The study of density functional theory (DFT) began in the early 20th century, based on quantum mechanics^[18]. The Schrödinger stationary equation can describe the law of motion of microscopic particles:

Where, \hat{H} is the Hamiltonian containing the nuclear kinetic energy term {\hat{T}}_{\mathrm{N}}, the electron kinetic energy term {\hat{T}}_{\mathrm{e}}, the nucleus-nucleus interaction term {\hat{V}}_{\mathrm{N}\mathrm{N}},Electron-electron interaction term {\hat{V}}_{\mathrm{e}\mathrm{e}}, nucleus-electron interaction term {\hat{V}}_{\mathrm{N}\mathrm{e}}; \mathrm{\Psi } \left( r \right) is the system wave function; E is the total energy of the system.

For a complex system, the number of atoms in it is so large that the Schrodinger stationary equation (1) can hardly be solved accurately. Due to the great difference in mass and velocity between the nucleus and the electron, the motion of the nucleus and the electron can be considered separately according to the Born-Oppenheimer approximation, so that the Schrodinger stationary equation (1) for a polyatomic system is approximately simplified to the Schrodinger equation for the electron:^[19]

Where r_1 , r_2 , r_3 \dots r_n are the positions of electrons numbered 1, 2, 3 … n, respectively. However, for many-electron systems, equation (2) is still very difficult to solve.

Until 1927, Thomas and Fermi established the Thomas-Fermi model, trying to use the microscopic electron density distribution to represent the properties of the macroscopic system, which provided a new way to solve the Schrodinger equation and was regarded as the embryonic form of DFT^[20]. In 1964, Hohenberg and Kohn proposed the Hohenberg-Kohn theorem on the basis of the former, which strictly proved the exact dependence between the energy of the system and the particle number density function^[21]. According to the Hohenberg-Kohn theorem, the functional form of the ground state electron density distribution function corresponding to the energy of a many-particle system can be expressed as

Where v \left( r \right) is the same local potential experienced by all electrons, including the correlation potential between electrons, nuclear potential field, external field, etc. Although the Hohenberg-Kohn theorem proves that the total energy of the system can be obtained by solving the ground state electron density distribution function, the specific functional form of the total energy and its practical application still need to be further explored.

In 1965, Kohn and Sham proposed the Kohn-Sham equation, which clarified the specific relationship between the energy of the system and the electron density distribution function, and made DFT formally enter the practical application stage^[22]. The Kohn-Sham equation is mainly based on the equation (3), using the relevant variables of the non-interacting electron system, the density function \mathrm{\rho } \left( r \right) is composed of N single-electron wave functions {\mathrm{\phi }}_i \left( r \right), and the electron kinetic energy term {\hat{T}}_{\mathrm{e}} as well as the electron-electron interaction term {\hat{V}}_{\mathrm{e}\mathrm{e}} are obtained. Subsequently, using the exchange-correlation functional V_{\mathrm{X}\mathrm{C}} to induce the interaction and correlation effects between particles in the system, the Kohn-Sham equation in one-electron form is obtained by functional variation:

Among,

The difficulty in solving the Kohn-Sham equations is that the specific form of the exchange-correlation functional is unknown. Therefore, it is necessary to obtain a parameterized empirical form of the exchange-correlation functional by approximately fitting the energy and charge density distributions of the system that has been solved accurately. At present, many approximation methods have been developed, such as local density approximation (LDA), generalized gradient approximation (GGA), etc. Correspondingly, a large number of functional forms have been obtained, such as B3LYP, M06-2X, etc^[23][24][25]. It is worth mentioning that in recent years, a number of new functional methods independently developed by China have emerged, such as XPBE, X3LYPX1, XYG3 and XYGJ-0S, which have also been widely used and recognized by researchers at home and abroad. In the actual calculation process, for different systems, the appropriate exchange-correlation functional is selected, and the basic information such as the stable structure and energy of the material can be obtained by solving the Kohn-Sham equation self-consistently. In general, most of the simulations in quantum chemical studies of electrolytes can be done using the highly universal B3LYP functional.

At present, many scientific research software based on DFT have been developed and widely used in quantum chemistry calculation in the field of materials, such as VASP, ABINIT, DMol3, Gaussian, ABACUS, etc. Among them, Gaussian software has the characteristics of comprehensive functions, simple operation and accurate calculation, which has attracted wide attention of researchers and has become the most widely used comprehensive software package for quantum chemistry. In addition, the domestic open source density functional calculation software ABACUS is developing rapidly at present. It supports two basis vectors of plane wave and numerical atomic orbital, and mainly uses norm-conserving pseudopotential. At present, it has complete functions and can be applied to electronic structure optimization, atomic structure relaxation, molecular dynamics simulation and other calculations from small systems to large systems with thousands of atoms.

Molecular dynamics (MD) simulation is an important simulation method to study the statistical properties and diffusion behavior of complex systems in short time, which is based on Newtonian classical mechanics^[26].

In a many-particle system, each atom can be regarded as a mass point, and its motion law conforms to Newton's second law:

Where F is the force on the atom, m is the atomic mass, and a is the atomic acceleration. Where F versus a can be further described by the potential gradient, atomic velocity, and atomic coordinates:

Where U is the atomic potential energy, r the atomic coordinate, v the atomic velocity, and t the time. Given the potential energy and initial coordinates of the atom, the microscopic information of the system, that is, the evolution of the position and velocity of the atom with time, can be derived from equations (6) and (7).

