Structural and Electronic Properties of Different Terminations for Quartz (001) Surfaces as Well as Water Molecule Adsorption on It: A First-Principles Study

Abstract

Structural and electronic properties of Si termination, O-middle termination, and O-rich terminations of a quartz (001) surface as well as water molecule adsorption on it were simulated by means of density functional theory (DFT). Calculated results show that the O-middle termination exposing a single oxygen atom on the surface is the most stable model of quartz (001) surface, with the lowest surface energy at 1.969 J·m⁻², followed by the O-rich termination and Si termination at 2.892 J·m⁻² and 2.896 J·m⁻², respectively. The surface properties of different terminations mainly depend on the surface-exposed silicon and oxygen atoms, as almost all the contributions to the Fermi level (E_F) in density of states (DOS) are offered by the surface-exposed atoms, especially the O2p state. In the molecular adsorption model, H₂O prefers to adsorb on the surface Si and O atoms, mainly via O₁–H₁ bond at 1.259 Å and Si₁–O_w at 1.970 Å by Van der Waals force and weak hydrogen bond with an adsorption energy of −57.89 kJ·mol⁻¹. In the dissociative adsorption model, the O-middle termination is hydroxylated after adsorption, generating two new Si–OH silanol groups on the surface and forming the O_wH₂···O₄ hydrogen bond at a length of 2.690 Å, along with a large adsorption energy of −99.37 kJ·mol⁻¹. These variations in the presence of H₂O may have a great influence on the subsequent interfacial reactions on the quartz surface.

1. Introduction

Quartz is an important mineral that has wide applications as a raw material in various fields in industry, such as glass, ceramics, and medicine [1,2,3]. It is the main component mineral of a series of important mineral resources such as siliceous phosphate ore, iron ore, tungsten ore, fluorite, and mica. Flotation is a widely accepted way to separate and utilize these ore resources based on the difference in wettability (hydrophilic and hydrophobic characteristics at a macroscopic-level) of the mineral particle surfaces by froth, which occurs at the interfaces of solid/air/water in the solution [4,5]. Furthermore, the surface chemical activities of minerals in flotation has a close relationship with its surface structure and properties. Therefore, it is crucial to accurately determine the mineral surface structure so that one can understand its interactions well with other molecules, such as water [6], calcium hydroxyl ions [7], and flotation reagents [5,8,9].

The surface structures and characteristics of quartz crystal have been investigated extensively using traditional means of analysis technologies, such as X-ray diffraction [10], scanning electron microscope [11], and photoelectron spectrum [12], but these studies have failed to offer more detailed surface structural and electronic properties at the level of electron and atom due to the limited resolution or accuracies of the above analysis methods. Even though atomic force microscopy can provide an overall characterization of the surface topography of a quartz (001) surface on a nanometer scale [13] and offer images of synthetically grown-quartz (0001) surfaces [14], it still fails to further determine the detailed microstructure of the exposing atoms on surface. With the development of quantum chemistry theory and computer technology, DFT calculations based on first principles have been widely used in acquiring the micro-structural information of various minerals with high accuracy, such as clay minerals [15,16,17], iron minerals [18], and sulfide minerals [19,20]. These studies have provided a theoretical basis for the quantitative interpretation of mineral properties.

In going from a bulk crystal to a surface, the atoms along the cleaved plane experience a loss of coordination, and this can manifest in new features in the electronic structure, as demonstrated in DFT studies in the literature [21,22]. Many researchers have focused on the surface properties of cleaved quartz using computational methods, and the consensus is that the (001) surface is the thermodynamically predominant plane [23,24,25,26]. Meanwhile, even for the single (001) plane, there are many possible terminations that are distinct in terms of the identity and number of terminal atoms. When the surface is in contact with an aqueous phase, water adsorption and dissociation processes can further modify the surface structure. As structure and composition affect reactivity, different surface terminations can thus exhibit unique properties, which go on to influence the bonding interactions with adsorbates [21,22,27].

While it is well-known that a mineral’s surface structure is transformed by contact with water, previous studies have investigated the interaction of flotation reagents with the surface modeled in the structure found under ultra-high vacuum conditions [28,29,30,31]. This may not be a realistic representation of the flotation process, as the reactivity of interest is actually occurring at a differently structured mineral–water interface. Therefore, the influence of water on the surface should also be investigated [7,32,33]. The quartz–water interface has been studied using molecular dynamics simulations (MDS), yielding information about how the surface was transformed by the presence of water [34,35,36,37]. However, a molecular-level understanding of the adsorption process and mechanism, such as that which can be attained through DFT modeling, is still lacking.

