# Adsorption of Water Molecule in Graphene/MoS2 Heterostructure with Vacancy Defects in Mo Sites

Authors: Hari Krishna Neupane; Narayan Prasad Adhikari
Journal: Advances in Condensed Matter Physics
 (2022)

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## Abstract

First-principle calculations based on the spin-polarized density functional theory (DFT) with vdW corrections by DFT-D2 approach have been carried out to study structural, electronic, and magnetic properties of water-adsorbed graphene/MoS2 heterostructures (system-I), and water-adsorbed graphene/MoS2 heterostructures with vacancy defects in Mo sites (systems-II). We consider vacancy defects in different Mo sites such as centre-1Mo atom vacancy defect (system-IIa), left-1Mo atom vacancy defect (system-IIb), and 2Mo atom vacancy defects (system-IIc). All the systems considered in this study are structurally stable; however, the stability of defected systems decreases with an increase in defect concentrations. The calculated binding energies of HS used in this study agree with the reported work. Electronic properties of system-I and systems-II reveal that they have metallic characteristics. Our investigation shows that system-I is nonmagnetic and systems-II are magnetic. The magnetic moment in the defected systems (system-IIa, system-IIb, and system-IIc) is developed by unpaired up and down-spins of electrons created in the orbitals of atoms due to vacancy defects in Mo atoms.


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## Body

## 1. Introduction

One of the ways to create 2D heterostructures is by two or more monolayers of different materials. The heterostructures improve the functional characteristics and bear novel properties. Therefore, they have intrigued the advanced compliance of researchers to predict other advantageous properties than the constituents [1, 2]. Presently, two-dimensional (2D) van der Waals (vdW) graphene/MoS2 (G/MoS2) heterostructure (HS) is a useful tool to design applicable electronic devices [3–6]. Graphene is an atom-thick 2D honeycomb lattice, and has a series of special electronic and physical properties. Its exceptional physical strength, large surface area, high electrical and thermal conductivities, low noise effect, controllable tunable band structure, and many more other interesting properties explore multiple possible applications such as electronic, spintronics, and gas sensors [1, 7–10]. 2D Molybdenum disulphide (MoS2) is the form of hexagonal plane crystal structure of S atoms on either side of a hexagonal plane of Mo atoms. It has certain bandgap in its electronic band known as the wide bandgap exotic semiconductor [11, 12]. MoS2 is used in the electronic, spintronic, and optoelectronic devices because of its impressive optical, electronic, and magnetic properties [11–13]. Defects are inherent in any system due to entropic reason. They (vacancy defect/impurity defect) can develop novel properties in 2D materials [14–18], and also electronic and magnetic properties of materials can be modified by defects [15, 19, 20]. People are using the pristine and defected G/MoS2 HS in electronic devices. Hence, it is highly demanding to study HS of 2D materials with defects. The devices made by pristine G/MoS2 HS and vacancy-defected G/MoS2 HS sometimes have to be used in the surrounding (moisture) environment. Due to which, moisture (water molecule) can affect the properties of HS materials [21, 22]. The molecular adsorption in vacancy-defected HS can bring new properties because vacancy defects are very keen locations for molecular adsorption due to the configuration of atoms around the vacancy. They play a particular role in determining the geometrical arrangement of layered materials [21–23]. Also, electronic and magnetic properties of defected materials can be modified by adsorbed water molecule [23]. Thus, it opens the way to tune novel properties of vacancy-defected HS materials. Therefore, it needs to study the adsorption of water molecule on G/MoS2 HS (system-I) and Mo sites vacancy defects G/MoS2 HS (system-II). To our best knowledge, literature studies do not contain a significant study of water-adsorbed 2D G/MoS2 HS materials with Mo defects. In this study, we have investigated the structural, electronic, and magnetic properties of Mo sites vacancy-defected water-adsorbed 2D G/MoS2 HS materials by using the spin-polarized density functional theory (DFT)-based first-principle calculations, within the DFT-D2 approach. Our calculations show that system-I and its Mo site vacancy defect (systems-II) materials could be promising candidates for the device applications.The rest part of the article is arranged as follows. Computational methods, interpretation of findings, and conclusions of this study are given in Sections2–4, respectively.


