Theoretical study on the role of magnesium chloride complexes induced by different magnesium-to-chlorine ratios in magnesium–sulfur batteries

Abstract

In magnesium–sulfur batteries, electrolyte exploration is vital for developing high-energy-density, safe, and reliable batteries. This study focused on cyclic THF and chain DME, representative solvents in ether electrolytes. MgCl₂, an ideal anionic salt, forms mono-nuclear (MgCl₂(DME)₂), bi-nuclear ([Mg₂(μ-Cl)₂(DME)₄]²⁺), and tri-nuclear ([Mg₃(μ-Cl)₄(DME)₅]²⁺) complexes in DME. With increasing salt concentration, these complexes sequentially form. Under lower salt concentrations, THF and MgCl₂ form mono-nuclear complexes ([MgCl₂(THF)₄]) and continue to form bi-nuclear complexes ([Mg₂(μ-Cl)₃(THF)₆]⁺). However, at higher salt concentrations, bi-nuclear complexes ([Mg₂(μ-Cl)₃(THF)₆]⁺) directly form in THF. Comparing HOMO–LUMO values, [Mg(DME)₃]²⁺ is easily oxidized. Energy gaps decrease with Cl⁻ ion addition, enhancing solution conductivity. Ratios of Mg²⁺ and Cl⁻ in S-reduction complexes differ, suggesting DME is better at a low Mg/Cl ratio, and THF at a high Mg/Cl ratio. This study contributes to understanding complexes and enhancing Mg–S battery performance.

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1. Introduction

There is an urgent need for economical, high energy density, and safe rechargeable batteries for applications in portable electronics, electric vehicles, and grid energy storage. Among potential candidates, magnesium–sulfur (Mg–S) batteries have emerged as promising contenders due to their high theoretical capacity, low cost, inherent safety, and the abundance of magnesium and sulfur in the Earth's crust. This has garnered significant research interest in recent years.¹ Mg–S batteries offer a theoretical energy density exceeding 3200 W h L⁻¹, surpassing even lithium-sulfur batteries (2800 W h L⁻¹) due to the two-electron conversion reaction Mg²⁺ + S + 2e⁻ ↔ MgS.^2–4 However, some challenges remain. Magnesium, being a highly reactive metal, presents a greater migration barrier for bivalent Mg²⁺ ions compared to traditional monovalent alkali metals. Additionally, the formation of passivation layers containing reduction products (MgO, Mg(OH)₂, MgCO₃, etc.) on the Mg anode hinders Mg²⁺ transfer, leading to higher impedance.^5–9 The electrolyte plays a crucial role in determining battery performance by providing the medium for ionic conduction and influencing the electrode–electrolyte interface for both cathode and anode reactions.¹⁰ In Mg–S batteries, electrolyte additives offer a cost-effective approach to enhance performance. For instance, incorporating a small amount of I₂ facilitates Mg²⁺ transfer by forming a conductive MgI₂ layer on the Mg anode.⁵ Similarly, adding MgCl₂ provides a readily available source of Mg ions, usually present as complexes (MgCl⁺ or Mg₂Cl₃⁺) in chlorine-based electrolytes. However, the dissociation of these complexes requires significant energy (around 3.0 eV).¹¹

