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Chemisorption of metallic radionuclides on a monolayer MoS2 nanosheet

In the process of developing nuclear energy, removing radioactive waste in the environment is a challenging problem that human beings have to face. The main work of this paper is to investigate the mechanism of the interaction between metallic radionuclides (Cs, Sr, and Ba) and a monolayer MoS2 nanosheet, and the work is completed by using the first principles calculation method. The results show that all of the three kinds of metallic radionuclides can be chemisorbed on the monolayer MoS2 nanosheet. The optimum adsorption site for the metallic radionuclides adsorbed on the monolayer MoS2 is TMo (top of the Mo atom), because the metallic radionuclides can interact with the three nearest S atoms when the metallic radionuclides are at the TMo site. The chemisorption strength of the metallic radionuclides on the monolayer MoS2 is Ba > Sr > Cs. The mechanism of the chemisorption is explored by using the total charge transfer, density of states, and electron density difference. The final analysis shows that the s orbital of S atoms plays an important role in the chemisorption.


Introduction
The disposal of radioactive materials has long been a difficult problem for nuclear power development; 1 especially, when a serious nuclear accident occurs, large amounts of radioactive waste water are produced in the damaged nuclear power plant. How to remove radionuclides from radioactive waste water quickly and efficiently has become a worldwide challenging problem, such as the Fukushima Daiichi nuclear disaster. 2,3 To solve this problem, many radioactive material removal methods, such as sorption, (co)precipitation, ion exchange, solidication, and membrane separation, have been extensively applied to eliminate radionuclides from waste water. Among these methods, the sorption technique has widely been applied in real environmental pollution management because of its simple operation, low cost, and applications on a large scale. 4 In the past few decades, a considerable number of materials were studied to nd out a candidate material for the efficient removal of radionuclides, and the related research on zeolites, molecular sieves, and other materials has achieved great progress. Since graphene was invented, the research on the twodimensional material has received increasing attention from scientists and engineers, due to its unique band structure, semiconducting or superconducting properties, excellent mechanical performance, and so on. The two-dimensional material is widely considered for use in electronic devices, catalysis, energy storage, tools used under extreme conditions, and other elds. With the deepening of the research, the two-dimensional material is considered as a new kind of candidate material, which is used in environmental remediation. Through the hard work of Wang's team, [5][6][7][8][9] the mechanism of graphene removing radionuclides from the environment has been claried, and their studies show that oxygen-containing functional groups are crucial for improving the adsorption capacity of graphene for radionuclides. Meanwhile, scientists have found that MoS 2 has some adsorption capacity for heavy metal ions 10,11 and toxic gas molecules, [12][13][14][15] and the optical properties of monolayer MoS 2 changed when some organic macromolecules were adsorbed on monolayer MoS 2 . 16 Monolayer MoS 2 can also be considered as a candidate cathode material for Li-ion batteries. 17 Based on the above research, MoS 2 is considered as a potential material for environmental restoration. 18 Especially, scientists believe that MoS 2 is a potential sensor material for toxic gases, such as CO, NO, HS 2 , NH 3 , SO 2 and so on. Using the rst principles calculation method, the electronic and magnetic properties of MoS 2 have been investigated, 19 and the adsorption energy and charge transfer of different kinds of toxic gas molecules adsorbed on monolayer MoS 2 have been reported, [20][21][22] and the result shows that MoS 2 can monitor toxic gases in the atmosphere. Based on this research, we think that MoS 2 might be a candidate material for radionuclide removal from the environment. As for the preparation of monolayer MoS 2 , three successful methods have been reported, such as mechanical exfoliation, liquid exfoliation, and chemical vapor deposition (CVD). The successful preparation of the material has provided the possibility for its large-scale application, especially in the eld of radioactive environmental restoration. 89  Cs are both the gamma source and the beta source, and the characteristic energy of the g ray from the emission of 137 Cs is about 661.66 keV. All of the metallic radionuclides have adverse impacts on the environment, and more importantly, they are harmful to public health. How to remove the three kinds of metallic radionuclides in waste water is very important for the treatment of radioactive waste water. Therefore, we focused on the adsorption of the three kinds of metallic radionuclides on monolayer MoS 2 . As we know, although the atomic mass of isotopes is different, their chemical properties are basically similar. The chemical properties of metallic radionuclides depend upon the electrons on the outside. The effects of the radioactivity of metallic radionuclides on the adsorption capacity of MoS 2 is beyond the scope of this study. In our previous work, 23 we just show that monolayer MoS 2 can adsorb metallic radionuclides, and the adsorption belongs to chemisorption according to the adsorption energies of the metallic radionuclides on monolayer MoS 2 . In this paper, we aim to study why monolayer MoS 2 can adsorb metallic radionuclides. The mechanism of monolayer MoS 2 adsorbing metallic radionuclides has been explored clearly, which may provide a theoretical basis for relevant experimental research in the future. Based on our previous work, we calculated the charge transfer, electron density difference, total densities of states (TDOS) and partial densities of states (PDOS), to clarify the mechanism of the adsorption. We hope that our work can shed some light on environmental remediation, especially the treatment of radioactive waste water.