In this paper, DFT calculations are carried out on the Si, O-middle, and O-rich terminations of a simulated (001) quartz surface. After each termination is geometry-optimized against a vacuum, the interaction of the most stable termination with water is investigated. The DFT results are analyzed in terms of energy, surface geometry, and electronic properties. As such, the information reported here contributes to a fundamental understanding of the ubiquitous quartz surface, which is of interest to those in the field of mineralogy as well as those interested in the many industrial applications of quartz. In particular, the results about the quartz–water interface are critical to understanding reagent adsorption and other surface-mediated processes occurring at the quartz–water interface.

2. Computational Method and Model

2.1. Computational Method

Calculations have been made using the Cambridge Serial Total Energy Package (CASTEP) [38] in the TCM Group of the Cavendish Laboratory in Cambridge, UK. CASTEP implements DFT using periodic boundary conditions and a planewave basis set [39]. Calculations in this study used ultrasoft pseudopotentials to model the electron–nucleus interactions at reduced computational cost [40]. The convergence tolerances for geometry optimization calculations were set to a maximum displacement of 0.002 Å, a maximum force of 0.05 eV·Å⁻¹, a maximum energy change of 2.0 × 10⁻⁵ eV·atom⁻¹, and a maximum stress of 0.1 GPa, and the SCF convergence tolerance was set to be 2.0 × 10⁻⁶ eV·atom⁻¹. The valence electron configurations considered in the work are Si 3s²3p², O 2s²2p⁴, and H 1s¹. Before adsorption, the H₂O was placed inside a 10 Å × 10 Å × 10 Å cubic cell for an optimization calculation. Computational parameters such as the planewave basis set cutoff energy and k-point sample were tested for convergence.

2.2 Quartz Crystal Cell Optimization

The quartz crystal space group ${\mathrm{D}}_3^6-\mathrm{P}{3}_{2}21$ belongs to a rhombohedral system with the starting unit cell parameters of a = b = 4.973 Å, c = 5.469 Å, α = β = 90.0°, and γ = 120.0° (see Figure 1). It is comprised of the structures of silicon oxygen tetrahedron, and the silicon atom was located at the tetrahedron center. Each silicon atom was coordinated with four oxygen atoms. The angles of O–Si–O were 110.1° and 108.7°, and the bond lengths of Si–O were 1.620 Å and 1.624 Å.

A bulk quartz cell was modeled to form a basis for the subsequent surface calculations. The dependence of the rationality of the quartz unit-cell on exchange-correlation functionals selection, the k-point set mesh, and cutoff energy was tested. Afterwards, the calculated crystal lattice parameters were compared with experimental values to determine the validity of the computed quartz crystal cell. After geometry optimization, the exchange correlation functional used was the generalized gradient approximation (GGA) developed via the Perdew–Wang generalized-gradient approximation (PW91) [41], and kinetic energy cutoff was set at 360 eV, and a 5 × 5 × 4 grid was chosen for all structure calculations. The quartz cell parameters obtained after minimization were a = b = 4.964 Å, c = 5.470 Å, with deviations of 0.14% and 0.02%, respectively, compared with experiment values [42]. This showed that the calculation conditions chosen were sufficient for the system, and the method was credible for the subsequent calculations. More detailed data for the above geometry optimization of bulk cell is provided in the supplementary material.

2.3. Surface Models and Calculation of Surface Energy

The quartz (001) surface was cleaved on the basis of an optimized 1 × 1 bulk structure. The (001) cleave plane forms three different exposed atoms, as shown in Figure 2. The cleaved surfaces are formed by breaking Si–O bonds to generate highly reactive Si and Si–O free radical species. The Si termination exposes a single silicon atom with double coordination bonds (Figure 2a), the O-middle termination exposes an oxygen atom with a single coordination and a silicon atom with three coordination bonds (Figure 2b), and the O-rich termination exposes two oxygen atoms both with a single coordination bonded with the first silicon atom with four coordination bonds (Figure 2c). The (1 × 1) terminations were used to test for a suitable number of atomic layers to create the slab model and to determine a sufficient vacuum thickness to prevent interactions between periodic images in the direction of the surface normal. For both the surface slab models and the H₂O molecule adsorption surface, the eight outermost atomic layers of the substrate were allowed to relax, while the 10 bottom-most atomic layers of the substrate were fixed to the bulk coordinates.

