# Application of First Principles Computations Based on Density Functional Theory (DFT) in Cathode Materials of Sodium-Ion Batteries

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle of DFT Calculation

## 3. Application of DFT Calculation in Transition-Metal Oxides/Chalcogenides

#### 3.1. Energy Calculation and Structural Stability Judgment

_{x}Ni

_{y}Co

_{1−y}O

_{2}material has thermodynamic stability or metastable state at the typical P2 synthesis temperature (≈1000 K) and can successfully synthesize new P2 compounds with Ni

_{3+/4+}and ${\mathrm{Co}}^{3+/4+}$.This work expanded the current knowledge of P2 materials.

^{1}-${\mathrm{O}}_{2}$, reduces the total energy of charged structures, and promotes the migration of transition metals.

#### 3.2. Ion/Molecular Diffusion Dynamics Simulation

_{2/3}Fe

_{2/3}Mn

_{1/3}O

_{2}with the same stoichiometry and used the DFT calculation to study the diffusion of ${\mathrm{Na}}^{+}$ in them. Through calculation and comparison, they found ${\mathrm{Na}}^{+}$ diffusion resistance of the P2 phase was still lower than that of the O3 phase after excluding factors, such as sodium-ion content and the oxidation state of transition metals. This also proves the diffusion ability of sodium ions in two phases is mainly related to the structure.

_{x}Se

_{y}@CN has higher ${\mathrm{Na}}^{+}$ ion diffusion coefficient than pure Fe

_{x}Se

_{y}through calculation. They thought the Ni-doped carbon layer coated on the surface of the ${\mathrm{Fe}}_{\mathrm{x}}{\mathrm{Se}}_{\mathrm{y}}$ micro rod may be the reason for accelerating charge transfer and Na

^{+}ion diffusion.

#### 3.3. Analysis of Electronic Structure

## 4. Application of DFT Calculation in Polyanionic Compounds

#### 4.1. Energy Calculation and Structural Stability Judgment

_{3.41}£

_{0.59}FeV(PO

_{4})

_{3}, in its original state and charged state, Mohammed et al. [47] determined the five most favorable original state structures and the eight most favorable charged state structures through coulomb energy analysis. Then, they used their DFT calculations, respectively, and finally obtained the structure with the lowest total energy. Jian et al. [48] also calculated the voltage curve of ${\mathrm{Na}}_{\mathrm{x}}{\mathrm{V}}_{2}{{(\mathrm{PO}}_{4})}_{3}$ before the experiment and found when x is between 1 and 3, the calculated voltage is 3.4 V, but when x is between 3 and 4, the calculated voltage is quite different from the experimental result, shown in Table 1.

_{3}Zr

_{2}(SiO

_{4})

_{2}(PO

_{4}) and Ge doped ${\mathrm{Na}}_{3}{\mathrm{Zr}}_{1.875}{\mathrm{Ge}}_{0.125}{\mathrm{Si}}_{2}{\mathrm{PO}}_{12}$ materials in the rhombohedral and monoclinic phases, respectively. They found before Ge doping, the free energies of the two phases had little difference, but after Ge doping, the energy difference of the two phases reached 13 kJ ${\mathrm{mol}}^{-1}$, and the rhombohedral phase was more stable, and the conductivity of the material was also improved.

#### 4.2. Ion/Molecular Diffusion Dynamics Simulation

#### 4.3. Analysis of Electronic Structure

## 5. Application of DFT Calculation in Prussian Blue

#### 5.1. Energy Calculation and Structural Stability Judgment

_{2}H

_{5}OH material using the DFT method. According to the results of calculation and simulation, they found the OH groups in the material are more inclined to adsorb on the edge and vertex of the crystal, which makes it difficult for the crystal core to grow at these positions, thus making the PB material to present a flower-like structure. To explore the role of ${\mathrm{Na}}^{+}$ ions in the structural evolution of NaMnHCF when they are introduced, through DFT calculation, Xiao et al. [51] found when sodium is added, the increase of ${\mathrm{Na}}^{+}$ makes the coulomb gravity of Na-N increase, thus reducing the distance between them and forming a rhombohedral lattice with less distortion.

#### 5.2. Ion/Molecular Diffusion Dynamics Simulation

_{sodiation}) of the unit cell in which a sodium ion is inserted into FeHCF and BR-FeHCF are 4.757 and 1.152 eV, respectively, indicating sodium ions can enter the latter more easily and effectively.

^{+}co-migration, the migration barrier of Na

^{+}collective migration one by one is the lowest, which is 0.28 eV. It indicates Na

^{+}is more inclined to co-migrate step by step.