Computation method and details
First principles calculations based on density functional theory 24,25 are used in this paper and all calculations are conducted in the Cambridge serial total energy package (CASTEP). 26 In the crystal periodic potential eld, the multi-electron system is expressed by the plane wave function through the threedimensional periodic boundary condition, and in order to reduce the number of plane wave bases, the CASTEP soware package uses the ultraso pseudopotential to describe the interaction between ions and electrons. As we know, metallic radionuclides exist in valence forms as metal ions (such as Cs + , Sr 2+ and Ba 2+ ) in radioactive waste water, and we set a corresponding charge on these metallic radionuclide atoms. In the reciprocal space, the plane wave cutoff energy is set to 500 eV, and the exchange and correlation functions among electrons are described by the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA). [27][28][29] Structure optimization is conducted using the Broyden-Fletcher-Goldfarb-Shanno minimization, modied to take into account the total energy as well as the gradients. The self-consistent eld (SCF) tolerance is set to 1.0 Â 10 À6 eV per atom. Aer the convergence test, all the calculations are performed using 3 Â 3 Â 1 Monkhorst-Pack k points. In order to avoid interlayer interactions, a vacuum layer of 16Å is used in the c direction. In the process of geometry optimization, all the structures are fully relaxed, and the optimal atomic positions are determined until satisfying the following conditions: (1) the maximal force on them is less than 0.03 eVÅ À1 ; (2) the maximal change of energy per atom is less than 1.0 Â 10 À5 eV; (3) the maximal displacement is less than 5.0 Â 10 À4Å ; (4) the maximal stress in the supercell is less than 0.02 GPa.
A 5 Â 5 Â 1 supercell of monolayer MoS 2 (containing 25 Mo atoms and 50 S atoms) with a single metallic radionuclide adsorbed onto it is constructed to be the calculation model.  For the adsorption of the metallic radionuclides, the adsorption energy is calculated using the following relationship: where E M+MoS 2 is the total energy of the metallic radionuclide atom adsorbed on monolayer MoS 2 . E MoS 2 is the total energy of monolayer MoS 2 . E M is the total energy of the single free metallic radionuclide atom. According to the relationship, a negative adsorption energy can make the metallic radionuclide atom adsorb on monolayer MoS 2 with higher stability. The more negative the adsorption energy, the stronger the interaction between the metallic radionuclides and the monolayer MoS 2 nanosheet. We calculated the charge transfer Q t based on Mulliken 30 and Hirshfeld 31 methods. To understand the difference between Mulliken and Hirshfeld methods, here we briey introduce these two methods of calculating atomic charge. First, the normalization condition of the molecular orbital wave function is considered, ð f i ðrÞ 2 dr ¼ 1: Where, r represents the space coordinates. The molecular orbitals f i are expanded by using atomic-centered basis functions c m , Where, C is the matrix of coefficient, and by substituting eqn (3) into eqn (2), a result can be obtained aer integration, X m C m;i 2 þ 2 X m X m $ n C m;i C n;i S m;n ¼ 1: Where, S m;n ¼ ð c m ðrÞc n ðrÞdr. The rst item in eqn (4) is the sum of independent contributions of each basis function to the orbit, and it is called the localized term. The second item is the cross term, and it represents the joint contribution to the orbit due to the coupling between each pair of basis functions. Mulliken denes the composition of the fundamental function m in molecular orbital i as: That is to say, the localized term is completely assigned to the corresponding base function, and the cross term is bisected into the corresponding two basis functions. The atomic populations can be obtained by adding up the populations of all the basis functions that belong to the same atom in all the orbitals, and the Mulliken atomic charge is given by the equation, Where, Z A is the nuclear charge number, and h is the orbital population.