## 2. Methods and Materials

The comprehensive intuition is gained into the physical properties of the system-I and its Mo site vacancy defect systems-II by the spin-polarized density functional theory (DFT) [24]-based first-principle calculations. DFT with the PWscf code of the Quantum ESPRESSO package [25] has been conducted to study the structural, electronic, and magnetic properties of system-I and system-II. The code uses ultra-soft pseudo-potentials (USPPs) to describe the interactions between ion cores and valence electrons. A plane-wave basis set, with cut-off values of 35 Ry and 350 Ry for wave functions and charge densities, respectively, was used. Exchange and correlation interactions were considered by generalized gradient approximation (GGA) [26]. London dispersion contributions for weak vdW force in between the constituents of supercells were described through the DFT-D2 scheme [27]. Self-consistent field (Scf) and structure optimization calculations were executed by Broyden–Fletcher–Goldfarb–Shanno (BFGS) method [28] with Γ-centered Monkhorst-Pack (MP) [29] k-Points mesh commensurate with (6 × 6 × 1) sampling of the heterostructures of system-I and system-II. The system-I was created by adsorbing water molecule (center position on the surface of MoS2) at 2.52 Å distance above the top surface of MoS2 in vertical G/MoS2 HS as shown in Figure 1, since vertical G/MoS2 HS was formed by (4 × 4) supercell structure of graphene and (3 × 3) supercell structure of MoS2 with 4.11% lattice mismatch. In HS, the lattice mismatch can be determined via differing the lattice constant, whereas there is no direct chemical bonding between the component layers. Systems-II were constructed by adsorbing water molecule in centre-1Mo atom vacancy defect G/MoS2 HS (system-IIa), left-1Mo atom vacancy defect G/MoS2 HS (system-IIb), and 2Mo atom vacancy defect G/MoS2 HS (system-IIc), which are illustrated in Figure 2. Convergence was sustained by using Marzari–Vanderbilt (MV) [30] smearing with an enlightening of 0.001 Ry. David diagonalization methods with plain mixing mode for self-consistency where a default value of mixing factor 0.6 was used. To reduce the interaction within periodic structures, a vacuum detachment of 18 Å was used along z-direction. All the atoms in structures were allowed to relax by the PBE functional until the forces conversed to less than 10−3 Ry/Bohr in each direction and energy to 10−4 Ry. To tune electronic and magnetic properties of materials, a mesh of (6 × 6 × 1) k-points was used for band structure calculations and meshes of (12 × 12 × 1) k-points were employed for density of states (DOS) and projected density of state (PDOS) calculations.Figure 1
(a) Adsorbed water molecule is at 2.52 Å distance above the top surface of graphene in G/MoS2 HS. (b) adsorbed water molecule is (left-position) at 2.52 Å distance above the top surface of MoS2 in G/MoS2 HS. (c) adsorbed water molecule is (right-position) at 2.52 Å distance above the top surface of MoS2 in G/MoS2 HS. (d) adsorbed water molecule is (center position) at 2.52 Å distance above the top surface of MoS2 in G/MoS2 HS.
(a)(b)(c)(d)Figure 2
Side view and top view of Mo site vacancy defect HS materials: (a) center-1Mo atom vacancy defect water-adsorbed G/MoS2 HS (system-IIa), (b) left-1Mo atom vacancy defect water-adsorbed G/MoS2 HS (system-IIb), and (c) 2Mo atoms vacancy defects water-adsorbed G/MoS2 HS (system-IIc).
(a)(b)(c)


## 3. Results and Discussion

In this section, we present, discuss, and analyze the main findings of this study. Findings of system-I and systems-II are obtained from band structure, DOS, and PDOS calculations.


### 3.1. Structural Study

The water-adsorbed G/MoS2 HS is constructed by putting water molecule at various locations on graphene and MoS2 surfaces of the G/MoS2 HS material as shown in Figures 1(a)–1(d). The adsorbed water molecule (at center position on the surface of MoS2) at a distance of 2.52 Å above the top surface of MoS2 in the HS is found to be most stable, as shown in Figure 1(d). To determine the stability, we have calculated the binding energy of system-I by using the following equation [31]:(1)Eb=Ew+G/MoS2HS−EG/MoS2HS−EwA,where Ew+G/MoS2HS,EG/MoS2HS,Ew are the total energy of the system-I, G/MoS2 HS, and adsorbed water molecule, respectively, and “A” is the surface area of heterostructure. The obtained binding energy of system-I is −23.82 meV/Å2, which means system-I is energetically stable at the ground state. It means physisorption interaction takes place in between them. The stable optimized system-IIa, system-IIb, and system-IIc are created by adsorbing water molecule in centre-1Mo atom, left-1Mo atom, and 2Mo atom vacancy defect G/MoS2 HS, respectively, as shown in Figures 2(a)–2(c). To determine the stability of such systems, we have also calculated binding energy using the following formalism [31]:(2)Eb=Ew+G/MoS2HSMo−d−EG/MoS2HSMo−d−EwA,where Ew+G/MoS2HSMo−d,EG/MoS2HSMo−d,Ew are the ground state energy of Mo site vacancy defect water-adsorbed G/MoS2 HS (systems-II), Mo site vacancy defect G/MoS2 HS, and adsorbed water molecule, respectively, and “A” represents the surface area of defected heterostructures. The estimated binding energy of system-IIa, system-IIb, and system-IIc are −20.09 meV/Å2, −20.03 meV/Å2, and −17.40 meV/Å2, respectively. The calculated binding energy of system-I, system-IIa, system-IIb, and system-IIc is comparable with the values of other vdW HSs [32, 33]. Thus, considered systems are stable because negative binding energy means that materials are energetically stable at the ground state. Lower value of binding energy indicates that the material is more stable than others. Hence, the stability of the above considered materials is decreased with an increase in the defect concentration. The defect formation energy of system-IIa, system-IIb, and system-IIc is found to be 0.21 eV, 0.21 eV, and 0.40 eV, respectively, which are calculated by using the following equation [34]:(3)Edf=Etd−Etp+nMoµMo,where (Et)d, (Et)p, nMo, and µMo are the total ground state energy of vacancy defect HS (systems-II), total ground state energy of pristine HS (system-I), numbers of vacancy defects (Mo) atoms, and chemical potential of a Mo atom, respectively. Materials have lower defect formation energy, which indicates that they can be favorable for computational work.In addition, we have also computed the interlayers distance between graphene and monolayer MoS2 of system-I, system-IIa, system-IIb, and system-IIc materials, and they are 3.72 Å, 3.81 Å, 3.83 Å, and 3.94 Å, respectively. These values are comparable with other graphene-based 2D HS materials [35, 36]. From this analysis, we conclude that system-I is more compact than Mo vacancy-defected systems. In systems-II, compactness of atoms and layers of constituents are increased with a decrease in their defect concentration. The estimation of binding energy and interlayer distance of the above considered systems shows that weak vdW force exists in between graphene and MoS2.


