Adsorption of hydrated Fe(OH) 2+ on the kaolinite surface: A density functional theory study

: The present study employed density functional theory (DFT) to analyze the adsorption configuration and mechanism of Fe(OH) 2+ on the kaolinite (001) surface. The findings demonstrated that Fe(OH) 2 (H 2 O) 4+ is the main type in which hydrated Fe(OH) 2+ can be found in aqueous solution. On the surface of kaolinite, Fe(OH) 2 (H 2 O) 4+ will be adsorbed. There are two forms of adsorption: outer-sphere and inner-sphere coordination (monodentate/bidentate) adsorption. Fe(OH) 2 (H 2 O) 4+ has a moderate propensity to adsorb on the alumina octahedral sheet of kaolinite when the outer-sphere coordination adsorption takes place. In cases of inner-sphere coordination adsorption, Fe exhibits a tendency to form monodentate adsorption compounds in conjunction with O u atoms. Additionally, it prefers to create bidentate adsorption compounds through coordination with both O t and O u atoms. The adsorption mechanism analysis results show that the ionic property of Fe atom decreases after outer-sphere coordination adsorption. After inner-sphere coordination adsorption, some electrons of Fe atom are transferred to the surface O atom. The presence of electrons between the Fe and O atoms enhances the formation of bonds, hence enhancing the covalent nature of the Fe-O bond. Theoretical FT-IR (Fourier transform infrared spectroscopy) calculations show that the formation of Fe-O chemical bonds. Because of the lower adsorption energy and more chemical bonds, hydrate Fe(OH) 2+ is more likely to be bidentate adsorbed on the kaolinite surface.


Introduction
Rare earths (especially medium and heavy rare earths) are of great strategic significance in the national defense industry and some high-tech fields.Ionic rare earth ores are rich in medium and heavy rare earth elements (Zhang et al., 2021;Luo et al., 2014;), and rare earth ions exist in the form of ion adsorption on clay minerals.Highly reactive cations like Mg 2+ , NH4 + , and similar species have the capacity to facilitate the desorption of rare earth ions from the surfaces of clay minerals into the leachate solution.(Wang et al., 2021) But in this process, other metal ions adsorbed on the clay minerals surface (especially Al 3+ , Fe 3+ ) can be desorption into the leachate in large quantities, which will seriously affect the quality of rare earth products (Qiu et al., 2014).Although researchers have carried out a lot of research on impurity inhibitors and impurity leaching technology, it will still cause the loss of rare earth resources while leaching (Qiu et al., 2014;Fang et al., 2018;Fang et al., 2012;Zhou et al., 2022;Wu et al., 2021;Zhao et al., 2007;Xu et al., 2005;Yin et al., 2012;).To enhance the efficiency of rare earth resource recovery and optimize the use rate of these resources, the occurrence state and adsorption mechanism of impurity metal ions in ionized rare earth minerals need to be studied, so as to further develop rare earth leaching agents with high selectivity.
In recent decades, researchers have conducted extensive research on adsorbent adsorption on the surface of clay minerals.Dousova et al. (2011) investigated the adsorption affinity for As oxyanions after Fe/Al/Mn pretreatment of clay minerals using low-grade calcined kaolin (MT) and bentonite (BT).To transform the surface charge of sodium smectite clays from negative to positive, ferric ions (Argel-Fe and Volclay-Fe) were added.Rodrigues et al. (2020) tested clay in a synthetic wastewater containing seven anionic dyes (a mixture of tartar, brilliant blue FCF, and amaranth).The maximum adsorption capacities for Argel-Fe were 88.68 mg g(-1) and 392.21 mg g(-1) for Volclay-Fe, while enrichment of clays with Fe(III) enhanced functionality to the clays and produced adsorbents with quick adsorption abilities and high discoloration capacities.Neumann et al. (2013) investigated electron transfer from Fe(II) sorbed to basal planes and edge OH-groups of the clay mineral NAu-1 using mossbauer spectroscopy in conjunction with selective chemical extractions.The results demonstrate that Fe(II) sorbed primarily to basal planes at pH values less than 6.0 and to edge OH-groups at pH values more than 7.5.At pH 7.5, significant electron transfer occurred from edge OH-group bound Fe(II), but at pH 4.0 and 6.0, electron transfer from basal plane-sorbed Fe(II) to structural Fe(III) occurred but to a considerably lesser amount than from edge-bound Fe(II).Feng et al. (2023) investigated how Fe co-adsorption affected the mechanism of REE uptake on kaolinite using inductively coupled plasma mass spectrometry (ICP-MS), powder X-ray diffraction (PXRD), and X-ray photoelectron spectroscopy (XPS).The findings indicate that FeOOH layers formed on top of REEs on the surface of kaolinite, and Fe is deleterious to REE ionexchange efficiency.Experiments were used in the preceding investigations.Quantum chemistry can study compound reaction processes and the structural properties of molecules at the atomic level.It includes ab initio algorithm, semi-empirical method and density functional theory method (Yan et al., 2019;).The density functional theory (DFT) method, which is suitable for the simulation calculation of large molecular systems and solids and has been widely utilized in mining, the chemical industry, and other industries, requires less calculation than the first two quantum chemical methods.It has also been used to study the adsorption configuration and mechanism of various adsorbents on mineral surfaces, such as the adsorption of Y 3+ 、Lu 3+ 、Al 3+ 、Pb 2+ and CaOH + on kaolinite surface (Qiu et al., 2021;Miao et al., 2022;Fang et al., 2020;Wang et al., 2014;Peng et al., 2017;Zhang et al., 2021;Jiang et al., 2023).The microscopic mechanism of Fe occurrence on the surface of clay minerals is rarely studied.It is critical to investigate the adsorption mechanism of Fe on the clay material surface since it is a typical impurity ion in rare earth leaching solutions.Vitaly et al. (2022) apply density functional theory (DFT) calculations to provide atomistic insights into the heterogeneous reaction between aqueous Fe(II) and the Fe-bearing clay mineral nontronite Fe2Si4O10(OH)2 by studying its adsorption mechanism and interfacial Fe(II)−Fe(III) electron transfer (ET) at edge and basal surfaces.Using DFT and moleculardynamics simulation techniques, Liu et al. (2012) investigated the inner-sphere coordination adsorption of Fe 2+ on the edge surfaces of kaolinite.However, this study did not consider the hydroxylation of Fe 2+ , and only the edge surface of kaolinite was studied.Fe, a significant contaminant in the processing of rare earths, can be found on the surface of carrier minerals in a variety of forms, primarily as a hydrated hydroxyl group in solution.The most common mineral for transporting rare earth ions is kaolinite, which is also the mineral that dissociates most readily in the 001 direction.Therefore, it is essential to investigate the hydrated hydroxyl iron's adsorption behavior on the kaolinite (001) surface.
Using a density generalized function theory analysis based on the firstness principle, the adsorption configuration of dihydroxy hydrates of Fe 3+ on kaolinite (001) surface and its fugacity mechanism on kaolinite surface were explored in this paper (Mulliken et al., 1955).The findings of this research contribute to the understanding of the metallogenic mechanism of ion-type rare earth ore.Additionally, they provide valuable insights for addressing the issue of iron impurities in ion-type rare earth ore.Furthermore, these results can be utilized as a reference for the development of iron inhibitors or more effective leaching agents.