The transition from microscopic information to macroscopic properties of a system mainly depends on the statistical mechanics method. Specifically, the statistical ensemble can be obtained by defining the macroscopic thermodynamic state of the system, and the corresponding macroscopic properties can be obtained by averaging the specific microscopic information of the ensemble:

Where, A is the macroscopic property of the system, A_i is the microstate corresponding to the macroscopic property, and p_i is the occurrence probability of the microstate.

molecular dynamics can be divided into Classical molecular dynamics (CMD) and Ab initio molecular dynamics (AIMD) according to the different ways of describing the interaction between atoms in the system.

In CMD simulation, the potential energy that determines the motion of atoms can be expressed in the form of a mathematical function, namely the potential energy function, also known as the molecular force field. Specifically, the molecular force field originates from the interaction between the atom itself and all other atoms in the system, including bonding interaction and non-bonding interaction.

For different simulation systems, the molecular force field and the corresponding function parameters can be derived from previous experimental work or calculated by quantum mechanical methods. At present, the commonly used molecular force fields include AMBER (for biomolecules), GAFF (for small organic molecules and polymers), OPLS (for ionic liquids), GROMOS (for biomolecules and gas-phase molecules), and ReaxFF (for chemical reactions)^{[27][28][29][30][31]}. In the past few decades, with the deepening of CMD research, more and more force field models have been developed and applied, such as APPLE & P force field (commonly used in liquids, electrolytes, polymers), AMOEBA (atomic multipole optimization energetics for biomolecular simulation) and so on. These force fields have greatly improved the simulation efficiency and accuracy of various models, but there is still a lack of high-quality force fields with universality. Therefore, in order to obtain ideal CMD simulation results, it is very important to select the appropriate force field and parameters.

Unlike CMD, AIMD is independent of empirical parameters, and its simulation uses quantum mechanics to calculate the potential energy and force on the atom. Specifically, the AIMD simulation uses the Hartree-Fock equation or DFT to deal with the Schrodinger equation to obtain the interatomic potential function, and then obtains the atomic motion trajectory according to equations (6) and (7), and then performs statistical analysis on the properties of the system.

AIMD simulation can not only accurately deal with all atoms in the periodic table of elements, but also simulate chemical reactions and polarization effects, which most CMD force fields can not do, so AIMD is also widely used in the simulation of electrolyte and electrode interface reactions in batteries. At the same time, AIMD is based on first-principles calculations, which can also eliminate the negative effects of empirical force fields. However, inheriting the characteristics of first-principles calculation, AIMD simulation can obtain high-precision simulation results, but the size of the simulation system and the simulation efficiency are also greatly limited.

Machine learning molecular dynamics (MLMD) has emerged in recent years, bringing new opportunities for computational simulation of materials. The MLMD method mainly establishes the information database of the materials of the research system through a small amount of Schrodinger equation calculation, and constructs the quantitative relationship between the material structure and the corresponding energy and force based on the machine learning model, that is, the machine learning potential function, and finally uses the machine learning potential function to carry out molecular dynamics simulation. The MLMD method can effectively balance the simulation speed of CMD and the simulation accuracy of AIMD, and has great application potential in electrolyte research. Based on the machine learning model of artificial neural network (ANN), Yao et al. Obtained the relationship between dielectric constant and electrolyte composition and salt concentration, which was consistent with the MD simulation results^[32]. This work applies machine learning methods to data analysis and property prediction, and clarifies the chemical origin of dielectric constant variation with electrolyte composition and temperature. Wang et al. Combined ab initio molecular dynamics with free energy calculation to calculate the redox potential of propylene carbonate electrolyte at a certain concentration, and established the structure-property relationship by using an unsupervised machine learning model with local structural descriptors^[33]. Furthermore, Wang et al. Proved the correlation between the solvation structure of water molecules in different concentrations of lithium salts (LiTFSI and LiBETI) and the redox potential of aqueous electrolyte by free energy calculation based on MLMD and AIMD^[34]. In this part, the effect of concentration on the electrochemical properties of electrolyte was systematically studied from the perspective of first-principles computational electrochemistry, which laid a theoretical foundation for the research and development of energy materials.

Binding energy is an important parameter to characterize the interaction ability between monomers in a coordination complex, and its definition formula is^[36]

Where E_{\mathrm{b}} is the binding energy, and E_{\mathrm{A}-\mathrm{B}} 、 E_{\mathrm{A}} 、 E_{\mathrm{B}} are the complex energy, monomer A energy, and monomer B energy, respectively. In the process of quantum chemical calculation, considering the difference in the use of basis functions, the binding energy in coordination complexes is usually corrected by adding the basis set overlap error on the basis of the above binding energy^[37]. In the study of electrolyte, binding energy is mainly used to describe the interaction between cations, anions and solvents, which has important reference value for analyzing the ion-solvent chemistry of bulk electrolyte and exploring the design ideas of low-temperature electrolyte (Fig. 1A)^{[38⇓⇓~41]}. Shakourian-Fard et al. Calculated the binding energy of Ethyl methyl carbonate with Ethylene carbonate (EC), Diethyl carbonate (DEC), Dimethyl carbonate (DMC), Ethyl methyl carbonate (EMC) and Propylene carbonate (PC) in electrolyte using M06-2X/6311 + + G (d, p) basis set^[42]. The calculated results show that the binding energy between PC and Li⁺ (-107. 84 kcal/mol) is about 10 ~ 50 kcal/mol smaller than that of other common carbonate solvents such as EC (-153. 69 kcall/mol), DMC (-116. 78 kcal/mole), EMC (-113. 15 kcal/mole) and DEC (-116. 66 kcall/mole). This calculation result can explain the difference of solvent coordination number of the first solvation shell of Li⁺ in different electrolytes to some extent, that is, in PC-based electrolyte, Li⁺ prefers to form coordination relationship with three solvents, while in other carbonate-based electrolytes, the solvent will form a stable tetrahedral configuration around Li⁺. Wu et al. Analyzed the binding energy between the components in the local high concentration electrolyte with LiFSI as the lithium salt and 1,2-Dimethoxyethane (DME) as the solvent by DFT method^[43]. The calculation results show that the weak diluent-anion binding energy is helpful to improve the stability of the solvated structure and inhibit the oxidation of the electrolyte at the high voltage positive electrode. They focused on 2H, 3H-Decafluoropentane (HFC) and Tris (2,2,2-trifluoroethyl) orthoformate (TFEO) diluents, which have different binding energies with FSI^-, and their binding energies with FSI^- are 13.9 and 19.5 kcal/mol, respectively. By analyzing the solvation structure stability of Li⁺, it was found that in the electrolyte containing TFEO, the strong diluent-anion binding energy stripped the Li⁺-FSI^- complex from DME, while the weak diluent-solvent binding energy "fixed" the coordinated DME in place, thus distorting the solvation structure and leading to the early desolvation of DME. However, in the electrolyte containing HFC with weak diluent-anion binding energy, the difficulty of DME de-coordination behavior increases, and the oxidation-intolerant components in the electrolyte decrease, thereby improving the oxidation stability of the electrolyte.