#### 5.3. Analysis of Electronic Structure

## 6. Application of DFT Calculation in Organic Materials

#### 6.1. Energy Calculation and Structural Stability Judgment

#### 6.2. Ion/Molecular Diffusion Dynamics Simulation

#### 6.3. Analysis of Electronic Structure

## 7. Outlook and Personal Perspectives

- DFT calculation can effectively predict the electronic structure of materials, such as the highest occupied molecular orbital, the lowest unoccupied energy level orbital, band gap, etc. Thus, it can predict the physical and chemical properties of various molecules and nanoparticles of the cathode materials of sodium-ion batteries, greatly accelerating the identification, characterization, and optimization of materials.
- The electron transport properties can be predicted by combining with DFT, which can effectively predict the transport and diffusion of sodium ions in materials, thus predicting their sodium-ion conductivity.
- Based on the existing material database, the stability of the sodium-ion battery can be predicted. Therefore, the feasibility prediction is carried out before the experiment, which greatly saves the time and costs of the experiment and has guiding significance for the experimental process.
- The combined DFT calculation with relevant characterization techniques were taken as a supplement and extension of experimental disciplines to better understand the structure–activity relationship between material structure and performance; it can provide a scientific theoretical basis for the development and design of cathode materials for sodium-ion batteries.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Dunn, B.; Kamath, H.; Tarascon, J.M. Electrical energy storage for the grid: A battery of choices. Science
**2011**, 334, 928–935. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lu, Y.X.; Zhao, C.L.; Rong, X.H.; Chen, L.Q.; Hu, Y.S. Research progress of materials and devices for room-temperature Na-ion batteries. Acta Phys. Sin.
**2018**, 67, 120601. [Google Scholar] - Delmas, C. Sodium and Sodium-Ion Batteries: 50 Years of Research. Adv. Energy Mater.
**2018**, 8, 1703137. [Google Scholar] [CrossRef] - Pan, H.L.; Hu, Y.S.; Chen, L.Q. Room-temperature stationary sodium-ion batteries for large-scale electric energy storage. Energy Environ. Sci.
**2013**, 6, 2338–2360. [Google Scholar] [CrossRef] - Kubota, K.; Komaba, S. Review-Practical Issues and Future Perspective for Na-Ion Batteries. J. Electrochem. Soc.
**2015**, 162, A2538–A2550. [Google Scholar] [CrossRef] - Palomares, V.; Casas-Cabanas, M.; Castillo-Martinez, E.; Han, M.H.; Rojo, T. Update on Na-based battery materials. A growing research path. Energy Environ. Sci.
**2013**, 6, 2312–2337. [Google Scholar] [CrossRef] - Coetzer, J. A new high-energy density battery system. J. Power Sources
**1986**, 18, 377–380. [Google Scholar] [CrossRef] - Okada, S.; Takahashi, Y.; Kiyabu, T. 210th ECS Meeting Abstracts; MA2006-02; Electrochemical Society (ECS): Pennington, NJ, USA, 2006. [Google Scholar]
- Winter, M.; Barnett, B.; Xu, K. Before Li ion batteries. Chem. Rev.
**2018**, 118, 11433–11456. [Google Scholar] [CrossRef] - Li, L.L.; Yu, D.S.; Li, P.; Huang, H.J.; Xie, D.Y.; Lin, C.C.; Hu, F.; Chen, H.Y.; Peng, S.J. Interfacial electronic coupling of ultrathin transition-metal hydroxide nanosheets with layered MXenes as a new prototype for platinum-like hydrogen evolution. Energy Environ. Sci.
**2021**, 14, 6419–6427. [Google Scholar] [CrossRef] - Xu, S.; Wu, X.; Li, Y. Novel copper redox-based cathode materials for room-temperature sodium-ion batteries. Chin. Phys. B
**2014**, 23, 118202. [Google Scholar] [CrossRef] - Shacklette, L.W.; Jow, T.R.; Townsend, L. Rechargeable electrodes from sodium cobalt bromzes. J. Electrochem. Soc.
**1988**, 135, 2669–2674. [Google Scholar] [CrossRef] - Asl, H.Y.; Manthiram, A. Reining in dissolved transition-metal ions. Science
**2020**, 369, 140–141. [Google Scholar] [CrossRef] [PubMed] - Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Phys. Rev. B
**1996**, 54, 11169–11186. [Google Scholar] [CrossRef] - Payne, M.C.; Teter, M.P.; Allan, D.C. Iterative minimization techniques for ab initio total-energy calculations-molecular-dynamics and conjugate gradients. Rev. Mod. Phys.