Materials and methods
The CASTEP module of Materials Studio 2019 was used to do the calculations, which were based on density functional theory first-principles.The cut-off energy is selected to 400 eV during computation following the convergence test and in accordance with the results (Hohenberg et al., 1964;Kohn et al., 1964;Clark et al., 1964).Ultrasoft pseudopotentials were employed for density generalization calculations, utilizing the WC generalization method within the framework of the generalized gradient approximation (GGA) (Wu et al., 1964;Ireta et al., 2004;Vanderbilt et al., 1990).The convergence value of the Self-Consistent Field (SCF) was determined to be 2.0×10 -6 eV•atom -1 , and the energy, atomic forces, and atomic displacements were all improved using the BFGS method.Structure optimisation and convergence tolerances for energy calculations were set at 2.0×10 -5 eV•atom -1 for energy convergence, 0.05 eV -1 for interatomic force convergence, 0.002 for atomic displacement convergence, and 0.1 GPa for intracrystal stress convergence.(Monkhorst et al., 1990;Pack et al., 1976;Pfrommer et al., 1997;Yin et al., 1997;He et al., 2021).Kaolinite's bulk type and surface's Brillouin zone integrals were estimated to be (2×1×3) and (2×1×1), respectively (Neder et al., 1999;Wu et al., 1964;Ireta et al., 2004).This investigation used the Monkhorst-Pack k-point grid sampling approach, as described by Zhang et al. (2021;2021).The structure of kaolinite was investigated using neutron powder diffraction at a low temperature of 1.5 K based on experimental data.The obtained structural parameters were: a = 10.40,b = 18.03, c = 25.30,α= 90°, β= 90°, and γ= 89.73°.The computer software applies dipole moment correction within an electrically neutral adsorption system to establish spin polarization (Luo et al., 2022).
Modeling of kaolinite crystals for geometric optimization.Cutting the optimum cell model along the 0 0 1 direction produced the Kaolinite (001) surface, which was then covered with a vacuum layer with a 20 Å height to eliminate interlayer interactions.To accurately describe the ion-surface interactions, a 2×2×1 supercell was created and geometrically optimized.Due to the small depth of ion-surface interaction, the alumina octahedral sheet and silica tetrahedral sheet of kaolinite were fixed separately for the surface optimization in order to save computational cost.After the optimization, the stabilization models of silica tetrahedral sheet and alumina octahedral sheet were obtained respectively, in which three forms of hydroxyl groups appeared on the alumina octahedral sheet.As illustrated in Fig. 1, the three distinct arrangements of hydroxyl groups are labeled as "lying" (Ol), "tilted" (Ot), and "up" (Ou).
In order to make the process of adsorption closer to the real situation, we placed Fe(OH)2 + in a 15×15×15 Å 3 periodic box and added 1 to 7 water molecules for each calculation.The atomic force, energy, and displacement converging criteria were 0.03 eV/atom, 1.0×10 -5 eV/atom, and 0.001 Å, respectively.The binding energy (Ebind), which is defined as follows (1), is used to assess the stability of the Fe(OH)2 + hydrate model, represented as [Fe(OH)2(H2O)n] + (1 ≤ n ≤ 7).
where   is the binding energy of hydrate Fe(OH)2 + ,  [() 2 ( 2 )] + ,   and   2  correspond to the energy of the entire system, Fe(OH)2 + , and H2O, respectively.After obtaining a stable model of hydrated Fe(OH)2 + , the method of adsorption of the dependable structure of Fe(OH)2 + on the alumina octahedral and silica tetrahedral sheets was examined.Two types of adsorption models were study: outer-sphere and inner-sphere coordination adsorption.When computing the outer-sphere coordination adsorption on the alumina octahedral sheet, hydrated Fe(OH)2 + is placed precisely above the center of the three hydroxyl groups on the surface.When computing the outer-sphere coordination adsorption on the silica tetrahedral sheet, the hydrated Fe(OH)2 + were placed precisely above the core of the six-membered silicon-oxygen ring.Adsorption compounds that are formed are referred to as "M" and "N", respectively.When calculating the monodentate adsorption of the adsorbate, a water in the adsorbate is removed, the adsorbate was placed directly above the three deprotonated hydroxyl oxygen atoms.When calculating the bidentate adsorption of the adsorbate on the alumina octahedral sheet, two water ligands in the adsorbate is removed, the adsorbate was placed above the bridge position between the two deprotonated hydroxyl groups, respectively.Fig 2 shows the initial inner-sphere coordination adsorption position.As can be seen from the figure, Fe(OH)2 + may undergo monodentate adsorption on three different hydroxyl groups to form monodentate adsorption compounds and may undergo bidentate adsorption on the bridge sites between two adjacent hydroxyl groups to form bidentate adsorption compounds.The compounds formed at the "Ol", "Ou" and "Ot" sites are named L, U and T. The compounds formed at the "Ou-Ot", "Ou-Ol" and "Ot-Ol" sites are named as UT, UL and TL.The adsorption energy (Eads) is used to characterize whether adsorption can occur on the surface and the strength of adsorption.A positive value of adsorption energy means that adsorption cannot occur.A negative value of adsorption energy means that adsorption can take place, and the more negative the value, the more likely adsorption will take place.Eads can be can be calculated by formula (2) (He et al., 2023;Qiu et al., 2021;Miao et al., 2022;).
where   is the adsorption energy,  / stand for the total energy of adsorption system,   stand for the total energy in an isolated system of hydrated Fe(OH)2 + .  stand for the isolated single-layer kaolinite (001) surface total energy.
Fig. 2. Initial adsorption position of inner-sphere coordination adsorption

