Electronic Structure and Lithium Diffusion in LiAl2(OH)6Cl Studied by First Principle Calculations

First-principles calculations based on the density functional theory (DFT) were carried out to study the atomic structure and electronic structure of LiAl2(OH)6Cl, the only material in the layered double hydroxide family in which delithiation was found to occur. Ab initio molecular dynamics (AIMD) simulations were used to explore the evolution of the structure of LiAl2(OH)6Cl during a thermally induced delithiation process. The simulations show that this process occurs due to the drastic dynamics of Li+ at temperatures higher than ~450 K, in which the [Al2(OH)6] host layers remain stable up to 1100 K. The calculated large value of the Li+ diffusion coefficient D, ~3.13×10−5cm2/s, at 500 K and the high stability of the [Al2(OH)6] framework suggest a potential technical application of the partially-delithiated Li1-xAl2(OH)6Cl1-x (0 < x < 1) as a superionic conductor at high temperatures.

In the past years, the anion exchange of Li-Al LDHs was extensively studied with respect to their properties and chemical stability. Dutta et al. [12] found that the anion exchange selectivity of the dehydrate LiAl-X (X = PO 4 3− , HPO 4 2− , Cl − , H 2 PO 4 − ) should follow the order PO 4 3− > HPO 4 2− > Cl − > H 2 PO 4 − by spectroscopic studies and free energy calculations. Fogg et al. [16] applied time-resolved in situ X-ray diffraction (XRD) measurements and obtained that the reaction rate constant into gibbsite Al(OH) 3 decreases in the series OH − > SO 4 2− > Cl − > Br − > NO 3 − . Lei et al. [17,18] studied the preferential anion intercalation of pyridine carboxylate and toluate isomers in LiAl-Cl-mH 2 O at different temperatures by nuclear magnetic resonance (NMR) spectra. Hou et al. [19] carried out XRD and NMR to study the hydration state and the factors controlling the expansion behaviors of Li-Al LDHs and Mg-Al LDHs. In a theoretical approach, Fogg et al. [20] used molecular dynamics to rationalize the structures of LiAl-X (Br − , Cl − , NO 3 − , CO 3 2− , SO 4 2− , C 2 O 4 2− ) and showed that this approach is a useful predictive tool for simulating interlayer spacings and the orientations of the guest ions in the related intercalates. The density functional theory (DFT) calculations were performed to study the structural stability of LiAl-X (X = F − , Cl − , Br − , OH − , NO 3 − , CO 3 2− , SO 4 2− ) and also the CO 2 capture capacity of LiAl-X (X = Cl − , NO 3 − , CO 3 2− ) [21]. In a later study, Cl − position changes were observed in LiAl-Cl by molecular dynamics simulation between −90 and 90 • C [22]. Among the Li-Al LDHs, LiAl-Cl-mH 2 O is the only compound in which a delithiation occurs [23]. However, the mechanism of this delithiation (~570 K), after the dehydration (~400 K), and the structural evolution of LiAl-Cl at higher temperatures has not been determined. In particular, the consequence of the delithiation has not been studied, which, however, is rather interesting since the rise of the diffusion rate of the Li + may be due to the increase of the number of vacant Li sites in the structure. A high migrant rate of Li + and a relatively stable structure is the prerequisite condition of an Li-ion battery material. In this paper, we applied the first principle calculations based on DFT to study the electronic structure and bonding of LiAl 2 (OH) 6 Cl. Besides, ab initio molecular dynamics (AIMD) simulations were performed to investigate the structural evolution at higher temperatures. The diffusion of the Li from the cation layer into the inter-layer space and the resulting high Li mobility followed by a further delithiation from the system were further investigated.

