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* E-mail: jlchu@home.ipe.ac.cn; Tel.: 0086-010-82544848; Fax: 0086-010-82544848 Received May 6, 2013; accepted June 23, 2013; published online XXXX, 2013. Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/cjoc.201300380 or from the author. Chin. J. Chem. 2013, XX, 1—6 © 2013 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1

DOI: 10.1002/cjoc.201300380

Study on Lithium Insertion in Lepidocrocite and λ-MnO2 Type TiO2: A First-Principles Prediction

Yahui Liu,a Jingyi Wu,b,c Wei Zhao,a Jinglong Chu,*,a and Tao Qia a National Engineering Laboratory for Hydrometallurgical Cleaner Production Technology,

Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China b Laboratory of Nuclear Analysis Techniques, Institute of High Energy Physics,

Chinese Academy of Sciences, Beijing 100049, China c Key Laboratory of Molecular Nanostructure and Nanotechnology, Beijing National Laboratory for Molecular

Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China

TiO2 is a latent anode material for rechargeable lithium batteries. Our simulation models, basing lepidocrocite and λ-MnO2 type TiO2, were investigated by density functional theory (DFT). The key issues are focused on the lithium insertion sites, electronic structures, and the conducting paths of Li＋ ions. Our calculated data indicate the calculated voltage of λ-MnO2 type TiO2 is higher than that of lepidocrocite type TiO2. The Li＋ ion migration en-ergy barrier of lepidocrocite type TiO2 along the [1 0 0] direction (0.45 eV) is lower than that of along the [1 1 0] direction (0.57 eV). The energy barriers of λ-MnO2 type TiO2 to move a Li＋ ion among the adjacent embedded sites (16c or 8a sites) is 0.68 eV.

Keywords titanium dioxide, lithium insertion, diffusion, density functional theory, transition state

Introduction Recently, lithium ion (Li＋ ion) batteries have at-

tracted significant interests because of their high capac-ity and the highest output voltage among the known rechargeable devices.[1-3] Graphite is a popular anode material of rechargeable lithium batteries due to its well-conductive, light-weight, low-price and eco- friendly characters.[4] However, the insertion potential of lithium into graphite is very close to that of lithium plating, which leads to limited inherent overcharge pro-tection.[1] Therefore, to develop new materials instead of graphite has been pay much attention at present.

Titanium dioxide (TiO2) is one of the few Li-embedded materials that can work at low potential conditions (around 1.5 V).[1] These materials have be-come attractive candidates for the Li＋ ions negative electrodes except theirs drawback of loss in battery en-ergy density. Usually, the study of TiO2 as a durable and safe anode was mainly focused on microcrystalline rutile, anatase, brookite and TiO2(B) forms.[5-9] Nowa-days, theoretical studies have been applied in many fields such as, describing electronic structure, optimiz-ing band structures and searching transition state at atomic level. Thereby, computer simulations have be-come a more and more powerful mean for the assistant research of experiments.

First principles calculations have been successfully applied in a range of lithium battery materials relating to rutile, anatase and TiO2(B).[10-15] In this work, we dis-cussed the lithium insertion sites and electronic confor-mations of ideal TiO2 with lepidocrocite and λ-MnO2 like structures by means of computer simulation. Then, the Li＋ ions conduction paths of lepidocrocite and λ-MnO2 type TiO2 were fully investigated, respectively. We demonstrated that both the lepidocrocite and λ-MnO2 type TiO2 will be the good anode materials for rechargeable lithium batteries.

Computational Details All unit cell parameters and geometry optimization

were calculated by the Dmol3 code[16,17] with the gener-alized gradient approximation (GGA) functional of Perdew-Wang exchange and correlation functional (PW91).[18,19] All-electron double-numerical basis set with polarization functions (DNP) was applied to all atoms. To take into account any relativistic effects, the effective core pseudopotentials (ECP) were chosen.[20] We recognized that some recent studies on Ti-based oxides have used the DFT＋U approach to treat Ti oxi-dation states. Morgan et al. emphasize GGA＋U can well describe the process of lithium intercalation into anatase TiO2.[21] Since the Dmol3 program does not

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have the＋U option, it seems not fit for the calculation of electronic property of transition-metals. However, for lepidocrocite and λ-MnO2 type TiO2, as the ideal struc-tures, their U values have not been obtained from ex-periment. Meanwhile, numerous recent studies on TiO2 defects and lithium insertion in transition metal materi-als have employed GGA methodology without the on-site U parameter.[13-15] Especially, Arrouvel et al. consider that the GGA method has a small systematic overestimation on cell volumes and the discrepancy (1.3%) of the experimental volume is smaller than that of GGA＋U (2.3%) for treating TiO2(B).[14] Therefore, the Dmol3 program as the fastest DFT algorithm has still been chosen to optimize the unit cell parameters.