The form of Fe(OH)2 + in water environment
Relevant studies have shown that metal ions are difficult to exist in the form of single ion in aqueous solution, and in most cases exist in the form of hydration or hydroxyl hydration.Fig. 3 shows the geometric configuration of Fe(OH)2 + present in aqueous solution, represented by Fe(OH)2(H2O)n + (n = 0-7).As illustrated in Fig. 3, coordination links between Fe atoms and O atoms in the surrounding water molecules develop in the first solvated shell layer of Fe(OH)2 + .As the number of water molecules grows from 1 to 4, these bonds become more evenly distributed around Fe(OH)2 + .When there are four water molecules present, a molecule with a shape like an octahedron is created.In instances when the quantity of water molecules exceeded four, it was discovered that the coordinated water molecules were situated at a considerable distance from the initial solvated shell layer of Fe(OH)2 + .Consequently, Fe(OH)2 + exhibited coordination with a maximum of four water molecules within the first solvated shell layer of Fe(OH)2 + .Table 1 presents the equilibrium geometry parameters and binding energies (Ebind) associated with several hydrated Fe(OH)2 + species.According to the data presented in Table 1, there is a clear trend observed as the number of water molecules surrounding Fe(OH)2 + grows from 1 to 4. Specifically, the maximum distance, minimum distance, and average distance between Fe and O (Ow) in water molecules, as well as the charge of Fe, exhibit a progressive increase.Conversely, the binding energy (Ebind) consistently decreases across this range.When the coordination number of water molecules surrounding Fe(OH)2 + grows to five, there is a significant increase in the maximum distance between Fe and Ow, from 1.969 Å to 3.467 Å.Additionally, the average distance between Fe and Ow also increases, from 1.969 Å to 2.272 Å.The phenomenon of Ebind experiences a notable upward trend.The sterichindrance effect between water molecules and between water molecules and hydroxyl groups is minimal when there are few water molecules surrounding Fe(OH)2 + .The quantity of water molecules increased, and the steric-hindrance effect increased.The water molecules crowd each other in order to stabilize their presence around Fe(OH)2 + resulting in a gradual increase in the distance between Fe and Ow.As the number of water molecules increases to 4, the Ebind continuously decreases from 702.39 to 1042.54 KJ/mol.The Ebind is smallest when Fe is coordinated with 4 water molecules, implying that the Fe(OH)2(H2O)4 + formed at this time is the most stable.When the number of water molecules in a system rises over four, a phenomenon known as steric hindrance becomes more pronounced.This results in the inability of water molecules to occupy the initial solvated shell layer of the Fe(OH)2 + .As a consequence of this, they migrate away from the range of bonding that can occur between the atoms of iron and oxygen, which results in an increase in the maximum bond length of iron increased.At this time, the Ebind suddenly jumps up to 717.17 KJ/mol, which indicates that the coordination of Fe(OH)2 + with five water molecules is not in the user's advantage.In conclusion, it can be inferred that the Fe(OH)2 + species attains its highest stability in an aqueous environment when coordinated with four water molecules, resulting in the production of Fe(OH)2(H2O)4 + .Therefore, Fe(OH)2(H2O)4 + was selected as the initial adsorbent for investigating the adsorption behaviour of Fe(OH)2 + on the surface of kaolinite in the conducted study.