The Hirshfeld atomic charge is dened as, where, and X A r 0 A ðrÞ represents the sum of the electron density of all atoms in the free state, also known as the promolecule density. Dr(r) is called the deformation density, and it stands for the change of electron density in the relaxation process aer atoms form molecules. w A (r) is the weight function of atom A, and it denes the entire real space that belongs to atom A. Hirshfeld's division has a clear physical meaning, and Nalewajski and Parr prove from the point of view of information theory that this division is a way to minimize the distance (Kullback-Leibler relative entropy) of information between atoms and molecules when the electron density is allowed to transfer between atoms. Because the results obtained by the Mulliken method depend too much on the basis group, scientists generally believe that the Hirshfeld method is more effective. We also draw a conclusion based on the results obtained by the Hirshfeld method. Nevertheless, the results obtained from the Mulliken method still have a good reference.
The atoms have a positive charge when the Mulliken or Hirshfeld charge (e) > 0, and the atom has a negative charge when the Mulliken or Hirshfeld charge (e) < 0. The positive value of Q t shows that the electrons transferred from the metallic radionuclides to monolayer MoS 2 , while the negative value of Q t indicates that the electrons transferred from monolayer MoS 2 to the metallic radionuclides. In order to explore the interaction mechanism between the metallic radionuclides and monolayer MoS 2 , we calculated the electron density difference, total densities of states (TDOS) and partial densities of states (PDOS).

Results and discussion
In order to explain the rationality of the calculation in this paper, we rst explore the structure and properties of monolayer MoS 2 . The lattice constant is 3.166Å, and the bond length of Mo-S and S-S bonds is 2.409Å, and 3.137Å, respectively. Our calculations are in good agreement with the available numerical results. 32,33  The adsorption energy, total charge transfer and adsorption height (the height of the radionuclide Cs above the MoS 2 surface) of the radionuclide Cs adsorbed on the monolayer MoS 2 nanosheet with different congurations are given in Table 1. When the initial conguration of the radionuclide Cs on the monolayer MoS 2 nanosheet is B, the radionuclide Cs is repelled from the initial site B and migrates to the rst nearest neighbor Mo atom aer relaxation, and the radionuclide Cs can interact with the three nearest S atoms. From the adsorption energy, it can be seen that the adsorption energy of the B initial structure is the lowest (À3.259 eV). Therefore, T Mo is the energetically favorable site. For the Ni adsorbed on monolayer MoS 2 , 42 T Mo is also the energetically favorable site. Fig. 3(a) shows the optimized structure of metallic radionuclide Cs adsorbed on the monolayer MoS 2 nanosheet with the B initial conguration. We can nd that the height of Cs atoms above the monolayer MoS 2 surface is 2.829Å. The bond length of Mo-S 1 and Mo-S 2 bonds increased to 2.421Å and 2.438Å, while the length of Mo-S 3 decreased to 2.405Å, respectively. The increase of the bond length indicates that the interaction between Mo atoms and S atoms is weakened. The distance between the radionuclide Cs and Mo atom is 4.462Å, while the distance between the radionuclide Cs and S 1 , S 2 , and S 3 is 3.459Å, 3.490 A, and 3.457Å, respectively.
In addition, it can be found that the total charge transfer Q t for different initial structures obtained by the Mulliken and Hirshfeld methods have the same trend. The total charge transfer of the radionuclide Cs adsorbed on the monolayer MoS 2 nanosheet with all of the initial congurations is positive, indicating that the radionuclide Cs acts as the electron donor and the monolayer MoS 2 nanosheet acts as the electron acceptor. For the adsorption of the radionuclide Cs on monolayer MoS 2 with all of the initial structures, the corresponding charge transfer value based on the Mulliken method is higher than that of the Hirshfeld method. And for the adsorption of the radionuclide Cs on monolayer MoS 2 with the B initial structure, the corresponding charge transfer obtained by Mulliken and Hirshfeld methods is 1.00 e and 0.59 e, respectively. Fig. 3(b) shows the band structure of a metallic radionuclide Cs adsorbed on monolayer MoS 2 . There is no band gap in the band structure, and this phenomenon means that the band gap disappeared in the band structure aer a metallic radionuclide Cs was adsorbed on monolayer MoS 2 .
In order to further explore the interaction mechanism between the radionuclide Cs and monolayer MoS 2 nanosheet, we calculated the TDOS, PDOS and electron density difference of the system before and aer adsorption. Fig. 3(c) shows the TDOS and PDOS of the Cs atom adsorbed on monolayer MoS 2 with the B initial structure. There are four regions in the valence band, including the high energy region (from À6 eV to 0 eV), the second high energy region (near À14 eV), the medium energy region (near À36 eV), and the low energy region (near À62 eV). The high energy region, the medium energy region, and the low energy region consist of Mo d, p, and s orbitals, and the S p orbital also makes a contribution to the high energy region; the second high energy region is composed of the S s orbital. Aer the radionuclide Cs was adsorbed on monolayer MoS 2 , two small peaks (near À10 eV and À23 eV) appeared in the valence band. According to the density of states, the adsorption of the radionuclide Cs on monolayer MoS 2 was mainly caused by the hybridization between Cs p and S s orbitals.