**1992**, 64, 1045–1097. [Google Scholar] [CrossRef] [Green Version] - Alder, B.J.; Wainwright, T.E. Studies in molecular dynamics. I. General Method. J. Chem. Phys.
**1959**, 31, 459–466. [Google Scholar] [CrossRef] [Green Version] - Car, R.; Parrinello, M. Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett.
**1985**, 55, 2471–2474. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Ong, S.P.; Chevrier, V.L.; Hautier, G.; Jain, A.; Moore, C.; Kim, S.; Ma, X.; Ceder, G. Voltage, stability and diffusion barrier differences between sodium-ion and lithium-ion intercalation materials. Energy Environ. Sci.
**2011**, 4, 3680–3688. [Google Scholar] [CrossRef] [Green Version] - Yang, L.; Chen, R.S.; Liu, Z.P.; Gao, Y.R.; Wang, X.F.; Wang, Z.X.; Chen, L.Q. Configuration-dependent anionic redox in cathode materials. Battery Energy
**2022**, 1, 2021001. [Google Scholar] [CrossRef] - Chevrier, V.L.; Ceder, G. Challenges for Na-ion Negative Electrodes. J. Electrochem. Soc.
**2011**, 158, A1011–A1014. [Google Scholar] [CrossRef] - Mo, Y.; Ong, S.P.; Ceder, G. Insights into Diffusion Mechanisms in P2 Layered Oxide Materials by First-Principles Calculations. Chem. Mater.
**2014**, 26, 5208–5214. [Google Scholar] [CrossRef] - Dacek, S.T.; Richards, W.D.; Kitchaev, D.A. Structure and Dynamics of Fluorophosphate Na-Ion Battery Cathodes. Chem. Mater.
**2016**, 28, 5450–5460. [Google Scholar] [CrossRef] [Green Version] - He, Q.; Yu, B.; Li, Z.H.; Zhao, Y. Density Functional Theory for Battery Materials. Energy Environ. Mater.
**2019**, 2, 264–279. [Google Scholar] [CrossRef] [Green Version] - Zhang, M.; Tong, Y.F.; Xie, J.; Huang, W.W.; Zhang, Q.C. Rechargeable Sodium-Ion Battery Based on Polyazaacene Analogue Anode. Chem. Eur. J.
**2021**, 27, 16754–16759. [Google Scholar] [CrossRef] - Li, J.Y.; Hu, H.Y.; Wang, J.Z.; Xiao, Y. Surface chemistry engineering of layered oxide cathodes for sodium-ion batteries. Carbon Neutralization
**2022**, 1, 96–116. [Google Scholar] [CrossRef] - Volkov, A. Ionic and Electronic Transportation Electrochemical and Polymer Based Systems; Linkoping University Electronic Press: Linköping, Sweden, 2017. [Google Scholar]
- Parr, R.G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, NY, USA, 1989. [Google Scholar]
- Dreizler, R.M.; Gross, E.K.U. Density Functional Theory: An Approach to the Quantum Many Body Problem; Springer: Berlin/Heidelberg, Germany, 1990. [Google Scholar]
- Kryachko, E.S.; Ludena, E.V. Density Functional Theory of Many Electron Systems; Kluwer: Dordrecht, The Netherlands, 1990. [Google Scholar]
- March, N.H. Electron Density Theory; Academic Press: London, UK, 1992. [Google Scholar]
- Chong, D.P. Recent Advances in Density Functional Methods; World Scientific: Singapore, 1995. [Google Scholar]
- Nalewajski, R.F.; Mrozek, J. Hartree-Fock difference approach to chemical valence: Three-electron indices in UHF approximation. Int. J. Quantum Chem.
**1996**, 57, 377–389. [Google Scholar] [CrossRef] - Parr, R.G.; Yang, W. Density-functional theory of the electronic structure of molecules. Annu. Rev. Phys. Chem.
**1995**, 46, 701–728. [Google Scholar] [CrossRef] - Kohn, W.; Sham, L.J. Self-consistent equations including exchange and correlation effects. Phy. Rev.
**1965**, 140, A1133–A1138. [Google Scholar] [CrossRef] [Green Version] - Szalewicz, K. Determination of Structure and Properties of Molecular Crystals from First Principles. Acc. Chem. Res.
**2014**, 47, 3266–3274. [Google Scholar] [CrossRef] - Patkowski, K.; Szalewicz, K. Argon Pair Potential at Basis and Excitation Limits. J. Chem. Phys.
**2010**, 133, 094304. [Google Scholar] [CrossRef] - Jensen, F. Introduction to Computational Chemistry, 2nd ed.; Wiley: Chichester, UK, 2007. [Google Scholar]
- Toumar, A.J.; Ong, S.P.; Richards, W.D.; Dacek, S.; Ceder, G. Vacancy Ordering in O3 -Type Layered Metal Oxide Sodium-Ion Battery Cathodes. Phys. Rev. Appl.