Atomic and Electronic Structure of LiAl 2 (OH) 6 Cl
The crystal structures of LiAl-X-mH 2 O (X = Cl − , NO 3 − , Br − ) and of their dehydrates, LiAl-X, were determined by Besserguenev et al. [15]. In the dehydrates LiAl-X, Li and X form Li· · · X· · · Li· · · X· · · chains along the c-axis, while the inter chain X· · · X distance is increased in LiAl-X-mH 2 O due to the presence of interlayer water molecules [20,21]. Fogg et al. [23,24] found that, in contrast to the rhombohedral modification, the hexagonal LiAl-Cl-mH 2 O can form a second-stage intermediate phase and can be isolated as pure crystalline phases during the intercalation reactions with some dicarboxylate anions. LiAl 2 (OH) 6 Cl crystallizes in the hexagonal space group P6 3 /mcm (Figure 1a). The optimized lattice parameters are a = 5.158 Å, c = 14.259 Å, which agree quite well with the experimental ones (a = 5.10 Å, c = 14.2994 Å) [15]. The cell parameters and atomic positions obtained from our calculations are all given in Tables S1 and S2 in the supporting information. Within each unit cell the Li, Al, Cl, O, and H atoms occupy five inequivalent atomic sites, respectively. The Cl atoms are located on a mirror plane between two neighboring [LiAl 2 (OH) 6 ] + layers forming Cl-centered trigonal prisms with the six nearest H atoms with Cl-H distances of 2.30 Å (Figure 1a). The Cl-Li distances are much longer (3.56 Å), indicating that the Cl atoms are mainly stabilized by bonding to the H atoms of the hydroxyl groups. As a result, the H atoms of the six hydroxyl groups point towards the Cl atoms in contrast to the situation found in Al(OH) 3 ( Figure S1). As shown in Figure 1b The diffusion of the Li from the cation layer into the inter-layer space and the resulting high Li mobility followed by a further delithiation from the system were further investigated. The crystal structures of LiAl-X-mH2O (X = Cl − , NO3 − , Br − ) and of their dehydrates, LiAl-X, were determined by Besserguenev et al. [15]. In the dehydrates LiAl-X, Li and X form Li⋯X⋯Li⋯X⋯ chains along the c-axis, while the inter chain X⋯X distance is increased in LiAl-X-mH2O due to the presence of interlayer water molecules [20,21]. Fogg et al. [23,24] found that, in contrast to the rhombohedral modification, the hexagonal LiAl-Cl-mH2O can form a second-stage intermediate phase and can be isolated as pure crystalline phases during the intercalation reactions with some dicarboxylate anions.

Atomic and Electronic Structure of LiAl2(OH)6Cl
LiAl2(OH)6Cl crystallizes in the hexagonal space group P63/mcm ( Figure 1a). The optimized lattice parameters are a = 5.158 Å, c = 14.259 Å, which agree quite well with the experimental ones (a = 5.10 Å, c = 14.2994 Å) [15]. The cell parameters and atomic positions obtained from our calculations are all given in Tables S1 and S2 in the supporting information. Within each unit cell the Li, Al, Cl, O, and H atoms occupy five inequivalent atomic sites, respectively. The Cl atoms are located on a mirror The calculated band structures, density of states (DOSs) and crystal orbital Hamilton population (COHP) of LiAl 2 (OH) 6 Cl are shown in Figure 2. The valence band maximum (VBM) is at the K point, while the conduction band minimum (CBM) is located at the Γ point. According to this calculation, LiAl 2 (OH) 6 Cl is a wide-gap insulator with an indirect band gap. The top valence bands are dominated by Cl 3p and O 2p orbitals (~98%) and exhibit small dispersion, as shown in Figure S2  The bonding properties were analyzed using COHP curves as shown in Figure 2c. Bonding

Lithium Diffusion in LiAl 2 (OH) 6 Cl during Heating
The structural evolution of LiAl 2 (OH) 6 Cl was studied by AIMD simulations at simulated temperatures ranging from 300 K to 1400 K with an increment of 50 K. To monitor the changes of the structure with increasing temperature, we calculated the pair distribution function (PDF), g ij (r), which gives the probability of finding a j-type atom at a distance, r, from an i-type atom [24,25]. The g ij (r) is defined as: where V is the volume of the system, and N i and N j are the numbers of the i-type and j-type atoms, respectively. r ij is the length of a vector connecting atom i and atom j. Figure 3 shows the PDF of Li-O and Al-O at various temperatures. The three relatively sharp peaks for both g LiO (r) and g AlO (r) at 400 K correspond to the atomic distances between the nearest, second, and third nearest neighbors of O atoms around Li and Al, respectively, in LiAl 2 (OH) 6 Cl, as expected. All three peaks of both g LiO (r) and g AlO (r) get broader in peak width and lower in intensity with increasing temperature, indicating that the Li-O and Al-O interactions become weaker at high temperatures. Due to the lower charge of Li compared to Al, the changes for g LiO (r) are much larger than for g AlO (r). For g AlO (r), the peak positions remain nearly unchanged in our simulations. In contrast, the situation is different for g LiO (r), where the Li-O distance of around~2.0 Å, indicated by the first peak contracts slightly with the increase of the temperature (Figure 3a). It is worth mentioning that in the g LiO (r) curve at 400 K, the first, second, and third nearest neighbor Li-O distances are still well defined, whereas at higher temperatures, the peaks are smeared out, indicating a higher dynamics of the Li atoms. This demonstrates that octahedral coordination around the Li atoms is not regular any more above 600 K. A similar situation was found in experiments by Hou and Kirkpatrick [23], where the decomposition of LiAl-LDH began at temperatures slightly below 573 K.