### 3.2. Electronic Properties

The electronic properties of the material are predicted based on the electronic band structure. Band structures of system-I, system-IIa, system-IIb, and system-IIc are illustrated in Figures3(a), 4(a), 5(a), and 6(a), respectively. We know that graphene and monolayer MoS2 have metallic [1, 9] and semiconducting properties, respectively [12, 13]. Band structure of graphene/MoS2 HS is a sum of band structures of those constituents in which properties of graphene are preserved, and hence, it also has metallic properties [20, 37]. Impressively, it is noted that Dirac point setup in the conduction band at 0.11 eV distance from the Fermi energy level in the band structure of water adsorbed Graphene/MoS2 HS (system-I). This small value of the Dirac cone is obtained because of the adsorption of water molecule in G/MoS2 HS. The formation of the Dirac cone in the conduction band means electrons spontaneously flow from the valence band to the conduction band. Hence, system-I has metallic properties. Also, the property of G/MoS2 HS is still preserved.Figure 3
(a) Band structure of system-I, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-I, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-I, (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-I. In all DOS and PDOS, the horizontal dot line separates spin states and the vertical dot line separates the electronic bands, and also in band plot, the horizontal dot line represents the Fermi energy level; insets in DOS and PDOS represent the spin states within a large energy range alongx-axis.
(a)(b)(c)(d)Figure 4
(a) Band structure of system-IIa, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIa, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIa, (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIa. In all DOS and PDOS, the horizontal dot line separates spin states and the vertical dot line separates the electronic bands, and also in the band plot, the horizontal dot line represents the Fermi energy level. Insets in DOS and PDOS represent spin states within large energy range alongx-axis.
(a)(b)(c)(d)Figure 5
(a) Band structure of system-IIb, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIb, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIb, (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIb. In all DOS and PDOS, the horizontal dot line separates spin states and the vertical dot line separates the electronic bands, and also in the band plot, the horizontal dot line represents Fermi energy level. Insets in DOS and PDOS represent the spin states within a large energy range alongx-axis.
(a)(b)(c)(d)Figure 6
(a) Band structure of system-IIc, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIc, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIc, and (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIc. In all DOS and PDOS, the horizontal dot line separates the spin states and the vertical dot line separates the electronic bands, and also in the band plot, the horizontal dot line represents the Fermi energy level. Insets in DOS and PDOS represent the spin states within a large energy range alongx-axis.
(a)(b)(c)(d)Moreover, we explored band structures of systems-II materials and found that the Dirac cone is formed at 0.72 eV, 0.71 eV, and 0.68 eV distance from the Fermi energy level in system-IIa, system-IIb, and system-IIc materials, respectively, which are shown in Figures4(a), 5(a) and 6(a). A few numbers of electronic bands of valence electrons cross the Fermi energy level in band structures, which is due to the effect of Mo vacancy atom in structures, which breaks the symmetry of system-I. Hence, defected materials are metallic. In systems-II, unpaired up-spin and down-spin states are appeared by Mo vacancy defects, due to which the movement of interfacial charges is developed in systems. Hence, the different values of the Dirac point, Fermi energy, and shift of the Fermi energy level towards the valence band are obtained in system-IIa, system-IIb, and system-IIc, which are presented in Table 1.Table 1
Fermi energy (Ef), fermi energy shifts (Es), amplitude of the Dirac point (Dp), Dirac point shifts in defected materials (Ds), defect formation energy (Edf), and total binding energy of the systems (Eb).
Systems ⟶System-I:System-IIa:System-IIb:System-IIc:SystemsEf (eV)Es (eV)Dp (eV)Ds (eV)Edf (eV)Eb (meV/Å2)System-I0.44—0.11——−23.82System-IIa−0.611.050.720.610.21−20.09System-IIb−0.601.040.710.590.21−20.03System-IIc−0.861.300.680.570.40−17.40In Table1, we can see that the values of Fermi energy and Fermi energy shift are increased with an increase in the concentration of Mo vacancy defects, but the distance of the Dirac point from the Fermi energy level decreases with an increase in the defect concentration in the systems. The reason is that vacancies are very precise place for adsorbed molecule. This is because we have calculated the bond length between nearest Mo-Mo atoms, S-S atoms, Mo-S atoms, and distance between adsorbed water molecule to MoS2 surface in vacancy defects HS and found that the compactness of materials decreases with an increase in defect concentrations. Thus, adsorbed molecule disturbed the atomic configurations in vacancy-defected HS materials, which influences the electronic properties of the systems. Dirac point setup in the conduction band reflects that the electron impulsively proceeds from the valence to the conduction band because the flow of current in metals and semiconductors depends on the amplitude of Dirac shift. Hence, system-IIa, system-IIb, and system-IIc have metallic properties.


