We are grateful for the detailed review of our manuscript. All comments have been addressed in the revised version of the manuscript

Comment 1: The author should use appropriate words, such as short time but not small time.

Response: corrected

Comment 2: There are a few grammatical errors that need to be improved in the revised version. For example, “The volume, corresponding to the as-defined voids, can be determined by constructing secondary VDPs for all the vertices in the primary construction with the same surrounding ions……”.

Response: The text of the manuscript was additionally proofread by authors. Terminology has been carefully checked and corrected.

Comment 3: Eq. 3 is the Nernst-Einstein equation, which should be pointed out. In addition, D stands for the diffusion coefficient of Li+ but not the chemical diffusion coefficient, and T represents the absolute temperature (K) in Eq. 3.

Response: The description of Eq.3 was revised in accordance with your remark. The text was changed: “ …The ionic conductivity of Li … in intercalation electrode materials is univocally connected with Li diffusivity via Nernst-Einstein equation … D is diffusion coefficient of Li … and T is absolute temperature”

Comment 4: ρ stands for the hop probability in Eq. 5, which should be pointed out.

Response: We pointed out that ρ stands for the hop probability. The text was changed in this way: “…where ρ is the geometric factor that can be interpreted as a hop probability … ”

Comment 5: This work should include recent work published in the field of energy storage. Please find some references: Chem. Eng. J. 2022, 433, 134506. Sub‐nanoscale Engineering of MoO2 Clusters for Enhanced Sodium Storage Appl. Surf. Sci. 2020, 533, 147511. Energy Storage Mater. 2020, 25, 416–425. ACS Energy Lett. 2019, 4, 2007–2012.

Response: We found useful information in the listed references regarding the ionic conductivity measurement techniques, and cited four of them in a new section named “Experimental techniques and computational methods for ionic conductivity investigation in intercalation materials”.

Comment 6: Based on the DFT, the nudged elastic band (NEB) and ab initio molecular dynamics (AIMD) methods are often used to calculate the diffusion of lithium ions in solids. Hence, all methods, including then experimental or numerical simulation methods for calculating the ionic conductivity of intercalation materials should be introduced in detail and summarized in a table.

Response: Thank you for your helpful suggestion. We have extended our manuscript by a new section named “Experimental techniques and computational methods for ionic conductivity investigation in intercalation materials” where experimental and computational methods are introduced and summarized in TABLE I “Experimental and computational methods for ionic conductivity and diffusivity investigation”, with their advantages/disadvantages.

Comment 7: The significance of this work is Relatively vague should be highlighted.

Response: We added an outlook section that highlights the significance of this review work.

Comment 8: In order to highlight the significance of this work, based on the cited works, the authors should point out how to design the new intercalation materials with the high ionic conductivity with a graphic abstract and summarize the strategies for improving the ionic conductivity in a table.

Response: We have summarized the possible strategies for improving the ionic conductivity in TABLE II. “Design principles for improving the ionic conductivity” (section Outlook), which was created based on the results discussed in the manuscript.

Comment 9: In order to make the structure of the article more hierarchical, titles at all levels can refer to the following format. The authors can refer to J. Phys.: Condens. Matter. 2022, 34, 345601. 3. Mechanisms of Ionic Conductivity in Intercalation Materials 3.1. Theory of ionic conductivity 4.2.1. Local coordination at initial and transition states

Response: The section numbering has been changed in accordance with your suggestion.

Comment 10: All factors affect the ionic conductivity of Li+ and the corresponding quantitative expressions should be summarized in a table.

Response: Most of the factors affecting the ionic conductivity are now summarized in the new ‘Outlook’ section and Table II. Unfortunately the quantitative expression exists only for strain vs migration barriers which is included in the manuscript text.

Comment 11: For a review paper, the outlook should be added.

Response: Outlook section has been added before the Conclusion section.

Comment 1: In the Subtitle II of the review, the last paragraph shall mention which is the most followed method for the determination of ionic conductivity based on its accuracy.

Response: The names of the methods have been added to the last paragraph. Additionally, we have extended our manuscript by a new section named “Experimental techniques and computational methods for ionic conductivity investigation in intercalation materials” where the main experimental and computational techniques are briefly overviewed mentioning their strong and weak points.

Comment 2: The manuscript can also include a separate section regarding the ionic conductivity studies of high-voltage battery materials.

Response: We have analyzed the correlation between redox potential of high-voltage battery materials and ionic conductivity, which have been included into a separate section 5.2.12.

Comment 3: Do any computational insight works related to computational insights into ionic conductivity and the electrolyte ion intercalation to the material sites have developed? If yes, the inclusion of this topic could increase the practical visibility of the manuscript.

