2 decomposes to HgCl and Cl. Then, the Hg atom in the HgCl part forms an Hg−S bond with the neighboring S atom in the (ZnS) n cluster, and the decomposed Cl atom forms a Zn−Cl bond with one Zn atom in the (ZnS) n cluster at a nearby position. The condition of HgCl and HgCl 2 adsorption, here, is similar to those on the Fe 3 O 4 (111) surface [32]. Based on the adsorption energies and newly formed covalent Hg−S and Zn−Cl bonds, HgCl and HgCl 2 adsorbed on (ZnS) n clusters are chemisorption. HgCl and HgCl 2 are also chemisorption on the ZnS(110) surface with adsorption energies being −174.33 kJ/mol and −132.79 kJ/mol, respectively [8].

Non−Covalent Interactions (NCI) and Electron Local Function (ELF) Analyses
An ELF analysis supplies quantitative criteria to investigate the Jellium−like behavior in clusters and the changes in bonding properties at different regions. The ELF values are in the range from 0.0 to 1.0, where the highest value 1.0 (in red) indicates strong binding interaction, while the lowest value 0.0 (in blue) indicates weak interaction. We calculate the ELF values of (ZnS) n Hg (n = 5, 7) clusters and plot them in Figure 4. As shown in Figure 4, there is no bonding interactions between Hg and Zn. Therefore, what maintains the interaction between Zn and Hg? The NCI analysis of (ZnS) 5 Hg and (ZnS) 7 Hg is performed. The NCI analysis for (ZnS) 5 Hg and (ZnS) 7 Hg is also depicted in Figure 4. The intramolecular interactions can be distinguished from the figure. Non−bond attraction presents on the left side of the graph, while non−bond repulsion presents on the right side of the NCI graph. In Figure 4a, one attractive spike presents at −0.009 a.u. associated with the Zn···Hg interaction and one repulsive spike presents at 0.006 a.u. related to the Zn···Zn repulsive interactions in (ZnS) 5 Hg. The NCI isosurface of (ZnS) 5 Hg reveals that non−bond attractive interactions exist between Hg 0 and its five neighboring Zn atoms in (ZnS) 5 . The non−bond attractive interactions play an important role in stabilizing the (ZnS) 5 Hg cluster. The ELF analysis of Hg 0 and two neighboring Zn atoms is shown in Figure 4c. From the figure, it is obvious that no Zn−Hg bond forms in (ZnS)5Hg. The Hg 0 and Zn interaction with each other mainly comes from non−bond interactions. From Figure  4b, there is one attractive spike at −0.033 a.u. and two repulsive spikes at −0.006 and 0.030 a.u. that correspond to Zn···Hg and Zn···Zn repulsive interactions, respectively. The isosurface of the (ZnS)7Hg cluster in the middle of Figure 4 reveals that the attractive interactions are in blue, whereas the repulsive interactions are in red. It is worth noting that the Zn···Hg interaction in the (ZnS)7Hg cluster is stronger than the hydrogen bond in water dimer (−0.025 a.u.) [35]. Thus, the Zn···Hg interaction in the (ZnS)7Hg cluster is strong and can stabilize it. The three atoms' ELF analysis of Hg and neighboring Zn and S atoms in Figure 4c reveals that the Zn−Hg bond does not form without red regions, while the Zn−S bond forms with red regions existing.
In order to determine why the adsorption energy of HgCl and HgCl2 on (ZnS)n clusters is relatively large, we carried out ELF and NCI analyses for (ZnS)5HgCl, (ZnS)7HgCl, (ZnS)5HgCl2, and (ZnS)7HgCl2 clusters with bigger adsorption energies. Figure 5   From the figure, it is obvious that no Zn−Hg bond forms in (ZnS) 5 Hg. The Hg 0 and Zn interaction with each other mainly comes from non−bond interactions. From Figure 4b, there is one attractive spike at −0.033 a.u. and two repulsive spikes at −0.006 and 0.030 a.u. that correspond to Zn···Hg and Zn···Zn repulsive interactions, respectively. The isosurface of the (ZnS) 7 Hg cluster in the middle of Figure 4 reveals that the attractive interactions are in blue, whereas the repulsive interactions are in red. It is worth noting that the Zn···Hg interaction in the (ZnS) 7 Hg cluster is stronger than the hydrogen bond in water dimer (−0.025 a.u.) [35]. Thus, the Zn···Hg interaction in the (ZnS) 7 Hg cluster is strong and can stabilize it. The three atoms' ELF analysis of Hg and neighboring Zn and S atoms in Figure 4c reveals that the Zn−Hg bond does not form without red regions, while the Zn−S bond forms with red regions existing.