### 3.3. Magnetic Properties

The magnetic properties of materials can be studied based on the density of states (DOS) and the projected density of states (PDOS) analysis. DOS are defined as the number of available electronic states per unit energy range. In computational physics/chemistry, it is one of the ways to represent electronic eigen states in the energy space of a molecule, where it counts the number of energy states nearby a given energy value. If Ψi and Ei represent the normalized eigen functions and eigen values, respectively, the total density of states (TDOS) can be defined as [17](4)DE=∑iδE−Ei,where D(E) represents the density of states, and its integral ∫DEdE in between the energies E1 and E2 gives the number of states within the specified energy range [38]. The density of states projected over any arbitrary state is defined as the projected density of states (PDOS). The present magnetic moment by reason of spin states of electrons in the individual orbital of atoms in the materials is calculated by using PDOS. It can be expressed as(5)n0E=∑if0|ψi2δE−Ei,with ∫n0(E)dE = 1, due to the normalization condition of chosen orbital │f0>. When plotted, PDOS gives the relative contributions to TDOS and hence helps to analyze the relative contributions of each atom or molecule in the larger systems. Unpaired up-spin and down-spin states of an isolated atom possess a nonzero value of total spin and cause finite magnetic moment [19]. It means spin states are asymmetrically distributed in DOS and PDOS of materials. Up-spin and down-spin states are totally symmetric in DOS and PDOS, indicating equal contributions of magnetic moment in materials from up- and down-spin electrons. This ensures that those materials have nonmagnetic properties. In the present work, we discuss magnetic properties of water-adsorbed G/MoS2 HS (system-I) and water-adsorbed Mo sites vacancy defect (systems-II) materials based on DOS and PDOS calculations. Magnetic moments due to spin states of C, Mo, S, O, and H atoms in PDOS of system-I and systems-II are given in Table 2.Table 2
Total magnetic moment (µT) due to up-spin and down-spin state of electrons in the orbitals of C, Mo, S, O, and H atoms in PDOS of system-I, system-IIa, system-IIb, and system-IIc.
µ by up-spin and down-spin in ↓System-IIc (µB/cell)System-IIb (µB/cell)System-IIa (µB/cell)System-I (µB/cell)2s of C0.010.000.000.002p of C0.020.030.030.004p of Mo0.00−0.02−0.030.004d of Mo0.04−0.75−0.750.005s of Mo0.01−0.02−0.020.003s of S0.02−0.03−0.040.003p of S0.07−1.72−1.700.002s of O0.000.000.000.002p of O0.000.000.000.001s of H0.000.000.000.00µT (µB/cell)+0.17−2.51−2.510.00DOS and PDOS plots for up-spin and down-spin electrons of system-I, system-IIa, system-IIb, and system-IIc are shown in Figures3(b)–3(d), Figures 4(b)–4(d), Figures 5(b)–5(d), and Figures 6(b)–6(d), respectively. In Figures 3(b)–3(d), the DOS and PDOS plots for up-spin and down-spin of system-I are found to be symmetric, which means system-I is a nonmagnetic material. The system-IIa and system-IIb behave as strongly magnetic materials with largely asymmetric DOS/PDOS plots for up-spin and down-spin states near the Fermi energy level as shown in Figures 4(b)–4(d) and Figures 5(b)–5(d), while system-IIc is found to be slightly asymmetric as shown in Figures 6(b)–6(d), depicting the weak magnetic nature. We have calculated that the magnetic moment as asymmetrically distributed up-spin and down-spin states of electrons in 2s and 2p orbitals of C atoms are 0.00 µB/cell & 0.03 µB/cell; 4p, 4d, and 5s orbitals of Mo atoms are −0.03 µB/cell, −0.75 µB/cell, and −0.02 µB/cell; and 3s and 3p orbitals of S atoms are −0.04 µB/cell and −1.70 µB/cell, respectively, of system-IIa. Thus, total magnetic moment of system-IIa has a value of −2.51 µB/cell. Also, we have computed the magnetic moment by asymmetrically distributed unpaired up-spin and down-spin states of electrons in 2s and 2p orbitals of C atoms are 0.01 µB/cell and 0.02 µB/cell; 4p, 4d, and 5s orbitals of Mo atoms are −0.02 µB/cell, −0.75 µB/cell, and −0.02 µB/cell; 3s and 3p orbitals of S atoms are −0.03 µB/cell and −1.72 µB/cell, respectively, in system-IIb. Hence, the total magnetic moment of system-IIb has a value of −2.51 µB/cell. Similarly, we have determined the magnetic moment of system-IIc material due to asymmetrically distributed up-spin and down-spin states around the Fermi energy level in DoS/PDoS as shown in Figures 6(b)–6(d). The magnetic moments given by total up-spin and total down-spin states of electrons in the orbitals of C, Mo, and S atoms are found to be 0.03 µB/cell, 0.05 µB/cell, and 0.09 µB/cell, respectively. Also, we individually calculated the magnetic moments given by asymmetrically distributed spin states in 2s and 2p orbitals of C atoms, which have values of 0.01 µB/cell and 0.02 µB/cell, respectively; 4p, 4d, and 5s orbitals of Mo atoms have values of 0.00 µB/cell, 0.04 µB/cell, and 0.01 µB/cell, respectively; and 3s and 3p orbitals of S atoms have values 0.02 µB/cell and 0.07 µB/cell, respectively, as given in Table 2. Therefore, we found that the total value of magnetic moment of system-IIc is +0.17 µB/cell. In summary, magnetic properties of materials are consistent with the spin-asymmetry theory for the origin of magnetism, where it is understood that the higher the net difference in electronic occupancy in between up-spin and down-spin, the higher the magnetic moment is. The calculated values of magnetic moment in system-IIa and system-IIb (i.e., −2.51 µB/cell and −2.51 µB/cell) are greater than those of system-IIc (+0.17 µB/cell) because unpaired spin states of electrons in the orbitals around the vacancy atoms of system-IIc seem to be more paired by absorbed water molecule than in system-IIa and system-IIb. Therefore, magnetic moment of system-IIc rapidly falls down compared to system-IIa and system-IIb. We also found that there is a bit stronger interaction of water molecule with 1Mo vacancy defects as compared to 2Mo vacancy defects in the systems; this is because of greater polarizability of atoms in system-IIa and system-IIb than in system-IIc.