Li intercalation of anatase usually is accompanied by a defect state (~1.0 eV) which is below the conduction band edge. Also, there exists a consequence of the self-interaction error inherent to pure GGA method when this method has been used to treat this open shell system.[21] Therefore, in order to make a probable accu-rate prediction, the electronic conformation and single- point energy of LixTiO2 were recalculated at GGA- PW91 level with CASTEP code[22] using LDA＋U op-tion. Generally, the value of U will be fitted to repro-duce some experimental property as a semi-empirical component to the computations. Thus, the optimized results were needed to determine the U value from ex-periment and the prediction accuracy was partly af-fected by the selection of U value. The correction of U＝4.2 eV is applied according to the result of anatase type TiO2.[21]

In order to determine the energy barrier of migrated Li＋ ions in lepidocrocite and λ-MnO2 type TiO2, a method combining the linear synchronous transition and the quadratic synchronous transition (LST/QST) with conjugate gradient (CG) refinements was em-ployed.[23,24]

The average cell potential of Li-embedded transition metal compounds[14] is calculated by the Nernst formula. The reaction is represented as follows:

TiO2＋xLi(metal) → LixTiO2 (1)

The expression for the potential can be written as follows:

( ) GV xxFΔ－

＝ (2)

in which, the F＝96485.34 C/mol, ΔG (the free energy change) is approximated by the internal energy change per intercalated Li＋, E(int).

2 2(Li TiO ) (Li) (TiO )(int) xE xE EEx

－ －＝ (3)

in which, E(LixTiO2) and E(TiO2) are the total energy of lithium ion doped and undoped in the structures of TiO2, respectively. E(Li) (the energy of lithium metal) is ob-tained by optimizing the body-centered cubic (space

group: Im-3m) Li metal with original a0＝3.500 Å (the optimized parameter of a is 3.455 Å).

Results and Discussion Structures of TiO2 and their lithium insertion sites

The bulk TiO has high-symmetrical face-centered cubic (rock-salt type, space group: Fm-3m) crystal structure. It is well-known that the bond length of Li－O and Ti－O is nearly equal,[13] therefore, the solid so-lution of Ti1-x-yLix□yO (□, vacancy) can exist stably with rock-salt type structure. When x＝0 and y＝1/2, they have a chemical formula Ti□O2. Typically, anatase- TiO2 is one kind of this structure and could carry Li＋

ions efficiently. Tielens et al. do a very intensive study on this system.[13]

The ideal layered Ti□O2 (lepidocrocite type TiO2

[25-27]) is constructed according to the crystal struc-ture of rock salt type TiO. It has the space group Pmmn, with original unit cell parameters of a＝2.83 Å, b＝4.00 Å, and c＝5.66 Å. After optimizing the parameters, unit cell parameters will be altered to a＝3.04 Å, b＝3.76 Å, and c＝6.24 Å together with the angle of Ti-O-Ti bend-ing from 180° to 152.5° on a-c plane. The optimized lattice parameters are very similar to the experimental cell parameters of Ti0.91O2 (a＝3.0 Å, b＝3.8 Å) derived from the crystallite of Cs0.7Ti1.825O4□0.175.[25] Our calcu-lations on lepidocrocite type TiO2 base on GGA-PW91 show good agreement with the experiment results. Also, the insertion sites and conduction paths would be close to the real experimental results. When lithium was em-bedded in the site (2a site, Wyckoff notation), the lay-ered Ti□O2 can keep its original periodicity (space group: Pmmn). After optimizing the LiTiO2 structure, all the atoms are almost aligned in the planes as in the original TiO structure.