The surface energy ($E_{surf}$) is the required energy to cleave the crystal into two independent surfaces in the crystal direction of the crystal cleavage under the action of external force, which is dependent on the interaction of surface atoms and closely related with the geometrical structure of the surface atoms. For surface systems without external force, the total surface energy of the system tends to be minimized. The $E_{surf}$ of creating the cleaved surface can be estimated by the following relation [27]:

$$E_{surf}={(E}_{slab}{-N·E}_{bulk})/2S$$

(1)

where $E_{slab}$ is the energy of the corresponding slab; $E_{bulk}$ is the energy of bulk crystal; N is the number of bulk units in the slab; S is the surface area of cell. The smaller the surface energy is, the higher the surface stability is.

It is quite necessary to test the atomic layer number and vacuum thickness to obtain the relative stable surface models of different terminations.

Table 1. Effects of atomic layer number on surface energy of different terminations of the quartz (001) surface (the vacuum thickness in these tests was set at 10 Å).

Atomic Layer Number	Surface Energy/(J·m−2)
	Si Termination	O-Middle Termination	O-Rich Termination
9	2.928	1.999	2.920
12	3.124	2.000	2.915
15	2.898	1.997	2.907
18	2.896	1.995	2.896
21	2.896	1.995	2.893
24	2.897	1.999	2.899

and

Table 2. Effects of vacuum thickness on surface energy of different terminations of the quartz (001) surface (the atomic layer number in these tests was set at 18).

Vacuum Thickness/Å	Surface Energy/(J·m−2)
	Si Termination	O-Middle Termination	O-Rich Termination
8	2.905	1.986	2.894
10	2.896	1.995	2.896
15	2.896	1.969	2.892
18	2.899	1.969	2.894
20	2.894	1.972	2.892

show the influence of the atomic layer number and vacuum thickness on the surface energy of three different terminations of the quartz (001) surface, respectively.

From the results of Table 1 and Table 2, it is obvious that the changes in surface energy for the different terminations are not very noticeable after simulation, which indicates that the testing range of the atomic layer number and vacuum layer thickness set in the calculation were reasonable, and the three terminations all showed a certain stability. For all of the surface terminations, it was determined that 18 atomic layers and 15 Å of vacuum is sufficient to converge the calculated surface energy. Based on convergence studies, structures for the three different surface terminations of quartz (001) were generated, as shown in Figure 3, with the atomic layers identified.

3. Results and Discussion

3.1. Surface Structural and Electronic Properties of Different Terminations for Quartz (001) Surface

3.1.1. Surface Energy

It is generally known that the lower the surface energy is, the more stable the surface is [21]. Among the three terminations, the O-middle termination has the lowest surface energy at 1.969 J·m⁻². Cleaving on this termination needs less energy than that of any other surfaces, which indicates that it is likely to be the most stable termination model of the quartz (001) surface by DFT calculation. The surface energies of Si termination and O-rich termination are higher at 2.896 J·m⁻² and 2.892 J·m⁻², respectively, showing the consistent surface stability. The DFT calculated values for the surface energy provides some guidance as to what surface termination is the most thermodynamically stable. However, as the DFT total energies are modeled at 0 K, effects such as temperature and pressure are neglected. Furthermore, it is possible that, in the real system, metastable surface terminations may be kinetically stabilized. Therefore, there are practical limitations to the interpretation of the DFT predictions based on the surface energies. Next, we calculated the surface relaxation, surface atomic Mulliken charge distribution, Mulliken bond population, and density of states to further investigate the property differences of the three terminations.

3.1.2. Surface Relaxation

In going from the bulk to a surface structure, the coordination number of the exposed atoms changes, and it is expected that the outermost atoms will undergo inward relaxations to recover a stable bonding environment. This is called the relaxation of minerals surface atoms. The relaxation formula is as follows [22]:

$$\Delta Z=\frac{Z_i-Z_{i,bulk}}{a}\times 100\%$$

(2)

where the $Z_i$ represents the corresponding atomic coordinate of Si and O atoms in the i-th layer after the relaxation; $Z_{i,bulk}$ denotes the bulk atomic coordinate of Si and O atoms in the i-th layer, which was established by the bulk of quartz after the geometry optimization; $a$ refers to the bulk lattice parameter along the z-axis before geometry optimization.