## 3.1. Structural Study

The water-adsorbed G/MoS2 HS is constructed by putting water molecule at various locations on graphene and MoS2 surfaces of the G/MoS2 HS material as shown in Figures 1(a)–1(d). The adsorbed water molecule (at center position on the surface of MoS2) at a distance of 2.52 Å above the top surface of MoS2 in the HS is found to be most stable, as shown in Figure 1(d). To determine the stability, we have calculated the binding energy of system-I by using the following equation [31]:(1)Eb=Ew+G/MoS2HS−EG/MoS2HS−EwA,where Ew+G/MoS2HS,EG/MoS2HS,Ew are the total energy of the system-I, G/MoS2 HS, and adsorbed water molecule, respectively, and “A” is the surface area of heterostructure. The obtained binding energy of system-I is −23.82 meV/Å2, which means system-I is energetically stable at the ground state. It means physisorption interaction takes place in between them. The stable optimized system-IIa, system-IIb, and system-IIc are created by adsorbing water molecule in centre-1Mo atom, left-1Mo atom, and 2Mo atom vacancy defect G/MoS2 HS, respectively, as shown in Figures 2(a)–2(c). To determine the stability of such systems, we have also calculated binding energy using the following formalism [31]:(2)Eb=Ew+G/MoS2HSMo−d−EG/MoS2HSMo−d−EwA,where Ew+G/MoS2HSMo−d,EG/MoS2HSMo−d,Ew are the ground state energy of Mo site vacancy defect water-adsorbed G/MoS2 HS (systems-II), Mo site vacancy defect G/MoS2 HS, and adsorbed water molecule, respectively, and “A” represents the surface area of defected heterostructures. The estimated binding energy of system-IIa, system-IIb, and system-IIc are −20.09 meV/Å2, −20.03 meV/Å2, and −17.40 meV/Å2, respectively. The calculated binding energy of system-I, system-IIa, system-IIb, and system-IIc is comparable with the values of other vdW HSs [32, 33]. Thus, considered systems are stable because negative binding energy means that materials are energetically stable at the ground state. Lower value of binding energy indicates that the material is more stable than others. Hence, the stability of the above considered materials is decreased with an increase in the defect concentration. The defect formation energy of system-IIa, system-IIb, and system-IIc is found to be 0.21 eV, 0.21 eV, and 0.40 eV, respectively, which are calculated by using the following equation [34]:(3)Edf=Etd−Etp+nMoµMo,where (Et)d, (Et)p, nMo, and µMo are the total ground state energy of vacancy defect HS (systems-II), total ground state energy of pristine HS (system-I), numbers of vacancy defects (Mo) atoms, and chemical potential of a Mo atom, respectively. Materials have lower defect formation energy, which indicates that they can be favorable for computational work.In addition, we have also computed the interlayers distance between graphene and monolayer MoS2 of system-I, system-IIa, system-IIb, and system-IIc materials, and they are 3.72 Å, 3.81 Å, 3.83 Å, and 3.94 Å, respectively. These values are comparable with other graphene-based 2D HS materials [35, 36]. From this analysis, we conclude that system-I is more compact than Mo vacancy-defected systems. In systems-II, compactness of atoms and layers of constituents are increased with a decrease in their defect concentration. The estimation of binding energy and interlayer distance of the above considered systems shows that weak vdW force exists in between graphene and MoS2.


## 3.2. Electronic Properties

The electronic properties of the material are predicted based on the electronic band structure. Band structures of system-I, system-IIa, system-IIb, and system-IIc are illustrated in Figures3(a), 4(a), 5(a), and 6(a), respectively. We know that graphene and monolayer MoS2 have metallic [1, 9] and semiconducting properties, respectively [12, 13]. Band structure of graphene/MoS2 HS is a sum of band structures of those constituents in which properties of graphene are preserved, and hence, it also has metallic properties [20, 37]. Impressively, it is noted that Dirac point setup in the conduction band at 0.11 eV distance from the Fermi energy level in the band structure of water adsorbed Graphene/MoS2 HS (system-I). This small value of the Dirac cone is obtained because of the adsorption of water molecule in G/MoS2 HS. The formation of the Dirac cone in the conduction band means electrons spontaneously flow from the valence band to the conduction band. Hence, system-I has metallic properties. Also, the property of G/MoS2 HS is still preserved.Figure 3