Response: The computational insights regarding ion intercalation processes in Li-ion batteries were collected in our recent review paper [D. A. Aksyonov and V. A. Nikitina Molecular Sciences and Chemical Engineering, “Charge transfer through interfaces in metal-ion intercalation systems”, 10.1016/B978-0-12-823144-9.00054-6]. We highlighted the importance of these processes in the Outlook section.

Comment 4: An outlook section can be included before the conclusion.

Response: Outlook section was added before the Conclusion section.

We are grateful to reviewers for the detailed review of our manuscript. All comments have been addressed in the revised version of the manuscript. Please find below our detailed response per each comment.

Comment 1: The greek letter nu with a * as superscript is defined twice in the article. Once as vibrational prefactor (equation 6 on page 6) and later as the hopping attempt frequency (equation 8 on page 10). Depending on how these are derived, and which thermodynamic quantities are incorporated (entropy term), they may not be the same. This should be elaborated in more detail.

Response: The vague term vibrational prefactor and corresponding ambiguity were removed. The definition of the hopping attempt frequency was added following equation 6: “$\nu^*$ being an effective frequency associated with vibration of \li in the direction of the saddle point. This frequency is a ratio of the products of N and N-1 normal frequencies in initial and transition states, respectively, and include change of entropic contribution. Later we refer to it as \it{hopping attempt frequency}” The discussion regarding equation 8 was inaccurate. It was rewritten.

Comment 2: Regarding the paragraph “5.2.4 Type of alkali cation”: there is one prominent example that is not listed at all albeit it is reported to span cations from H+, Li+, Na+, Li+ to Rb+. A2Ti6O13, the alkali hexatitanates. This example material could also be addressed in section 5.2.3. but it is up to the authors to include this example. The also show a nice correlation between the cation size, tunnel size, and activation energy.

Response: Now we mentioned hexatitanates in paragraph 5.2.4: “Another example is \ce{A2Ti6O13} ($C2/m$) which shows much smaller barrier for \na migration (0.17 eV - classical potentials~\cite{zulueta2019lithium}, 0.24 eV - PBE+U~\cite{ling2017anomalously} ) than that for \li (0.47 eV - classical potentials~\cite{zulueta2019lithium}) or \ka (0.92 eV - GGA)~\cite{li2021atomic}, 1.28 eV - PBE~\cite{xu2018boosting}).” The barrier values were added to tables 4-6 and Figure 14.

Comment 3: The proportionality between the hopping attempt frequency and the average phonon frequency is given in equation 11. This Equation is erroneous since the average phonon frequency must be of unit hertz (Hz) and not that of an energy while “Ea” is of unit of an energy. Response: There was a typo. The proportionality should be written for D0 (pre-exponential constant). D0 ~ exp(Ea/<ω>). However, in this case the units on the left and right parts are still different, which is not a problem, because it is not an exact equation, but just a proportionality. By adding a constant with the required dimensionality the exact equation will be correct.

Comment 4: Further suggestions to improve the readebility: i) 30.000 instead of 30 thousand would increase the readability (page 4) ii) Figure 18 b shows Lix+1Ti2O4 while in the text (page 17) the material is referred to as Li1+xTi2O4. iii) spelling mistake in the caption of figure 6 (mirgration should be migration), (page 9)

Response: corrected

Comment 1: Title, Abstract, Introduction: I think it would be good to directly direct the reader's attention to cathode materials or at least to mention that in this article compounds with transition metal ions are in the focus of interest. I am not sure if all the materials covered by the authors can be regarded as intercalation materials. Therefore one might think about the title once again.

Response: Title has been changed into “Computational insights into ionic conductivity of transition metal electrode materials for metal-ion batteries - A review”. Abstract and Introduction are slightly updated to narrow the focus of interest.

Comment 2: Table 1: NMR, „very limited information on lithium diffusion coefficient due to the coupling between electronic spins and spin-lattice relaxation rate“ This statement is of course right for paramagnetic materials, such as, cathode materials. However, see also page 2, I would recommend to at least say that NMR is a powerful tool in studying the dynamic parameters of diamagnetic compounds. And, do not forget to mention at least some of the papers that indeed use high-resolution NMR to look at local structural changes during charging and discharging the various cathode materials, see studies by C.P. Grey etc. I would suggest working out these advantages briefly a better way though the paper focusses on dynamic properties.

Response: We added a short discussion based on Grey’s works into the text: “NMR is a powerful tool for elucidation of local structure and dynamics, such as diffusion in diamagnetic materials (Li4SiO3 [25] , Li4+xTi5O12 [26] , Li12Si7[27] , Li2ZrO3 [28] ). However the studying of cation migration processes in transition metal cathode materials being paramagnetic in the discharged state is difficult due to large dipolar interactions between the Li nucleus and unpaired electrons of transition metals (V, Ni, Co, Fe, etc) which is dominated in the NMR spectra [29]. Despite this, the combination of different NMR techniques, such as spin-lock (SLR), allows studying the local structures and electronic properties of paramagnetic cathode materials as a function of state of charge [29,30] and extracting diffusion properties, for example in LiTiS2 [31], LiMn2O4 [32], Li3V2(PO4)3 [33], Li1.5Al0.5Ti1.5(PO4)3 [34] .”