The atomic displacements and coordination of three different terminations of the quartz (001) surface are given in

Table 3. Atomic displacement and coordination of different terminations of the quartz (001) surface (C* represents the coordination number of atoms).

Atoms	Si Termination				O-Middle Termination				O-Rich Termination
	C*	$\Delta$x	$\Delta$y	$\Delta$z	C*	$\Delta$x	$\Delta$y	$\Delta$z	C*	$\Delta$x	$\Delta$y	$\Delta$z
O1	2	0.12	0.07	−0.02	1	0.07	0.05	0.20	1	−2.24	0.06	−0.11
O2	2	−0.11	−0.21	−0.01	2	0.58	0.17	0.05	1	2.11	0.49	0.21
O3	2	0.12	−0.03	0.03	2	−0.10	−0.29	−0.05	2	0.40	0.69	−0.35
O4	2	0.06	0.04	0.01	2	0.26	−0.30	−0.04	2	−0.77	0.02	−0.21
O5	2	0.03	−0.11	0.06	2	−0.01	0.00	0.04	2	−0.25	−0.46	−0.22
O6	2	0.11	0.04	0.03	2	−0.05	−0.32	0.04	2	−0.40	−0.17	−0.08
O7	2	0.05	0.08	0.01	2	0.20	0.20	−0.03	2	0.33	−0.61	−0.12
O8	2	0.41	0.22	0.09	2	−0.01	0.03	−0.05	2	0.63	−0.04	0.11
Si1	2	−2.76	−0.29	0.05	4	−1.81	−0.77	−0.18	4	−0.04	0.23	−0.31
Si2	4	0.08	−0.06	0.00	4	0.19	0.02	0.01	4	−0.23	0.07	−0.22
Si3	4	0.10	−0.02	0.24	4	0.18	−0.02	0.01	4	0.08	−0.29	−0.09
Si4	4	0.13	0.02	0.05	4	0.18	0.02	−0.01	4	0.20	−0.05	0.05

. The displacements of surface silicon and oxygen atoms in the top three layers changed in variety after relaxation duo to the dangling bond on the surface. They move toward or away from the bulk in the direction of the x-, y-, and z-axes. In the special ring structure of the silicon oxygen tetrahedron of quartz, the atoms of the top three layers show a certain stretching effect on the atoms under them, with the result that some atoms in the bulk layer that bonded with them also have different degrees of contraction relaxation. The surface structure of different terminations before and after relaxation from the same side view are shown in Figure 4 as the direct display of relaxation results.

For the Si termination, the Si₁ atom only shows a displacement along the x-axis (−2.76%), and the overall structural relaxation degree is relatively low. This may be because the full ring structure of silicon oxygen tetrahedron show a strong binding and stretching effect on the Si atom in it. For the O-middle termination, the O₁ and Si₁ atoms have dangling bonds, and they show the reverse displacement along the x- and z-axes. The first O₁ atom has a small displacement along the z-axis at 0.20% away from the bulk, while the Si₁ atom bonded with it has an opposite displacement along the z-axis at −0.18% toward the bulk. Additionally, the Si₁ atom also has a large displacement along the x-axis at −1.81% and a slight displacement along the y-axis at −0.77%. The displacements of O-middle termination atoms are larger than that of Si termination. For the O-rich termination, the top O₁ and O₂ atoms have large displacements toward the opposite direction, and the major movement is along the x-axis direction (respectively at −2.24% and at 2.11%). The O₂ atom also has a relative obvious displacement along the y-axis at 0.49% compared with that of the O₁ atom at 0.06%. Furthermore, the O₁ and O₂ atoms has a slight displacement along the z-axis, respectively, at −0.11% for the O₁ atom toward the bulk and 0.21% for the O₂ atom away from the bulk. Over all, the O-rich termination is the most obvious one in all three terminations, and it can be seen directly from Figure 4 that the exposing two O atoms in double dangling Si–O bonds show a larger angle rotation around the central Si₁ atom, adjusting the spacing of the atoms and rearranging the electron distribution. The angles of O–Si–O on the surface changed substantially; in particular, the angle of O–Si–O decreased from 108.69° to 60.90°.