**2015**, 4, 064002. [Google Scholar] [CrossRef] [Green Version] - Wang, Q.C.; Lin, C.; Li, J.B.; Gao, H.C.; Wang, Z.G.; Jin, H.B. Experimental and theoretical investigation of Na
_{4}MnAL(PO_{4})_{3}cathode material for sodium-ion batteries. Chem. Eng. J**2021**, 425, 130680. [Google Scholar] [CrossRef] - Matteo, B.; Wang, J.Y.; Clément, R.; Ceder, G. A First-Principles and Experimental Investigation of Nickel Solubility into the P2 NaxCoO2 Sodium-Ion Cathode. Adv. Energy Mater.
**2018**, 8, 1801446. [Google Scholar] - House, R.A.; Maitra, U.; Pérez-Osorio, M.A.; Lozano, J.G.; Jin, L.; Somerville, J.W.; Duda, L.C.; Nag, A.; Walters, A.; Zhou, K.J.; et al. Superstructure control of first-cycle voltage hysteresis in oxygen-redox cathodes. Nature
**2020**, 577, 502–508. [Google Scholar] [CrossRef] - Zhu, Y.F.; Xiao, Y.; Dou, S.X.; Kang, Y.M.; Chou, S.L. Spinel engineering on layered oxide cathodes for sodium-ion batteries. eScience
**2021**, 1, 13–27. [Google Scholar] [CrossRef] - Nakayama, M.; Kaneko, M.; Wakihara, M. First-principles study of lithium-ion migration in lithium transition metal oxides with spinel structure. Phys. Chem. Chem. Phys.
**2012**, 14, 13963–13970. [Google Scholar] [CrossRef] - Pandit, B.; Rondiya, S.R.; Dzade, N.Y.; Shaikh, S.F.; Kumar, N.; Goda, E.S.; Al-Kahtani, A.A.; Mane, R.S.; Mathur, S.; Salunkhe, R.R. High Stability and Long Cycle Life of Rechargeable Sodium-Ion Battery Using Manganese Oxide Cathode: A Combined Density Functional Theory (DFT) and Experimental Study. ACS Appl. Mater. Interfaces
**2021**, 13, 11433–11441. [Google Scholar] [CrossRef] - Lee, D.H.; Xu, J.; Meng, Y.S. An advanced cathode for Na-ion batteries with high rate and excellent structural stability. Phys. Chem. Chem. Phys.
**2013**, 15, 3304–3312. [Google Scholar] [CrossRef] - Jiang, L.W.; Lu, Y.X.; Wang, Y.S.; Liu, L.L.; Qi, X.G.; Zhao, C.L.; Chen, L.Q.; Hu, Y.S. A High-Temperature β-Phase NaMnO
_{2}Stabilized by Cu Doping and Its Na Storage Properties. Chin. Phys. Lett.**2018**, 35, 048801. [Google Scholar] [CrossRef] - Mohammed, H.; Najma, Y.; Payam, K.; Tan, M.X.; Liu, J.; Sang, P.F.; Fu, Y.Z.; Huang, Y.H.; Ma, J.W. Fast sodium intercalation in Na
_{3.41}£_{0.59}Fe(PO_{4})_{3}: A novel sodium-deficient NASICON cathode for sodium-ion batteries. Energy Storage Mater.**2020**, 35, 192–202. [Google Scholar] - Jian, Z.L.; Sun, Y.; Ji, X.L. A new low-voltage plateau of Na
_{3}V_{2}(PO_{4})_{3}as an anode for Na-ion batteries. Chem. Commun.**2015**, 51, 6381–6383. [Google Scholar] [CrossRef] - El Kacemi, Z.; Mansouri, Z.; Benyoussef, A.; El Kenz, A.; Balli, M.; Mounkachi, O. First principle calculations on pristine and Mn-doped iron fluorophosphates as sodium-ion battery cathode materials. Comput. Mater. Sci.
**2022**, 206, 111292. [Google Scholar] [CrossRef] - Zhao, L.N.; Zhao, H.L.; Du, Z.H.; Chen, N.; Chang, X.W.; Zhang, Z.J.; Gao, F.; Trenczek-Zajac, A.; Świerczek, K. Computational and experimental understanding of Al-doped Na
_{3}V_{2-x}Al_{x}(PO_{4})_{3}cathode material for sodium ion batteries: Electronic structure, ion dynamics and electrochemical properties. Electrochim. Acta**2018**, 282, 510–519. [Google Scholar] [CrossRef] - Xiao, P.; Song, J.; Wang, L.; Goodenough, J.B.; Henkelman, G. Theoretical Study of the Structural Evolution of a Na
_{2}FeMn(CN)_{6}Cathode upon Na Intercalation. Chem. Mater.**2015**, 27, 3763–3768. [Google Scholar] [CrossRef] [Green Version] - Nasir, N.A.M.; Badrudin, F.W.; Idrus, A.; Sazman, F.N.; Taib, M.F.M.; Yahya, M.Z.A. First-principles study on structural and electronic properties of Prussian blue cathode material for sodium-ion battery. Mol. Cryst. Liq. Cryst.
**2019**, 693, 115–122. [Google Scholar] [CrossRef] - Xu, Y.; Wan, J.; Huang, L.; Ou, M.Y.; Fan, C.Y.; Wei, P.; Peng, J.; Liu, Y.; Qiu, Y.G.; Sun, X.P.; et al. Structure Distortion Induced Monoclinic Nickel Hexacyanoferrate as High-Performance Cathode for Na-Ion Batteries. Adv. Energy Mater.
**2018**, 9, 1803158. [Google Scholar] [CrossRef] - Wu, X.Y.; Jin, S.F.; Zhang, Z.Z.; Jiang, L.W.; Mu, L.Q.; Hu, Y.S.; Li, H.; Chen, X.L.; Armand, M.; Chen, L.Q. Unraveling the storage mechanism in organic carbonyl electrodes for sodium-ion batteries. Sci. Adv.