Comment 3: NMR, see also 4.2.: For example, in the case of LTO (Li4+xTi5O12) several SLR (spin-lock) NMR studies exist that provide deep insights into the Li+ diffusion properties. The same holds for LATP.

Response: Added to Section 4.2 according to the previous response

Comment 4: GITT: Well, the accuracy of diffusion coefficients from GITT is debatable.

Response: agree, mentioned in the text

EIS: I would not call it EIS, but only impedance spectroscopy (IS), as it is usually carried out in the solid state here. EIS would refer to IS in liquid systems.

Response: corrected

Comment 5: LiFePO4: There might be a study of Maier and co-workers directly addressing the 1D nature in LiFePO4 which the authors might also consider. LiTiS2, apart from ref. 38 there is another paper of almost the same authors (PRB) that also looks on the exact diffusion pathway with SAE NMR: oct-tet-oct

Response: The articles of Maier et.al. regarding 1D diffusion in LFP are now cited in Section 4.4 during discussion of diffusion dimension (10.1016/j.ssi.2008.01.079, 10.1149/1.2388240). The mentioned work of M. Wilkening and P. Heitjans (10.1103/PhysRevB.77.024311) is now cited in Section 1 while discussing the NMR methodology.

Comment 6: The part about the Meyer-Neldel rule needs some clarification, see page 18. The authors are encouraged to look up in literature what this rule is indeed about as it relates E_a and the pre-factor of the Arrhenius line; this pre-factor does contain more than just the attempt frequency.

Response: Thank you for this comment. In fact we made a typo. Indeed it should be D0 proportional to Ea. References to original studies related to Meyer-Neldel rule were added. It was clarified that equation 8 corresponds to a modified rule where the average phonon frequency is additionally incorporated.

We would like to express our sincere gratitude to the reviewers and editor for dedicating their time and expertise to evaluating our manuscript and providing valuable feedback. We have carefully considered all of their constructive comments and have made revisions accordingly. These changes have been documented in the manuscript_diff.pdf file, along with minor corrections. We believe these enhancements have strengthened the quality and clarity of our work.

This manuscript reports the surface segregation of LiCoO2 materials with several doping elements. The authors performed DFT+U calculations on a doped LiCoO2 surface with various metals and calculated relevant solubility and surface segregation energies. Using these results, they point out the importance of segregating elements that can improve surface stability and reduce degradation. The manuscript is recommended for publishing in Physical Review Materials; however, it needs a little more revision as follows:

Loss of oxygen and transition metal migration inside the Li sites are mainly observed at high SOC when Li vacancies are formed. However, this study is entirely done on the fully lithiated stoichiometries with zero or low SOC. Does the reported result also hold at high SOC with partially delithiated structures? If authors can show one or two example simulations on partially delithiated systems, that will enhance the significance of this research.

We suggest that the extremely slow diffusion of transition metals (TMs), as evidenced by estimations below, limits segregation phenomenon to high-temperature annealing during synthesis. Consequently, calculating segregation tendencies for zero SOC is a suitable and accurate approach. However, we acknowledge the necessity of assessing the impact of segregation on various properties at high SOC, a scope beyond our study. Nonetheless, in response to your suggestion, we considered two examples involving Ti and Al. Our findings suggest that upon partial delithiation, segregation trends may undergo significant changes.

Delithiation to Li0.5CoO2 induces substantial changes in E seg , shifting from -0.94 to -0.3 eV for Ti 4+ and from -0.04 to 0.84 eV for Al3+ compared to fully lithiated states. These pronounced alterations underscore the importance of investigating the impact of SOC more comprehensively. However, such an endeavor is highly resource-intensive and warrants a dedicated study. Partial delithiation introduces additional complexities, including symmetry lowering from R-3m to P2/m, the emergence of lithium vacancies, and the presence of two types of cobalt: Co 3+ and Co 4+ . These factors increase the number of possible configurations for bulk solutions and at the surface, necessitating careful consideration and analysis.

The following text was added at the beginning of Results IIIC

“We investigate the surface segregation trends of LiCoO2 in its fully lithiated state, as obtained immediately after synthesis. This inquiry is driven by the recognition that equilibrium segregation of TMs primarily occurs during the high-temperature annealing process of synthesis, rather than through cycling at room temperature, given the inherently low diffusivity of TMs. We provide a brief overview of the influence of lithium concentration on segregation energies in Section S6.”

The following text was added to SI Section S6:

We consider equilibrium segregation to result primarily from high-temperature annealing during synthesis, rather than from cycling. Transition metals (TM) exhibit very low diffusivity, making it unlikely for TM dopants to equilibrate their surface concentrations in a charged state at room temperature. Estimations of TM diffusivity in layered oxides, based on experimentally measured interdiffusion coefficients of Ni/Co pairs (using LiNi 0.8 Co 0.2 O 2 /LiCoO 2 pair), with an activation energy of 2.2 eV and a pre-exponential coefficient of D 0 = 2.6 × 10 –6 m 2 /s, suggest diffusion lengths of approximately 10 –8 - 10 –6 Å/year at T ranging from 25 to 60 °C (based on sqrt(2Dt) estimation). This illustrates that TM metals are effectively immobile at typical battery operation temperatures [1]. Consequently, the segregation observed after synthesis, corresponding to the fully lithiated state, will persist during delithiation, thereby influencing the structural stability of the surface.

However, to ascertain whether segregation may become thermodynamically unstable upon delithiation, we examined the segregation of Ti and Al in a partially delithiated system. Specifically, we constructed the (104) slab with a composition of Li 24 Co 56 O 112 , derived from the ideal P2/m-Li 0.5 CoO 2 structure, as previously performed by other researchers [2] (Fig. S6). The Co atoms at the surface are in 4+ states. Due to the slab’s non-stoichiometry we calculated the segregation energy as E seg = E slab (X at surface) - E slab (X in the bulk).

We obtained E seg (Ti) = −0.3 eV and E seg (Al) = 0.84 eV vs −0.94 eV and –0.04 eV in the fully lithiated slabs, respectively (Table S20). The obtained differences can be attributed to the emergence of Co 4+ in partially delithiated slab. In such a slab the Ti 4+ for Co 4+ substitution both in bulk and at surface does not require the formation of Co 2+ polaron in the 1nn position as observed in a fully lithiated slab. Indeed, using the Ti-doped fully lithiated slab with a Li vacancy created near the Ti, we were able to consider Ti 4+ segregation without Co 2+ polaron, and obtained E seg lying in the range of −0.3 - −0.5 eV depending on the Ti-Li vac configuration (Table. S21), which is comparable to that in partially delithiated slab.

For Al 3+ , in the partially delithiated slab, the substitution occurs differently: Al 3+ substitutes for Co 3+ when located in the bulk, whereas it substitutes for Co 4+ at the surface. In the latter case an additional Co 4+ is formed in the bulk, increasing the energy of the system. Conversely, in the fully lithiated slab Al 3+ substitutes for Co 3+ both in bulk and at surface. Our findings for these selected elements suggest that delithiation can significantly impact segregation energies, particularly when a mismatch of dopant and host metal valency is present. This underscores the necessity for further investigations in this area.

1. Li, J., Doig, R., Camardese, J., Plucknett, K., & Dahn, J. R. (2015). Measurements of interdiffusion coefficients of transition metals in layered Li–Ni–Mn–Co oxide core–shell materials during sintering. Chemistry of Materials, 27(22), 7765-7773.

2. Ben Yahia, H., Shikano, M., & Kobayashi, H. (2013). Phase Transition Mechanisms in LixCoO2 (0.25≤x≤1) Based on Group–Subgroup Transformations. Chemistry of Materials, 25(18), 3687-3701.

The authors used a Hubbard-like correction for the DFT calculation. What is the rationale for using the provided U values? How do the U values correlate with the experimental band gap of bulk LiMO2?

In our selection of Hubbard U values, our premise was that achieving accurate reproduction of formation enthalpies would lead to precise calculation of segregation energies. Thus, we opted for the U values initially published by Jain et al. [1], as they were fitted to accurately describe experimental binary oxide formation enthalpies. Additionally, we considered that the impact of U values on segregation energies would be of secondary importance, given the differential nature of segregation energy and the resulting compensation of U impact. Therefore, we favored the use of published values rather than fitting our own. It's worth noting that while these values were originally fitted for binary oxides, they have beensuccessfully applied to layered oxides in previous studies. To support our assumption, we conducted additional benchmarks and included them in the SI.

The following text explaining the rationale was added to SI Section S7.4 and referenced from the methodology:

The impact of the Hubbard U value used for Co and the dopant on the segregation energy is illustrated in Figure S7. We observed that the effect of U(Co) on Mn and Al segregation energies is relatively weak, with E seg showing a slight synchronous increase for both Al and Mn. Additionally, we found that E seg for Mn exhibits minimal dependency on U(Mn) when U(Co) is fixed at 3 eV. The decrease in E seg (Mn) observed at lower U(Mn) values of 1 and 2 eV may be attributed to the transition of Mn from a high-spin (HS) to a low-spin (LS) state in the bulk, although at the surface, Mn remains stabilized in the HS state across the entire range of U(Mn). For more detailed information about the magnetic structure of each supercell, please see below.

Figure S7. Segregation energy of Mn and Al as a function of the U Hubbard value when a) the U value is changing on Co, but fixed on Mn, and b) the U value is fixed on Co, but changing on Mn.

Regarding the correlation of U values with the experimental band gap of bulk LiMO2, we compiled available data in Table S28. Specifically focusing on LiCoO2, U values in the range from 3.0 to 3.4 eV (our value is 3.2 eV) yield a band gap of 2-2.2 eV, while theexperimental value falls between 2.1-2.7 eV. For LiNiO2, the calculated band gap at U=6.2 eV and the experimental band gaps are 0.8 eV and 0.4-1.0 eV, respectively. In the case of LiMnO2, the theoretical and experimental band gaps are 1.0 and 1.6 eV, respectively. Reasonable agreement is also observed for LiCrO2, but unsatisfactory for LiVO2, where the computational gap (1.5 eV) noticeably overestimates the experimental value (0.18 eV). No experimental data for LiFeO2 is available. Overall, the selected U values generally enable reasonable reproduction of band gaps.

Table S28. Computed and experimental band gaps (eV) of layered LiTMO 2 using different density functional combinations.

1. A. Jain, G. Hautier, C. J. Moore, S. Ping Ong, C. C. Fischer, T. Mueller, K. A. Persson, and G. Ceder, A High-Throughput Infrastructure for Density Functional Theory Calculations, Comput Mater Sci 50, 2295 (2011).

2. O. Y. Long, G. Sai Gautam, and E. A. Carter, Assessing Cathode Property Prediction via Exchange-Correlation Functionals with and without Long-Range Dispersion Corrections, Physical Chemistry Chemical Physics 23, 24726 (2021).

3. W. Tian, M. F. Chisholm, P. G. Khalifah, R. Jin, B. C. Sales, S. E. Nagler, and D. Mandrus, Single Crystal Growth and Characterization of Nearly Stoichiometric LiVO2, Mater Res Bull 39, 1319 (2004).

4. H. I. Elsaeedy, Synthesis and Characterization of LiCrO2 Thin Films As Potential Cathode Material for Lithium Ion Batteries, J Electron Mater 49, 282 (2020).

5. А. Chakraborty, M. Dixit, D. Aurbach, and D. T. Major, Predicting Accurate Cathode Properties of Layered Oxide Materials Using the SCAN Meta-GGA Density Functional, NPJ Comput Mater 4, 60 (2018).

6. F. Kong, R. C. Longo, M.-S. Park, J. Yoon, D.-H. Yeon, J.-H. Park, W.-H. Wang, S. KC, S.-G. Doo, and K. Cho, Ab Initio Study of Doping Effects on LiMnO2 and Li2MnO3 Cathode Materials for Li-Ion Batteries, J Mater Chem A Mater 3, 8489 (2015).

7. V. R. Galakhov, E. Z. Kurmaev, St. Uhlenbrock, M. Neumann, D. G. Kellerman, and V. S. Gorshkov, Electronic Structure of LiNiO2, LiFeO2 and LiCrO2: X-Ray Photoelectron and X-Ray Emission Study, Solid State Commun 95, 347 (1995).

8.K. Kushida and K. Kuriyama, Narrowing of the Co-3d Band Related to the Order–Disorder Phase Transition in LiCoO2, Solid State Commun 123, 349 (2002).

9. J. van Elp, J. L. Wieland, H. Eskes, P. Kuiper, G. A. Sawatzky, F. M. F. de Groot, and T. S. Turner, Electronic Structure of CoO, Li-Doped CoO, and LiCoO2, Phys Rev B 44, 6090 (1991).

10. S. Laubach, S. Laubach, P. C. Schmidt, D. Ensling, S. Schmid, W. Jaegermann, A. Thißen, K. Nikolowski, and H. Ehrenberg, Changes in the Crystal and Electronic Structure of LiCoO2 and LiNiO2 upon Li Intercalation and De-Intercalation, Physical Chemistry Chemical Physics 11, 3278 (2009).

11. D.-H. Seo, A. Urban, and G. Ceder, Calibrating Transition-Metal Energy Levels and Oxygen Bands in First-Principles Calculations: Accurate Prediction of Redox Potentials and Charge Transfer in Lithium Transition-Metal Oxides, Phys Rev B 92, 115118 (2015).

12. Boev, A. O., Fedotov, S. S., Abakumov, A. M., Stevenson, K. J., Henkelman, G., & Aksyonov, D. A. (2021). The role of antisite defect pairs in surface reconstruction of layered AMO2 oxides: A DFT+ U study. Applied Surface Science, 537, 147750.

The authors did not provide any information on the DFT correction of the layered system. LiCoO2 is a layered material and van der Waals’ correction needs to be incorporated in the DFT total energy calculation. Why van der Walls’s correction was not included in their DFT simulation?

We discovered that the influence of van der Waals correction on segregation energies in fully lithiated oxide is relatively minor, resulting in a decrease of less than 0.1 eV. Nonetheless, we acknowledge that its significance may increase for delithiated structures.

To confirm our statement the following additional results were added to SI Section7.3:

To evaluate the impact of van der Waals' (vdW) contribution, we conducted calculations of the segregation energy for several cases, including Al, Mn, and Ti, using the D3 van der Waals correction, which is one of the most commonly employed dispersion correction methods [1-2]. The resulting values are summarized in Table S25. It is evident that for all cases, the energy decreases by less than 0.1 eV, without altering the overall trend.

The limited impact of van der Waals correction on segregation energies aligns with previous findings, which demonstrated that in lithiated layered oxides LixMO 2 (M = Ni, Co, Mn), the influence of vdW correction on lattice constants, band gaps (see Table S26), local magnetic moments, and intercalation potentials is negligible [3]. However, as highlighted by Chakraborty et al. [3], upon delithiation (x<0.5), the intercalation potential increases by 0.5 V, indicating that vdW correction should not be disregarded when studying segregation energy in strongly delithiated oxides.

Table S25. Impact of vdW correction on segregation energy (E seg ) in eV, calculated for LiCoO 2 (104) surface.

References 1.Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem.Phys. 2010, 132, 154104.

2.Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J.Comput. Chem. 2011, 32, 1456-1465.

3. A. Chakraborty, M. Dixit, D. Aurbach, and D. T. Major, Predicting Accurate Cathode Properties of Layered Oxide Materials Using the SCAN Meta-GGA Density Functional, Npj Comput. Mater. 4, 60 (2018).

4. J. van Elp, J. L. Wieland, H. Eskes, P. Kuiper, G. A. Sawatzky, F. M. F. de Groot, and T. S. Turner, Electronic Structure of CoO, Li-Doped CoO, and LiCoO2, Phys. Rev. B 44, 6090 (1991).

5. Rosolen, J. M., & Decker, F. (2001). Photoelectrochemical behavior of LiCoO2 membrane electrode. Journal of Electroanalytical Chemistry, 501(1-2), 253-259.

6. Rao, M. C., & Hussain, O. M. (2009). Spectroscopic investigations on tetravalent doped LiCoO2 thin film cathodes. The European Physical Journal-Applied Physics, 48(2), 20503.

7. Kushida, K., & Kuriyama, K. (2001). Optical absorption related to Co-3d bands in sol–gel grown LiCoO2 films. Solid state communications, 118(12), 615-618.

8. O. Y. Long, G. Sai Gautam, and E. A. Carter, Assessing Cathode Property Prediction via Exchange-Correlation Functionals with and without Long-Range Dispersion Corrections, Phys. Chem. Chem. Phys. 23, 24726 (2021).

What is the “n” value for different doped systems in Eq. 1 that the authors used in their calculation? How does that compare with the experimental maximum concentration of M (“x” values in Table 1)? How does the solubility and surface segregation vary with the concentration of M (n value)?

While we did not conduct a comprehensive study on the impact of concentration (n = = 32, x = 1/n = 3%) on solubility and segregation, a single benchmark revealed that transitioning from a dilute regime (6%) to a surface concentration of 25% monolayer increased segregation energy by 0.05 eV, from −0.35 to −0.30 eV. This suggests that dopant-dopant interactions remain insignificant up to relatively high concentrations. However, the implications of a monolayer-like concentration warrant further investigation.

The following section about the impact of concentrations was added to SI Section S7.1:

All solution energies presented in the main text are computed for n = 32, corresponding to our bulk supercell with 128 atoms. The corresponding x value is calculated as 1/n, which equals 1/32 = 3%. Our convergence study (Table S22) demonstrates that the interaction between dopants at these concentrations is minimal (<0.1 eV), indicating that our calculated values pertain to the dilute solid solution regime. This concentration is notably smaller than some experimentally observed solubilities with x values ranging from 0.1 to 1, where solute-solute interactions may contribute additionally. However, we did not investigate solute-solute interactions extensively, as it diverges somewhat from our primary objective. The concept of segregation is typically applied with average dopant concentrations relatively low, such as 0.1-1%, but with significant segregation energies leading to higher enrichment at surfaces. Therefore, we consider choosing a bulk concentration of 3% as a reasonable reference for calculating segregation energies.

In the case of surface segregation, the concentration can reach up to 100%, corresponding to a full monolayer of dopant. Despite this, we consistently adhered to the dilute solid solution regime for surface segregation by employing relatively large 224-atom slabs with a surface concentration of 0.7 nm -2 (6%). A single benchmark revealed that transitioning from a diluteregime (6%) to a surface concentration of 25% monolayer increased segregation energy by 0.05 eV, from -0.35 to -0.30 eV (Table S23). This suggests that dopant-dopant interactions remain insignificant up to relatively high concentrations. However, the implications of a monolayer-like concentration warrant further investigation.

Table S22. Solution energy (eV) of substitution defects in LiCoO 2 as a function of supercell size (Å) and number of atoms.

Table S23. Influence of (104) surface area on Fe segregation energy in NaCoO 2 , calculated relative to Fe solution in a 128-atom bulk supercell. Magnetic moments (μ B ) on surface atoms are indicated in bold. Surface concentration is provided per surface area (nm -2 ) and per number of TM atoms in the surface layer (%).

The authors have used density functional theory (DFT)-based calculations to examine the surface segregation of dopants (Mg, Al, Ti, V, Cr, Mn, Fe, and Ni) in LiCoO2. The understanding of surface segregation will be helpful in designing layered-oxide-based electrodes in Li-ion materials that are better resistant to structural degradation and/or oxygen loss upon anionic oxidation. The comparison with experimental data is patchy (i.e., there are notable disagreements with experimental observations), this can be due to the nature of the experimental data that is available. Overall, the study is quite well-structured, the analysis sound, and the calculations are rigorous. I recommend the publication of the manuscript in Physical Review Materials with minor revision, after the authors address the following comments.

I don't think solution energies as the authors have defined are giving them the right tendency of ions to occupy the bulk Co sites within LiCoO2. This is simply due to the kind of 'isostructure' reference energy that the authors take. Why not take defect formation energies as the scale? Or always take the most stable set of phases thermodynamically as the reference composition?

We fully agree that the right way to estimate solubilities would be to take the most thermodynamically stable set of phases as the reference composition. This is what we tried for Mg, Ti, and V and provided data in Table S3. The problem is that once we switch to a set of phases, we should refer to the synthesis conditions and correctly define the chemical potentials of Li and O at finite temperatures and pressure leading us to the necessity to construct the complete quaternary phase diagrams (Li - Co - M - O). This is a highly complex task, which we suggest to avoid to focus on the main goal of the work.

In Table I, we provide E s (SG), calculated relative to the thermodynamically most stable LiMO 2 phase. The latter serves as an improved estimate of solubility than the ‘isostructure’ reference energy - E s (R-3m), also we expect that it gives correct tendencies for Ni, Mn, Al, Cr, and Fe. For these elements, LiMO 2 is more stable than any combination of other phases basedon the Materials Project database. Nevertheless, to avoid confusion of readers we add the following remark at the start of of Section IIIA:

“The solution energies provided are model-based, assuming that the most stable phase within LiCoO2 during synthesis is LiMO2, which is expected to be the case for Al, Ni, Mn, Fe, and Cr. However, establishing this assumption rigorously, particularly for Mg, V, and Ti, would necessitate constructing quaternary phase diagrams. As this is beyond the scope of our current objectives, any correlation drawn between our calculated solution energies (Es) and experimental solubilities should be considered conjectural.”

The higher segregating energies that the authors obtain for the low-spin surfaces is not due to the higher energy of the low-spin surface than the intermediate-spin surface? The explanation given (of Co switching from low-spin to intermediate-spin state, page 4) seems a little strange.

We acknowledge your point, which presents a very reasonable perspective. Upon further analysis, we recognize that the segregation process can be decomposed into two distinct processes: (i) the migration of the dopant from the bulk to the surface, and (ii) the relocation of the surface Co atom into the bulk. Upon focusing on the second process, a significant contrast emerges between LS and IS surfaces. In the case of the LS surface, the Co atom consistently maintains a low spin state, whereas for the IS surface, the Co atom must alter its spin state upon transitioning into the bulk. Consequently, the second process is more favorable for the LS surface, a consequence of its higher energy in comparison to the IS surface. We have incorporated this refined explanation into Section IIIC for clarity.

Nevertheless, our original explanation is still valid, albeit it may not have been articulated clearly. We have revised it in Section IIIC as follows:

“Another contributing factor in the case of the LS surface is the transformation of one surface Co atom, positioned adjacent to the dopant, from a LS to an IS state (Figure S3). However, when the dopant resides within the bulk, all surface Co atoms remain in the LS state. Consequently, when computing the energy difference between the two slabs, our segregation energy ($E_{seg}$) can be expressed as the sum of two terms: $E_{seg}$ (all surface Co in LS) + $\Delta E$ (Co LS → IS). This latter term accounts for the decrease in energy resulting from the transition of one surface Co atom from the LS to the IS state, thus contributing to the decrease in our $E_{seg}$.”

The authors can include a little bit more discussion on what could be possible scenarios for a dopant that is segregating vis-a-vis oxygen generation within the bulk. The motivation of the study, as described in their introduction, doesn't seem well-connected in the discussion.

We extended the discussion section in the following way:

“ Experimental studies have widely established that LiNiO2 or Ni-rich layered oxides exhibit a higher tendency for oxygen release compared to LiCoO2 [83, 84]. This observation is further supported by DFT calculations of surface oxygen vacancies formation energies (Evac), commonly utilized as a descriptor of oxygen stability [85,86]. For instance, Evac in LiNiO2 is calculated at 1.1 eV, while in LiCoO2, it stands at 1.8 eV in the fully intercalated state, with a significant decrease upon deintercalation [87]. Consequently, the segregation of nickel is expected to facilitate oxygen release, potentially elucidating the observed negative impact of nickel segregation reported in previous studies [17, 18].

The trends observed in Evac across different transition metals and levels of intercalation are not straightforward. During deintercalation, Evac in LiCoO2 decreases from 1.8 to 0.4 eV, whereas in LiMnO2, it decreases from 3.2 to 0.8 eV [87]. This indicates that manganese segregation can enhance oxygen stability, particularly in deintercalated states. However, this analysis is valid only if the surface maintains its layered structure and remains unreconstructed. Upon reconstruction into spinel or rocksalt structures, the role of dopants may vary, as demonstrated by Yoon, where Ni-induced reconstruction proved beneficial[23]. Such surfacetransformations to reduced spinel-like and rocksalt structures are well-documented [83]. While they are often viewed as detrimental, they also serve a protective function by mitigating further oxygen release. The issue arises when the layer becomes too thick, hindering lithium diffusion. In this manner, surface segregation may serve as a catalyst for electrochemically more favorable reconstructions.

Another indirect consequence of surface segregation may lie in its influence on the migration barriers of oxygen vacancies. Studies have shown that oxygen vacancies formed at the surface have a propensity to diffuse inward, contributing to material degradation [83]. It is conceivable that certain segregating elements, while facilitating the formation of vacancies, may also immobilize them by promoting stronger M-v O bonding and increasing the migration barrier for oxygen vacancies. This impediment could restrict their diffusion either inward towards the bulk or across the surface, preventing the formation of oxygen vacancy clusters. The clustering of oxygen vacancies is known to be highly detrimental [83], therefore, the impact of segregation on clustering should also be thoroughly investigated.

In addition to oxygen vacancies, the formation of surface Li/TM antisites represents another crucial process, particularly during the transformation from layered to spinel and rocksalt structures. Previous research employing DFT+U calculations has demonstrated that the formation of Li/TM antisite pairs is more favorable at the surface compared to the bulk [8], thus providing insight into the surface's inclination towards reconstruction. However, the influence of segregation on surface antisites remains an open question and warrants further investigation. ”

8. A. Boev, S. Fedotov, A. Abakumov, K. Stevenson, G. Henkelman, and D. Aksyonov, Applied Surface Science 537, 147750 (2021)

17. H. Dixit, W. Zhou, J.-C. Idrobo, J. Nanda, and V. R. Cooper, Acs Nano 8, 12710 (2014).

18 P. Yan, J. Zheng, J. Zheng, Z. Wang, G. Teng, S. Kuppan, J. Xiao, G. Chen, F. Pan, J.-G. Zhang, et al., Advanced Energy Materials 6, 1502455 (2016)

23. M. Yoon, Y. Dong, Y. Yoo, S. Myeong, J. Hwang, J. Kim, S.-H. Choi, J. Sung, S. J. Kang, J. Li, et al., Advanced Functional Materials 30, 1907903 (2020)

83. H. Zhang, H. Liu, L. F. Piper, M. S. Whittingham, and G. Zhou, Chemical reviews 122, 5641 (2022).

84. S. S. Zhang, Energy Storage Materials 24, 247 (2020)

85. Y. Gao, X. Wang, J. Ma, Z. Wang, and L. Chen, Chemistry of Materials 27, 3456 (2015).

86. A. V. Morozov, I. A. Moiseev, A. A. Savina, A. O. Boev, D. A. Aksyonov, L. Zhang, P. A. Morozova, V. A.Nikitina, E. M. Pazhetnov, E. J. Berg, et al., Chemistry of Materials 34, 6779 (2022)

87.W. Hu, H. Wang, W. Luo, B. Xu, and C. Ouyang, Solid State Ionics 347, 115257 (2020)