Molecules 2019, 24, x 4 of 9 which gives the probability of finding a j-type atom at a distance, r, from an i-type atom [24,25]. The is defined as: where V is the volume of the system, and Ni and Nj are the numbers of the i-type and j-type atoms, respectively. is the length of a vector connecting atom i and atom j. Figure 3 shows the PDF of Li-O and Al-O at various temperatures. The three relatively sharp peaks for both and at 400 K correspond to the atomic distances between the nearest, second, and third nearest neighbors of O atoms around Li and Al, respectively, in LiAl2(OH)6Cl, as expected. All three peaks of both and get broader in peak width and lower in intensity with increasing temperature, indicating that the Li-O and Al-O interactions become weaker at high temperatures. Due to the lower charge of Li compared to Al, the changes for are much larger than for . For , the peak positions remain nearly unchanged in our simulations. In contrast, the situation is different for , where the Li-O distance of around ~2.0 Å, indicated by the first peak contracts slightly with the increase of the temperature (Figure 3a). It is worth mentioning that in the curve at 400 K, the first, second, and third nearest neighbor Li-O distances are still well defined, whereas at higher temperatures, the peaks are smeared out, indicating a higher dynamics of the Li atoms. This For a more detailed analysis of the changes of the Li and Al atomic positions, we calculated the partial coordination numbers (PCNs), N ij , which give the average number of j-type atoms within the cut-off distance, R cut , of an i-type atom from the PDF according to: where ρ is the number density [26,27]. The cut-off distance, R cut , was selected to be the distance corresponding to the tail of the first peak in the PDF. Figure 4 shows the evolution of the PCN with an increasing temperature for Li-O and Al-O. For temperatures below 400 K, N LiO is 6, which indicates that Li is octahedrally coordinated with O atoms. At temperatures above 450 K, N LiO starts to decrease, suggesting that the Li atoms do not have an octahedral coordination any more, which may also be caused by a partial delithiation from the positively charged layers. Above 650 K, N LiO stops decreasing and fluctuates around 2 with the further increasing temperature. and get broader in peak width and lower in intensity with increasing temperature, indicating that the Li-O and Al-O interactions become weaker at high temperatures. Due to the lower charge of Li compared to Al, the changes for are much larger than for . For , the peak positions remain nearly unchanged in our simulations. In contrast, the situation is different for , where the Li-O distance of around ~2.0 Å, indicated by the first peak contracts slightly with the increase of the temperature (Figure 3a). It is worth mentioning that in the curve at 400 K, the first, second, and third nearest neighbor Li-O distances are still well defined, whereas at higher temperatures, the peaks are smeared out, indicating a higher dynamics of the Li atoms. This demonstrates that octahedral coordination around the Li atoms is not regular any more above 600 K. A similar situation was found in experiments by Hou and Kirkpatrick [23], where the decomposition of LiAl-LDH began at temperatures slightly below 573 K.  The evolution of the Al-O coordination environment with the temperature is quite different from the Li-O case. From the g AlO (r) shown in Figure 3b, it can be clearly seen that g AlO (r) shows a well-ordered structure even up to 1000 K. This result indicates that within the time-scale of MD simulations, the oxygen octahedron around Al is stable, which can also be seen from the PCN versus temperature curve, as presented in Figure 4. At temperatures above 1100 K, N AlO starts to drop, which means that after the breakdown of the octahedral Li coordination above 450 K, the framework made up of the AlO 6 octahedra remains stable until 1100 K. Above 1300 K, the octahedral coordination around Al becomes unstable.
To further study the different behaviors of Li and Al in LiAl 2 (OH) 6 Cl during the heating process, the mean square displacement (MSD) of Li and Al at 500 K were calculated and are presented in Figure 5. MSD is defined as [28]: where N represents the number of type-c atoms in the system, while < A > denotes the ensemble average of a physical quantity, A. As it is known that the timescale of the Li diffusion process is of the order of picoseconds, it can be analyzed by MD simulations. It can be seen from Figure 5 that the Li atoms show a larger dynamics than the Al atoms. This can be explained by the heavier mass and higher charge of Al compared to Li. Within larger time intervals, the values of MSD increase with time as observed in [28]. In many kinds of lithium superionic conductors, e.g., Li 3 Y(PSO 4 ) 2 , Li 5 PSO 4 Cl 2 [29], and Li 7 P 3 S 11 [30], an open site due to Li + diffusion is found to be occupied by another Li + within 10 ps. From the MSD vs. t curve, the diffusion coefficient, D, can be calculated as follows: where d indicates the dimension of the system [28,29]. Equation (4) reduces to Equation (5) if the time dependence of MSD is approximately linear, which holds true in most cases. Thus, Equation (5) is also widely used in the literature to calculate the diffusion coefficient [29,31]. The calculated value of the Li + diffusion coefficient by using Equation (5) is 3.13 × 10 −5 cm 2 /s, which is higher than that of the Li + ion calculated for Li 5 YPS 4 Cl 2 (~2.5 × 10 −6 cm 2 /s) at 500 K [29]. The Li ion conductivity can be estimated by the Nernst-Einstein relation [29]: where ρ, R, and F represent the molar density of Li in the unit cell, gas constant (8.314 J·mol −1 ·K −1 ), and the Faraday's constant (96,485 C·mol −1 ), respectively. z is the charge number of Li, z = +1.