**2015**, 1, e1500330. [Google Scholar] [CrossRef] [Green Version] - Chen, Y.Q.; Luder, J.; Ng, M.F.; Michael, S.; Sergei, M.G. Polyaniline and CN-functionalized polyaniline as organic cathodes for lithium and sodium ion batteries: A combined molecular dynamics and density functional tight binding study in solid state. Phys. Chem. Chem. Phys.
**2018**, 20, 23. [Google Scholar] [CrossRef] - Katcho, N.A.; Carrasco, J.; Saurel, D.; Gonzalo, E.; Han, M.; Aguesse, F.; Rojo, T. Commercial Prospects of Existing Cathode Materials for Sodium Ion Storage. Adv. Energy Mater.
**2017**, 7, 1601477. [Google Scholar] [CrossRef] - Zhai, L.F.; Yu, J.M.; Yu, J.P.; Xiong, W.W.; Zhang, Q.C. Thermodynamic Transformation of Crystalline Organic Hybrid Iron Selenide to Fe
_{x}Se_{y}@CN Microrods for Sodium Ion Storage. ACS Appl. Mater. Interfaces**2022**, 14, 49854–49864. [Google Scholar] [CrossRef] - Zuo, W.H.; Ren, F.C.; Li, Q.H.; Wu, X.H.; Fang, F.; Yu, X.Q.; Li, H.; Yang, Y. Insights of the anionic redox in P2–Na
_{0.67}Ni_{0.33}Mn_{0.67}O_{2}. Nano Energy**2020**, 78, 105285. [Google Scholar] [CrossRef] - Caballero, A.; Hernán, L.; Morales, J.; Sánchez, L.; Peña, J.S.; Aranda, M.A.G. Synthesis and characterization of high-temperature hexagonal P2-Na
_{0.6}MnO_{2}and its electrochemical behaviour as cathode in sodium cells. J. Mater. Chem.**2002**, 12, 1142–1147. [Google Scholar] [CrossRef] - Han, M.H.; Gonzalo, E.; Casas-Cabanas, M.; Rojo, T. Structural evolution and electrochemistry of monoclinic NaNiO
_{2}upon the first cycling process. J. Power Sources**2014**, 258, 266–271. [Google Scholar] [CrossRef] - Wang, S.H.; Sun, C.L.; Wang, N.; Zhang, Q.C. Ni- and/or Mn-based Layered Transition Metal Oxides as Cathode Materials for Sodium Ion Batteries: Status, Challenges and Countermeasurements. J. Mater. Chem. A
**2019**, 7, 10138–10158. [Google Scholar] [CrossRef] - Wang, J.Y.; Wang, Y.; Seo, D.H.; Shi, T.; Chen, S.P.; Tian, Y.S.; Haegyeom, K.; Gerbrand, C. High-performance trifunctional electrocatalysts based on FeCo/Co
_{2}P hybrid nanoparticles for Zinc–Air battery and self-powered overall water splitting. Adv. Energy Mater.**2020**, 10, 1903968. [Google Scholar] [CrossRef] - Kim, J.; Yoon, G.; Lee, H.M.; Hyungsub, K.; Lee, S.; Kang, K. New 4V-Class and Zero-Strain Cathode Material for Na-Ion Batteries. Chem. Mater.
**2017**, 29, 7826–7832. [Google Scholar] [CrossRef] - Ran, L.B.; Ardeshir, B.; Li, M.; Yin, Y.; Baris, D.; Lin, T.G.; Li, M.; Masud, R.; Ian, G.; Wang, L.Z.; et al. Ge co-doping NASICON boosts solid-state sodium ion batteries’ performance. Energy Storage Mater.
**2021**, 40, 282–291. [Google Scholar] [CrossRef] - Li, X.Q.; Zhang, Y.; Zhang, B.L.; Qin, K.; Liu, H.M.; Ma, Z.F. Mn-doped Na
_{4}Fe_{3}(PO_{4})_{2}P_{2}O_{7}facilitating Na^{+}migration at low temperature as a high-performance cathode material of sodium ion batteries. J. Power Sources**2022**, 521, 230922. [Google Scholar] [CrossRef] - Sun, S.; Zhao, Y.J.; Ni, Q.; Sun, A.; Yuan, X.Y.; Li, J.B.; Jin, H.B. Revealing excess Al
^{3+}preinsertion on altering diffusion paths of aluminum vanadate for zinc-ion batteries. Energy Storage Mater.**2022**, 52, 291–298. [Google Scholar] [CrossRef] - Song, W.X.; Ji, X.B.; Wu, Z.P.; Zhu, Y.R.; Yang, Y.C.; Chen, J.; Jing, M.J.; Li, F.Q.; Banks, C.E. First exploration of Na-ion migration pathways in the NASICON structure Na
_{3}V_{2}(PO_{4})_{3}. J. Mater. Chem.**2014**, 2, 5358–5362. [Google Scholar] [CrossRef] [Green Version] - Chen, M.Z.; Hua, W.B.; Xiao, J.; David, C.; Chen, W.H.; Wang, E.H.; Hu, Z.; Gu, Q.F.; Wang, X.L.; Indris, S.; et al. NASICON-type air-stable and all-climate cathode for sodium-ion batteries with low cost and high-power density. Nat. Commun.
**2019**, 10, 1480. [Google Scholar] [CrossRef] [Green Version] - Wei, Y.B.; Zhang, Y.; Huang, Y.D.; Wang, X.C.; Cheng, W.H.; Sun, Y.; Jia, D.Z.; Tang, X.C. Simple synthesis and electrochemical performance of NaVSi
_{2}O_{6}as a new sodium-ion cathode material. Int. J. Energy Res.**2021**, 45, 10746–10751. [Google Scholar] [CrossRef] - Li, W.; Yao, Z.J.; Liu, Y.; Zhang, S.Z.; Wang, X.L.; Xia, X.H.; Gu, C.D.; Tu, J.P. Optimizing quasi-solid-state sodium storage performance of Na