Chen et al. Modeled ethylene carbonate, diethyl carbonate, ethylene glycol dimethyl ether, 1,3-Dioxolane (DOL) solvents and LiPF₆, LiFSI, LiTFSI, LiNO₃ lithium salts and discussed the solvation effect on the interaction between electrolyte species^[11]. DFT simulations show that the solvation effect can significantly reduce the binding energy of Li⁺- solvent, Li⁺- anion and solvent-solvent, while increasing the coordination bond length in the solvated complex. On this basis, they predicted the dissolution behavior of lithium salt in electrolyte by comparing the binding energy between Li⁺- solvent/anion and the dielectric constant of solvent. Specifically, LiPF₆ has good solubility in both ether (DOL and DME) and ester (EC and DEC) solvents due to its weak cation-anion interaction in the electrolyte. LiNO₃ has poor solubility due to strong cation-anion interaction. EC solvent has a high dielectric constant, which can significantly reduce the cation-anion interaction strength in lithium salts, so it has a good solubility for various lithium salts. DME solvent can provide strong ion-solvent interaction and also has good solubility of lithium salt. This study provides a microscopic understanding of the interaction between electrolyte components under solvation, which provides a reference and thinking for the design of new electrolytes.

Different from the normal temperature electrolyte, the special working temperature of the low temperature electrolyte makes the basic interaction between different species change dramatically. Among them, as the rate-determining step of ion migration in low temperature electrolyte, the ion precipitation process at the solid-liquid interface determined by the cation-solvent/anion interaction has become the focus of researchers. Ma et al. Selected the structurally similar ether solvents ethylene glycol dimethyl ether and Dimethoxymethane (DMM) as the research objects, and analyzed the relationship between the solvating ability of solvents in lithium metal batteries and the desolvation behavior of Li⁺ at low temperature^[44]. In general, the number of solvent molecules in the solvated structure and the solvating power determine the resistance of the cation ion desolvation process. The theoretical calculation results show that the binding energy of DMM and Li⁺ is lower than that of DME at all coordination numbers, which proves that DMM has weak solvation ability (Fig. 1b). Compared with DME-based electrolyte, the solvation structure of DMM-based electrolyte contains less solvent with weak solvation ability, so the Li⁺ has faster desolvation kinetics (Fig. 1C). Benefiting from the lower Li⁺ desolvation barrier, the DMM-based weak solvated electrolyte exhibits higher lithium plating/stripping efficiency than DME-based electrolyte at a low temperature of -40 ℃, and the assembled Li ‖ Cu battery has a high coulombic efficiency of 97. 87%.

According to the frontier molecular orbital theory, the redox stability of electrolyte components can be described by the Highest occupied molecular orbital (HOMO) and Lowest unoccupied molecular orbital (LUMO). Generally speaking, a higher HOMO energy indicates that the outermost electron of the molecule is unstable, and the molecule is more likely to lose electrons and be oxidized. For molecules with lower LUMO energy, the foreign electron is more likely to occupy the corresponding orbital, resulting in the reduction of the molecule at high voltage^[45,46]. Wu et al. Calculated the frontier orbital energies of common carbonate solvents in lithium batteries by using Gaussian software with B3LYP/6-31 + G (d, p) as the basis set, and the results are shown in Table 1^[47]. According to the simulation information, the reduction order of different solvents under the same conditions is EC > DMC > DEC > EMC, that is, EMC has the strongest resistance to reduction; DEC is the least susceptible to oxidation according to the HOMO energy. The above calculation results are in good agreement with the results of redox potential measurement, which proves the applicability of DFT calculation method in the study of molecular redox stability.

In general, the calculation of molecular or anionic frontier orbital energies is performed under vacuum conditions or in a specific solvent (ester, ether, water) environment. However, in the electrolyte, different species will interact with each other and form a complex system, which will have a certain impact on the frontier orbital energy of each component of the electrolyte^[48]. Chen et al. Explored the relationship between solvation structure and solvent redox stability in lithium battery electrolyte by DFT calculation^[12]. The calculated results show that the HOMO and LUMO energies of the Li⁺ coordination solvent decrease in different degrees due to the solvation effect in the single-solvent electrolyte, and the decrease of the HOMO and LUMO energies is approximately linearly proportional to the average binding energy of the Li⁺- solvent complex. In the binary solvent electrolyte simulation, they found that the electrolyte solvation environment also affected the redox stability of the coordinated solvent. In general, the larger the dielectric constant of the solvation environment, the weaker the Li⁺- solvent interaction, and the smaller the amount of change in frontier orbital energy. The above research results provide valuable reference for the design and construction of high chemical stability electrolyte.