The electron density difference of radionuclide Cs adsorbed on monolayer MoS 2 with the B initial structure is shown in Fig. 3(d). The red and blue regions in the gure indicate the increase and decrease of the electron density, respectively. It can be found that the electron density near the S atom increased obviously and the electron density near the Mo and Cs atoms decreased aer the radionuclide Cs was adsorbed on monolayer MoS 2 , which further conrmed that the radionuclide Cs acts as the electron donor and monolayer MoS 2 acts as the electron acceptor; more precisely, the S atoms near the radionuclide Cs act as the electron acceptor. Table 2 shows the adsorption energy, total charge transfer, and adsorption height of the radionuclide Sr atom adsorbed on the monolayer MoS 2 nanosheet with different initial  Paper congurations. The result shows that the adsorption energy of the radionuclide Sr atom on the monolayer MoS 2 nanosheet is higher than that of the radionuclide Cs; therefore, the interaction between the radionuclide Sr and monolayer MoS 2 nanosheet is weaker than that of the radionuclide Cs. When the initial conguration of the radionuclide Sr on monolayer MoS 2 is B, the radionuclide Sr migrates to the rst nearest neighbor Mo atom (T Mo ) aer relaxation, and T Mo is the optimum adsorption site. The adsorption energy of the Sr atom adsorbed on the monolayer MoS 2 nanosheet with T Mo conguration is À3.863 eV. Fig. 4(a) shows the optimized structure of radionuclide Sr adsorbed on monolayer MoS 2 with the B initial conguration. Aer relaxation, the bond length of Mo-S 1 , Mo-S 2 , and Mo-S 3 bonds increased to 2.412Å, 2.466Å, and 2.424Å, respectively. Due to the radionuclide Sr adsorbed on monolayer MoS 2 , the length of Mo-S bonds (near the radionuclide Sr) becomes longer than that in MoS 2 , and this result means that the interaction between the Mo atom and S atom is weakened by the radionuclide Sr. The distances between the radionuclide Sr and Mo, S 1 , S 2 , and S 3 are 3.517Å, 2.776Å, 2.778Å, and 2.764Å, respectively. These values indicate that the interaction between the radionuclide Sr and S atoms is stronger than the interaction between the radionuclide Cs and S atoms.

Adsorption of Sr on the monolayer MoS 2 nanosheet
Although the total charge transfer Q t for different initial congurations obtained by the Mulliken and Hirshfeld method is different, they have the same trend. In the interaction process, the Sr atom acts as electron donor and monolayer MoS 2 acts as electron acceptor. For the adsorption of Sr on monolayer MoS 2 with B initial conguration, the corresponding charge transfer Q t obtained by Mulliken and Hirshfeld method is 1.24 e and 0.72 e, respectively. Fig. 4(b) shows the band structure of a radionuclide Sr on monolayer MoS 2 with the initial conguration B, and the band gap of this conguration is 0.271 eV. The decrease of the band gap is due to the adsorption of the radionuclide Sr. Fig. 4(c) shows the TDOD and PDOS of the radionuclide Sr adsorbed on monolayer MoS 2 . There is a hybridization exists between the s orbital of the S atom and the p orbital of the Sr atom and the Mo p orbital. When the radionuclide Sr is at the T Mo site, there is an interaction between the radionuclide Sr and the three nearest S atoms. Fig. 3 The relaxed configuration, band structure (from À10 eV to 5 eV), density of states, and electron density difference of the radionuclide Cs on monolayer MoS 2 .  Fig. 4(d) shows the electron density difference of the radionuclide Sr adsorbed on monolayer MoS 2 with T Mo conguration. The S atoms act as the electron accepter, and the Mo and Sr atoms act as the electron donor. This result is in good agreement with the total charge transfer Q t obtained by Mulliken and Hirshfeld methods.