_{3}V_{2}(PO_{4})_{2}F_{2.5}O_{0.5}cathode by structural design plus nitrogen doping. Chem. Eng. J.**2022**, 433, 133557. [Google Scholar] [CrossRef] - Zuo, D.X.; Wang, C.P.; Han, J.J.; Wu, J.H.; Qiu, H.J.; Zhang, Q.; Lu, Y.; Lin, Y.J.; Liu, X.J. Oriented Formation of a Prussian Blue Nanoflower as a High-Performance Cathode for Sodium Ion Batteries. ACS Sustain. Chem. Eng.
**2020**, 8, 16229–16240. [Google Scholar] [CrossRef] - Hurlbutt, K.; Giustino, F.; Volonakis, G.; Pasta, M. Origin of the High Specific Capacity in Sodium Manganese Hexacyanomanganate. Chem. Mater.
**2022**, 34, 4336–4343. [Google Scholar] [CrossRef] - Shao, M.M.; Wang, B.; Liu, M.C.; Wu, C.; Ke, F.S.; Ai, X.P.; Yang, H.X.; Qian, J.F. A High-Voltage and Cycle Stable Aqueous Rechargeable Na-Ion Battery Based on Na
_{2}Zn_{3}[Fe(CN)_{6}]_{2}-NaTi_{2}(PO_{4})_{3}Intercalation Chemistry. ACS Appl. Energy Mater.**2019**, 2, 5809–5815. [Google Scholar] [CrossRef] - Huang, Y.X.; Xie, M.; Zhang, J.T.; Wang, Z.H.; Jiang, Y.; Xiao, G.H.; Li, S.J.; Li, L.; Wu, F.; Chen, R.J. A novel border-rich Prussian blue synthetized by inhibitor control as cathode for sodium ion batteries. Nano Energy
**2017**, 39, 273–283. [Google Scholar] [CrossRef] - Peng, J.; Zhang, W.; Hu, Z.; Zhao, L.F.; Wu, C.; Peleckis, G.; Gu, Q.F.; Wang, J.Z.; Liu, H.K.; Dou, S.X.; et al. Ice-Assisted Synthesis of Highly Crystallized Prussian Blue Analogues for All-Climate and Long-Calendar-Life Sodium Ion Batteries. Nano Lett.
**2022**, 22, 1302–1310. [Google Scholar] [CrossRef] - You, Y.; Xin, S.; Hooman; Asl, Y.; Li, W.D.; Wang, P.F.; Guo, Y.G. Subzero-Temperature Cathode for a Sodium-Ion Battery. Adv. Mater.
**2016**, 28, 7243–7248. [Google Scholar] [CrossRef] - Wojdeł, J.C.; Moreira, I.D.R.; Bromley, S.T.; Illas, F. On the prediction of the crystal and electronic structure of mixed-valence materials by periodic density functional calculations: The case of Prussian Blue. J. Chem. Phys.
**2008**, 128, 044713. [Google Scholar] [CrossRef] - Wojdeł, J.C.; Bromley, S.T. Efficient calculation of the structural and electronic properties of mixed valence materials: Application to Prussian Blue analogues. Chem. Phys. Lett.
**2004**, 397, 154–159. [Google Scholar] [CrossRef] - Xu, Y.; Wan, J.; Huang, L.; Ou, M.Y.; Fan, C.Y.; Wei, P.; Peng, J.; Liu, Y.; Qiu, Y.G.; Sun, X.P.; et al. Dual redox-active copper hexacyanoferrate nanosheets as cathode materials for advanced sodium-ion batteries. Energy Storage Mater.
**2020**, 33, 432–441. [Google Scholar] [CrossRef] - Wu, Z.Z.; Xie, J.; Xu, Z.C.J.; Zhang, S.Q.; Zhang, Q.C. Recent Progress in Metal-Organic Polymers as Promising Electrodes for Lithium/Sodium Rechargeable Batteries. J. Mater. Chem. A
**2019**, 7, 4259–4290. [Google Scholar] [CrossRef] - Kim, H.J.; Kim, Y.; Shim, J.; Jung, K.H.; Jung, M.S.; Kim, H.; Lee, J.C.; Lee, K.T. Environmentally Sustainable Aluminum-Coordinated Poly(tetrahydroxybenzoquinone) as a Promising Cathode for Sodium Ion Batteries. ACS Appl. Mater. Interfaces
**2018**, 10, 3479–3486. [Google Scholar] [CrossRef] [PubMed] - Huangfu, C.; Liu, Z.; Lu, X.L.; Liu, Q.; Wei, T.; Fan, Z.J. Strong oxidation induced quinone-rich dopamine polymerization onto porous carbons as ultrahigh-capacity organic cathode for sodium-ion batteries. Energy Storage Mater.
**2021**, 43, 120–129. [Google Scholar] [CrossRef] - Zhou, G.Y.; Mo, L.L.; Zhou, C.Y.; Wu, Y.; Lai, F.L.; Lv, Y.; Ma, J.M.; Miao, Y.E.; Liu, T.X. Ultra-strong capillarity of bioinspired micro/nanotunnels in organic cathodes enabled high-performance all-organic sodium-ion full batteries. Chem. Eng. J.
**2021**, 420, 127597. [Google Scholar] [CrossRef] - Wang, L.B.; Ni, Y.X.; Hou, X.S.; Chen, L.; Li, F.J.; Chen, J. A two-dimensional metal-organic polymer enabled by robust nickel-nitrogen and hydrogen bonds for exceptional sodium-ion storage. Angew. Chem. Int. Ed.
**2020**, 59, 22126–22131. [Google Scholar] [CrossRef] - Xiong, W.X.; Huang, W.W.; Zhang, M.; Hu, P.D.; Cui, H.M.; Zhang, Q.C. Pillar [5] quinone–Carbon Nanocomposites as High-Capacity Cathodes for Sodium-Ion Batteries. Chem. Mater.
**2019**, 31, 8069–8075. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**)The step of determining crystal structure by the first principles [35]. (