Outer-sphere coordination adsorption
The kaolinite (001) surface comprises two distinct layer, silica tetrahedral sheet and alumina octahedral sheet, and the adsorbent can be outer layer adsorbed on both surfaces.Consequently, a comprehensive investigation was conducted to examine the adsorption configurations and processes of Fe(OH)2(H2O)4 + on both the silica tetrahedral and alumina octahedral sheets of kaolinite individually.The findings of the investigation are depicted in Fig. 4 and Table 2.As depicted in picture 4, the adsorbent's approach to the surface results in the formation of hydrogen bonds between the oxygen (O) and hydrogen (H) atoms of the adsorbent and the hydrogen (H) and oxygen (O) atoms of the kaolinite surface.This bonding interaction occurs within the specified range, as indicated by the black dashed line in the image.
There are two types of hydrogen bonds, the Os-Hw type hydrogen bond formed between the surface O (Os) and the H (Hw) atoms of the adsorbent, and the Ow-Hs type hydrogen bond formed between the O (Ow) atoms of the adsorbent and the surface H (Hs). Related studies have shown that interatomic interactions occur in the range of 3 Å.In order to investigate the length and number of hydrogen bonds formed, the maximum bonding length (2.58 Å), which is the default of the software, was used to investigate the hydrogen bonding state generated during the outer-sphere coordination adsorption.The results obtained from the calculations are presented in Table 2.It is evident from the table that the adsorption of the adsorbent onto the Silica tetrahedral sheet resulted in the formation of Os-Hw type hydrogen bonds with lengths of 1.917 and 2.451 Å.The adsorption of the adsorbent on the alumina octahedral sheet resulted in the formation of hydrogen bonds of Os-Hw type with lengths ranging from 1.613 to 2.412 Å, and Ow-Hs type with lengths ranging from 1.462 to 2.334 Å.The adsorption of the adsorbent on the alumina octahedral sheet resulted in the formation of hydrogen bonds that were both shorter in length and more abundant as compared to the adsorption on the silica tetrahedral sheet.The increased occurrence of hydroxyl groups in the alumina octahedral sheet contributes to a higher likelihood of interaction between the hydrogen and oxygen atoms in these groups and the oxygen and hydrogen atoms in the adsorbent.Consequently, a greater number of hydrogen bonds are formed.
Following the process of adsorption, it was seen that Fe(OH)2 + retained coordination with four water molecules.The mean separation distance between iron (Fe) atoms and oxygen (Ow) atoms exhibited variations within the range of 0.003-0.029Å.The adsorption energy of adsorbate on the silica tetrahedral and alumina octahedral sheet was determined to be 580.50 and 590.53 KJ/mol, respectively.The adsorption energy of the adsorbent on the alumina octahedral sheet exhibits a marginal decrease compared to that on the silica tetrahedral sheet, with a difference of around 1.73%.
In a general sense, it can be observed that the adsorbent formed a greater quantity of hydrogen bonds with shorter bond lengths on the alumina octahedral sheet in comparison to the adsorption of adsorbate on the silica tetrahedral sheet.Additionally, the adsorbent exhibited a lower adsorption energy on the alumina octahedral sheet as opposed to the silica tetrahedral sheet.Hence, the adsorption of adsorbate on the kaolinite (001) surface primarily occurs by outer-sphere coordination, with a minor inclination towards adsorption in the alumina octahedral sheet.
The investigation focused on analysing the partial density of states of Fe, silica tetrahedral sheet, and alumina octahedral sheet in order to get insights into the adsorption mechanism.Fig. 5 (A) displays the density of states for both iron (Fe) and the silica tetrahedral sheet.Following the process of adsorption, it was seen that the 3d orbital of iron (Fe) underwent a little displacement towards higher energy levels.Additionally, the locality of the 3d orbital experienced a modest increase.Simultaneously, it can be shown that the 3d orbital of iron (Fe) retains a significant contribution at the Fermi level, suggesting that Fe maintains a substantial amount of reactivity even after being adsorbed onto the silica tetrahedral sheet.Following the process of adsorption, it was seen that the overall density functional theory (DFT) of the silica tetrahedral sheet saw a downward shift in energy.Additionally, there was a modest rise in the non-locality of the 2s and 2p orbitals.These findings suggest that the silica tetrahedral sheet achieved a higher level of stability.