Adsorption of Ba on the monolayer MoS 2 nanosheet
We calculated the adsorption energy, total charge transfer, and adsorption height of the radionuclide Ba adsorbed on the monolayer MoS 2 nanosheet, as shown in Table 3. The radionuclide Ba migrates from the initial conguration B to the rst nearest neighbor Mo atom aer relaxation. The adsorption energy of the radionuclide Ba on monolayer MoS 2 is the lowest, followed by the radionuclide Sr, and the adsorption energy of the radionuclide Cs on monolayer MoS 2 is the highest. Therefore, the strength of the adsorption of the three kinds of metallic radionuclides on the monolayer MoS 2 nanosheet is: Ba > Sr > Cs. For the radionuclide Ba, T Mo is the energetically favorable site, and the corresponding adsorption energy is À4.137 eV. According to the magnitude of the adsorption energy, all of the three kinds of metallic radionuclides can be chemisorbed on monolayer MoS 2 . The adsorption height of the radionuclide Ba on monolayer MoS 2 is about 2.1Å, and the adsorption height of the radionuclide Ba on monolayer MoS 2 is higher than that of the radionuclide Sr, while the adsorption height of the radionuclide Ba on monolayer MoS 2 is lower that of the radionuclide Cs. The length of the S-Mo bond is longer than that of the pristine Mo-S bond, and the result means that the adsorption of the radionuclide Ba weakens the interaction between S and Mo. The distance between radionuclides Ba and Mo is 3.726Å, and the value is higher than that of the radionuclide Sr, but the value is lower than that of the radionuclide Cs. The distance between Ba and S1, S2, and S3 is 2.969 eV, 2.921 eV, and 2.922 eV, respectively. The distance between Ba and S and Mo indicates that the interaction between Ba and monolayer MoS 2 is weaker than the interaction between Sr and monolayer MoS 2 , while the interaction between Ba and monolayer MoS 2 is stronger than the interaction between radionuclide Cs and monolayer MoS 2 . Fig. 4 The relaxed configuration, band structure (from À10 eV to 5 eV), density of states, and electron density difference of the radionuclide Sr on monolayer MoS 2 . When we calculated the total charge transfer, the difference in the total charge transfer obtained by the Mulliken and Hirshfeld methods still exists, but the total charge transfer obtained by the two methods has the same trend. Like Cs and Sr adsorbed on monolayer MoS 2 , the Ba atom acts as the electron donor and monolayer MoS 2 acts as the electron acceptor. For Ba adsorbed on monolayer MoS 2 with B initial conguration, the total charge transfer obtained by the Mulliken and Hirshfeld methods is 0.94 e and 0.80 e, respectively. The relationship between charge transfer and adsorption energy is analyzed, but the effect of the charge transfer on the adsorption energy is not obvious. Fig. 5(b) shows the band structure of the radionuclide Ba adsorbed on monolayer MoS 2 . When compared with pristine monolayer MoS 2 , the band gap of monolayer MoS 2 has narrowed due to the adsorption of the radionuclide Ba, and all of the three kinds of metallic radionuclides have similar effects on the band structure of monolayer MoS 2 . Fig. 5(c) shows the TDOS and PDOS of the radionuclide Ba adsorbed on monolayer MoS 2 , and there is a hybridization between the S s orbital and Ba p orbital, and the main reason for the adsorption of the radionuclide Ba on monolayer MoS 2 might be the hybridization. Fig. 5(d) shows the electron density difference of the radionuclide Ba adsorbed on monolayer MoS 2 with the T Mo conguration (relaxed from the B initial conguration). The red and blue regions in the gure indicate the increase and decrease of the electron density, respectively. The radionuclide Ba and Mo atoms act as the electron acceptor and the S atoms near the radionuclide Ba act as the electron donor, and the result is in agreement with the total charge transfer Q t obtained by the Mulliken and Hirshfeld methods.

Conclusions
In this paper, we investigated the adsorption of three kinds of metallic radionuclides, Cs, Sr, and Ba, on monolayer MoS 2 by using the rst principles calculation method. The result shows that all of the three kinds of metallic radionuclides can be chemisorbed on the monolayer MoS 2 nanosheet, according to the magnitude of the adsorption energy. The adsorption strength of the three kinds of metallic radionuclides on the monolayer MoS 2 nanosheet is Ba > Sr > Cs. All of the radionuclides act as the electron donor, while monolayer MoS 2 acts as the electron acceptor; more precisely, the S atoms near the radionuclides act as the electron acceptor. For the three kinds of Fig. 5 The relaxed configuration, band structure (from À10 eV to 5 eV), density of states, and electron density difference of the radionuclide Ba adsorbed on monolayer MoS 2 with the initial configuration B. metallic radionuclides, the optimum adsorption site is T Mo , because the radionuclides can interact with the three nearest S atoms.

Conflicts of interest
There are no conicts to declare.