(a) Band structure of system-I, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-I, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-I, (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-I. In all DOS and PDOS, the horizontal dot line separates spin states and the vertical dot line separates the electronic bands, and also in band plot, the horizontal dot line represents the Fermi energy level; insets in DOS and PDOS represent the spin states within a large energy range alongx-axis.
(a)(b)(c)(d)Figure 4
(a) Band structure of system-IIa, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIa, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIa, (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIa. In all DOS and PDOS, the horizontal dot line separates spin states and the vertical dot line separates the electronic bands, and also in the band plot, the horizontal dot line represents the Fermi energy level. Insets in DOS and PDOS represent spin states within large energy range alongx-axis.
(a)(b)(c)(d)Figure 5
(a) Band structure of system-IIb, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIb, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIb, (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIb. In all DOS and PDOS, the horizontal dot line separates spin states and the vertical dot line separates the electronic bands, and also in the band plot, the horizontal dot line represents Fermi energy level. Insets in DOS and PDOS represent the spin states within a large energy range alongx-axis.
(a)(b)(c)(d)Figure 6
(a) Band structure of system-IIc, (b) DOS of up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIc, (c) PDOS of total up-spin and total down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIc, and (d) PDOS of individual up-spin and down-spin states of electrons in the orbitals of C Mo, S O, and H atoms of system-IIc. In all DOS and PDOS, the horizontal dot line separates the spin states and the vertical dot line separates the electronic bands, and also in the band plot, the horizontal dot line represents the Fermi energy level. Insets in DOS and PDOS represent the spin states within a large energy range alongx-axis.
(a)(b)(c)(d)Moreover, we explored band structures of systems-II materials and found that the Dirac cone is formed at 0.72 eV, 0.71 eV, and 0.68 eV distance from the Fermi energy level in system-IIa, system-IIb, and system-IIc materials, respectively, which are shown in Figures4(a), 5(a) and 6(a). A few numbers of electronic bands of valence electrons cross the Fermi energy level in band structures, which is due to the effect of Mo vacancy atom in structures, which breaks the symmetry of system-I. Hence, defected materials are metallic. In systems-II, unpaired up-spin and down-spin states are appeared by Mo vacancy defects, due to which the movement of interfacial charges is developed in systems. Hence, the different values of the Dirac point, Fermi energy, and shift of the Fermi energy level towards the valence band are obtained in system-IIa, system-IIb, and system-IIc, which are presented in Table 1.Table 1
Fermi energy (Ef), fermi energy shifts (Es), amplitude of the Dirac point (Dp), Dirac point shifts in defected materials (Ds), defect formation energy (Edf), and total binding energy of the systems (Eb).
Systems ⟶System-I:System-IIa:System-IIb:System-IIc:SystemsEf (eV)Es (eV)Dp (eV)Ds (eV)Edf (eV)Eb (meV/Å2)System-I0.44—0.11——−23.82System-IIa−0.611.050.720.610.21−20.09System-IIb−0.601.040.710.590.21−20.03System-IIc−0.861.300.680.570.40−17.40In Table1, we can see that the values of Fermi energy and Fermi energy shift are increased with an increase in the concentration of Mo vacancy defects, but the distance of the Dirac point from the Fermi energy level decreases with an increase in the defect concentration in the systems. The reason is that vacancies are very precise place for adsorbed molecule. This is because we have calculated the bond length between nearest Mo-Mo atoms, S-S atoms, Mo-S atoms, and distance between adsorbed water molecule to MoS2 surface in vacancy defects HS and found that the compactness of materials decreases with an increase in defect concentrations. Thus, adsorbed molecule disturbed the atomic configurations in vacancy-defected HS materials, which influences the electronic properties of the systems. Dirac point setup in the conduction band reflects that the electron impulsively proceeds from the valence to the conduction band because the flow of current in metals and semiconductors depends on the amplitude of Dirac shift. Hence, system-IIa, system-IIb, and system-IIc have metallic properties.