The 3-dimension (3-D) pore structure of TiO2 (space group: Fd-3m) is formed to be very similar to the λ-MnO2 structure.[28] In fact, we found that the λ-MnO2 type TiO2 was also derived from rock salt type Ti□O2 with the original unit cell parameters of a＝4.000×2 Å. The optimized parameter of a is 8.44 Å. Unfortunately, there are only few experimental data about λ-MnO2 type TiO2. For Li saturated structures, they have the similar result as lepidocrocite type TiO2: all the atoms are aligned in planes. The Li＋ ions embed at □ position (16c sites, Wyckoff notation) form a closely packed type array surrounding O atoms with an octahedral co-ordination. And more, it exhibits NaCl type crystal structure. For Li half-saturated structure, the Li＋ ions can embed at two probable positions, the 16c sites or 8a sites. The 8a sites are the position that Li＋ surrounds O atoms with tetrahedral coordination and it exhibits spinel type crystal structure with chemical formula of Li4Ti8O16. The optimized parameter of a is 8.38 Å, which is slightly smaller than that of experimental data for spinel type Li4Ti5O12 (8.375 Å).[29]

In short, our calculations of the lepidocrocite type

Study on Lithium Insertion in Lepidocrocite and λ-MnO2 Type TiO2

Chin. J. Chem. 2013, XX, 1—6 © 2013 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cjc.wiley-vch.de 3

TiO2 and spinel type Li4Ti8O16 based on GGA-PW91 method using Dmol3 code show good agreement with the experiment results in unit cell parameters.

All TiO2 and LiTiO2 structures (see Figure 1) exhibit a stable electronic conformation of closed or opened shells, respectively. The λ-MnO2 type TiO2 has the highest energy among these structures. However, its corresponding LiTiO2 structure has the most stable structure. The geometry parameters of the optimized structure are shown in Table 1. Based on these opti-mized results, it can be found that the embedded Li atom leads to an increased O－O distance and a de-creased Ti－Ti distance compared to original TiO2, moreover, the O-Ti-O angle is close to 90°. Among them, the structure change of λ-MnO2 type is the mini-mum while it has the highest potential.

It obviously indicates that the potential change is relative to the structure before and after Li insertion. If the structure deforms greatly, the potential should be

lower. The potential usually is ~1.5 V vs Li＋ for dif-ferent type TiO2. We calculated data using Dmol3 code, and the potential of lepidocrocite type TiO2 is 1.36 V for Li saturation. This corresponding value is much lower than that of λ-MnO2 type TiO2 (2.11 V).

In contrast to the Dmol3 code, the calculated voltage using CASTEP code with LDA＋U option (calculated for the Dmol3 optimized unit cell parameters) is a little lower and the value is 1.29 and 1.61 V, respectively. Especially, the result of λ-MnO2 type TiO2 shows that the choice of code strongly affects the prediction of voltage data. Our calculated data, presented in Table 2, indicate that voltage range calculated by Dmol3 is 1.36－1.57 V for lepidocrocite type TiO2 and 2.11－3.36 V for λ-MnO2 type TiO2, respectively. The energies of lepidocrocite and λ-MnO2 type TiO2, corrected by CASTEP code supplement with LDA＋U, are 1.29－1.44 and 1.61－2.72 V, respectively.

Figure 1 Lithium insertion sites of lepidocrocite and λ-MnO2 type TiO2.

Table 1 Calculated lattice parameters of two types of TiO2 and their corresponding Li embedded LiTiO2 structurea

Types of TiO2 Space group Z a/Å b/Å c/Å V/Å3 Atom x/a y/b z/c lepidocrocite type TiO2 Pmmn 2 3.043 3.756 6.237 71.28 Ti 0 0 0.8211 O 0.5 0 0.6565 O 0 0.5 0.9208lepidocrocite type LiTiO2 Pmmn 2 3.055 3.787 6.719 77.73 Ti 0 0 0.8506 O 0.5 0 0.6441 O 0 0.5 0.9196Li embedded at 2a sites Li 0.5 0.5 0.5655λ-MnO2 type TiO2 Fd-3m 4 8.437 300.26 Ti 0.125 0.875 0.375 O 0.8908 0.1092 0.6092NaCl type LiTiO2 Fd-3m 4 8.380 294.24 Ti 0.125 0.875 0.375 O 0.8798 0.1202 0.6202Li embedded at 16c sites` Li 0.625 0.625 0.125 a Li embedded at 2b sites of lepidocrocite type LiTiO2 and Li embedded at 8a sites of spinel type Li2Ti4O8 can be found in supporting information. The λ-MnO2 type TiO2 was optimized using the primitive of the face-centered cube.