According to the MSD, the Li conductivity for the current simulated system was calculated to be 708 mS/cm at 500 K.
For a more detailed analysis of the changes of the Li and Al atomic positions, we calculated the partial coordination numbers (PCNs), , which give the average number of j-type atoms within the cut-off distance, Rcut, of an i-type atom from the PDF according to: where is the number density [26,27]. The cut-off distance, Rcut, was selected to be the distance corresponding to the tail of the first peak in the PDF. Figure 4 shows the evolution of the PCN with an increasing temperature for Li-O and Al-O. For temperatures below 400 K, NLiO is 6, which indicates that Li is octahedrally coordinated with O atoms. At temperatures above 450 K, NLiO starts to decrease, suggesting that the Li atoms do not have an octahedral coordination any more, which may also be caused by a partial delithiation from the positively charged layers. Above 650 K, NLiO stops decreasing and fluctuates around 2 with the further increasing temperature.
The evolution of the Al-O coordination environment with the temperature is quite different from the Li-O case. From the shown in Figure 3b, it can be clearly seen that shows a well-ordered structure even up to 1000 K. This result indicates that within the time-scale of MD simulations, the oxygen octahedron around Al is stable, which can also be seen from the PCN versus temperature curve, as presented in Figure 4. At temperatures above 1100 K, NAlO starts to drop, which means that after the breakdown of the octahedral Li coordination above 450 K, the framework made up of the AlO6 octahedra remains stable until 1100 K. Above 1300 K, the octahedral coordination around Al becomes unstable. To further study the different behaviors of Li and Al in LiAl2(OH)6Cl during the heating process, the mean square displacement (MSD) of Li and Al at 500 K were calculated and are presented in Figure 5. MSD is defined as [28]: where N represents the number of type-c atoms in the system, while 〈 〉 denotes the ensemble average of a physical quantity, . As it is known that the timescale of the Li diffusion process is of the order of picoseconds, it can be analyzed by MD simulations. It can be seen from Figure 5 that the Li atoms show a larger dynamics than the Al atoms. This can be explained by the heavier mass and higher charge of Al compared to Li. Within larger time intervals, the values of MSD increase with time as observed in [28]. In many kinds of lithium superionic conductors, e.g., Li3Y(PSO4)2, Li5PSO4Cl2 [29], and Li7P3S11 [30], an open site due to Li + diffusion is found to be occupied by another Li + within 10 ps. From the MSD vs. t curve, the diffusion coefficient, D, can be calculated as follows: Among several possibilities, we chose two for the movements of the Li atoms, i.e., within the layers or between the layers in LiAl 2 (OH) 6 Cl, see Figure 6, which we found reasonable from the structural point of view. The calculated structural energy is plotted against the diffusion coordinates, which shows an energy barrier of about 202 meV for the intra-layer diffusion within the Li-Al layers and 177 meV for the inter-layer diffusion path. Such low energy barriers may give rise to a high Li conductivity of partially delithiated Li 1-x Al 2 (OH) 6 Cl 1-x (0 < x < 1). Although the Li conductivity may not be the only factor that determines a battery performance, its high value strongly recommends the possibility of utilizing this compound as a lithium superionic conductor.
where indicates the dimension of the system [28,29]. Equation (4) reduces to Equation (5) if the time dependence of MSD is approximately linear, which holds true in most cases. Thus, Equation (5) is also widely used in the literature to calculate the diffusion coefficient [29,31]. The calculated value of the Li + diffusion coefficient by using Equation (5) is 3.13 × 10 / , which is higher than that of the Li + ion calculated for Li5YPS4Cl2 (~2.5 × 10 / ) at 500 K [29]. The Li ion conductivity can be estimated by the Nernst-Einstein relation [29]: where , R, and F represent the molar density of Li in the unit cell, gas constant (8.314 J·mol −1 ·K −1 ), and the Faraday's constant (96,485 C·mol −1 ), respectively. z is the charge number of Li, z = +1. According to the MSD, the Li conductivity for the current simulated system was calculated to be 708 mS/cm at 500 K. Among several possibilities, we chose two for the movements of the Li atoms, i.e., within the layers or between the layers in LiAl2(OH)6Cl, see Figure 6, which we found reasonable from the structural point of view. The calculated structural energy is plotted against the diffusion coordinates, which shows an energy barrier of about 202 meV for the intra-layer diffusion within the Li-Al layers and 177 meV for the inter-layer diffusion path. Such low energy barriers may give rise to a high Li