In order to determine why the adsorption energy of HgCl and HgCl 2 on (ZnS) n clusters is relatively large, we carried out ELF and NCI analyses for (ZnS) 5 HgCl, (ZnS) 7 HgCl, (ZnS) 5 HgCl 2 , and (ZnS) 7 HgCl 2 clusters with bigger adsorption energies. Figure 5 plots the NCI and ELF analyses for (ZnS) 5 HgCl and (ZnS) 7 HgCl clusters. The results, in Figure 5a, for (ZnS) 5 HgCl reveal two attractive spikes at −0.011 and −0.043 a.u. which are associated with the Zn···Zn and S···Hg attractive interactions, respectively. Two repulsive spikes, in Figure 5a, at 0.011 and 0.024 a.u. are Zn···Zn repulsive interactions in Zn 2 S 2 and ZnSClZn units, respectively. The ELF analysis of Hg and neighboring S and Zn atoms is shown in the upper part of Figure 5c. According to the figure, it is obvious that the S−Hg bond forms in (ZnS) 5 HgCl because of the red region between Hg and S and the Zn−S bond also presents. The ELF analysis of Cl and two neighboring Zn atoms reveals that the Zn−Cl bond forms in (ZnS) 5 HgCl. Figure 5b shows the NCI analysis of the (ZnS) 7 HgCl cluster. From the figure, one attractive and two repulsive spikes present that are locating at −0.025, 0.007, and 0.029 a.u., which correspond to Hg···S attractive interactions and Zn···Zn repulsive interactions, respectively. The ELF analysis reveals that the Hg atom in the HgCl molecule forms an Hg−S bond with the S atom, and the Cl atom forms a Zn−Cl bond with the Zn atom in the (ZnS) 7 cluster.    Figure 6c. According to the figure, it is obvious that the Cl−Hg bond forms in (ZnS)5HgCl2 according to the red region between Hg and Cl. The ELF analysis of Hg and two neighboring S and Zn atoms reveals that Hg−S and Zn−S bonds form. The ELF analysis of Cl and two neighboring Zn atoms reveals that two Zn−Cl bonds form in the ZnSZnCl unit. Figure 6b is the NCI analysis of the (ZnS)7HgCl2 cluster. According to the figure, two attractive spikes are located at −0.022 and 0.005 a.u. which are the Zn···Zn and Hg···S attractive interactions, respectively; two repulsive spikes present at 0.005 and 0.029 a.u. which correspond to Zn···Zn repulsive interactions. The ELF analysis of Cl, Hg, and S reveals that the Hg atom forms Hg−Cl and Hg−S bonds in the (ZnS)7HgCl2 cluster. According to the ELF analysis of the remaining Cl and neighboring Zn and S atoms, the Cl−Zn bond forms. The ELF analysis of Hg and neighboring S and Zn reveals that the Hg−S bond forms in the (ZnS)7HgCl2   Figure 6c. According to the figure, it is obvious that the Cl−Hg bond forms in (ZnS) 5 HgCl 2 according to the red region between Hg and Cl. The ELF analysis of Hg and two neighboring S and Zn atoms reveals that Hg−S and Zn−S bonds form. The ELF analysis of Cl and two neighboring Zn atoms reveals that two Zn−Cl bonds form in the ZnSZnCl unit. Figure 6b is the NCI analysis of the (ZnS) 7 HgCl 2 cluster. According to the figure, two attractive spikes are located at −0.022 and 0.005 a.u. which are the Zn···Zn and Hg···S attractive interactions, respectively; two repulsive spikes present at 0.005 and 0.029 a.u. which correspond to Zn···Zn repulsive interactions. The ELF analysis of Cl, Hg, and S reveals that the Hg atom forms Hg−Cl and Hg−S bonds in the (ZnS) 7 HgCl 2 cluster. According to the ELF analysis of the remaining Cl and neighboring Zn and S atoms, the Cl−Zn bond forms. The ELF analysis of Hg and neighboring S and Zn reveals that the Hg−S bond forms in the (ZnS) 7 HgCl 2 cluster.

