Experimental and mechanistic study on the enrichment of heavy metals by modified calcium oxide during MSW pyrolysis

ABSTRACT Experimental and density functional theory (DFT) calculations show that NaCl modified can promote the adsorption of heavy metals Cr, Cd, and Pb by CaO in the municipal solid waste (MSW) pyrolysis. CrCl3 (g), CdCl2 (g) and PbCl2 (g) are the main form of Cr, Cd and Pb in MSW pyrolysis gas. The DFT calculations show that the adsorption energy of NaCl modified CaO (NaCl/CaO) increased from 285.37 kJ/mol, 130.58 kJ/mol and 145.72 kJ/mol to 373.80 kJ/mol, 216.03 kJ/mol and 214.67 kJ/mol for Cr, Cd and Pb compared with CaO. Similarly, the experimental average adsorption rates increased from 43.32%, 40.13% and 25.54% to 56.42%, 46.44% and 46.22%. The bondings between CaO and CrCl3, CdCl2, PbCl2 molecules are the outermost 2p orbitals of O in CaO hybridizes with the 3d and 3p orbitals of Cr, the 5s and 4d orbitals of Cd, and the 6p and 6s orbitals of Pb. After the adsorption of NaCl, the total charge change on the CaO surface changed from 0.12e to 0.01e, and the number of electrons obtained by CrCl3, CdCl2 and PbCl2 molecules from the adsorbent increased from 0.51, 0.26 and 0.22 e to 0.94, 0.53 and 0.34 e. NaCl promoting the electron-losing ability of calcium oxide surface. Meanwhile the Cl atom of NaCl form new chemical bonds with heavy metal atoms, increasing adsorption sites of heavy metal molecules with calcium oxide. This study contributes to the adsorption of heavy metals during MSW pyrolysis by CaO and NaCl/CaO.