In addition to the conventional quantum chemical calculation method, the AIMD method can also be used to simulate the electronic structure of the electrolyte system to analyze the redox priority of the electrolyte components, in which the position of LUMO/HOMO can be intuitively obtained from the PDOS diagram. Yamada et al. Found that with the increase of electrolyte concentration, the LUMO orbital of the electrolyte system was gradually transferred from acetonitrile (AN) to TFSI^- anions (Fig. 2)^[49]. This change allows the preferential reduction of TFSI^- anions in the high-concentration LiTFSI AN electrolyte to form AN inorganic-rich SEI layer on the anode surface, which inhibits the further decomposition of the electrolyte and greatly improves the reduction stability of the AN-based electrolyte.

At present, the simulation of the redox stability of electrolyte components is more used in the study of Solid electrolyte interphase (SEI) and Cathode-electrolyte interface (CEI)^[50⇓~52]. Kim et al. Added LiNO₃ and LiDFBP as additives into 1 mol/L LiTFSIDME electrolyte to regulate the electrode-electrolyte interface of lithium metal batteries^[53]. DFT calculations show that additives LiDFBP (− 3.19 eV) and LiNO₃(-1.53 eV) have lower LUMO energy compared to lithium salt LiTFSI (− 0.03 eV) and solvent DME (1.50 eV). LiDFBP and LiNO₃ with different electron-accepting abilities were reduced on the surface of Li anode to construct a dense and robust inner-layer SEI rich in LiF and an outer-layer SEI rich in Li₃N with high ionic conductivity, respectively. In addition, the CEI of NCM811 cathode is further enhanced due to the lowest HOMO energy of LiDFBP in each component of the electrolyte. The final DME ether electrolyte containing LiDFBP and LiNO₃ resulted in a Li ‖ NCM811 full cell achieving a long cycle life (600 cycles) at 0.5 C with a capacity retention of 80.9% and a coulombic efficiency of 99.94%. In addition to common film-forming additives, diluents can also play a role in optimizing the electrode-electrolyte interface. Zhu et al. Used fluorinated aromatic diluents Trifluoromethoxybenzene (TFMB) and Benzotrifluoride (BZTF) to prepare a localized high concentration electrolyte (LiFSIDME/Diluent), and compared the frontier orbital energies of both TFMB and BZTF with those of other electrolyte components^[54]. The results of quantum chemical calculations show that TFMB and BZTF have lower LUMO energy than the commonly used 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether (TTE) diluent, which promotes the synergistic reductive decomposition of FSI^- and diluent in the electrolyte and the formation of uniform and robust SEI on the surface of lithium metal (Fig. 3A, B. The Li(20μmol/L)‖LiNi_0.8Mn_0.1Co_0.1O₂(NCM811, positive electrode loading :3.5 mAh/cm²) full cell using LiFSIDME/TFMB electrolyte achieved an initial capacity of 210 mAh/G and > 80% capacity retention over 260 cycles. Li ‖ NCM811 soft pack cell with an energy density of about 340 Wh/kg (positive loading :3.5 mAh/cm²; Capacity: 1.8 Ah) also showed a good capacity retention of 80% after 200 cycles.

Electrostatic potential (ESP) is a potential field generated by the nucleus and electrons in the space around the molecule, and its definition formula is:^[55]

Where Z_{\mathrm{A}} is the charge carried by the nucleus, \mathrm{\rho } \left( r \text{'} \right) is the electron density, r_A and r are the nuclear and electron coordinates, respectively, and the two terms on the right side of the equation represent the potential field formed by nuclear charge and electron density dominance, respectively. For the region close to the nucleus, the electrostatic potential is always dominated by the nuclear charge, and its value is positive, so it is generally not meaningful to study. For the region outside the van der Waals surface of the system, the electrostatic potential is always dominated by the electron density, and its value can be positive or negative, which has a relatively high research value. In the study of electrolyte system, electrostatic potential is usually used to judge the binding site between solvent and Li⁺, to analyze the influence of functional groups on the solvation ability of electrolyte components, and to predict the nucleophilic/electrophilic reaction site of solvation structure^{[56⇓⇓~59]}. Zhao et al. Judged the binding site of solvent and Li⁺ in the electrolyte by simulating the solvent electrostatic potential of ethylene glycol dimethyl ether and 2,2-Dimethoxy-4- (trifluoromethyl) -1,3-dioxolane (DTDL), and the simulation results are shown in Figure 4A^[60]. The negative electrostatic potential region on the DME molecule is distributed around the oxygen atom and the potential magnitude is similar, while the negative electrostatic potential around the oxygen atom in the DTDL molecule is quite different. The special structure of DTDL makes it and Li⁺ have two possible binding sites, which are the O atom in the cyclic ether and the O atom in the linear ether segment, respectively. The presence of the -CF₃ group in DTDL reduces the electron density of the O atom in the cyclic ether, which weakens the solvating ability of DTDL and changes the coordination of Li⁺ with the solvent. Zhang et al. Used electrostatic potential simulation to study the nucleophilic/electrophilic reaction sites of different solvation structures in the electrolyte of lithium metal batteries, and then analyzed the formation process of SEI on the surface of lithium metal electrodes (Fig. 4B, C)^[61]. For Conventional carbonate electrolyte electrolyte (CCE), the EC molecule in the representative solvated structure has more positive electrostatic potential values, which is considered to be the highly active site for nucleophilic reaction^[62]. The preferential decomposition of EC will directly lead to the formation of organic-rich SEI layer on the surface of lithium anode. Upon the additional addition of In(OTf)₃ and LiNO₃(Solubilizer mediated conventional carbonate electrolyte,SCCE) to the CCE electrolyte, the In³⁺-NO₃^- complex can effectively alter the reaction sites in the solvated structure. EC forms a negative electrostatic potential by interacting with NO₃^-, while NO₃^- with higher electrostatic potential can undergo site-selective reactions within the Helmholtz layer, eventually forming an inorganic SEI layer rich in N and O elements on the electrode surface.