3.1.3. Surface Atomic Mulliken Charge Distribution

In the Mulliken scheme of charge partitioning, the charges in the overlap region are distributed evenly between the relevant atomic orbitals. This is a relatively simple and effective method, but also has its shortcomings, since the charge apparently tends to be distributed to the atoms with high electronegativity in the actual process. Additionally, it is also pointless to compare the absolute values of the atomic Mulliken charge simply, as the Mulliken charge is quite sensitive to the chosen basis set, and different basis sets vary greatly [43]. Even so, the results obtained under the same basis set conditions still make sense when the relative values of the Mulliken atomic charges are compared, which has been widely used as an efficient method to describe the charge transfer and bond strengths between different atoms [7,20,33,44]. In this section, the Mulliken atomic charge populations of surface atoms in each termination are calculated and compared with those of the bulk (

Table 4. Surface atomic Mulliken charge distribution of different terminations of the quartz (001) surface and bulk.

Atoms		s	p	Total	Charge/e
Bulk	Si	0.57	1.07	1.64	+2.36
	O	1.83	5.35	7.18	−1.18
Si termination	Si1	1.66	1.14	2.80	+1.20
	O1	1.84	5.33	7.17	−1.17
	O2	1.84	5.33	7.17	−1.17
	Si2	0.57	1.09	1.66	+2.34
	O3	1.83	5.36	7.19	−1.19
O-middle termination	O1	1.94	5.10	7.04	−1.04
	Si1	0.59	1.21	1.80	+2.20
	O2	1.85	5.34	7.19	−1.18
	O3	1.83	5.34	7.17	−1.18
	Si2	0.57	1.06	1.63	+2.37
O-rich termination	O1	1.95	4.67	6.62	−0.63
	O2	1.95	4.69	6.64	−0.64
	Si1	0.54	1.00	1.54	+2.46
	O3	1.83	5.36	7.19	−1.19
	O4	1.83	5.37	7.20	−1.20

).

It can be seen that the Mulliken atomic charges populations of Si and O atoms on the surface layers are different from the bulk after relaxation. For the Si termination, 2s and 2p states of the Si₁ atom gain electrons from 0.57 to 1.66 and from 1.07 to 1.14, respectively, and the overall charge reduction 1.16 e varies from +2.36 to +1.20 e, and the charges of the O₁ and O₂ atoms each reduce 0.01 e. For the O-middle termination, the O₁ atom gains electrons 0.11 at 2s states and loses electrons 0.25 at 2p states, respectively. The overall charge reduction 0.14 e varies from −1.18 e to −1.04 e, while the overall charge of the Si atom reduction 0.16 e varies from +2.36 to +2.20 e. For the O-rich termination, the O₁ and O₂ atoms both lose electrons at 2p states, 0.68 and 0.66, and the final charge reduces from −1.18 e to −0.63 e and −0.64 e, respectively. Furthermore, the charge of Si₁ atom increases 0.1 e. It can be concluded that, for all the terminations, the electrons of surface-exposed atoms are redistributed due to the creation of dangling bonds relative to the bulk coordination.

3.1.4. Surface Atomic Mulliken Bond Population

It is well known, in general, that an ionic or covalent character can be determined according to Mulliken bond population. High populations indicate that the bond is covalent. On the contrary, low populations suggest that the interaction between bonds is ionic.

Table 5. Surface atomic Mulliken bond population of different terminations of the quartz (001) surface and bulk.

Termination	Bond	Surface Population (Bulk)	Bond Length (Bulk)/Å
Si	Si1–O1	0.27 (0.52)	1.67 (1.624)
	Si1–O2	0.52 (0.53)	1.61 (1.632)
	O1–Si2	0.4 (0.51)	1.61 (1.625)
	O2–Si2	0.5 (0.63)	1.62 (1.622)
	O3–Si3	0.5 (0.52)	1.62 (1.617)
O-middle	O1–Si1	0.9 (0.52)	1.51 (1.620)
	Si1–O2	0.4 (0.53)	1.60 (1.618)
	Si1–O3	0.4 (0.53)	1.62 (1.628)
	O2–Si2	0.5 (0.53)	1.61 (1.631)
	O3–Si2	0.5 (0.52)	1.62 (1.624)
O-rich	O1–Si1	0.3 (0.53)	1.62 (1.624)
	O2–Si1	0.3 (0.52)	1.62 (1.626)
	Si1–O3	0.4 (0.53)	1.60 (1.616)
	Si1–O4	0.5 (0.53)	1.61 (1.625)
	O3–Si2	0.5 (0.51)	1.61 (1.625)

summarizes the Mulliken bond populations of the three terminations.