Introduction
The amount of urban MSW generated in large and medium-sized cities in China in 2020 is 235.602 million tons.Among many waste treatment methods, pyrolysis is an important development direction for municipal solid waste treatment due to the advantages of effective reduction of dioxin generation and diversification of product utilization (Lei et al. 2018).Cr, Cd and Pb, as three of the five heavy metal toxins, have high contents in MSW and are harmful to the people and environment after their emission (Viczek et al. 2020).As semi-volatile heavy metals, they are volatilized in a significant amount into pyrolysis gas and oil during the pyrolysis of MSW, which affects product utilization (Du et al. 2021;Miskolczi, Ates, and Borsodi 2013).Therefore, the control of heavy metals, Cr, Cd and Pb, in MSW pyrolysis process becomes an urgent problem to solve.
In the control technology of heavy metals, the in-furnace additive control technology is simple and accessible.The additives are cheap and easy to obtain, thus it is considered as a promising technology for heavy metal control (Li et al. 2016).Wang et al. (2016) investigated the control of heavy metals by Al 2 O 3 , SiO 2 and CaO, and the results illustrated that CaO showed better adsorption of Pb and Cd compared with Al 2 O 3 and SiO 2 .Meanwhile Chen et al. (2013) showed that the removal efficiency of CaO for heavy metal Cr in coal combustion flue gas was better than that of Al 2 O 3 and Fe 2 O 3 .CaO is considered as a promising heavy metal adsorption material because of its large specific surface area and adsorption capacity (Luo et al. 2019).The form of heavy metals during the pyrolysis of MSW varies with the physical and chemical properties of the waste, the pyrolysis temperature, and the pyrolysis atmosphere (Dong et al. 2015).Generally, due to the high chlorine content in MSW and the small particle size and volatility of heavy metal chlorides, gaseous heavy metals during waste pyrolysis are mostly present in the form of heavy metal chlorides (Zhang et al. 2013).Furthermore, Peng and Lin (2014) showed that the higher the Cl content in the fuel, the more effective the calcium-based adsorbent was in adsorbing heavy metals.The excellent performance of calcium oxide for heavy metal adsorption has been reported in heavy metal steam experiments or solid waste incineration experiments, but the adsorption of heavy metals in the pyrolysis of MSW has been rarely studied.Therefore, it is significant to investigate the adsorption effect of CaO on heavy metals during MSW pyrolysis.
Although CaO has a relatively good performance in trapping heavy metals, the adsorption effect of natural calcium-based adsorbents on heavy metals is still limited.Therefore, the modification of calcium-based adsorbent materials to improve their adsorption performance has gradually received attention and research from scholars, and among which the addition of metal oxides and inorganic salts for modification is the main idea.Li et al. (2021) showed that the addition of CeO 2 can effectively prevent the sintering of CaO particles, thus enhancing the CaO adsorption performance on heavy metals at high temperatures.Meanwhile, CeO 2 can be used as oxygen donors to provide O 2-and increase the active functional groups for heavy metal adsorption (Yoon and Lee 2019).Liang et al. (2017) used NaCl to modify heavy calcium carbonate, and the removal of heavy metal ions such as Cd 2 + and Cu 2+ from water by the modified adsorbent increased from 60% to 98%.In addition, (Lu, Wang, and Guo 2008).adopted NaCl to modify CaO, the results showed that NaCl could increase the layer spacing of CaO, and after the modification, the adsorption capacity of CaO on CdCl 2 increased from 0.5 g/g to 0.73 g/g.In summary, CaO does not have the problem of sintering at the pyrolysis temperature of 400°C − 600°C, and the doping of Ce, Zr and other oxygen-rich cavities is more expensive, which restricts the large-scale industrial application.NaCl exists in large quantities in seawater and the extraction process is mature, so compared with CaO modification methods such as loading metal oxides, the use of NaCl modification to improve the adsorption capacity of CaO has the advantages of low cost and simple operation.Meanwhile, the effect of sodium chloride on the adsorption of heavy metals in the pyrolysis of domestic waste by calcium oxide is not yet known.Therefore, a related study was conducted in this paper.
Some progress has been made in the study of the control of CaO adsorption on heavy metals during waste pyrolysis, but the traditional experimental techniques can only reflect the macroscopic effects and cannot avoid the interference of certain experimental factors.With the rapid development of computers, the use of computer simulations has become a trend to the adsorption mechanism study.Lu et al. (2021).used DFT to calculate the migration and transformation mechanisms of Pb 0 and PbCl 2 on CaO surface, whereas Yu et al. (2020).investigated the adsorption energy of CaO, Al 2 O 3 , and SiO 2 on PbO and As 2 O 3 using DFT calculations, and the results showed that the adsorption energy of CaO on As 2 O 3 was the largest.However, previous DFT studies have focused on the adsorption of pure heavy metals on calcium oxide.The morphology of the presence of multiple heavy metals during waste pyrolysis and the microscopic mechanisms of their interactions with calcium oxide are not understood.Moreover, the effect of NaCl on the adsorption effect of CaO and its microscopic mechanisms have not been widely recognized so far.Therefore, it is important to investigate the adsorption mechanism of CaO on Cr, Cd and Pb using DFT for the control of heavy metals in MSW pyrolysis process.
The effects of CaO and NaCl/CaO on the adsorption of various heavy metals in the lowtemperature (400°C −600°C) anoxic atmosphere of MSW pyrolysis have not been studied.Moreover, there are research gaps in the morphological changes of heavy metals during MWS in a low-temperature anoxic atmosphere and the microscopic mechanism of their adsorption by CaO and NaCl/CaO.In this paper, based on the thermodynamic simulation calculation to obtain the presence morphology of heavy metals Cr, Cd and Pb during the MSW pyrolysis process in the temperature range of 400°C − 600°C.The adsorption energies, charge transfer, bond population values and density of states of Cr, Cd and Pb adsorption by CaO and NaCl/CaO were calculated by DFT, which enabled to obtain the microscopic mechanism of heavy metal Cr, Cd and Pb adsorption by CaO, mainly including the adsorption active site, bonding type and bonding hybridization mode.The differences in bonding of CaO and NaCl/CaO with heavy metals were also obtained, which led to the reason why NaCl affects the adsorption of heavy metals by CaO.And then, the adsorption of CaO and NaCl/CaO on heavy metals in MSW pyrolysis was experimentally investigated.The results were combined with simulation calculations to establish a bridge between microscopic simulations and macroscopic experiments, afterward to reveal the mechanism of heavy metal adsorption by CaO and NaCl/CaO at a deeper level.The study in this paper provides insight into the microscopic mechanism of heavy metal adsorption by CaO and NaCl/CaO, and contributes to the exploration of CaO and its modifiers in heavy metal adsorption during the pyrolysis of MSW.

Materials
Regarding the real MSW is complex and inhomogeneous, it is problematic to get gram-scale experimental regulation from real waste.Therefore, simulated waste was used in this experiment.Configuration of simulated waste based on real waste components (collected from a landfill in Guangdong, China), with a morphological simulation.The composition of the simulated waste is shown in Table S1, and the industrial analysis and elemental composition of the simulated waste are shown in Table S2.The list of the main reagents used in the experiment is shown in Table S3.