In the electrolyte of lithium metal battery, lithium ion has the characteristics of small volume and high positive charge density. Driven by coordination bonds, hydrogen bonds, van der Waals forces and other forces, it is very easy to interact with nucleophilic aprotic polar solvents and negatively charged anions to form solvated structures. In general, the solvation structure largely affects the physicochemical properties of the bulk electrolyte. Therefore, it is of great significance to systematically study the solvation structure of electrolyte and its control strategy for optimizing the design of electrolyte and improving the performance of battery.

The electrolyte solvation structure is mainly described by the radial distribution function and coordination number, and is visualized by the simulation snapshots. The radial distribution function ( g \left( r \right)) represents the spatial distribution probability of other particles based on one reference particle. It is defined as

Where r is the distance from the study particle to the reference particle, \rho \left( r \right) is the average density of the study particle between r and r + \mathrm{d} r, and \rho is the total density of the study particle in the electrolyte. Integration of equation (11) yields the coordination number ( N \left( r \right)), which is defined by

The solvation structure is closely related to the electrolyte composition (lithium salt and solvent). Among them, the influence of different anions on the solvation structure is mainly attributed to the difference of geometry or charge distribution^[63,64]. Reber et al. Used LiFSI, LiFTFSI and LiTFSI lithium salts with different symmetries for low-temperature lithium battery electrolytes with a mass molar concentration of 35 (35 mol/kg, 35 m)^[65]. The MD-simulated snapshots of the radial distribution functions and solvation structures of the three electrolytes are shown in Fig. 5, and the anions with different geometries exhibit different coordination States with Li⁺. In that radial distribution function, the characteristic peak at about 3.99Å (marked as B) and 4.55Å correspond to the bidentate and monodentate coordination of the anion with the Li⁺ through the O atom, respectively. Among them, the monodentate coordination of FSI^- is the most prominent, both monodentate and bidentate coordination of FTFSI^- are common, and bidentate coordination is dominant in TFSI^-. It is worth mentioning that the asymmetric geometry of FTFSI^- makes its uncoordinated —SO₂CF₃ functional group have high rotational mobility, which hinders the close packing of solvated structure and greatly improves the supercooling performance of electrolyte. Lytle et al. Analyzed the origin of the coordination differences between OTf^- and TFSI^- and Li⁺ by AIMD and enhanced sampling metadynamics^[66]. The simulation results show that although the Lennard-Jones parameters and charges of most atoms in OTf^- and TFSI^- are similar, there is a difference of 0.1 e in the Charge on the sulfonyl oxygen (Charge- {\mathrm{O}}_{\mathrm{O}\mathrm{T}\mathrm{f}}^{-} = − 0.63 e, Charge- {\mathrm{O}}_{\mathrm{T}\mathrm{F}\mathrm{S}\mathrm{I}}^{-} = − 0.53 e), and this subtle Charge difference leads to a major change in the ion pairing behavior of the electrolyte, which in turn affects the ionic conductivity and Li⁺ transference number of the electrolyte.

In addition to anions with special geometry and charge distribution, anions with strong coordination ability are also considered to play an important role in regulating the solvation structure, and they are usually used to replace weak solvation anions to change the species distribution and coordination in the solvation structure^[67]. Zhang et al. Designed a LiPF₆/LiNO₃EC/DMC two-salt electrolyte applied to lithium metal batteries^[68]. Using MD method, it was found that there was a strong competition between NO₃^-, PF₆^- and solvent in the solvated structure. Among them, NO₃^- with strong coordination ability weakens the interaction between Li⁺ and PF₆^- in the solvated structure and increases its own solvation participation for lithium ions. The substitution of NO₃^- for PF₆^- in the solvated structure promotes the formation of a SEI rich in Li₃N. The stable SEI with high conductivity effectively adjusts the nucleation form of lithium at the solid-liquid interface, inhibits the formation of lithium dendrites, and improves the battery cycle performance. In addition, the strong oxidizability and hygroscopicity of LiNO₃ inhibit the degradation of PF₆^- and the leaching of its decomposition products (PF₅ and HF) from the SEI, which greatly improves the coulombic efficiency of the battery while avoiding the continuous reaction of deposited lithium metal with the electrolyte.