M N
1.917  ) illustrates the density of states on the Fe and alumina octahedral sheet.The activity of Fe atoms remains very high following their adsorption onto the alumina octahedral sheet, a characteristic that is comparable to their adsorption onto the silica tetrahedral sheet.The DFT of the alumina octahedral sheet clearly changes to the lower energy direction, with a larger amplitude than that of the silica tetrahedral sheet.The findings indicate that iron (Fe) exhibits a minor propensity to adsorb onto the alumina octahedral sheet, resulting in the formation of a more stable outer-sphere coordination adsorption compound.
Table 3 presents the Mulliken charge population analysis of the outer-sphere coordination adsorption on two distinct surfaces.According to the data presented in Table 3, it is evident that the Fe 3p orbital experienced a loss of 0.02 electrons, while the Fe 3d orbital gained 0.1 electrons following the outer-sphere coordination adsorption of adsorbate on the silica tetrahedral sheet.Additionally, Fe exhibited an overall gain of 0.08 electrons after adsorption, resulting in a decrease in its charge by 0.08 and a decrease in ionicity.On the other hand, when hydrated Fe(OH)2 + was adsorbed on the alumina octahedral sheet, the Fe 3s orbital gained 0.01 electrons, the Fe 3d orbital gained 0.28 electrons, and the Fe 3p orbital lost 0.03 electrons.Consequently, Fe displayed an overall gain of 0.26 electrons after adsorption, leading to a decrease in its charge by 0.26.In comparison to adsorption on the silica tetrahedral sheet, Fe received more electrons, and its ionicity is lower and more stable.

Monodentate adsorption structure
Since all three different hydroxyl groups on the alumina octahedral sheet of kaolinite (001) can be deprotonated, the deprotonated kaolinite surface can be coordinated with iron ions, thus allowing the inner-sphere coordination adsorption of iron ions on the alumina octahedral sheet of kaolinite.The absorbent has the capability to undergo monodentate adsorption on the "Ol", "Ou", and "Ot" sites of the kaolinite surface, resulting in the formation of three distinct monodentate adsorption compounds.The investigation focused on the monodentate adsorption configuration of the adsorbate on the alumina octahedral sheet of kaolinite.The findings of this investigation are presented in Fig. 6.

1.620
Ol Ou Ot L U T Fig. 6.Monodentate adsorption configuration of absorbent at "Ol" (L), "Ou" (U) and "Ot" (T) positions As shown in Fig. 6, Fe atoms form coordination bonds with surface deprotonated O atoms after adsorption.Compared to the outer-sphere coordination adsorption process, hydrogen bonds were formed between Ow and Hw atoms in the adsorbent and hydroxyl groups on the kaolinite surface in the default bonding range of the system (0-2.58Å) (black dashed lines in Fig. 6) during the inner-sphere coordination adsorption process.Table 4 displays the structural parameters and adsorption energies of the adsorption compounds formed.The table reveals that the length ranges of the "Os...Hw" bonds are 1.422-2.133Å, 1.467-1.770Å, and 1.545-2.412Å, respectively, while the length ranges of the "Ow...Hs" bonds are 1.620-1.979Å, 1.573-2.483Å, and 1.819-2.219Å, respectively.These observations are made when Fe is adsorbed on "Ol", "Ou", and "Ot".When hydrated Fe(OH)2 + is adsorbed on "Ou", the length of hydrogen bonds is marginally diminished.
In conjunction with hydrogen bonding, the Fe atom established chemical connections with the O atom located on the kaolinite surface.Chemical bonding exerts a significantly greater influence compared to hydrogen bonding, rendering it of more significance in ensuring the stability of the adsorption compound.According to the data presented in Table 4, the measured bond lengths of Fe-O in the L-, U-, and T-type compounds are 1.879, 1.887, and 2.076 Å, respectively.The Fe-Os bond length in L and U type compounds has a shorter distance compared to that in C-type compounds, whereas the disparity in chemical bonding between the L-and U-type compounds is relatively smaller.The adsorption energies of compounds L-, U-, and T-type are recorded as 848.27, 861.91, and 855.60 KJ/mol, respectively.In contrast to type L and T compounds, the U type chemical exhibits the most minimal absorption energy.
In general, it is widely accepted that the adsorption of Fe at the "Ou" position leads to the formation of shorter hydrogen bonds, slightly shorter chemical bonds, and lower adsorption energy.Consequently, it is hypothesised that hydrated Fe(OH)2 + is more prone to adsorb onto the "Ou" position, resulting in the formation of a U-type adsorption compound during monodentate adsorption on the surface of kaolinite.