Materials preparation and characterization
The preparation of sodium chloride modified calcium oxide is shown in Fig. S1: mix 5 g CaCO 3 with 0.35 mol/L NaCl solution, stir in a water bath at 25°C for 48 h, take out and centrifuge, after that dry in an oven at 105°C for 24 h, then calcine in a nitrogen atmosphere at 900°C for 3 h, cool and grind to below 100 mesh to obtain loaded sodium chloride Calcium oxide (NaCl/CaO), dried and stored.The crystal structure of CaO and CaO/NaCl were analyzed via a D8 Advance X-ray diffractometer (XRD) instrument purchased from Bruker, Germany, which used the Cu Kα (λ = 0.154056 nm) radiation at 40 kV and 40 mA in the scanning range of 30° − 85°.

Experimental method
The MSW pyrolysis experiments were carried out in a tube furnace with gas source, reactor, condenser tube, and flue gas cleaning system as shown in Fig. S2.The tube furnace in the experiment has a tube diameter of 60 mm and a tube length of 1000 mm, using a silicon molybdenum rod as the heating element for programmed heating.
In each experiment, the 0.5 g additive and 5 g simulated waste were mixed and sent into the tube furnace with corundum porcelain boat.Meanwhile, Nitrogen was fed to the tube furnace through the control of a rotameter with a flow rate of 2 L/min.Afterwards, the pyrolysis temperature was adjusted to set points (400°C − 600°C), keeping the pyrolysis for 1 hour.At the end of the experimental device, there are condenser tubes behind the tube furnace to condense the pyrolysis oil, and two absorption bottles were connected to purify the flue gas, which contain 5% HNO 3 and 10% H 2 O 2 absorption solution respectively.
Pyrolysis residue was digested on the graphite digester at 120°C (HNO 3 : HClO 4 : HF = 8 : 2 : 2).When there was no solid in the digestion tube and the solution was clear, adjust the digestion temperature to 160°C to drive out the acid.In addition, fixing the digestion solution in a 50 mL volumetric flask and filtering after 1-2 mL solution was left in the digestion tube.At last, the content of heavy metals after digestion was tested by ICP-AES, and the retention rate (R) of heavy metals in solid product was defined as shown in Eq. ( 1), the heavy metal adsorption rate (D) of the adsorbent is shown in Eq. ( 2).
In Eq. ( 1), C char and C waste indicate the concentration of one heavy metal in solid char and simulated waste, respectively (mg/kg).M char and M waste denote the weight of generated char and raw simulated waste, respectively(kg).
In Eq. ( 2), D represents the adsorption rate of the added additive on heavy metals except the enrichment rate of pyrolysis carbon on heavy metals.R raw and R ad represent the retention rate of the original waste without the additive and the retention rate after the additive is added, respectively.

Thermodynamic calculation method
The thermodynamic system equilibrium calculation in this work was via the equilibrium composition module of HSC Chemistry 6.0 thermodynamic software.The heavy metals species was obtained based on the Gibbs free energy minimization principle, which is minimizing the Gibbs free energy of a constant temperature and pressure system under the condition of material equilibrium (Holler 1996).Thermodynamic equilibrium calculations can analyze the trend of some variables, such as the trend analysis of heavy metal fugacity patterns (Poole et al. 2008).Therefore, the morphological transformation of heavy metals during pyrolysis was analyzed as a research object to provide the gas phase morphology of Cr, Cd and Pb for DFT calculation.The input elements are listed in Table S2.
The temperature range was from 350°C to 650°C and the temperature interval is 20°C.The simulated atmosphere is N 2 .