Projected Density of State (PDOS) Analysis
In order to obtain the interaction behaviors between the (ZnS)n cluster and Hg, HgCl, and HgCl2 molecules, we take the projected density of states (PDOS) of (ZnS)7Hg, (ZnS)7HgCl, and (ZnS)7HgCl2 as examples. Figure 7 shows the PDOS maps of bare Hg 0

Projected Density of State (PDOS) Analysis
In order to obtain the interaction behaviors between the (ZnS) n cluster and Hg, HgCl, and HgCl 2 molecules, we take the projected density of states (PDOS) of (ZnS) 7 Hg, (ZnS) 7 HgCl, and (ZnS) 7 HgCl 2 as examples. Figure 7 shows the PDOS maps of bare Hg 0 when the adsorption does not happen, and the Hg and Zn atoms of the Zn−Hg bond in (ZnS) 7 Hg.      Figure 10 presents the relative stability analysis. Figure 10a shows the second−order energy differences (Δ2E) versus cluster size and Figure 10b shows the plots of the energetic gaps (Eat-Eave) of (ZnS)nHg, (ZnS)nHgCl, and (ZnS)nHgCl2 (n = 1-12) clusters as a function  Figure 10 presents the relative stability analysis. Figure 10a shows the second−order energy differences (∆ 2 E) versus cluster size and Figure 10b shows the plots of the energetic gaps (E at -E ave ) of (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 (n = 1-12) clusters as a function of cluster size n, where E at is the atomization energy and E ave is average energy. For (ZnS) n Hg, E ave = −4163.15552 − 22.15309 × n 1/3 + 15.08148 × n 2/3 − 59251.4955 × n. For (ZnS) n HgCl, E ave = −16705.92608 + 16.58575 × n 1/3 − 6.2664 × n 2/3 − 59247.58793 × n. For (ZnS) n HgCl 2 , E ave = −29236.31971 + 36.76056 × n 1/3 − 19.12771 × n 2/3 − 59244.98538 × n. The rules of their stability changing as n is given in Figure 10a. In cluster science, ∆ 2 E is a parameter reflecting cluster stability. The higher the value of ∆ 2 E, the more stable the cluster is. There are four peaks in Figure 10a corresponding to n = 2, 5, 7, and 10, manifesting that the clusters at these sizes are more stable than the neighboring sizes for (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 . In addition, there are four downward peaks at n = 3, 6, 9, and 11, which indicate that they are less stable sizes for (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 .

Stability
of cluster size n, where Eat is the atomization energy and Eave is average energy. For (ZnS)nHg, Eave = −4163.15552 − 22.15309*n 1/3 + 15.08148*n 2/3 − 59251.4955*n. For (ZnS)nHgCl, Eave = −16705.92608 + 16.58575*n 1/3 − 6.2664*n 2/3 − 59247.58793*n. For (ZnS)nHgCl2, Eave = −29236.31971 + 36.76056*n 1/3 − 19.12771*n 2/3 − 59244.98538*n. The rules of their stability changing as n is given in Figure 10a. In cluster science, Δ2E is a parameter reflecting cluster stability. The higher the value of Δ2E, the more stable the cluster is. There are four peaks in Figure 10a corresponding to n = 2, 5, 7, and 10, manifesting that the clusters at these sizes are more stable than the neighboring sizes for (ZnS)nHg, (ZnS)nHgCl, and (ZnS)nHgCl2. In addition, there are four downward peaks at n = 3, 6, 9, and 11, which indicate that they are less stable sizes for (ZnS)nHg, (ZnS)nHgCl, and (ZnS)nHgCl2.  In Figure 10b, the size at the upward peak is more stable, and that at the downward peak is less stable. There are upward peaks at n = 2, 5, 7, and 10, representing that they are more stable than their neighbor sizes. There are downward peaks at n = 3, 6, and 9, which indicates that they are less stable.
Not only from the results of ∆ 2 E, but also from those of E at − E ave , (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 clusters are relative more stable sizes at n = 2, 5, 7, and 10.

Computational Methods
The structures of (ZnS) n clusters were investigated by using the genetic algorithm combined with density functional theory (GA−DFT) method. The GA algorithm is a search heuristic algorithm that simulates the evolution process [36]. A concrete description of the GA−DFT method has been given in our former paper [37]. In the GA−DFT program, the initial search of clusters is conducted at the PBE0/def2−SVP level [38,39]. After checking the similarity of the searched structures, the top 20 low−energy isomers in the structure library are optimized at the PBE0/def2−TZVP level. The isomers are arranged according to the energy order. The structure with the lowest energy is the global minimum (GM) structure of the cluster. The PBE0/def2−TZVP method [38,39] has been widely used in zinc compounds [40][41][42][43][44]. The structures of (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 clusters have been obtained based on the GM structures of (ZnS) n . Concretely, isomers with different structures are obtained by adding an Hg atom, HgCl, and HgCl 2 to the GM structures of (ZnS) n clusters, and the isomers with the lowest energies are the global optimal structures of (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 clusters, respectively. In the computational processes of (ZnS) n , (ZnS) n Hg, and (ZnS) n HgCl 2 , the charge and density are set to zero and one, respectively. The charge and density are set to zero and two for (ZnS) n HgCl clusters. For Zn, S, and Cl atoms, all the electrons are included in the calculations, whereas an effective core potential (ECP) and 20 valence electrons are considered for the Hg atom. Vibrational energies of each structure are computed to verify whether it is a stable structure. All the structures reported here are stable without one imaginary frequency. The D3(BJ) correction of van der Waals force is used in geometric optimization and vibration frequency calculation processes [45]. The D3 balance correction method proposed by Boys and Bernadi can correct the calculated lower binding energy value, thus, effectively making up for the precision defect of the PBE0 method in the research process [34]. All calculations are performed in the Gaussian 16 program [46]. The convergence threshold parameters of Gaussian 16 during optimization are 4.5 × 10 −4 for maximum force, 3 × 10 −4 for RMS force, 1.8 × 10 −4 for maximum displacement, and 1.2 × 10 −4 for RMS displacement. When geometric optimization is performed, the atoms of Hg 0 , HgCl, and HgCl 2 are completely relaxed. The Gauss view 6.0.16 visualization software is used to obtain the molecular structures [47], and all the structures of the clusters are viewed and obtained through the software. The Multiwfn 3.8 software [48] is used to calculate electron localization function (ELF), non−covalent interactions (NCI), and projected density of state.
