## Density Functional Theory (DFT) in Cathode Materials of Sodium‐Ion Batteries

As early as the 1970s, sodium‐ion batteries (SIB) and lithium‐ion batteries (LIB) were investigated almost at the same time. However, due to the excellent characteristics of LIBs and the limitations of research conditions, research on SIBs was developing slowly. In recent years, with the huge demand for renewable energy and the attentions paid to environmental pollution, the research on sodium‐ion batteries has returned to people’s attention. Additionally, because it can alleviate the resource shortage caused by excessive exploitation of LIB raw materials and the limited development of energy storage batteries caused by rising material prices, to a certain extent, it has attracted extensive attentions from researchers all over the world. The cathode material is an important part of SIBs, which directly determines the battery performance and the upper limit of cell energy density . The cathode materials that can be widely used must meet the following requirements. First, the cathode material should have a high‐redox potential so that a high‐output voltage can be obtained by maintaining the electrodynamic force of the SIBs. At the same time, the embedding and stripping of charged ions have a minor impact on the electrode potential so there will be no excessive voltage fluctuation during the charging and discharging process, which will not bring adverse effects to other electrical devices in the system.

Second, the sodium content of the material is high, and the sodium‐ion insertion is

reversible. This is a prerequisite for high capacity. Third, as the Na+ diffusion coefficient

is higher, the Na+ moves more quickly in the material so the ability to insert and de‐insert

is stronger. Fourth, in the process of sodium‐ion inserting/deinterlacing, the structure of

the positive electrode material should not change significantly to ensure the long‐term

stability of the battery. Fifth, it has good conductivity to ensure the sodium‐ion battery

can be charged and discharged with a high current. Sixth, the materials are easy to be

obtained and have good processing performance.

To obtain the ideal cathode material, it is especially important to better understand

its working mechanism. Theoretical calculation and simulation can help us to further

understand the nature of electrode materials. Analyzing the energy storage mechanism of

battery materials by theoretical calculation can analyze the electrochemical reaction

kinetic from the nanometer scale, and the relationship between structure and performance

can often be well explained by combining high‐precision experimental characterization

techniques. Density functional theory is widely used as a representative. At

present, the DFT calculation is widely used to estimate the structural stability of battery

materials, study the sodium insertion voltage of electrode materials, calculate the

diffusion barrier and diffusion path, analyze the electronic structure of battery materials,

and simulate the adsorption process of ions or molecules. Given the importance

and contribution of DFT calculation in the study of SIBs, this perspective summarizes the

latest progress in the DFT calculation of SIB cathode materials from transition‐metal

oxides/chalcogenides, polyanionic compounds, Prussian blue, and organic cathode

materials, respectively. This perspective focuses on the key role of the DFT calculation in

the development of cathode materials for SIB and guides the further developments of DFT

in the field of electrode materials in the future.

**Principle of DFT Calculation**

As long as some basic physical quantities (such as reduced Planck constant, atomic mass, and electronic electric quantity) are used, the physical and chemical properties of materials can be calculated through the Schrodinger Equation. Therefore, theoretical calculations based on the Schrodinger equation are generally first‐principles calculations. The Schrodinger equation has the following form:

iℏ ∂ ∂t ψ(r,t)=Ĥψ(r,t) ………………………..(1)

In the equation, i is an imaginary unit; ℏ represents the reduced Planck constant; ∂

∂t

is the item partial derivative operator; ψ(r,t) represents the wave function of the system;

Ĥ is the Hamiltonian operator of the system.

To solve the problem that the equations are difficult to solve due to the multi‐body

interaction in the first principle calculation, researchers have proposed a series of

simplification and approximation methods, among which the DFT is the most widely

used. The core idea of DFT is not to directly solve the electron wave function of

the multi‐body interaction system but to link the Hamiltonian with the electron density

and express the total energy, E, as the function of electron density. After the Kohn–Sham

hypothesis is introduced, the problem of the interaction system was transformed into

a non‐interaction problem that is easy to separate variables; the process of solving the

electron ground state energy was transformed into a self‐consistent iterative process of

the Kohn–Sham equation. After obtaining a self‐consistent convergent charge

density, the total energy of the system can be obtained. The first‐principles

calculation is widely used in crystallography. For example, the first principles are used to

determine the crystal structure.