DFT calculation method
All DFT calculations are based on the CASTEP module (Segall et al. 2002), the exchange-correlation functional for the geometric optimization of calcium oxide crystals are chosen as generalized GGA-PBE (Perdew-Burke-Ernzerh of generalized gradient approximation) (Perdew, Burke, and Ernzerhof 1997).The results of plane wave kinetic energy and k-point convergence tests are shown in Table S4.And according to the result, the plane wave kinetic energy and k-point were set 500 eV and 3 × 3 × 1 respectively.The convergence criteria for the geometrical optimization: maximum atomic displacement of 5.0 × 10 −4 nm, interatomic force of 0.01 eV/Å, interatomic internal stress of 0.02 GPa, and total energy change of the system of 5.0 × 10 −6 eV/atom.The convergence accuracy of the selfconsistent field is set to 1 × 10 −6 eV/atom.The optimized lattice parameters of calcium oxide are a = b = c = 4.886 Å, α = β = γ = 90°.The experimental values of CaO crystals are a = b = c = 4.811 Å and α = β = γ = 90° (Zintl, Harder, and Dauth 1934), with a relative deviation of 1.56% < 2%.Therefore, the parameter settings are reasonable.Since 001 surface is considered to be the lowest and most stable surface for CaO surface energy (Yang et al. 2020), this study chooses 001 surface as the surface for adsorption calculation.The model was built with a 3 × 3× 1 supercell of structurally optimized CaO as the source cell, with crystallographic surface cut along the 001 direction, and a vacuum layer of 15 Å thickness was created.The bottom two layers of atoms were fixed and the top layer was surface chirped.Fig. S3 shows the NaCl/CaO model for structural optimization, whose construction method is similar to the study by (Wang, Zhong, and Du 2021).
In this paper, the adsorption energy is used to evaluate the stability of the adsorption system, and the electron density difference and population distribution are used for analyzing the electron transfer and bonding type between the adsorbent and the adsorbate, and the density of states is used to analyze the bonding orbital hybridization.
The adsorption energy (E ads ) in this paper is calculated from Eq. ( 3).
In Eq. ( 3), E total is the total energy of the system after adsorption, E slab is the energy of the surface model, and E A is the energy of the adsorbed mass before adsorption.When there has been already one small molecule adsorbed on the surface of the solid adsorbent, the adsorption energy E adsA of another small molecule can be described as Eq. ( 4).
In Eq. ( 4), E A/B/slab is the total energy of both A and B adsorbed molecules after adsorption on the surface of the solid adsorbent, and E B/slab is the total energy of B molecules when adsorbed on the surface alone.

Thermodynamic calculation
The heavy metals species form results during MSW pyrolysis are shown in the Figure 1.Cr 2 O 3 is the main form of Cr species and gradually transformed to CrCl 3 (g) after 450°C.It is considered that CrCl 3 (g) is main existing form in the pyrolysis gas.CdCl 2 (g) is the stable Cd species in the pyrolysis temperature range and a small amount of CdCl 2 (g) converted to Cd (g) after 550°C.In the temperature range of 350°C to 450°C, PbCl 2 (s) transformed to PbCl 2 (g) progressively, and after 600°C, PbCl 2 (g) started to decompose to PbCl (g) slowly.Therefore, in the pyrolysis gas, CrCl 3 (g), CdCl 2 (g) and PbCl 2 (g) are the main forms of Cr, Cd and Pb species in temperature from 400 to 600°C.It can be seen that, in contrast to the MSW combustion process where heavy metals exist in the form of oxides (Guo et al. 2018), in the waste pyrolysis process heavy metals are more inclined to exist in the form of chlorides.Above all, the above three substances were selected as adsorbents in the DFT calculation for in-depth study.
Based on the thermodynamic calculations, Figure 2

Adsorption configuration analysis
It has been shown that adsorption occurs mainly between heavy metal atoms and oxygen atoms (Lu et al. 2021), DFT calculations were performed by placing heavy metal molecules on the adsorbent surface.Figure 3 shows the adsorption configurations of CrCl 3 , CdCl 2 and PbCl 2 on the CaO (001) and NaCl/CaO (001) surfaces.The distance between the surface O atom and the heavy metal atom is less than the sum of the atomic radius, so there is a bond between the O atom and the heavy metal atom.When CaO adsorbs CrCl 3 , CdCl 2 and PbCl 2 molecules, the surface O atoms move upward in the vertical direction and close to the heavy metal molecules.While the chlorine atoms of heavy metal molecules are far away from the surface of calcium oxide, resulting in an increase in the bond length  and a decrease in the bond angle of the heavy metal chloride molecules.After loading NaCl, the mutual attraction between the chlorine atoms of sodium chloride and the heavy metal atoms leads to the deflection of the heavy metal molecules on the surface of calcium oxide after adsorption.Moreover, the bond length of M (heavy metal atom) -O changes and the bond angle further decreases.The distance between the Cr atom and the surface O atom is shortened from 1.806 Å to 1.774 Å, which indicates that the attraction between the atoms is stronger and the bonding is more stable.Different from the O-Cr bond, the O-Cd and O-Pb bond lengths increase with the adsorption of NaCl/CaO.The heavy metal atoms approach from the positive upward direction of the O atoms toward the Cl atoms, resulting the elongation of the distance between the heavy metal atoms and the O atoms.Therefore, the loading of sodium chloride increases the interaction between the chlorine atoms and the heavy metal atoms and affects the attraction between the oxygen atoms and the heavy metals.