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Table 2 Calculated cell voltages for different lithium concentrations in lepidocrocite and λ-MnO2 type LixTiO2a

Li content (x) a/Å b/Å c/Å V/Å3 Voltage/V Corrected voltage/V

Spinel-LixTi4O8 (primitive cell) Dmol3 CASTEP LDA＋U

x＝0 5.966 150.13

x＝1 5.956 (5.964) 149.33 (149.93) 2.68 (3.36) 2.17 (2.72)

x＝2 － (5.957) － (149.41) － (2.94) － (2.37)

x＝3 5.947 148.66 2.29 1.77

x＝4 5.926 147.12 2.11 1.61

Lepidocrocite-LixTi2O4

x＝0 3.043 3.756 6.237 71.29

x＝1 (*) 3.055 3.787 6.719 77.73 1.57 1.44

x＝2 3.055 3.787 6.719 77.73 1.36 1.29 a Structure of (*) is optimized with fixing the unit cell. Generally, the results are no convergence with full optimization, so we have to fix the unit cell in stand of only optimization of the atom positions. The contents in bracket are the values of Li embedded at 8a sites.

All different types LixTiO2 show that an increase of

voltage can be found in contrast with a decrease of Li＋

ion concentration. There are two group data of λ-MnO2 type TiO2 in Table 2 (the values in brackets are obtained as the Li＋ ion at 8a sites).

Electronic structure The DOS of lepidocrocite and λ-MnO2 type TiO2 are

shown in Figure 2a, 2c respectively. There are some

predictable resemblances among the DOS of these two structures. The main contributions to the valence bands are O2p states which are bonded with Ti3d states, while the Ti 3d states are the dominant component of conduc-tion band (anti-bonding band). Mostly, there are many obvious differences among the DOS of those structures. For instance, there is a single d band in the DOS pat-terns of λ-MnO2 type TiO2 due to five-fold degenerate state of d orbitals. Meanwhile the corresponding d band

Figure 2 Total density of states for (a) lepidocrocite type TiO2; (b) lepidocrocite type LiTiO2; (c) λ-MnO2 type TiO2; (d) λ-MnO2 type LiTiO2.

Study on Lithium Insertion in Lepidocrocite and λ-MnO2 Type TiO2

Chin. J. Chem. 2013, XX, 1—6 © 2013 SIOC, CAS, Shanghai, & WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cjc.wiley-vch.de 5

of lepidocrocite type TiO2 splits into t2g and eg symme-try components. The DOS patterns of embedded Li＋ ion for those two types TiO2 are shown in Figure 1b, 1d respectively. In all Li embedded structures, the Fermi level (EF) shifts from high-energy edge p band to the adjacent edge d band, which means the electron of Li atom entering into the conduction band of TiO2. In ad-dition, the shifting of Fermi level situated within the d band implies that the LiTiO2 structures should become conductors.[30] If the embedded Li was treated as an atom (see formula 1), it can be found that the electron will transfer from Li2s band to Ti3d band, and finally those electrons could reduce Ti4＋ to Ti3＋.

According to the ligand field theory, the valence state of central ion can observably affect the splitting energy (Δ0). Therefore, the Δ0 value of lepidocrocite type LiTiO2 is only 1.81 eV, which is much smaller than the value (2.38 eV) of corresponding structural type of TiO2 (Figures 2c and 2d).

Li＋ ions conduction energy barrier and transition state

When considering the structure of TiO2 as an anode material for lithium ion batteries the rate of conduction energy barrier of intercalated lithium ions will be a critical parameter since it determines power output and battery charging times. Simulation methods can greatly enhance our understanding of ion conduction paths by evaluating the activation energies for various possible mechanisms at atomic level.