Similar to anion, solvent is an important component of solvation structure, and its molecular configuration and solvation level also have a significant impact on solvation structure^[42,69,70]. Yu et al. Modified DME to obtain 1,4-dimethoxylbutane (DMB) and Fluorinated 1,4-Dimethoxylbutane (FDMB), and used the three solvents in the electrolyte of lithium metal battery with LiFSI as lithium salt^[71]. The MD simulation results show that DME has a short alkyl chain between the O atoms that can coordinate with Li⁺, so it can form a bidentate coordination with Li⁺, while DMB with a long alkyl chain can not fold like DME, so it only coordinates with Li⁺ through ether oxygen. In the FDMB-based electrolyte, the ether bond oxygen in FDMB and the F atom on β-C can act together on the Li⁺ to form a five-membered ring. Among them, the interaction between F atom and Li⁺ is weaker than the chelating ability of two ether bond oxygen in DME, which makes FDMB not good at solvating Li⁺. In 1 mol/L LiFSIDME and LiFSIDMB electrolytes, the ratio of anions to solvent in the solvated structure of Li⁺ is 2.31 ∶ 1 and 2.29 ∶ 1, respectively, while in the same concentration of LiFSI FDMB electrolyte, the ratio of anions to solvent in the solvated structure of LiFSI FDMB is 2.The ratio of anions to solvent in the solvated structure of Li⁺ is as high as 3.29 ∶ 1, that is, more anions appear in the solvated structure in FDMB-based electrolyte, which effectively promotes the formation of anion-dominated SEI on the surface of lithium metal electrode and further improves the electrochemical performance of lithium metal full battery. However, the LiFSI/FDMB electrolyte system has the problem of high lithium deposition overpotential, which may be attributed to the decrease of ionic conductivity or the high SEI impedance caused by the introduction of fluorinated solvents into the system. In order to solve this problem, on the basis of FDMB, they further designed Fluorinated-1,2-diethoxyethane (Fluorinated DEE) solvents with different degrees of fluorination to control the microstructure and physicochemical properties of electrolytes^[72]. The computational simulation results show that the interaction between the solvent and the Li⁺ is weakened with the increase of the degree of fluorination of DEE, and the number of solvents in the solvated structure is decreasing, while the number of anions is increasing. By controlling the fluorination position and degree of DEE, adjusting the solvation structure of electrolyte, alleviating the serious Li⁺-FSI^- aggregation in electrolyte system, forming more mobile Li⁺ charge carriers, they successfully overcome the problems of poor ionic conductivity and high overpotential of FDMB electrolyte, and further improved the performance of batteries.

In addition to the electrolyte composition, the concentration can also significantly affect the formation of solvated structures. Since the wide application of lithium batteries, researchers have been committed to improving the electrolyte formulation to improve the electrochemical performance of batteries, but neglected the important influence of concentration on the microstructure and physicochemical properties of electrolytes. At present, 1 mol/L is the most widely used concentration standard in electrolyte design. Although 1 mol/L electrolyte has the highest bulk conductivity, it does not necessarily bring the best electrochemical performance to the battery, especially the rate performance^[73]. Therefore, it has become an important means to improve the electrochemical performance of batteries by controlling the electrolyte concentration to control the microstructure and physicochemical properties of the electrolyte^{[74⇓⇓~77]}.

According to the concentration difference, the electrolyte can be divided into low concentration electrolyte and high concentration electrolyte. The use of lithium salt in low concentration electrolyte is economical, but it also promotes the formation of unstable SEI rich in organic matter and the occurrence of side reactions between free solvent and electrode. In high concentration electrolyte, the amount of free solvent in the electrolyte system is greatly reduced due to the increased coordination between solvent molecules and Li⁺, which effectively inhibits the undesirable solvent-electrode side reaction in low concentration electrolyte. At the same time, because lithium salt can not be completely dissociated in high concentration electrolyte, the participation of anions in the solvation structure has been greatly improved, which promotes the formation of stable SEI rich in inorganic components^[78].

Wang et al. Used MD method to simulate the solvation structure evolution of LiFSIDMC electrolyte from low concentration to ultra-high concentration (Fig. 6a)^[79]. Under low concentration simulation conditions (1 LiFSI and 25 DMC, < 1 mol/L), all DMC solvents in the electrolyte system are free due to the high molar ratio of solvent to lithium salt; At moderate concentrations (12 LiFSI and 24 DMC, ≈ 4 mol/L), a large number of solvent molecules participate in the four-coordinated or five-coordinated solvated complexes of Li⁺, and anions mainly coordinate to Li⁺ in the form of aggregates. Under the condition of ultra-high concentration simulation (10 LiFSI and 11 DMC, ≈ 5.5 mol/L), the coordination degree between anions and Li⁺ is improved, so that the whole electrolyte system presents a complex three-dimensional network structure, and free solvent molecules and anions can hardly be observed.

The increase of electrolyte concentration usually increases the proportion of anions in the solvation structure, which leads to the decrease of HOMO and LUMO energy of the whole electrolyte to the level of salt anions, which not only promotes the pre-reduction and decomposition of salt anions replacing solvents on the surface of lithium anode, but also improves the oxidation resistance of electrolyte to positive electrode. Fan et al. Reported a high-concentration electrolyte (10 mol/L LiFSI EC/DMC) for lithium metal batteries, and found that L LiFSI EC was preferentially decomposed at the negative electrode to form LiF-rich SEI^[80]. Moreover, FSI^- plays a dominant role in the formation of fluorinated CEI on Ni-rich cathode as the solvent content decreases. Finally, the capacity retention of the Li‖LiNi_0.6Co_0.2Mn_0.2O₂(NCM622) battery with the prepared high-concentration electrolyte reached 86% after 100 cycles at a high cut-off voltage of 4.6 V.

The strong interaction between anions and cations in high concentration electrolyte can effectively increase the proportion of anions in the solvated structure and promote the formation of anion-derived SEI, but it also reduces the ionic conductivity of the electrolyte and the wettability of the electrode and separator^[81]. The above problems can be well solved by the local high concentration electrolyte, which is mainly obtained by adding a non-solvated inert diluent to the high concentration electrolyte. Since the interaction force between the diluent and the Li⁺ is weak, it generally does not appear in the first solvation shell, which allows the solvation characteristics of the high-concentration electrolyte to be maintained in the local high-concentration electrolyte^[82⇓~84]. Although the diluent does not participate in the local solvated complex of Li⁺, it changes the microstructure of the electrolyte system, which in turn affects the physical properties of the electrolyte.