Adsorption bonding analysis
To further investigate the interaction between the heavy metals and adsorbents surface, the electron density differences are calculated as shown in Figure 4.The blue regions denote charge depletion, while red regions represent charge accumulation.It is generally considered that covalent bonding occurs when the charge densities between atoms overlap and the electron density differences accumulate.When the charge densities between atoms do not overlap but there is charge transfer, the bonding is considered to be ionic (Ma, Zhao, and Yan 2013).As calcium oxide adsorbs heavy metal molecules, there is a significant charge density overlap and charge accumulation between the heavy metal atoms and the raised oxygen atoms, demonstrating the covalent characteristic of the M (heavy metal atom)-O bond.Meanwhile, red electron clouds are formed between Cl atoms of NaCl and Cr, Cd, and Pb atoms after loading NaCl, which is consistent with the conclusion drawn from the analysis of the adsorption configuration that sodium chloride has an attractive effect on heavy metals.Compared with Cd and Pb atoms, the charge accumulation between Cr atom and O atom of CaO and Cl atom of NaCl is deeper in color, which represents more shared electrons between the Cr-O and Cr-Cl bonds.And it also represents that the bonding is more stable, the Mulliken bonding residence in Table 1 also confirm this conclusion.The adsorption effect increases the bonding of heavy metal atoms with chlorine atoms in addition to the original oxygen atoms after NaCl modification.Moreover, the values of the bonding population between the modified O atoms and the heavy metal atoms are all increased, especially the Cr-O bond, demonstrating that the bonding orbital interactions were enhanced after the modification.Simultaneously, the value of the bonding residence formed by chlorine atoms with heavy metals is smaller than that formed by oxygen atoms with heavy metals.Therefore, the adsorption of heavy metals by oxygen atoms dominates after modification.
The Mulliken charge can be adopted to calculate the distribution of atomic charges and to quantitatively analyze the tendencies of charge transfer between atoms (Liu et al. 2011).The adsorption energies and the Mulliken charge change were listed in Table 2.The adsorption energies of CaO for the three heavy metals are as follows: CrCl 3 > PbCl 2 > CdCl 2 .All adsorption energies are above 50 kJ/mol, demonstrating that it is chemisorption between CaO and heavy metal molecules.Furthermore, the adsorption energies of the three heavy metals are improved by NaCl loading.After NaCl modification, the adsorption energy magnitudes are changed to CrCl 3 > CdCl 2 > PbCl 2 .Specifically, the adsorption energy of CrCl 3 was enhanced the most, with an increase of 88.435 kJ/mol.The number of electrons obtained by CrCl 3 , CdCl 2 and PbCl 2 molecules from the adsorbent increased from 0.51, 0.26 and 0.22 e to 0.94, 0.53 and 0.34 e.The loading of sodium chloride increases the ability of chlorine to transfer electrons to heavy metals, which induces more electron transfer to the heavy metal molecules and enhances the connection between the heavy metal molecules and the adsorbent.To better illustrate the effect of NaCl loading on calcium oxide, the charge changes of atoms on the calcium oxide surface before and after NaCl adsorption were calculated and supplemented in the paper.The relevant atoms are numbered in Fig. S4 and the results of the calculations are shown in Table S5.After the adsorption of NaCl, the surface charge distribution of O and Ca atoms on the surface of CaO ( 001) is disrupted.Compared to before the adsorption of NaCl molecules, the charge number at the p orbitals of O3 atoms increases, resulting in an increase in the number of negative charges carried by O3 atoms and a decrease in the number of negative charges carried by the remaining atoms, and the adsorption of NaCl molecules enhances the localized charged nature of the CaO (001) surface.s and d orbitals of Ca atoms increase in charge number, and the number of lost electrons decreases compared to that before the adsorption of NaCl molecules, which still have a certain electron loss.After the adsorption of NaCl molecule, the s-orbital charge of Na atom increases and the p-orbital charge of Cl atom decreases.The change of charge during the adsorption process is mainly completed by the transfer of valence electrons of the atom, and after the adsorption is completed, the NaCl molecule gets 0.02e electrons from the surface of CaO (001).After the adsorption of NaCl, the total charge change on the adsorbent surface changed from 0.12e to 0.01e, and the positive charge on the adsorbent surface was weakened, and the electron gaining ability was reduced and the electron losing ability was enhanced.