The Li＋ ion conduction barrier of lepidocrocite type TiO2 has been analyzed in theory using transition searching method. There exist obvious conduction paths between the adjacent Li＋ ions along [1 1 0], [1 0 0] and [0 1 0] directions. The energy barrier of Li＋ ions along [1 0 0] direction is calculated by searching the transition state which links the conformations between Li embed-ded at 2a sites bias＋0.05 Å and its corresponding ad-jacent 2a sites along [1 0 0] direction bias −0.05 Å. The embedded status of Li in 2b site, which located in the middle of opposite O atoms original from adjacent layer, is the transition state with conduction energy barrier of 0.45 eV along [1 0 0] direction. The conduction path along [1 1 0] direction has larger energy barrier of 0.57 eV. The transition state is located in the middle of O from the adjacent layer (Figure 3a). Therefore, all of the three conduction paths can provide significant contribu-tions to Li motion. In a short, the layered structure is helpful to easy migration of Li＋ ion in the interlayer.

The same optimization strategy is also used for λ-MnO2 type TiO2, however, some interests are en-countered when the TS research method was used be-tween adjacent Li＋ ions. In order to reduce computa-tion load and improve convergence speed, simple mod-els of primitive cell derived from the original cubic sys-tem are described. Those simple models are composed of four Ti, eight O and one Li. The Li can embed at 8a sites or 16c sites (labeled as that in the original cubic

system) in the unit cell.

Figure 3 Predicted energy barriers for lepidocrocite type TiO2 with a single Li+ ion (LiTi2O4) between the adjacent 2a sites along (a) [1 1 0] and (b) [1 0 0] direction; (c) The energy barrier for λ-MnO2 type TiO2 with a single Li+ ion (LiTi4O8) between the adjacent 16c sites.

There are two possible conduction paths between adjacent Li＋ ions: The path (I) is between the adjacent Li＋ ions of 8a sites; the path (II) is between the adja-cent Li＋ ions of 16c sites. However, the path (II) does not exist since the migration between the adjacent Li＋ ions is not following a linear route according to the re-

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sults of TS research. It requires the Li＋ ions to follow a zigzag path and pass the 8a sites when Li＋ ions migrate along the path (II). For the energy barriers, it is straight forward to observe that the Li＋ ion at 8a sites is more stable than that at 16c sites. Moreover, based on the TS research, the energy of Li＋ ion embedded at 16c is the transition state along the path (I). Therefore, wherever the Li＋ located at 8a or 16c site, the energy barrier of migration from 8a or 16c site to its adjacent sites (8a or 16c) is 0.68 eV.

Conclusions Periodic density functional theory calculations based

on Dmol3 code was performed successfully on the TiO2 with different dimension structures, including lepido-crocite and λ-MnO2 type TiO2 to investigate their ge-ometry and Li＋ ion conduction path. To obtain more rational results, all the electronic structure and single point energy were corrected with an LDA＋U option correction at GGA-PW91 level using CASTEP code.

Before and after Li insertion, the frame of λ-MnO2 type TiO2 has more deformation, and its Li-embedded state has the more stable structure compared to other type of LiTiO2. In the Li-inserted structures, the Fermi level shifts from p band to d band, which means the electron from Li atom will enter into the conduction band of TiO2.

A voltage range calculated by Dmol3 code is 1.36－1.57 V for lepidocrocite type TiO2 and 2.11－3.36 V for λ-MnO2 type TiO2, respectively. While, the energies of lepidocrocite and λ-MnO2 type TiO2, corrected by CASTEP code supplement with LDA＋U, are 1.29－1.44 and 1.61－2.72 V, respectively. All different types LixTiO2 show that an increase of voltage can be found in contrast with a decrease of Li＋ ion concentration. The energy barriers of lepidocrocite type TiO2 to move a Li from 2a site to its adjacent 2a site along [1 1 0] and [1 0 0] are 0.45 eV and 0.57 eV, respectively. By com-parison, it needs 0.68 eV for λ-MnO2 type TiO2 to move a Li＋ ion, wherever, the Li＋ located at 8a or 16c site.

Acknowledgement This work was financially supported by the Major

Program of the Natural Science Foundation of China (Grant No. 51090380), the National Science Foundation for Distinguished Young Scholars of China (Grant No. 51125018), the Knowledge Innovation Program of the Chinese Academy of Sciences (KGCX2-YW-214) and the special funds of “Mountain Tai Scholar” construc-tion project. The computing platform was supported by the Computer Facility for Theoretical and Computa-

tional Chemistry, Institute of Chemistry (CFCC), Chi-nese Academy of Sciences (CAS).

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