Bidentate adsorption
In the process of bidentate adsorption, iron (Fe) has the capability to create three distinct bidentate adsorption compounds at the "Ou-Ot," "Ou-Ol," and "Ot-Ol" sites, as visually depicted in Fig. 7.In compounds of UT-, UL-, and TL-types, the detachment of water molecules from the initial solvation shell is observed due to the steric hindrance effect.Specifically, one water molecule is detached in UTtype, two water molecules in UL-type, and one water molecule in TL-type compounds.Analogous to monodentate adsorption, the interaction between the adsorbate and the kaolinite surface involves the formation of hydrogen bonds.The hydrogen bond is illustrated by the black dashed line in Figure 7.
The maximum length of a hydrogen bond is set to 2.58 Å.The compounds of types UT and UL have "Os...Hw" bond lengths measuring 1.650 Å and 1.849 Å, respectively.However, the compound of TLtype does not possess a "Os...Hw" bond.In the UL-type compound, the bond length between "Os" and "Hw" is comparatively shorter.The TL-type compound exhibits the formation of two hydrogen bonds, with bond lengths of 1.879 Å and 2.207 Å.On the other hand, the UL-type compound forms a hydrogen bond denoted as "Ow...Hs" which has a bond length of 1.870 Å.The generation of the "Ow...Hs" phenomenon does not occur in the UL-type compound.The "Ow... Hs" present in the TL-type compound exhibit a little greater length, albeit with a higher quantity.

UT UL TL
1.849 Fig. 7. Bidentate adsorption configuration of absorbent at positions "Ou-Ot" (UT), "Ou-Ol" (UL) and "Ot-Ol" (TL), respectively The length of "Fe-Os" in UT-, UL-and TL-types compounds is between 1.761 and 1.872 Å, 1.766 and 1.771 Å, and 1.710 and 1.920 Å, respectively.The chemical bonds formed in the bidentate adsorption compounds are shorter in length and more numerous than those in the monodentate adsorption compounds.Therefore, the bidentate adsorption compounds are more stable from the view of chemical bonding.Among the three types of compounds formed, the chemical bond formed in UL-type compound is slightly shorter.
According to the data presented in Table 4, it can be observed that the adsorption energy associated with bidentate adsorption is significantly lower compared to that of monodentate adsorption.This discrepancy suggests that the bidentate adsorption compound exhibits more stability, implying a higher likelihood for the hydrated Fe species to undergo bidentate adsorption on the surface of kaolinite.The adsorption energy of UT-type compounds exhibits a little decrease in comparison to the other two compounds.
Typically, when the adsorbate is adsorbed at the "Ou-Ot" position, it is observed that the hydrogen bond exhibits a reduced length, the chemical bond experiences a little reduction in length, and the adsorption energy is diminished.Hence, upon comparing the adsorption characteristics of the adsorbate at three distinct locations on the kaolinite (001) surface, it becomes evident that there is a minor inclination for the adsorbate to adsorb at the "Ou-Ot" position.

Adsorption of water molecules on kaolinite surface
Kaolinite has a hydrophilic surface, making it easy to adsorb water molecules and form a hydration film.The adsorption of metal ions on the surface of kaolinite requires displacing the water molecules on the surface before forming an adsorption structure.Therefore, it is necessary to calculate the adsorption capacity of water molecules on the kaolinite (001) surface (He et al., 2021).By replacing the hydrated Fe(OH)2 + in the aforementioned adsorption model with water molecules, the adsorption structure and adsorption energy of water molecules on the ideal kaolinite surface and the deprotonated kaolinite surface can be calculated.Finally, it can be determined whether the hydrated Fe(OH)2 + can replace water molecules on the kaolinite surface.From Fig. 8 and Table 5, it can be seen that when water molecules adsorb on the surface of ideal kaolinite, the main interaction occurs through hydrogen bonds formed between the Hw and Ow atoms of water molecules and the Os and Hs atoms on the kaolinite surface.When water molecules adsorb on the Al-OH surface of ideal kaolinite, they form a Os-Hw bond with a length of 1.831 Å and Ow-Hs bond with a length of 1.851 Å.On the Si-O surface, water molecules form a Os-Hw bond with a length of 2.443 Å.The number of hydrogen bonds formed on the Al-OH surface is greater and the strength is stronger.Furthermore, the adsorption energy of water molecules on the Al-OH surface (24.87 KJ/mol) is much lower than that on the Si-O surface (1.82 KJ/mol).Both the adsorption structure and adsorption energy results indicate that water molecules are more prone to adsorb on the Al-OH surface of ideal kaolinite.This result is the same as that of chen et al.
When water molecules adsorb on kaolinite surface with one proton removed, they produce an Os-Hw hydrogen bond with a length of 2.140 Å and an adsorption energy of -61.21 KJ/mol.When water molecules adsorb on kaolinite surface with two protons removed, they produce five Os-Hw hydrogen bonds with a length ranging from 1.457 to 2.449 Å, and the adsorption energy of a single water particle is 64.17KJ/mol.The results showed that the higher the degree of deprotonation, the more easily the adsorption of water molecules occurred.However, the adsorption energy of hydrated Fe(OH)2 + on ideal kaolinite (001) surface (590.53KJ/mol) is much lower than that of water molecules on the ideal kaolinite surface (24.87 KJ/mol).Similarly, the adsorption energy of hydrated Fe(OH)2 + on the deprotonated kaolinite surface is also much lower than that of water molecules on the deprotonated kaolinite surface.The results show that the hydrated Fe(OH)2 + can push out the water molecules on the surface of kaolinite, and then adsorb on the surface of kaolinite.