Density of states analysis
The total density of states (TDOS) is shown in Figure 5.After adsorption, the shift of the higher to lower energy level states indicates that the adsorption structure becomes stable.Particularly, the larger shift of each energy level state to the lower energy level after adsorption of Cr shows a stronger adsorption interaction with Cr.The creation of new peaks after adsorption of different heavy metals illustrated the introduction of new bonds or the creation of new bonds, which will be analyzed in terms of the partial-wave state density.
The electrons density distribution and partial-wave state density (PDOS) of CaO adsorbed heavy metals were shown in Figure 6, where the analysis position was marked by the yellow box.There was an electronic overlap between the Cr, Cd, Pb atoms in CrCl 3 , CdCl 2 , PbCl 2 molecules and the oxygen atom on CaO ( 001   The electron overlap area between Pb atoms and O atoms is smaller than that of the other two heavy metals, thus the Pb-O bonding interaction is weaker, which is consistent with the analysis of the bonding population in Table 1.
The electron density distribution of NaCl/CaO adsorbed heavy metals were depicted in Figure 7.The partial-wave state density of each atomic orbital is slightly shifted to lower energy levels after the addition of CaO loaded with NaCl, illustrating that the loading of NaCl can make the adsorption reaction more stable.The orbitals that resonate after adsorption do not change, demonstrating that the hybridization mode of bonding between heavy metal molecules and CaO remains unchanged.Obviously, all bondings are formed by the interaction of the electron in the outer layers of the atoms.In particular, the charge density distribution of the Cl atoms in NaCl overlaps with that of the heavy metal atoms.The PDOS also shows the chlorine atom has resonance with Cr, Cd and Pb atoms at 0.044 eV, −4.132 eV and 2.436-4.333eV respectively.The chlorine atoms are bonded with the heavy metal molecules to form species similar to CrCl 4 − , CdCl 3 − , PbCl 3 − , and the added chlorine atoms of NaCl have mutual attraction and electron overlap with both heavy metal molecules and calcium oxide, which increases the pathway of electron interaction between calcium oxide and heavy metals.Table 2 also indicates that more electrons are received by the original heavy metal molecule after the addition of sodium chloride.In general, the increased number of interacting electrons and the formation of new bonds increase the adsorption capacity of the modified calcium oxide for heavy metals.
So far, DFT calculations have shown that CaO is chemisorbed to CrCl 3 , PbCl 2 , and CdCl 2 .Furthermore, sodium chloride enhances the adsorption energy of calcium oxide to heavy metals.The differential electron density diagram shows that there is an electron transfer between the oxygen atoms of calcium oxide and the heavy metal atoms.Also, there is a similar electron transfer between the chlorine atoms and the heavy metal atoms after loading sodium chloride.Therefore, it is presumed that chemical bonds were formed between the chlorine atoms, oxygen atoms and heavy metal atoms.This conjecture was confirmed by the population distribution, which calculated the bonding parameters between the oxygen atom, the chlorine atom and the heavy metal atom.The loading of sodium chloride provides a new electron transfer pathway for heavy metal adsorption by calcium oxide, which increases the adsorption energy of heavy metals adsorbed by calcium oxide.The hybridization between CaO and CrCl 3 , CdCl 2 , and PbCl 2 molecules is the hybridization of the 2p orbital of O in CaO with the 3d and 3p orbitals of Cr, the 5s and 4d orbitals of Cd and the 6p and 6s orbitals of Pb.The loading of sodium chloride does not change the bonding hybridization mode, but makes the adsorbed electron energy lower and the structure more stable.