## 3.3. Magnetic Properties

The magnetic properties of materials can be studied based on the density of states (DOS) and the projected density of states (PDOS) analysis. DOS are defined as the number of available electronic states per unit energy range. In computational physics/chemistry, it is one of the ways to represent electronic eigen states in the energy space of a molecule, where it counts the number of energy states nearby a given energy value. If Ψi and Ei represent the normalized eigen functions and eigen values, respectively, the total density of states (TDOS) can be defined as [17](4)DE=∑iδE−Ei,where D(E) represents the density of states, and its integral ∫DEdE in between the energies E1 and E2 gives the number of states within the specified energy range [38]. The density of states projected over any arbitrary state is defined as the projected density of states (PDOS). The present magnetic moment by reason of spin states of electrons in the individual orbital of atoms in the materials is calculated by using PDOS. It can be expressed as(5)n0E=∑if0|ψi2δE−Ei,with ∫n0(E)dE = 1, due to the normalization condition of chosen orbital │f0>. When plotted, PDOS gives the relative contributions to TDOS and hence helps to analyze the relative contributions of each atom or molecule in the larger systems. Unpaired up-spin and down-spin states of an isolated atom possess a nonzero value of total spin and cause finite magnetic moment [19]. It means spin states are asymmetrically distributed in DOS and PDOS of materials. Up-spin and down-spin states are totally symmetric in DOS and PDOS, indicating equal contributions of magnetic moment in materials from up- and down-spin electrons. This ensures that those materials have nonmagnetic properties. In the present work, we discuss magnetic properties of water-adsorbed G/MoS2 HS (system-I) and water-adsorbed Mo sites vacancy defect (systems-II) materials based on DOS and PDOS calculations. Magnetic moments due to spin states of C, Mo, S, O, and H atoms in PDOS of system-I and systems-II are given in Table 2.Table 2
Total magnetic moment (µT) due to up-spin and down-spin state of electrons in the orbitals of C, Mo, S, O, and H atoms in PDOS of system-I, system-IIa, system-IIb, and system-IIc.
µ by up-spin and down-spin in ↓System-IIc (µB/cell)System-IIb (µB/cell)System-IIa (µB/cell)System-I (µB/cell)2s of C0.010.000.000.002p of C0.020.030.030.004p of Mo0.00−0.02−0.030.004d of Mo0.04−0.75−0.750.005s of Mo0.01−0.02−0.020.003s of S0.02−0.03−0.040.003p of S0.07−1.72−1.700.002s of O0.000.000.000.002p of O0.000.000.000.001s of H0.000.000.000.00µT (µB/cell)+0.17−2.51−2.510.00DOS and PDOS plots for up-spin and down-spin electrons of system-I, system-IIa, system-IIb, and system-IIc are shown in Figures3(b)–3(d), Figures 4(b)–4(d), Figures 5(b)–5(d), and Figures 6(b)–6(d), respectively. In Figures 3(b)–3(d), the DOS and PDOS plots for up-spin and down-spin of system-I are found to be symmetric, which means system-I is a nonmagnetic material. The system-IIa and system-IIb behave as strongly magnetic materials with largely asymmetric DOS/PDOS plots for up-spin and down-spin states near the Fermi energy level as shown in Figures 4(b)–4(d) and Figures 5(b)–5(d), while system-IIc is found to be slightly asymmetric as shown in Figures 6(b)–6(d), depicting the weak magnetic nature. We have calculated that the magnetic moment as asymmetrically distributed up-spin and down-spin states of electrons in 2s and 2p orbitals of C atoms are 0.00 µB/cell & 0.03 µB/cell; 4p, 4d, and 5s orbitals of Mo atoms are −0.03 µB/cell, −0.75 µB/cell, and −0.02 µB/cell; and 3s and 3p orbitals of S atoms are −0.04 µB/cell and −1.70 µB/cell, respectively, of system-IIa. Thus, total magnetic moment