Bonding mechanism
From 3.3.1 and 3.3.2,U-type compound and the UT-type compound are the optimal adsorption structures of the two adsorption modes respectively.These two compounds were chosen to analyze their bonding mechanisms.Table 6 shows the Mulliken populations of Fe and Os atoms and Mulliken overlap populations of Fe-Os bonds in the two predominance adsorption compounds.It can be seen that in the U-type compound, the electronic orbitals (3s and 3d) of the Fe atom lost 0.28 e after adsorption, and the 2p orbitals gains 0.07 e, so the Fe atom as a whole behaves as an electron-deficient state.For the O atom, the 2s orbitals lost 0.05 e, but the 2p orbitals gain 0.20 e, so the O atom as a whole behaves as electron-rich state.Part of the electrons of the Fe atoms are transferred to the Os atoms, which leads to the enhancement of the ionicity of Fe； According to the data presented in Table 6, it can be observed that in the UT-type compound, the Fe atom experiences a loss of 0.26 e in both its 3s and 3d orbitals, while its 3p orbital gains 0.07 e.The adsorption process resulted in a total loss of 0.38 electrons by the iron (Fe) atom.Ot lost 0.03 and 0.04 e in its 2s and 2p orbitals, respectively.The overall loss incurred by Ot amounted to 0.07 e.The 2p receives 0.10 e, while the 2s of Ou loses 0.04 e. Ou has a total gain of 0.06 e. Table 7 illustrates the charge transfer mechanisms involving oxygen (O) and hydrogen (H) atoms occurring at the kaolinite surface and within hydrated Fe(OH)2 + .As can be seen in table 7, the O atom in the adsorbate loses a lot of electrons after adsorption, the H atom only gets a small amount of electrons, and the kaolinite surface gets a lot of electrons after adsorption.In general, most of the electrons of O and Fe in the adsorbate are transferred to the kaolinite surface, and the ionicity of Fe is enhanced.
The larger the Mulliken overlap layout value, the more electron overlap between the two atoms, indicating that the chemical bonds formed between the atoms are more stable.The Mulliken overlap layout value in the U-type compound is 0.32, and the values in the UT-type compound are 0.24 and 0.36. the overlap layout value of Fe-Os in UT-type compound is significantly larger than that of Fe-Os in U-type compound, indicating that in the bidentate adsorption compound, Fe interacts more strongly with the surface and the formed compound page is more stable, which is the same as the results of the previous study.In addition, since the overlap layout value is all positive, this indicates that the electrons of both Fe and surface O interact in a bonding state, forming covalent bonds.The non-localization of the Fe 3d orbit and the 2p orbit of the surface O increases noticeably after the monodentate adsorption, as can be observed in Fig. 10(a), meaning that the Fe and the surface O atoms develop less unstable after adsorption.Furthermore, both the density of state of the Fe atom and the O atom of the kaolinite surface shift to the lower energy level.The Fermi level contribution from Fe 3d and 3s orbitals is drastically reduced, indicating that Fe is more secure and the activity is lower.The contribution of the O atom's 2p orbital to the Fermi level is likewise greatly lowered, suggesting that the atom's activity has been significantly reduced as a result of adsorption as well as that it has become more stable.Following adsorption, the O atom yields four consecutive 2p orbital peaks in the 2.5 to 2.5 eV range, a fresh 3d orbital peak in the range of 2.5 to 1.25 eV, and a weak 3d orbital peak in the range of 2.5-2.75 eV.The Fe and surface O atoms form bonding orbitals, shown by the strength of the O 2p orbital peak being stronger than that of the Fe 3d orbital peak in the range of 2.5 to -1.25 eV; a weak 3d orbital peak appears at 2.5-2.75 eV; and the O atom yields four consecutive 2p orbital peaks in the range of 2.5 to 2.5 eV.O 2p orbital peak strength is higher than Fe 3d orbital peak strength between 2.5 and  As demonstrated in Fig. 10(b), the contribution of Fe's 3d orbital electrons to the Fermi level reduces by half and the 3s orbital electrons vanish following the bidentate adsorption.The surface O atom's contribution to the 2p orbital electrons decreases substantially, and the non-localization of the s and p orbitals has been substantially enhanced.This implies the stability and activity of the Fe and surface O atoms after adsorption have both been significantly improved.Fig. 10b shows that following adsorption, Fe and Ou atoms produce new 3d orbital peaks and 2p orbital peaks in the ranges of 1.58-2.8eV and 3.7-0.9eV.After adsorption, the electrons of Fe and Ou atoms on the surface are filled with antibonding orbitals because the intensity of 3d orbital peaks is higher in the excited state than that of 2p orbital peaks.After adsorption, the Fe atom and surface Ou atom's electrons are filled with bonding orbitals because the 2p orbital peak in the ground state is stronger than the 3d orbital peak and has a broader range.In summary, the Fe-Ou bond layout value of 0.32, as presented in Table 6, corresponds to the prevailing bonding condition seen between the Fe atom and the surface Ou atom subsequent to adsorption.Similarly, the PDOS of Ot atoms appear more 2p impure peaks near the Fermi level, and produce new 2s orbital peaks in the range of 17.28 to 16.5 eV.These impure peaks correspond to the Fe 3d orbital peaks, which is also the reason why Fe and Ot atoms form bonding orbitals (corresponding layout value is 0.45).Fig. 11 presents the theoretical FT-IR calculations for the bidentate adsorption compound of hydrated Fe(OH)2 + on the surface of kaolinite.As depicted in the figure, multiple peaks with varying intensities appear at different wavenumbers.By analyzing the vibrations of these peaks with different intensities, the vibrational patterns of various chemical bonds within the adsorption compound are illustrated in Fig. 12.It is evident that the peak at 1279 cm -1 exhibits the highest intensity, and this peak arises from the stretching vibration of the Fe-O bond formed after the bidentate adsorption.This indicates that the adsorption of hydrated Fe(OH)2 + on the kaolinite surface is a result of chemical adsorption.
Furthermore, the peaks at 587 cm -1 , 655 cm -1 , 938 cm -1 , 2599 cm -1 , 3136 cm -1 , 3265 cm -1 , and 3360 cm -1 correspond to the vibrations of the hydroxyl groups on the kaolinite surface, vibrations of the inner Al-O bonds, bending vibrations of water molecules in the adsorbate, vibrations of hydroxyl groups in water molecules, vibrations of hydroxyl groups in the adsorbate, vibrations of hydrogen bonds, and stretching vibrations of hydroxyl groups in water molecules, respectively.