Analysis of adsorption experiment results
In order to confirm the effect of loaded sodium chloride on the adsorption of heavy metals by calcium oxide, pyrolysis experiments were carried out.The XRD spectra of the original CaO and modified CaO are shown in Figure 8.The diffraction peaks of the original CaO have orderly kurtosis, sharp peak shape and well-balanced symmetry.There is little difference in peak strength and peak position between NaCl/CaO and original CaO in XRD patterns, which illustrates that NaCl modification does not destroy the basic structure of CaO.However, the peak of NaCl/CaO modified NaCl is weakened, which is attributed to the enlargement of the interlayer spacing of CaO due to the insertion of NaCl molecules.It is confirmed that NaCl has been loaded on CaO.
Figure 9 shows the retention rate of CaO and NaCl/CaO to the three heavy metals.From Figure 9(a), the retention rate of heavy metal Cr decreased from 70% to 50% in the range of 400°C to 450°C, which is related to the gradual transformation of Cr 2 O 3 to CrCl 3 (g) after 450°C in the results of thermodynamic simulation.After the addition of CaO, the overall increase of the  retention rate was observed, and the retention rate was above 65% at 400°C − 600°C.The modification of NaCl can effectively improve the retention rate of CaO at high temperature, which can improve the retention rate by about 8% at 550°C and 600°C.From Figure 9(b), the retention rate was improved by 25% to 30%, and ranged from 50% to 73% in the temperature range of 400°C to 600°C after the addition of CaO.Meanwhile, the addition of NaCl/CaO adsorbent, the retention rate was improved by 5% − 8% compared to CaO, and the retention rate was greater than 60% up to 550°C.From Figure 9(c), the retention rate of Pb without adsorbent decreases significantly from 75.3% to 55.6% with increasing temperature within 400°C to 500°C, which is related to the conversion of PbCl 2 to PbCl 2 (g).After the addition of CaO, the retention rate of Pb was above 62.9% in the whole temperature range.The retention rate of CaO on Pb increased after NaCl modified.In the temperature range of 400°C − 600°C, the retention rate of Pb could be above 74.9%.It can be seen that CaO can enhance the retention effect of all three heavy metals.Interestingly, the loading of NaCl can enhance the retention effect of CaO, which shows consistency with the conclusion reached by quantum chemistry.
From Figures 1 and 9, it can be seen that in the range of 400°C − 500°C, the retention rate of heavy metals still has a large variation because the morphology of the three heavy metals is still in change.At 500°C − 600°C, the morphology of heavy metals in the gas phase is stable as heavy metal chlorides, and there is less variation in the heavy metal retention rate without additives.Therefore, the relationship between adsorption energy and adsorption rate was explored with the adsorption rate at 500°C − 600°C.Figure 10 demonstrates the relationship between adsorption energy and adsorption rate of heavy metals adsorbed by CaO and NaCl/CaO.For the three heavy metals, the adsorption rate increases equally with the increase of adsorption energy.Moreover, the adsorption energy of chromium is greater than the other two heavy metals, and the adsorption rate of chromium is similarly greater than the other two heavy metals.It is shown that there is a positive correlation between adsorption energy and adsorption rate, which linking quantum chemical calculations with experiments.Overall, both the experimental results and quantum chemical calculations present the effectiveness of NaCl loading, showing consistency in the results.

Microscopic mechanism of heavy metal adsorption by CaO and NaCl/CaO
The results of quantum chemical simulations in this paper provide good theoretical guidance for the modification of adsorbents and the control of heavy metals.The consistency of the adsorption energy calculation results and the pyrolysis experimental retention rate results build a bridge between the microscopic world and macroscopic experiments, thus allowing us to explore more microscopic adsorption mechanism by more and more subtle means such as density of states and electron density difference.Therefore, the microscopic mechanisms of heavy metal adsorption by CaO and NaCl/CaO are discussed in depth below.
CaO has adsorption effect on heavy metals during MSW pyrolysis (Jiao et al. 2016); (Xie et al. 2020), but the details of adsorption of specific forms of heavy metals at low temperatures and low oxygen are still unclear.The loading of NaCl has a facilitating effect on the adsorption of heavy metals by CaO, and Chen and Zhang (1997) concluded that the loading of NaCl can effectively change the microporous structure of CaO and increase the specific surface area by modeling calculations of the pore structure.Lu, Wang, and Guo (2008) concluded that the loading of NaCl can form co-crystals by the characterization analysis of the material, increasing the CaO layer spacing and enhancing the adsorption capacity.In order to describe the adsorption of CaO and NaCl/CaO on the heavy metals CrCl 3 , CdCl 2 and PbCl 2 in a more detailed and clear manner, Figure 11 shows the adsorption mechanism of CaO and NaCl/CaO on CrCl 3 , CdCl 2 and PbCl 2 .
CaO is chemisorbed to CrCl 3 , CdCl 2 and PbCl 2 .CaO adsorbed CrCl 3 , CdCl orbitals of Cd, and the O-Pb bond is the hybridization of the 2p orbital of O with the 6p and 6s orbitals of Pb.The loading of NaCl does not change the bonding mode of CaO adsorbed heavy metals.The addition of chlorine interacts with heavy metal molecules to form species similar to CrCl 4 − , CdCl 3 − , PbCl 3 − .The additional chlorine atoms also interact with calcium oxide, leading to an increase in the electron transfer to the heavy metal molecule.The change in charge transfer results in larger bonding population for the M-O bonds, causing some of the M-O bond length to become shorter and the bonds more stable.Meanwhile, the formation of new bonds leads to more adsorption sites for heavy metal molecules on calcium oxide and an increase in adsorption energy.