Beltran et al. used the AIMD method to reveal the microstructure evolution of an electrolyte with LiFSI as the lithium salt, DMC as the solvent, and Bis (2,2,2-trifluoroethyl) ether (BTFE) as the diluent from a high concentration state to a local high concentration state (Fig. 6B)^[85]. In high concentration electrolyte (LiFSI ∶ DMC ∶ BTFE = 1.00 ∶ 1.10 ∶ 0.00, molar ratio), the FSI^- interacts with multiple Li⁺ to form a complex three-dimensional network structure. When a small amount of diluent was introduced into the electrolyte system (LiFSI ∶ DMC ∶ BTFE = 0.94 ∶ 1.10 ∶ 0.65, molar ratio), the complex network structure was not destroyed but opened by the diluent. When the diluent content is further increased (LiFSI ∶ DMC ∶ BTFE = 0. 64 ∶ 1. 10 ∶ 1. 65, molar ratio), the three-dimensional network structure is completely divided to form island solvated complexes, but most of the Li⁺still maintain the special solvated structure in the original high concentration electrolyte.

Ionic conductivity is an important factor affecting the rate performance and low temperature performance of batteries, which has a high reference value in the design process of high performance electrolyte^[86]. In general, the ion diffusion coefficient should be preferentially calculated before the ionic conductivity is simulated. Specifically, the ion diffusion coefficient (Mean square displacement) of the electrolyte was obtained from the Mean square displacement (MSD) method based on MD trajectories. Its expression is

Where d is the diffusion dimension, N is the number of diffusing ions, and r_{\mathrm{i}} \left( t \right) is the coordinate of ion i at time t. Based on this, the electrolyte ionic conductivity ( \sigma) can be obtained by the Nernst – Einstein equation:

Where Z_{\mathrm{c}} is the ion valence, e is the electron charge, C is the ion concentration, k_{\mathrm{B}} is the Boltzmann constant, and T is the temperature.

Because ionic conductivity is studied for cations and anions, the salt concentration of the electrolyte usually has a direct effect on ionic conductivity. Ravikumar et al. Studied the ion dynamic characteristics of LiPF₆EC system in the concentration range of 0.06 ~ 4 mol/L (Fig. 7A)^[87]. The MD simulation results show that the ionic conductivity of the electrolyte increases with the increase of the concentration, reaches the peak at 1 mol/L, and then decreases gradually. The diffusion coefficient of ions (Li⁺ and PF₆^-) in the electrolyte and the molar conductivity of the solution decrease with the increase of the concentration. The above simulation results are mainly attributed to the difference of solvation state of different concentrations of electrolyte. In low concentration electrolyte, Li⁺ forms coordination with five EC molecules. Subsequently, its average coordination number decreased with increasing salt concentration, reaching 2.8 at 4 mol/L concentration. In high concentration electrolyte, the contact ion pair and the cluster in the form of aggregate replace the common solvent-separated ion pair in low concentration, and the ion diffusion is greatly limited, so the ionic conductivity is significantly reduced, and the low mobility of the contact ion pair and the aggregate also leads to the decrease of the molar conductivity of the electrolyte. It is worth noting that the number of solvent-separated ion pairs in the electrolyte, similar to the ionic conductivity, reaches a maximum at a concentration of 1 mol/L, which to some extent confirms the correlation between solvent-separated ion pairs and the properties of the electrolyte.

In addition, according to the thermodynamic theory, high temperature usually triggers more violent particle motion in the system, so the ion transport characteristics of the electrolyte will also be affected by temperature. Wang et al. Studied the ionic conductivity of commercial electrolyte (L LiBOB PC) and multi-salt electrolyte (E1 ∶ 0.1 mol/L LiDFBOP + 0.4 mol/L LiBOB PC/FEC/EMC, E2∶0.1 mol/L LiDFBOP+0.2 mol/L LiBOB+0.2 mol/L LiPF₆PC/FEC/EMC) at different temperatures by means of experiment and simulation^[88]. Similar to the expected results, the electrolyte ionic conductivity shows a positive correlation with temperature (Figure 7 B). The STD electrolyte exhibits higher ionic conductivity than the other two electrolytes due to the higher lithium salt concentration and the degree of dissociation of anions and cations. It is worth noting that the calculated values of ionic conductivity obtained from MD simulation are in good agreement with the experimental values, which confirms the reliability of MD method in describing the properties of electrolyte.

Dielectric constant is one of the important physical and chemical properties of electrolyte. According to the classical laws of physics, the dielectric constant can significantly affect the interaction between solute and solvent, thus regulating the solvation structure of electrolyte. Specifically, the electrostatic interaction between ions or molecules is greatly weakened by the solvation effect, in which the dielectric constant plays a major role; The change of cation-solvent, cation-anion and solvent-solvent interactions in the electrolyte will further affect the formation of solvation structure. Therefore, the in-depth study of dielectric constant is helpful to regulate the interaction between species at the micro level and the electrolyte properties at the macro level, which is of great significance for optimizing the electrolyte design and improving the battery performance. However, the complexity of electrolyte composition brings great challenges to the test and research of dielectric constant. Fortunately, the dielectric constant of the electrolyte can be calculated by MD simulating the temporal fluctuation of the sum of the charge dipole moments of individual atoms in the system^[89,90]. The dielectric constant (ε) of the liquid electrolyte is defined as

Where ε₀ is the dielectric constant in the vacuum state, V is the volume of the simulation box, k_{\mathrm{B}} is the Boltzmann constant, T is the temperature and M = \sum \mathrm{\mu } = \sum q r is the total dipole moment of the system, where q is the charge of the atom and r is the position of the atom.