The Si–O population and length in the quartz bulk is about 0.52 and 1.624 Å, respectively, showing a covalence effect. The bond population and length of three terminations change to a certain extent due to the surface atomic charge transfer. For Si termination, as the charge of a Si₁ atom gains 1.16 e, the Si₁–O₁ bond population reduces from 0.52 to 0.27, and the length increases 0.052 Å, which indicates that the covalence of the Si–O bond is weakened and ionicity is strengthened. For O-middle termination, as the charge of the O₁ atom and the Si₁ atom is reduces by −0.14 e and +0.16 e, respectively, the O₁–Si₁ population increases from 0.52 to 0.96 with a 0.107 reduction in bond length, which indicates that the covalence interaction has been strengthened and the surface tends to be stable. For the O-rich termination, as O₁ and O₂ atoms do not lose many electrons, the O₁–Si₁ and O₂–Si₁ populations are reduced by 0.19 and 0.18, with a 0.005 and 0.002 increase in bond length, indicating that the O–Si covalent interactions weaken. Generally, the bonds near the surface mainly show extension compared with the bulk, which means that the ionicity between these atoms is enhanced due to the dangling bonds at the surface, and the results are in line with that of the tendency of the atomic displacements and surface charge distribution.

3.1.5. Density of States

Density of states (DOS) is one of the most important parameters for describing the states of motion of electrons in solid physics. In order to obtain a chemically intuitive description of the electronic structure, a state-by-state and atom-by-atom projected density of states (PDOS) analysis can be used. It has been widely used in solid physics, surface science, and interface absorption [7,28,45,46]. For further investigation, the PDOSs of the three terminations are shown in Figure 5. The PDOSs of surface Si and O atoms compared with that of the corresponding Si and O atoms in bulk are also presented in Figure 6 in order to reveal the surface properties of different terminations. The Fermi level (E_F) is referenced at 0 eV. It has been reported that the region near the Fermi level is very important for various physical and chemical properties such as conductor type, reaction activity of surface atoms, and electrochemical potential of minerals [7,20,33]. Therefore, great attention has been paid to the details near the Fermi surface.

It is can be seen from Figure 5 that the energy range distributions of electrons for the three terminations are almost the same. For the quartz surface, the activity of electrons at p states are much larger than that at s states, and the p states occupy the top of the valence band and the bottom of the conduction band, especially in the vicinity of the E_F level. Overall, the activity of O-middle termination was greater than that of Si termination and O-rich termination when only considering the details near the Fermi surface, especially of the 2p state electrons.

Figure 6 indicates that, for the Si termination, the s and p states of Si₁ atoms occupy the vicinity of the E_F level compared with that in the bulk; for the O-middle termination, the p states of O₁ and Si₁ atoms occupy in the vicinity of the E_F level, and the contribution of O₁ is much larger than the Si₁ atom; for the O-rich terminations, the p states of the O₁ and O₂ atoms entirely occupy the vicinity of the E_F level. Comparing the result of Figure 6 with Figure 5, we can see that the surface properties of different terminations are mainly formed by the surface-exposed atoms, as almost all contributions to E_F in the DOS of the surface are made by the surface-exposed atoms, which is a conclusion consistent with studies about the electronic properties of fluorapatite (001) surfaces [21] and AlCMn₃ (111) surfaces [22].

3.2. Adsorption of an Isolated Water Molecule on Quartz (001) Surface

The adsorption of an isolated H₂O molecule on a quartz (001) surface was studied based on the most stable quartz (001) termination (O-middle termination). A 4 × 3 × 1 supercell surface with atomic layer number 18 and vacuum thickness 18 Å was built to accommodate the isolated H₂O adsorption.

In terms of quartz surfaces, both the molecular and dissociative adsorptions have been considered based on research showing that the adsorption of water, depending on water coverage, can be either molecular or partially dissociative [25]. The optimized geometries are shown in Figure 7 and Figure 8, where the yellow and red balls represent silicon and oxygen atoms of quartz, and the blue and light gray balls represent oxygen and hydrogen atoms of water; parts of atoms are displayed as lines in order to see the whole adsorption structure clearly in Figure 7a and Figure 8a, and the zoomed-in views of the H₂O adsorption structure are shown in Figure 7b and Figure 8b; the bond length of newly formed bonds after adsorption are highlighted in blue, and the unit of bond length is Å.