**b**) Density functional theory combined with various theoretical methods. (

**c**) Performance comparison of argon dimer by different DFT methods. The datum curve [36] is accurate to its line width. The acronyms define various DFT methods, for example, see Reference [37]. Reprinted (adapted) with permission from Ref. [35]. Copyright 2014, American Chemical Society.

**Figure 2.**(

**a**) Sodium content configuration energy diagram of ${\mathrm{Na}}_{\mathrm{x}}{\mathrm{CrO}}_{2}$ materials. (

**b**) Calculation curve of O3 type ${\mathrm{Na}}_{\mathrm{x}}{\mathrm{MO}}_{2}(\mathrm{M}=\mathrm{Ti},\mathrm{V},\mathrm{Mn},\mathrm{Co},\mathrm{Ni},\mathrm{Cr},\mathrm{Fe})$ sodium−embedding voltage. Reprinted (figure) with permission from Ref. [38]. Copyright 2015, American Physical Society. Diffusion paths of sodium in ${\mathrm{Na}}_{4}{\mathrm{MnAl}(\mathrm{PO}}_{4}{)}_{3}$ and DFT calculation results of corresponding energy barrier of (

**c**,

**f**) Path1: Na(2)–Na(1), (

**d**,

**g**) Path2: Na(3)−Na(1) and (

**e**,

**h**) Path3: Na(2)−Na(3). Reprinted (adapted) with permission from Ref. [39]. Copyright 2021, Elsevier.

**Figure 3.**(

**a**) Charge-density diagram of ${\mathrm{Fe}\left[\mathrm{Fe}\right(\mathrm{CN})}_{6}]$. Reprinted (adapted) with permission from Ref. [52]. Copyright 2019, Informa UK Limited, trading as Taylor & Taylor & Francis Group. (

**b**) Geometry optimized structure of monoclinic NiHCF. Reprinted (adapted) with permission from Ref. [53] Copyright 2021, Elsevier. (

**c**) The charge density difference with an identical distortion and (

**d**) hydrate ${\mathrm{Na}}_{2}{\mathrm{Cu}\left[\mathrm{Fe}\right(\mathrm{CN})}_{6}{]}_{0.75}$ ·1.5${\mathrm{H}}_{2}\mathrm{O}$ at different Na concentrations, including Na-1 and Na-1.5. Reprinted (adapted) with permission from Ref. [79]. Copyright 2020, Elsevier.

Material Type | DFT Calculation Purpose | Calculation Results | Experimental Result | Reference |
---|---|---|---|---|

α-MnO_{2} | lattice parameters | a [Å]: 9.763 b [Å]: 9.763 c [Å]: 2.872 | a [Å]: 9.815 b [Å]: 9.815 c [Å]: 2.847 | [44] |

α-${\mathrm{MnO}}_{2}$ | reaction voltages | 3.42 V | 3.23 V | [44] |

α-${\mathrm{MnO}}_{2}$ | electronic band | 2.42 eV | 2.23 eV | [44] |

β-NaMnO_{2} | migration energy barrier | 0.3 eV | 0.27 eV | [46] |

${\mathrm{Na}}_{3.41}{\mathsf{\pounds}}_{0.59}{\mathrm{FeV}(\mathrm{PO}}_{4}{)}_{3}$ (Pristine) | lattice parameters | a [Å]: 8.9675 c [Å]: 21.6030 V [${\mathsf{\AA}}^{3}$]: 1504.48 | a [Å]: 8.8818 c [Å]: 21.5092 V [Å ^{3}]: 1469.95 | [47] |

${\mathrm{Na}}_{3.41}{\mathsf{\pounds}}_{0.59}{\mathrm{FeV}(\mathrm{PO}}_{4}{)}_{3}$ (cutoff voltage at 4.4 V vs. Na + /Na.) | lattice parameters | a [Å]: 8.5344 c [Å]: 21.7468 V [${\mathsf{\AA}}^{3}$]: 1371.74 | a [Å]: 8.6726 c [Å]: 21.789 V [${\mathsf{\AA}}^{3}$]: 1419.3 | [47] |

${\mathrm{Na}}_{\mathrm{x}}{\mathrm{V}}_{2}{{(\mathrm{PO}}_{4})}_{3}$ (1 < x < 3) | reaction voltages | 3.4 V | 3.3 V | [48] |

${\mathrm{Na}}_{2}$Fe${\mathrm{PO}}_{4}$F | band gap energy | 2.19 eV | 2.80 eV | [49] |