of system-IIa has a value of −2.51 µB/cell. Also, we have computed the magnetic moment by asymmetrically distributed unpaired up-spin and down-spin states of electrons in 2s and 2p orbitals of C atoms are 0.01 µB/cell and 0.02 µB/cell; 4p, 4d, and 5s orbitals of Mo atoms are −0.02 µB/cell, −0.75 µB/cell, and −0.02 µB/cell; 3s and 3p orbitals of S atoms are −0.03 µB/cell and −1.72 µB/cell, respectively, in system-IIb. Hence, the total magnetic moment of system-IIb has a value of −2.51 µB/cell. Similarly, we have determined the magnetic moment of system-IIc material due to asymmetrically distributed up-spin and down-spin states around the Fermi energy level in DoS/PDoS as shown in Figures 6(b)–6(d). The magnetic moments given by total up-spin and total down-spin states of electrons in the orbitals of C, Mo, and S atoms are found to be 0.03 µB/cell, 0.05 µB/cell, and 0.09 µB/cell, respectively. Also, we individually calculated the magnetic moments given by asymmetrically distributed spin states in 2s and 2p orbitals of C atoms, which have values of 0.01 µB/cell and 0.02 µB/cell, respectively; 4p, 4d, and 5s orbitals of Mo atoms have values of 0.00 µB/cell, 0.04 µB/cell, and 0.01 µB/cell, respectively; and 3s and 3p orbitals of S atoms have values 0.02 µB/cell and 0.07 µB/cell, respectively, as given in Table 2. Therefore, we found that the total value of magnetic moment of system-IIc is +0.17 µB/cell. In summary, magnetic properties of materials are consistent with the spin-asymmetry theory for the origin of magnetism, where it is understood that the higher the net difference in electronic occupancy in between up-spin and down-spin, the higher the magnetic moment is. The calculated values of magnetic moment in system-IIa and system-IIb (i.e., −2.51 µB/cell and −2.51 µB/cell) are greater than those of system-IIc (+0.17 µB/cell) because unpaired spin states of electrons in the orbitals around the vacancy atoms of system-IIc seem to be more paired by absorbed water molecule than in system-IIa and system-IIb. Therefore, magnetic moment of system-IIc rapidly falls down compared to system-IIa and system-IIb. We also found that there is a bit stronger interaction of water molecule with 1Mo vacancy defects as compared to 2Mo vacancy defects in the systems; this is because of greater polarizability of atoms in system-IIa and system-IIb than in system-IIc.


## 4. Conclusions

In this work, system-I, system-IIa, system-IIb, and system-IIc materials are constructed and investigated their structural, electronic, and magnetic properties by first-principles calculations based on the spin-polarized DFT-D2 method under computation package Quantum ESPRESSO. By analyzing the structures, we found that system-I is more compact than system-IIa, system-IIb, and system-IIc materials. Compactness of system and defect concentration in structures is related to each other because the more the defect concentrations in structures, the less the compactness of atoms in structures. Therefore, compactness of systems decreases with an increase in its defect concentration. On the analysis of band structures, system-I, system-IIa, system-IIb, and system-IIc have metallic properties. By studying DoS and PDoS calculations, we found that system-I has nonmagnetic properties and system-IIa, system-IIb, and system-IIc have magnetic properties. The total magnetic moment of system-IIa, system-IIb, and system-IIc has values −2.51µB/cell, −2.51 µB/cell, and +0.17 µB/cell, respectively. Higher values of magnetic moment are claimed by allotted up- and down-spins in 2p orbital of C atoms, 3p orbital of S atoms, and 4d orbital of Mo atoms in defected systems.



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*Source: 2135213-2022-04-11.xml*