According to the following formula [33], the adsorption energy (E ads ) is obtained: where E (adsorbate/substrate) represents the energy of (ZnS) n Hg, (ZnS) n HgCl, or (ZnS) n HgCl 2 ; E adsorbate is the energy of Hg 0 , HgCl, or HgCl 2 ; E substrate is the energy of (ZnS) n clusters. All the energies are those for the global minimum structures. Basis set superposition error (BSSE) has been considered during the adsorption energy (E ad ) calculations of Hg 0 , HgCl, and HgCl 2 over (ZnS) n clusters. If the value of E ads is negative, the adsorption process is exothermic and it favors to occur. When studying adsorption, it is particularly important to distinguish between physical adsorption and chemical adsorption of adsorbate. Whether new chemical bonds are formed is an important basis for distinguishing physical adsorption from chemical adsorption. In this study, chemisorption is judged by two points: new chemical bonds form between the adsorbate and the substrate during adsorption; the adsorption energy is relatively large.
The non−covalent interaction (NCI) analysis method can be used to analyze the stability of clusters. The NCI method [35] proposed by Yang et al. has been used to analyze many systems [49][50][51]. During the NCI analysis, the function is reduced density gradient (RDG) and the variable is electron density (ρ). The expression of RDG is: The electron density Hessian matrix (i.e., sign(λ 2 )) can be used to differentiate bonding (λ 2 < 0) and non−bonded (λ 2 > 0) interactions. The NCI diagram is a scatter plot, where the ordinate is s (RGB) and the abscissa is ρ * sign (λ 2 ) . Low−density peaks in the NCI map stand for non−covalent interactions. Using the VMD program, the gradient isosurface can be obtained [52]. Based on the values of sign(λ 2 ) * ρ, the gradient isosurfaces are colored [52] according to a RGB (red−blue−green) scale.
Average energies (E ave ) of the GM structures for the (ZnS) n Hg, (ZnS) n HgCl, and (ZnS) n HgCl 2 series are also calculated to study the relative stability of the clusters. E ave are four−parameter fitting functions of the GM energies, which can be expressed as: E ave = a + b × n 1/3 + c × n 2/3 + d × n, where n is the size of the cluster; a, b, and c are fitting coefficients. E at is the GM energies of the clusters.

Conclusions
Hg 0 is able to be physisorbed on (ZnS) n (n = 1-12) clusters with adsorption energy in the range from −13.33 to −4.04 kcal/mol. The orbitals of Hg 0 can hybridize with the orbitals of Zn. The interactions between (ZnS) n (n = 1-12) and Hg 0 are mainly non−convalent interactions. HgCl and HgCl 2 can interact with the S and Zn to form Hg−S and Zn−Cl bonds, which induce strong chemisorptions on (ZnS) n (n = 1-12) clusters. Considering that the adsorption energies of HgCl and HgCl 2 on (ZnS) n (n = 1-12) clusters predicted in this study are large and new chemical bonds are formed between HgCl, HgCl 2 , and (ZnS) n clusters, we believe that (ZnS) n clusters have great potential as efficient mercuric chloride capture materials for coal−fired power plants. Our future work will focus on the reaction mechanism of Hg 0 , HgCl, and HgCl 2 adsorption on (ZnS) n clusters, which is another important issue of Hg 0 , HgCl, and HgCl 2 capture. We will also consider various zinc−related materials, including pure zinc, to further explore the role of sulfur in enhancing Hg 0 , HgCl, and HgCl 2 binding.