${\mathrm{Na}}_{2}{\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}{\mathrm{PO}}_{4}$F | band gap energy | 1.36 eV | 1.93 eV | [49] |

${\mathrm{Na}}_{3}{\mathrm{V}}_{2}{{(\mathrm{PO}}_{4})}_{3}$ | band gap energy | 1.75 eV | 4.89 eV | [50] |

Na_{3}V_{1.8}Al_{0.2}(PO_{4})_{3} | band gap energy | 1.58 eV | 4.64 eV | [50] |

${\mathrm{FeMn}\left(\mathrm{CN}\right)}_{6}$ | lattice parameters | a [Å]: 7.09 b [Å]: 7.31 c [Å]: 10.69 | a [Å]: 7.15 b [Å]: 7.15 c [Å]: 10.54 | [51] |

${\mathrm{NaFeMn}\left(\mathrm{CN}\right)}_{6}$ | lattice parameters | a [Å]: 7.19 b [Å]: 7.97 c [Å]: 10.67 | a [Å]: 7.54 b [Å]: 7.54 c [Å]: 10.66 | [51] |

FeMn${\left(\mathrm{CN}\right)}_{6}$ | lattice parameters | a [Å]: 6.55 b [Å]: 6.55 c [Å]: 19.51 | a [Å]: 6.58 b [Å]: 6.58 c [Å]: 18.93 | [51] |

FeMn(CN)_{6}·2${\mathrm{H}}_{2}$O | lattice parameters | a [Å]: 7.08 b [Å]: 7.30 c [Å]: 10.73 | a [Å]: 7.15 b [Å]: 7.15 c [Å]: 10.54 | [51] |

NaFeMn${\left(\mathrm{CN}\right)}_{6}$·2${\mathrm{H}}_{2}$O | lattice parameters | a [Å]: 7.40 b [Å]: 7.63 c [Å]: 10.69 | a [Å]: 7.50 b [Å]: 7.50 c [Å]: 10.60 | [51] |

${\mathrm{Na}}_{2}$FeMn${\left(\mathrm{CN}\right)}_{6}$·2H2O | lattice parameters | a [Å]: 7.39 b [Å]: 7.47 c [Å]: 10.61 | a [Å]: 7.34 b [Å]: 7.53 c [Å]: 10.59 | [51] |

${\mathrm{Na}}_{2}$Fe[Fe${\left(\mathrm{CN}\right)}_{6}]$ | lattice parameters | a [Å]: 10.302 b [Å]: 10.302 c [Å]: 10.302 | a [Å]: 10.259 b [Å]: 10.259 c [Å]: 10.259 | [52] |

NaFe[Fe${\left(\mathrm{CN}\right)}_{6}$] | lattice parameters | a [Å]: 10.244 b [Å]: 10.244 c [Å]: 10.244 | a [Å]: 10.194 b [Å]: 10.194 c [Å]: 10.194 | [52] |

${\mathrm{Na}}_{2}$Fe[Fe(CN)6] | reaction voltages | 3.32 V | 3.23 V | [52] |

C-NiHCF | lattice parameters | a [Å]: 10.143 b [Å]: 10.143 c [Å]: 10.143 | a [Å]: 10.227 b [Å]: 10.227 c [Å]: 10.227 | [53] |

M-NiHCF | lattice parameters | a [Å]: 10.617 b [Å]: 7.601 c [Å]: 7.398 | a [Å]: 10.361 b [Å]: 7.417 c [Å]: 7.219 | [53] |

${\mathrm{Na}}_{2}{\mathrm{C}}_{6}{\mathrm{H}}_{2}{\mathrm{O}}_{4}$ | reaction voltages | 1.17 V | 1.21 V | [54] |

${\mathrm{Na}}_{3}{\mathrm{C}}_{6}{\mathrm{H}}_{2}{\mathrm{O}}_{4}$ | reaction voltages | 0.95 V | 1.31 V | [54] |

${\mathrm{Na}}_{4}{\mathrm{C}}_{6}{\mathrm{H}}_{2}{\mathrm{O}}_{4}$ | reaction voltages | 1.38 V | 1.49 V | [54] |

polyaniline (PANI) and cyano (CN) functionalized | increased voltage | 0.7–1.1 V | 1.3 V | [55] |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Yu, B.; Xiao, J.; Zhou, L.; Chen, M.
Application of First Principles Computations Based on Density Functional Theory (DFT) in Cathode Materials of Sodium-Ion Batteries. *Batteries* **2023**, *9*, 86.
https://doi.org/10.3390/batteries9020086

**AMA Style**

Wang Y, Yu B, Xiao J, Zhou L, Chen M.
Application of First Principles Computations Based on Density Functional Theory (DFT) in Cathode Materials of Sodium-Ion Batteries. *Batteries*. 2023; 9(2):86.
https://doi.org/10.3390/batteries9020086

**Chicago/Turabian Style**

Wang, Yuqiu, Binkai Yu, Jin Xiao, Limin Zhou, and Mingzhe Chen.
2023. "Application of First Principles Computations Based on Density Functional Theory (DFT) in Cathode Materials of Sodium-Ion Batteries" *Batteries* 9, no. 2: 86.
https://doi.org/10.3390/batteries9020086