Related studies have shown that magnesium chloride complexes have excellent magnesium deposition activity and reversibility, which also helps to dissolve Mg metal passivating surface films, such as (MgO/Mg(OH)₂ layer.^6,10 Mg and Cl ions will form different complexes in dimethoxyethane, 2015 Cheng et al.¹⁰ first proposed that the complex [Mg₂(μ-Cl)₂(DME)₄]²⁺ is formulated in dimethoxyethane (DME) through dehalodimerization of non-nucleophilic MgCl₂ by reacting with either Mg salts or Lewis acid salts. The results show that the complex has excellent magnesium deposition activity and reversibility. It is proved that they are feasible for practical magnesium batteries. 2017 Salama et al.⁶ found that DME, as a ligand, can stabilize the formation of multivalent cations through intrinsically bound DME molecules, such as [Mg₂(μ-Cl)₂(DME)₄]²⁺ and [Mg₃(μ-Cl)₄(DME)₅]²⁺, which are chlorinated complexes that help to dissolve away Mg metal passivating surface films. 2017 Du et al.¹² identified a unique tetra-nuclear cationic complex [Mg₄Cl₆(DME)₆]²⁺ for the first time and demonstrated to show high Mg plating/striping reversibility. 2019 Chaffin et al.¹³ studied the equilibrium between trans-[MgCl₂(DME)₂] and cis-[MgCl₂(DME)₂] isomers using Raman and infrared spectroscopy, and indicating the presence of [Mg₂(μ-Cl)₂(DME)₄]²⁺ complex. In 2020, Huang et al.'s¹⁴ study showed that the irreversible deposition of Al³⁺ leaded to an ionic configuration of magnesium trifluoromethanesulfonate based (MTB) electrolyte transformation from [Mg₂(μ-Cl)₂(DME)₄]²⁺ to [Mg₃(μ₃-Cl)(μ₂-Cl)₂(DME)₇]³⁺ ([Mg₂(μ-Cl)₂(DME)₄]²⁺ + [Mg(DME)₃]²⁺ + Cl⁻ = [Mg₃(μ₃-Cl)(μ₂-Cl)₂(DME)₇]³⁺). 2020 Attias et al.¹⁵ suggested that chlorine-containing complexes (such as [Mg₃(μ-Cl)₄(DME)₅]²⁺) adsorbed on to the Chevrel Phase (CP) surface (e.g., in the 0.25 M MgTFSI₂ + 0.5 M MgCl₂/DME (ICD = Imid/Chloride/DME)) electrolyte solution) reduce the activation energy of magnesium ions in the charge transfer reaction stage across the solid/solution interface. 2021 Yang et al.¹⁶ believed that the high ionic conductivity and unique solvation structure of [Mg₂(μ-Cl)₂(DME)₄]²⁺ accelerated the charge transfer process of Mg ions. 2022 Eilmes et al.¹⁷ observed that besides Raman bands at 213 and 221 cm⁻¹ of the respective MgCl₂(DME)₂ and [Mg₂(μ-Cl)₂(DME)₄]²⁺ complexes, a new band at 236 cm⁻¹, which was belonging to the [Mg₃(μ-Cl)₄(DME)₅]²⁺ species for the first time. It is suggested that the presence of both dimer and trimer could be the reason for the unprecedented electrochemical performance of the MMAC (Mg powder, MgCl₂ and AlCl₃)–DME system.

Tetrahydrofuran (THF), as a cyclic ether compound, has been widely used for its advantages of low boiling point, good fluidity, and strong solubility to many chemical substances. Studies on magnesium chloride cationic complexes have been conducted earlier. 2011 Kim et al.¹⁸ studied the electrochemically active substance [Mg₂(μ-Cl)₃(THF)₆]⁺ formed from the reaction of an Hauser base compound HMDSMgCl and a Lewis acid AlCl₃. This crystallization resulted in a dramatic improvement in the potential stability and coulombic efficiency. 2014, Liu et al.¹⁹ also reacted to produce [Mg₂(μ-Cl)₃(THF)₆]⁺ cations with electrochemical activity using the method of mono-Cl⁻ abstraction. This dimer has exceptional oxidation stability, improved electrophilic susceptibility, high current density and reversible Mg plating and stripping. 2015, Liu et al.²⁰ believed that [Mg₂(μ-Cl)₃(THF)₆]⁺ and [MgCl(THF)₃]⁺ could both be used as active substances for Mg deposition. 2015 See et al.²¹ suggested that the active Mg complex in conditioned magnesium aluminum chloride complex (MACC) is very likely the [Mg₂(μ-Cl)₃(THF)₆]⁺ complex that is observed in the solid state structure. Later See et al. confirmed in 2017²² that [Mg₂(μ-Cl)₃(THF)₆]⁺ is the main active complex for Mg electrodeposition, and the higher the concentrations, the higher the deposition currents. 2019, B. Moss et al.'s,²³ calculation results showed that MgCl₂(THF)₃ dichloride species and [MgCl(THF)₅]⁺ monochloride species are the dominant mononuclear species in solution, and they combine to form a binuclear species [Mg₂(μ-Cl)₃(THF)₆]⁺. Both mono-cation species can act as active species for Mg deposition, but the dinuclear species in the electrolyte have significant dominance and it is the primary species involved in reversible Mg deposition. 2020, Chaffin et al.'s,²⁴ spectral results showed that [Mg(THF)₆]²⁺ is the major species and responsible for the lower electrochemical performance of the 1 : 1 MACC-THF electrolyte, whereas [MgCl₂(THF)₄] and [Mg₂(μ-Cl)₃(THF)₆]⁺ are the complexes related with the higher electrochemical activity of the 2 : 1 MACC-THF electrolyte. 2021 Eilmes et al.²⁵ also proved the research results of Chaffin, and also proposed the existence of [MgCl(THF)₅]⁺ complex in the electrolyte solvent of 1 : 1 MACC-THF. By calculating the infrared spectrum, it is also shown that [MgCl(THF)₅]⁺ and [Mg₂(μ-Cl)₃(THF)₆]⁺ preferentially formed at in 1 : 1 and 2 : 1 electrolyte solutions, respectively. 2022 Xiao et al.²⁶ formed an all-magnesium salt electrolyte by co-dissolving Mg(pftb)₂ and MgCl₂ in THF. Complex [Mg₂(μ-Cl)₃(THF)₆]⁺ is the main electrochemically active species of the electrolyte. The higher MgCl₂ concentration, corresponding to more active ions [Mg₂(μ-Cl)₃(THF)₆]⁺, gives higher redox reaction current density. 2022 Cheng et al.²⁷ found that the chlorine-containing cation in the novel MgCl₂–B(Otfe)₃ (MCBB) electrolyte is [Mg₂(μ-Cl)₂(THF)₆]²⁺, which has a lower de-solvation energy barrier in terms of Mg plating.