For the molecular adsorption, it was found that water prefers to adsorb on the surface Si and O atom mainly via O₁–H₁ bond at 1.259 Å and Si₁–O_w at 1.970 Å. Furthermore, there are also two weak bonds O₂–H₂ at 2.444 Å and O₄–H₂ at 2.579 Å in the form of hydrogen bonds. The calculated adsorption energy of molecular adsorption is 600 meV/molecule (−57.89 kJ·mol⁻¹), mainly contributed by the Van der Waals force and weak hydrogen bond, which is close to the result of 618.9 meV derived from the plane-wave-based Vienna ab initio Simulation Package (VASP) calculation in [47] and is comparable with hydrogen bonds between water molecules in Ice-XI bulk (∼710 meV/molecule in DFT [48] and ∼610 meV/molecule in experiment [49]). Compared with other minerals, the adsorption energy is substantially larger than that of −29.1 kJ·mol⁻¹ on a hydrophobic galena surface and agrees well with that of −56.2 kJ·mol⁻¹ on a hydrophilic pyrite surface by DFT [32].

For the dissociative adsorption model, the structure of Si termination is quite different from the previous relaxed surface after adsorption. As we can see, the H₂O molecule dissociates into H⁺ and OH⁻ bonded with the O₁ and Si₁ atoms, respectively, generating two new Si–OH silanol groups on the quartz surface. At the same time, the Si₁–O_wH₂ group is bonded with the O₄ atom forming the O_wH₂···O₄ hydrogen bond. This indicates that the surface of quartz can be hydroxylated after adsorption of the H₂O molecule, and the hydroxylation was also reported on the quartz (101) surface [50] and a single methanol molecule in water [51] by DFT. The calculated adsorption energy of dissociative adsorption is 1.03 eV/molecule (−99.37 kJ·mol⁻¹), mainly contributed by the chemical bond of new Si–OH silanol groups and hydrogen bond. This energy is greater than that of −82.4 kJ·mol⁻¹ on hydrophilic pyrite surface by DFT [32]. In order to reveal the electron transfer and covalent interaction of new formed bonds after H₂O molecule dissociative adsorption, the surface atomic Mulliken charge distribution and surface Mulliken bond population before and after adsorption of H₂O were analyzed as shown in

Table 6. Surface atomic Mulliken charge distribution of O-middle termination before and after H₂O adsorption.

Atom	Adsorption	s	p	Total	Charge/e
H1	Before	0.48	0	0.48	0.52
	After	0.46	0	0.46	0.54
H2	Before	0.48	0	0.48	0.52
	After	0.50	0	0.50	0.50
Ow	Before	1.89	5.15	7.05	−1.05
	After	1.85	5.24	7.09	−1.09
O1	Before	1.94	5.10	7.04	−1.04
	After	1.86	5.26	7.12	−1.12
O2	Before	1.85	5.34	7.19	−1.18
	After	1.83	5.36	7.19	−1.19
O3	Before	1.83	5.34	7.17	−1.18
	After	1.84	5.36	7.20	−1.20
O4	Before	1.94	5.10	7.04	−1.04
	After	1.91	5.14	7.06	−1.06
Si1	Before	0.59	1.21	1.80	2.20
	After	0.58	1.05	1.63	2.37

and

Table 7. Surface Mulliken bond populations of O-middle termination before and after H₂O adsorption.

Bond	Population		Bond Length/Å
	Before	After	Before	After
Si1–O1	0.96	0.51	1.513	1.637
Si1–O2	0.42	0.45	1.600	1.630
Si1–O3	0.43	0.45	1.625	1.645
Ow–H2	0.51	0.53	0.978	1.000
Si1–Ow	-	0.59	-	1.594
O1–H1	-	0.54	-	0.972

(the atomic numbers correspond to the labels in Figure 8).