Conclusions
The study employed density functional theory (DFT) to investigate the primary constituent of hydrated Fe(OH)2 + in water environment.Additionally, the research examined the various adsorption configurations and mechanisms by which it occurs on the kaolinite (001) surface and the theoretical FT-IR calculations of bidentate adsorption compound was given to demonstrate the models are realistic.The findings of the investigation are presented as follows: (1) When water is present, the predominant form of Fe(OH)2 + is Fe(OH)2(H2O)4 + , which has a tendency to create an outer-sphere coordination adsorption compound through hydrogen bonding on the silica tetrahedral sheet of kaolinite.The production of a monodentate/bidentate compound on the alumina octahedral sheet of kaolinite is attributed to chemical bonding and hydrogen bonding.All three deprotonated oxygen atoms in the alumina octahedral sheet of kaolinite are linked to Fe atoms.After undergoing monodentate adsorption, the primary interaction of Fe atoms is with surface Ou atoms.However, in the case of bidentate adsorption, Fe atoms are prone to make surface connections with Ou and Ot atoms.
(2) Both types of compounds have strong bonding orbitals surrounding the Fe and surface O atoms, as evidenced by the bonding mechanism and Mulliken population analysis and theoretical FT-IR calculations show that the formation of Fe-O chemical bonds.The results of the study indicate a significant degree of covalency in the Fe-Os bonds.The bidentate adsorption process, in comparison to monodentate adsorption, forms a greater number of chemical bonds, resulting in a bidentate adsorption compound that exhibits reduced energy, increased stability, and lower adsorption energy.

Table 4 .
Structure parameters (Å) and adsorption energy (KJ/mol) of the adsorption compounds a Number of aqua ligands b The measurement of the distance between the iron (Fe) and oxygen (O) on the surface c The length of the bond between Fe and O in a hydroxyl group d The measurement of the distance between Fe and O of aqua ligand

Fig. 8 .
Fig. 8. Adsorption structure of water molecules on kaolinite surface (a: Ideal kaolinite Si-O surface; b: Ideal kaolinite Al-OH surface; c,d: Kaolinite surface with one and two protons removed, respectively)

Fig. 9
Fig. 9 (a) and (b) show the differential charge density diagrams between Fe and surface O atoms in the monodentate and bidentate adsorption compound, respectively.The blue part represents electron deficiency and the red part represents electron accumulation.It can be seen from the figure that Fe atoms in the two adsorption compounds are in electron deficiency state, and surface O atoms are in electron accumulation state, indicating that the charge of Fe atoms shifts to the surface O atoms after adsorption.In addition, the red part of O atom appear to shift towards the Fe atom, and the shift pattern of the O atom electrons in (b) is more significant.It is shown that Fe and O atom have strong covalency, and the Fe-O bond formed by bidentate adsorption is stronger than that formed by monodentate adsorption, which is consistent with the Mulliken layout results in Table 6.The study further explored the density of states (PDOS) of Fe and O atoms to confirm the distribution and contribution of electronic states between bonded atoms.

Fig. 9 .
Fig. 9. Differential charge density diagram of U-type (a) and UT-type compounds

Fig
Fig. 11 Theoretical FT-IR calculations of UT-type compound

Table 1
a The minimum separation distance observed b The maximum separation distance observed c The average distance observed d The charge of Fe

Table 3 .
Mulliken charge population of Fe atom after outer-sphere coordination adsorption

Table 6 .
Mulliken populations of Fe and Os atom and Mulliken overlap populations of Fe-Os bonds in U-, and UTtype compound Q = Q′-Q, where Q and Q′ are the total charges of H, O and kaolinite surface before and after adsorption, respectively a , indicating that Fe and surface O atoms form bonding orbitals.Between 2.5 and 2.75 eV, Fe 3d orbital peak strength is greater than O 2p orbital peak strength, indicating that Fe and surface O atoms form weak anti-bonding orbitals.The observed layout value of Fe-Os in Table6(0.32)can be attributed to the phenomenon where the electrons between Fe and the surface O occupy bonding states, resulting in the formation of a relatively stable chemical bond.