Conclusion
In this paper, DFT calculations were used to obtain the adsorption mechanism, including the adsorption energy, bonding parameters (bond length, bond population, differential charge), and bond hybridization types of CaO and NaCl/CaO for the heavy metals Cr, Cd and Pb.Experimental studies were conducted to investigate the retention of Cr, Cd and Pb by CaO and NaCl/CaO.The obtained calculation results were compared with the experimental results, and a similar pattern was found.The combination of experiments and calculations was used to confirm with each other, and the main conclusions of this paper were drawn as follows.
(1) In the temperature range of 400°C − 600°C, CrCl 3 (g), CdCl 2 (g) and PbCl 2 (g) are the main form of Cr, Cd and Pb in the MSW pyrolysis gas.All adsorption energies between heavy metals and adsorbent are above 50 kJ/mol, indicating that CaO and NaCl/CaO are mainly chemisorbed for the three heavy metals.
(2) The adsorption mechanism of CrCl 3 , CdCl 2 and PbCl 2 is mainly based on the formation of covalent bonds between O atoms and heavy metal atoms.Specifically, the bondings between CaO and CrCl 3 , CdCl 2 , PbCl 2 molecules are formed by hybridizing the outermost 2p orbitals of O in CaO with the 3d and 3p orbitals of Cr, the 5s and 4d orbitals of Cd, and the 6p and 6s orbitals of Pb.Sodium chloride modification does not change the way of bond hybridization, simultaneously increases the hybridization of the p orbitals of chlorine atoms with heavy metal atoms to form bonds.
(3) The experimental results showed that the retention rate decreased gradually with the increase of temperature in the temperature range of 400°C − 600°C, which could reach more than 65%, 50% and 60%.The heavy metal form is stable in the range of 500°C-600°C, and the adsorption rate and adsorption energy of this temperature range are selected for comparison.on the one hand, the interaction of NaCl with CaO changes the charge transfer on the CaO surface.
After the adsorption of NaCl, the total charge change on the adsorbent surface changed from 0.12e to 0.01e, and the positive charge on the adsorbent surface was weakened, and the electron gaining ability was reduced and the electron losing ability was enhanced.The number of electrons obtained by CrCl 3 , CdCl 2 and PbCl 2 molecules from the adsorbent increased from 0.51, 0.26 and 0.22 e to 0.94, 0.53 and 0.34 e.The number of bonding electrons increased, resulting in more stable bonding, and some of the bond lengths become shorter, which makes the adsorption energy increase.On the other hand, the addition of NaCl increases the bonding between Cl and heavy metal atoms.The additional chlorine in the heavy metal molecule interacts with the calcium oxide surface, increasing the adsorption sites between the heavy metal and the calcium oxide surface.The combination of the above two reasons led to the modification of sodium chloride to enhance the adsorption of heavy metals by calcium oxide.
CaO has good adsorption effect on Cr, Cd and Pb under low-temperature reducing atmosphere, and its loading with NaCl can enhance the adsorption capacity of heavy metals.This study provides a reliable basis for the development of calcium-based adsorbents and their modified substances to control heavy metals Cr, Cd and Pb under the environment of MSW pyrolysis.
shows the geometrically optimized molecular models of CrCl 3 , CdCl 2 and PbCl 2 constructed in the DFT calculations, which are similar to the model parameters constructed by (Noble-Eddy et al. 2010).

Figure 2 .
Figure 2. Molecular model of each heavy metal after geometric optimization.
) surface demonstrating chemical interaction.From PDOS, the p orbital of the O atom hybridize with the p and d orbitals of the Cr atom at −5.210 eV, 0.739 eV, which further confirm the chemical adsorption.The covalent bonds between Cd atoms and O atoms on CaO (001) surface were attributed to the overlap of electron clouds in the p orbitals of O atoms and the s and

d
orbitals of Cd atoms at −8.202 eV, −4.132 eV.The electron density distribution overlap between Pb-O after PbCl 2 was adsorbed on CaO (001) surface.The p and s orbitals of the Pb atom and the p orbital of the O atom on CaO surface had obvious overlapping peaks at −7.448 eV and −2.799 eV confirming covalent action.

Figure 10 .
Figure 10.Adsorption energy and adsorption rate of CaO and NaCl/CaO.

Table 1 .
Mulliken bonding residence of heavy metals after adsorption on CaO, NaCl/CaO.

Table 2 .
Adsorption energies and Mulliken charge change before and after adsorption on CaO, NaCl/CaO.
a Mulliken charge change is defined as the charge difference after and before adsorption.+ indicates electron donation while − indicates electron acceptance.
Compared with calcium oxide, the adsorption rate of Cd and Pb changed from 43.32%, 40.13% and 25.54% to 56.42%, 46.44% and 46.22% after the addition of NaCl/CaO.The adsorption energy of NaCl/CaO increased from 285.37 kJ/mol, 130.58 kJ/mol and 145.72 kJ/mol to 373.80 kJ/mol, 216.03 kJ/mol and 214.67 kJ/mol for Cr, Cd and Pb, demonstrating the same pattern as the retention rate.(4) The effect of adding loaded NaCl on the adsorption of heavy metals by CaO is mainly in two aspects: