#
First Principles Calculations of the Optical Response of LiNiO_{2}

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## Abstract

**:**

## 1. Introduction

## 2. Computational Methods

## 3. Results and Discussions

#### 3.1. Structural Properties

#### 3.2. Electronic Structures

#### 3.3. Optical Properties

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BZ | Brillouin Zone |

DFT | Density Functional Theory |

DOS | Density of states |

GGA | Generalized Gradient approximation |

LIB | Lithium-Ion Battery |

LNO | Lithium Nickel Oxide |

PAW | Projector-Augmented-Wave |

PBE | Perdew–Burke–Ernzerhof |

PDOS | Partial density of states |

RIXS | Resonant Inelastic X-ray Scattering (RIXS) |

SCAN | Strongly constrained and appropriately normed |

XRD | X-ray diffraction |

## References

- Larcher, D.; Tarascon, J. Towards greener and more sustainable batteries for electrical energy storage. Nat. Chem.
**2015**, 7, 19–29. [Google Scholar] [CrossRef] [PubMed] - Arumugam, M.; James, C.; Seung-Taek, M.; Seung-Min, O.; Yang-Kook, S. Nickel-Rich and Lithium-Rich Layered Oxide Cathodes: Progress and Perspectives. Adv. Energy Mater.
**2016**, 6, 1501010. [Google Scholar] [CrossRef] - Arumugam, M. A reflection on lithium-ion battery cathode chemistry. Nature
**2020**, 11, 1550. [Google Scholar] [CrossRef] - Zhang, H.; Li, C.; Eshetu, G.; Laruelle, S.; Grugeon, S.; Zaghib, K.; Julien, C.; Mauger, A.; Guyomard, D.; Rojo, T.; et al. From Solid-Solution Electrodes and the Rocking-Chair Concept to Today’s Batteries. Angew. Chem. Int. Ed.
**2020**, 59, 534–538. [Google Scholar] [CrossRef] [PubMed] - Du Pasquier, A.; Plitz, I.; Menocal, S.; Amatucci, G. A comparative study of Li-ion battery, supercapacitor and nonaqueous asymmetric hybrid devices for automotive applications. J. Power Sources
**2003**, 115, 171–178. [Google Scholar] [CrossRef] - Kim, Y.; Seong, W.M.; Manthiram, A. Cobalt-free, high-nickel layered oxide cathodes for lithium-ion batteries: Progress, challenges, and perspectives. Energy Storage Mater.
**2021**, 34, 250–259. [Google Scholar] [CrossRef] - Schipper, F.; Erickson, E.M.; Erk, C.; Shin, J.; Francois, F.C.; Aurbach, D. Review—Recent Advances and Remaining Challenges for Lithium Ion Battery Cathodes. J. Electrochem. Soc.
**2016**, 164, A6220–A6228. [Google Scholar] [CrossRef] - Bianchini, M.; Roca-Ayats, M.; Hartmann, P.; Brezesinski, T.; Janek, J. There and Back Again—The Journey of LiNiO
_{2}as a Cathode Active Material. Angew. Chem. Int. Ed.**2019**, 58, 10434–10458. [Google Scholar] [CrossRef] - Anisimov, V.I.; Zaanen, J.; Andersen, O.K. Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B
**1991**, 44, 943–954. [Google Scholar] [CrossRef] - Devi, A.A.S.; Nokelainen, J.; Barbiellini, B.; Devaraj, M.; Alatalo, M.; Bansil, A. Re-examining the giant magnetization density in α -Fe
_{1}6N_{2}with the SCAN+U method. Phys. Chem. Chem. Phys.**2022**, 24, 17879–17884. [Google Scholar] [CrossRef] - El-Bana, M.; El Radaf, I.; Fouad, S.; Sakr, G. Structural and optoelectrical properties of nanostructured LiNiO
_{2}thin films grown by spray pyrolysis technique. J. Alloys Compd.**2017**, 705, 333–339. [Google Scholar] [CrossRef] - Wang, Y.J.; Barbiellini, B.; Lin, H.; Das, T.; Basak, S.; Mijnarends, P.E.; Kaprzyk, S.; Markiewicz, R.S.; Bansil, A. Lindhard and RPA susceptibility computations in extended momentum space in electron-doped cuprates. Phys. Rev. B
**2012**, 85, 224529. [Google Scholar] [CrossRef] - Barbiellini, B.; Hancock, J.N.; Monney, C.; Joly, Y.; Ghiringhelli, G.; Braicovich, L.; Schmitt, T. Inelastic x-ray scattering from valence electrons near absorption edges of FeTe and TiSe
_{2}. Phys. Rev. B**2014**, 89, 235138. [Google Scholar] [CrossRef] - Li, N.; Sallis, S.; Papp, J.K.; Wei, J.; McCloskey, B.D.; Yang, W.; Tong, W. Unraveling the cationic and anionic redox reactions in a conventional layered oxide cathode. ACS Energy Lett.
**2019**, 4, 2836–2842. [Google Scholar] [CrossRef] - Kresse, G.; Furthmüller, J. Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci.
**1996**, 6, 15–50. [Google Scholar] [CrossRef] - Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B
**1999**, 59, 1758–1775. [Google Scholar] [CrossRef] - Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B
**1994**, 50, 17953–17979. [Google Scholar] [CrossRef] [PubMed] - Perdew, J.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef] - Tuccillo, M.; Palumbo, O.; Pavone, M.; Muñoz-García, A.; Paolone, A.; Brutti, S. Analysis of the Phase Stability of LiMO
_{2}Layered Oxides (M = Co, Mn, Ni). Crystals**2000**, 10, 526. [Google Scholar] [CrossRef] - Wang, L.; Maxisch, T.; Ceder, G. Analysis of the Phase Stability of LiMO
_{2}Layered Oxides (M = Co, Mn, Ni). Phys. Rev. B**2006**, 73, 195107. [Google Scholar] [CrossRef] [Green Version] - Jain, A.; Hautier, G.; Ping Ong, S.; Moore, C.; Fischer, C.; Persson, K.; Ceder, G. Formation enthalpies by mixing GGA and GGA + U calculations. Phys. Rev. B
**2011**, 84, 045115. [Google Scholar] [CrossRef] - Sun, J.; Ruzsinszky, A.; Perdew, J.P. Strongly Constrained and Appropriately Normed Semilocal Density Functional. Phys. Rev. Lett.
**2015**, 115, 036402. [Google Scholar] [CrossRef] [PubMed] - Sun, J.; Remsing, R.C.; Zhang, Y.; Sun, Z.; Ruzsinszky, A.; Peng, H.; Yang, Z.; Paul, A.; Waghmare, U.; Wu, X.; et al. Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional. Nat. Chem.
**2016**, 8, 831–836. [Google Scholar] [CrossRef] [PubMed] - Monkhorst, H.J.; Pack, J.D. Special points for Brillouin-zone integrations. Phys. Rev. B
**1976**, 13, 5188–5192. [Google Scholar] [CrossRef] - Gajdoš, M.; Hummer, K.; Kresse, G.; Furthmüller, J.; Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Phys. Rev. B
**2006**, 73, 045112. [Google Scholar] [CrossRef] - Liu, Y.; Lian, J.; Sun, Z.; Zhao, M.; Shi, Y.; Song, H. The first-principles study for the novel optical properties of LiTi
_{2}O_{4}, Li_{4}Ti_{5}O_{1}2, Li_{2}Ti_{2}O_{4}and Li_{7}Ti_{5}O_{1}2. Chem. Phys. Lett.**2017**, 677, 114–119. [Google Scholar] [CrossRef] - Altarelli, M.; Dexter, D.L.; Nussenzveig, H.M.; Smith, D.Y. Superconvergence and Sum Rules for the Optical Constants. Phys. Rev. B
**1972**, 6, 4502–4509. [Google Scholar] [CrossRef] - Laubach, S.; Laubach, S.; Schmidt, P.C.; Ensling, D.; Schmid, S.; Jaegermann, W.; Thißen, A.; Nikolowski, K.; Ehrenberg, H. Changes in the crystal and electronic structure of LiCoO
_{2}and LiNiO_{2}upon Li intercalation and de-intercalation. Phys. Chem. Chem. Phys.**2009**, 11, 3278–3289. [Google Scholar] [CrossRef] - Hoang, K.; Johannes, M.D. Defect chemistry in layered transition-metal oxides from screened hybrid density functional calculations. J. Mater. Chem. A
**2014**, 2, 5224–5235. [Google Scholar] [CrossRef] - Hoang, K.; Johannes, M.D. Defect physics in complex energy materials. J. Phys. Condens. Matter
**2018**, 30, 293001. [Google Scholar] [CrossRef] [Green Version] - Chakraborty, A.; Dixit, M.; Aurbach, D.; Major, D.T. Predicting accurate cathode properties of layered oxide materials using the SCAN meta-GGA density functional. NPJ Comput. Mater.
**2018**, 4, 1–9. [Google Scholar] [CrossRef] - Jain, A.; Ong, S.P.; Hautier, G.; Chen, W.; Richards, W.D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; et al. Commentary: The Materials Project: A materials genome approach to accelerating materials innovation. APL Mater.
**2013**, 1, 011002. [Google Scholar] [CrossRef] - Välikangas, J.; Laine, P.; Hietaniemi, M.; Hu, T.; Tynjälä, P.; Lassi, U. Precipitation and Calcination of High-Capacity LiNiO
_{2}Cathode Material for Lithium-Ion Batteries. Appl. Sci.**2020**, 10, 8988. [Google Scholar] [CrossRef] - Sicolo, S.; Mock, M.; Bianchini, M.; Albe, K. Furthermore, Yet It Moves: LiNiO
_{2}, a Dynamic Jahn–Teller System. Chem. Mater.**2020**, 32, 10096–10103. [Google Scholar] [CrossRef] - Setyawan, W.; Curtarolo, S. High-throughput electronic band structure calculations: Challenges and tools. Comput. Mater. Sci.
**2010**, 49, 299–312. [Google Scholar] [CrossRef] - Fox, M. Optical Properties of Solids, 2nd ed.; Oxford Master Series in Condensed Matter Physics; Oxford University Press: Oxford, UK, 2010. [Google Scholar]
- Craco, L.; Leoni, S. Electrodynamics and quantum capacity of Li
_{x}FePO_{4}battery material. Appl. Phys. Lett.**2011**, 99, 192103. [Google Scholar] [CrossRef] - Radha, S.K.; Lambrecht, W.R.L.; Cunningham, B.; Grüning, M.; Pashov, D.; van Schilfgaarde, M. Optical response and band structure of LiCoO
_{2}including electron-hole interaction effects. Phys. Rev. B**2021**, 104, 115120. [Google Scholar] [CrossRef] - Scafetta, M.D.; Cordi, A.M.; Rondinelli, J.M.; May, S.J. Band structure and optical transitions in LaFeO
_{3}: Theory and experiment. J. Phys. Condens. Matter**2014**, 26, 505502. [Google Scholar] [CrossRef] - Tan, G.; DeNoyer, L.; French, R.; Guittet, M.; Gautier-Soyer, M. Kramers–Kronig transform for the surface energy loss function. J. Electron Spectrosc. Relat. Phenom.
**2005**, 142, 97–103. [Google Scholar] [CrossRef] - Jia, Y.; Ye, Y.; Liu, J.; Zheng, S.; Lin, W.; Wang, Z.; Li, S.; Pan, F.; Zheng, J. Breaking the energy density limit of LiNiO
_{2}: Li_{2}NiO_{3}or Li_{2}NiO_{2}? Sci. China Mater.**2022**, 65, 913–919. [Google Scholar] [CrossRef] - Prange, M.P.; Rehr, J.J.; Rivas, G.; Kas, J.J.; Lawson, J.W. Real space calculation of optical constants from optical to x-ray frequencies. Phys. Rev. B
**2009**, 80, 155110. [Google Scholar] [CrossRef] - Hafiz, H.; Suzuki, K.; Barbiellini, B.; Tsuji, N.; Yabuuchi, N.; Yamamoto, K.; Orikasa, Y.; Uchimoto, Y.; Sakurai, Y.; Sakurai, H.; et al. Tomographic reconstruction of oxygen orbitals in lithium-rich battery materials. Nature
**2021**, 564, 213–216. [Google Scholar] [CrossRef] [PubMed] - Chabaud, S.; Bellin, C.; Mauri, F.; Loupias, G.; Rabii, S.; Croguennec, L.; Pouillerie, C.; Delmas, C.; Buslaps, T. Electronic density distorsion of NiO
_{2}due to intercalation by Li. J. Phys. Chem. Solids**2004**, 65, 241–243. [Google Scholar] [CrossRef] - Suzuki, K.; Otsuka, Y.; Hoshi, K.; Sakurai, H.; Tsuji, N.; Yamamoto, K.; Yabuuchi, N.; Hafiz, H.; Orikasa, Y.; Uchimoto, Y.; et al. Magnetic Compton Scattering Study of Li-Rich Battery Materials. Condens. Matter
**2022**, 7, 4. [Google Scholar] [CrossRef]

**Figure 1.**Crystallographic monoclinic (mC8) structure of LiNiO${}_{2}$ [ Li (green), Ni (blue), and Oxygen (red)]. The image was obtained from DFT structure relaxation.

**Figure 2.**X-ray diffraction pattern (Cu-K$\alpha $ radiation) of the monoclinic (mC8) structure of LiNiO${}_{2}$ using the VESTA software.

**Figure 3.**Partial densities of states (PDOSs) associated with the Li-s, Ni-d, and O-p states in various LNO crystal structures based on GGA (left column) and GGA+U (right column). GGA based results: (

**a**) mC8, (

**c**) op8, and (

**e**) P2${}_{1}$/C. GGA+U based results: (

**b**) mC8, (

**d**) op8, and (

**f**) P2${}_{1}$/C. The dashed vertical line marks the Fermi level.

**Figure 4.**Band structure of LiNiO${}_{2}$. Solid and dashed lines denote the spin-up and spin-down band structure, respectively.

**Figure 5.**(

**a**) The computed real part, ${\epsilon}_{1}\left(\omega \right)$, and (

**b**) the imaginary part, ${\epsilon}_{2}\left(\omega \right)$, of the dielectric function as a function of energy in LNO.

**Figure 7.**(

**a**) The computed Tauc plot of ${\left(\alpha h\nu \right)}^{0.5}$ in units of ${\left(eVc{m}^{-1}\right)}^{0.5}$ and (

**b**) the energy-loss spectrum of LNO.

**Table 1.**Lattice parameters and the volume per atom after full relaxation with GGA, GGA+U with U = 4 eV, SCAN, and SCAN+U with U = 2 eV. Experimental values are given [8].

Lattice Parameters | GGA | GGA+U | SCAN | SCAN+U | Exp. |
---|---|---|---|---|---|

a (Å) | 4.839 | 4.799 | 4.779 | 4.749 | 4.99 |

b (Å) | 2.799 | 2.789 | 2.778 | 2.765 | 2.83 |

c (Å) | 5.109 | 5.129 | 5.093 | 5.054 | 5.07 |

$\beta $ (${}^{o}$) | 112.701 | 112.429 | 112.064 | 112.195 | 109.7 |

V (Å${}^{3}$/atom) | 7.980 | 7.932 | 7.833 | 7.681 | 8.426 |

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**MDPI and ACS Style**

Kothalawala, V.N.; Sasikala Devi, A.A.; Nokelainen, J.; Alatalo, M.; Barbiellini, B.; Hu, T.; Lassi, U.; Suzuki, K.; Sakurai, H.; Bansil, A.
First Principles Calculations of the Optical Response of LiNiO_{2}. *Condens. Matter* **2022**, *7*, 54.
https://doi.org/10.3390/condmat7040054

**AMA Style**

Kothalawala VN, Sasikala Devi AA, Nokelainen J, Alatalo M, Barbiellini B, Hu T, Lassi U, Suzuki K, Sakurai H, Bansil A.
First Principles Calculations of the Optical Response of LiNiO_{2}. *Condensed Matter*. 2022; 7(4):54.
https://doi.org/10.3390/condmat7040054

**Chicago/Turabian Style**

Kothalawala, Veenavee Nipunika, Assa Aravindh Sasikala Devi, Johannes Nokelainen, Matti Alatalo, Bernardo Barbiellini, Tao Hu, Ulla Lassi, Kosuke Suzuki, Hiroshi Sakurai, and Arun Bansil.
2022. "First Principles Calculations of the Optical Response of LiNiO_{2}" *Condensed Matter* 7, no. 4: 54.
https://doi.org/10.3390/condmat7040054