Yao et al. Studied the variation of dielectric constant of liquid electrolyte with temperature and electrolyte composition by molecular dynamics simulation^[32]. Specifically, the dielectric constant decreases with increasing temperature due to the intense motion of the molecules and their enhanced ability to overcome intermolecular dipole-dipole interactions at high temperatures (Figure 8 a). For the binary solvent mixture, the dielectric constant changes with the composition as a polynomial function and a linear function, respectively, depending on the strength of the intermolecular interaction (Fig. 8 B, C). In addition, they also explored the variation of dielectric constant of high concentration electrolyte and local high concentration electrolyte. Because ions not only contribute to the dielectric constant, but also change the arrangement of solvent molecules by forming solvated complexes. Therefore, with the increase of electrolyte salt concentration, the change of dielectric constant shows a volcano trend of first increasing and then decreasing (Fig. 8d). In the local high concentration electrolyte, the increase of diluent will also increase the dielectric constant of the electrolyte.

Different from the bulk electrolyte, the electrolyte at the interface is in direct contact with the electrode, and its microstructure has important reference value for analyzing the chemical properties of the interface. Generally, the electrode surface of the battery will attract specific ions and molecules from the electrolyte through physical electrostatic interaction or chemical adsorption, forming an Electric double layer (EDL). The concept of EDL was first described and modeled by von Helmholtz in 1853, and further modified by Gouy, Chapman, and Stern. Stern divided the EDL into a dense layer and a diffuse layer. The Inner structure of the dense layer on the electrode is defined as the Inner Helmholtz plane (IHP). The species distributed in the IHP are mainly anions and neutral molecules. Due to the limitation of space, there are almost no solvated molecules in the IHP. The Outer structure near the IHP is defined as the Outer Helmholtz plane (OHP), in which some complete solvation structures gradually emerge^[91].

The microstructure of the electrode-electrolyte interface is generally directly affected by the composition of the electrolyte. Zhang et al. Constructed a novel EDL structure with adaptive and passivation properties by introducing a functional anionic additive (LiNO₃) into the electrolyte^[92]. The MD simulation results of the Helmholtz interfacial region within the positive electrode surface are shown in Fig. 9. For the LiFSIDME system, when the electrode voltage is gradually increased, anions are adsorbed and enriched on the surface of the cathode, while Li⁺ is discharged from the inner layer of the EDL, resulting in a large amount of DME in the free state (Figure 9 A). In contrast, a large amount of Li⁺ still remains in the inner layer of the EDL of the LiFSI/LiNO₃DME system. Most of the DMEs form a coordination relationship with Li⁺, thus forming multiple polymer-like chain structures with high electrochemical stability at the electrode interface (Fig. 9b). Based on this special design, the decomposition of ether-based electrolyte is significantly inhibited at the high voltage cathode interface, which makes the battery show outstanding performance such as ultra-high speed charge and discharge and ultra-low temperature application.

Because the desolvation of Li⁺ at the electrode interface is the rate-determining step in the electrochemical process at low temperature, which highly affects the electrochemical kinetics, the interfacial microstructure, which is closely related to the desolvation process of Li⁺, has become an important part of the research on low-temperature electrolytes. Holoubek et al. Simulated the desolvation path of Li⁺ in DEE and DOL/DME-based electrolytes at low temperature by molecular dynamics (Fig. 9 B, C)^[93]. The results show that the anionic solvated structure is more favorable for Li⁺ to desolvate and migrate to IHP due to the electrostatic repulsion. This work provides a reference for the electrolyte design of low temperature lithium metal batteries.

Because of the high reactivity of lithium metal, its surface electrolyte is easy to decompose spontaneously, forming SEI. Ideally, SEI not only has the characteristics of "ion transport, electronic insulation", but also can block the further decomposition of electrolyte, which is an important role in regulating the interface of lithium metal anode. Understanding and mastering the reaction mechanism of the anode-electrolyte interface is of great significance for the design of high-quality SEI and the construction of stable lithium anode. AIMD simulation is widely used to explore the decomposition mechanism of electrolyte components because it can intuitively simulate chemical reactions. Gomez-Ballesteros et al. Simulated the decomposition process of EC molecule under the reduction of different electron numbers^[94]. In the case of one-electron reduction, EC will decompose to form EC radicals, whereas in the case of two-electron reduction, EC will decompose to form ethylene (C₂H₄) and carbonate ions (CO₃^2-). Clarke-Hannaford et al. Used AIMD simulation to study the decomposition mechanism of TFSI^- and FSI^- on Li (001) surface^[95]. Fig. 10 shows that these two anions achieve dissociation through the cleavage of C-F, S-C, S-F, S-O and N-S bonds, among which, the dissociation of FSI^- is faster and more thorough than that of TFSI^-. Furthermore, Zheng et al. Analyzed the reaction mechanism of 1 mol/L LiFSIDME/TFEO local high concentration electrolyte on the surface of lithium metal anode by AIMD^[83]. The results show that when LiFSI and TFEO molecules are close to each other and contact the anode surface, the fluorine-containing radicals produced by the rapid decomposition of salt anions can initiate the decomposition of TFEO, and finally the LiF-rich SEI is rapidly formed on the surface of lithium metal, which improves the cycle stability of lithium metal batteries.