It can be seen from Table 6 that, after adsorption of H₂O, the electrons transfer from Si₁ atoms to O₁ and O_w1 atoms. The 2p orbital of O₁ and O_w atoms gain electrons 0.16 and 0.09, respectively, leading to their charge increasing from −1.04 e to −1.12 e and from −1.05 e to −1.09 e. This indicates that the activities of O atoms in the two new Si–OH silanol group are strengthened. The results of Table 7 show that, due to the new Si–OH silanol group, the populations of O₁–Si₁ are reduced from 0.96 at the relaxation surface to 0.51 at the adsorption surface, which is almost equivalent to the bulk value 0.52, indicating that the covalence of Si–O bond is strengthened. The population of Si₁–O_w at 0.59 is higher than that of Si₁–O₁ at 0.51, so the bond length of Si₁–O₁ is longer, suggesting that the two Si–OH silanol groups are not completely consistent. The bond length of O_w–O₄ is 2.690 Å with an H₂···O₄ length of 1.718 Å and an O_wH₂···O₄ angle of 163.03°, which is close to the reference hydrogen bond with an OO distance of 2.70 Å after water adsorption on a quartz surface by VASP calculation [25]. The bond of O_w–O₄ belongs to a strong hydrogen bond based on classification criterion (the strong one is within an OO distance of 2.72 Å and an OH···O angle of 168°) originating from those reported in the 2D water layers on metal Pt (111) [52] and hydroxylated cristobalite (100) [53].

During bonding between two atoms, there are two types of bond orbitals—a bonding orbital and an antibonding orbital—that always appear in pairs. The bonding orbital is dominated by atomic orbitals with high electronegativity, whereas the antibonding orbital is dominated by atomic orbitals with low electronegativities [43]. To further investigate the bonding mechanism of H₂O molecule after the dissociative adsorption, the PDOSs of O₁–H₁ bonding and Si₁–O_w bonding in the dissociative adsorption model are given in Figure 9.

Based on the PDOSs of O₁–H₁ bonding in Figure 9a, it can be clearly seen that the O₁ 2p–H₁ 1s bonding DOS peak appears between −1.5 and −4.8 eV, and the antibonding DOS peak resonances are at 2.5–5.5 eV. The bonding effect is stronger than that of the antibonding bond. The bonding orbital has a quite wide energy level, indicating that the delocalization of electrons is high, which is also beneficial to bonding [28]. Additionally, the splitting effect of bonding and antibonding is quite large due to the whole energy (−1.5–5.5 eV) across the Fermi level [54]. All of these both indicating that the bonding effect of O₁–H₁ is quite strong, mainly contributed by the O₁ 2p–H₁ 1s. It is consistent with the Mulliken analysis results that the O₁ 2p orbital gains electrons 0.16 and forms a strong O₁–H₁ bond with a length of 0.972 Å. Similarly, for the PDOSs of Si₁–O_w bonding in Figure 9b, the Si₁–O_w bond also showed a strong covalent interaction, mainly contributed by the Si₁ 2p–O_w 2p with a bonding DOS peak between 0 and −11.5 eV and an antibonding DOS peak from −17.0 to −21.0 eV, and the Si₁ 2s–O_w 2p with a bonding DOS peak between 0 and −7.5 eV and an antibonding DOS peak from −7.5 to −11.0 eV. The results of the bonding DOS analysis are therefore in agreement with the analysis of Mulliken charge distribution and bond populations.

According to the adsorption energies in calculation, it is suggested that both the molecular adsorption and dissociative adsorption are favorable for isolated water molecules on the O-middle termination of a quartz (001) surface. The structure and electronic properties of the quartz surface are influenced by H₂O molecule adsorption; that is, the reactivity site and the surface hydrophilic character changes. This is supported by a similar study on the relaxation and electronic structure of sulfide minerals surfaces in the presence of H₂O molecules [55]. Thus, the adsorption of a flotation reagent at quartz–water interfaces would be different from that at a direct quartz surface without H₂O interactions, which has already been identified in studies on thiol collector interaction on galena (PbS) and sphalerite (ZnS) in the presence of water molecules in DFT [20,33].

4. Conclusions

DFT calculations were employed to investigate the structural and electronic properties of three distinct terminations of a (001) quartz surface, with subsequent water adsorption studies carried out on the surface that was predicted to be the most stable. It was found that a so-called O-middle termination, characterized by a single exposed oxygen atom at the surface, is most likely predominant in real samples, as it has the lowest associated surface energy. Water adsorption on the O-middle termination was therefore modeled. It is shown here that the structure and electronic properties of the surface are transformed by both molecular and dissociative water adsorption. Based on this information, it can be expected that exposure to a water environment will affect a quartz surface’s structure and reactivity. Thus, the formation of the quartz–water interface must be accounted for when modeling processes, such as the flotation process, involve reagents. The results here provide valuable insight on how to represent the flotation process in a pulp environment through atomistic calculations.