The above studies show that different proportions and concentrations of Mg²⁺ and Cl⁻ in solution will produce different types of cations, which will have different effects on deposition overpotential, current density and regulation process. The related literature show that, Mg/Cl = 1 : 1 corresponds to MgCl⁺,^20,23,25 Mg₂Cl₂²⁺,^{6,10,13,14,16,17,27} Mg₃Cl₃³⁺ (ref. 14) cations, Mg/Cl = 1 : 2 corresponds to MgCl₂,^13,17,23,24 Mg/Cl = 2 : 3 corresponds to Mg₂Cl₃⁺,^18–26 Mg₄Cl₆²⁺ (ref. 12) cations, and Mg/Cl = 3 : 4 corresponds to Mg₃Cl₄²⁺ (ref. 6, 15 and 17) cations. These cations combine with different solvent molecules (such as DME or THF) to form different complexes, which have the effect of improving the battery interface and improving the battery performance. The degree of de-solvation of Mg ions from the electrolyte is an important factor affecting the performance of Mg–S batteries, but the mechanism of the interaction between the magnesium anode and the electrolyte interface is still unclear. The generation process of these magnesium chloride complexes and the thermodynamic behavior in the discharge process have not been studied systematically.

In this paper, we first determined the stable complex structures of different anions and Mg²⁺ in DME solution by calculation. It was observed that Cl⁻ had a better de-solvation effect on Mg²⁺ in solvent. Then, the structure and properties of magnesium chloride complexes formed in DME and THF electrolytes were investigated in detail according to the different proportion of Mg/Cl. According to the concentration of Mg/Cl in different proportions, we determined the magnesium chloride cationic complexes in different solvents. The DME molecule has a di-oxygen chain structure, forming the [Mg₂(μ-Cl)₂(DME)₄]²⁺ complex at Mg/Cl = 1 : 1, the [Mg₃(μ-Cl)₄(DME)₅]²⁺ complex at Mg/Cl = 3 : 4. THF has a mono-oxygen ring structure, forming the [MgCl₂(THF)₄] complex at Mg/Cl = 1 : 2, the [Mg₂(μ-Cl)₃(THF)₆]⁺ complex at Mg/Cl = 2 : 3. According to the free energy calculation results, we analyzed the formation process of magnesium chloride complexes. With the increase of MgCl₂ salt concentration, the proportion of Mg/Cl also increased, and MgCl₂(DME)₂ was first formed in DME solution. With the increase of MgCl₂ salt concentration, the main complex in the solution was [Mg₂(μ-Cl)₂(DME)₄]²⁺, and as MgCl₂ continues to increase, the reaction mainly produces [Mg₃(μ-Cl)₄(DME)₅]²⁺ complex. Similarly, the [MgCl₂(THF)₄] complex was first formed in THF solution, and with the increase of salt, the main complex becomes [Mg₂(μ-Cl)₃(THF)₆]⁺. In addition, we drew a flow chart of the action of magnesium chloride complexes in the process of S-reduction under different solvation conditions. In contrast, the Mg/Cl ratio in DME is lower, while the Mg/Cl ratio in THF is higher. If the two solvents are mixed, then the Mg/Cl ratio of the electrolyte can be kept constant.

2. Computational methods

In order to find the preferred structures of magnesium chloride complexes, we employed the swarm-intelligence based ABCluster structure prediction method,^28,29 which can efficiently search for the stable structures. Furthermore, a global search should be an effective method to avoid missing candidates of ground state structures. To improve the search efficiency, point group symmetry and the bond characterization matrix technique were included to eliminate similar structures.

The underlying local structure optimization and electronic property calculations were performed at the density functional theory (DFT) level using the B3LYP³⁰ hybrid functional as implemented in the Gaussian 16 package. Since there are thousands of structures generated during the structure search, an economic basis set, i.e. 3-21G for Mg and S, was chosen to optimize these structures. These settings are enough for evaluating the relative energies of the generated structures. After the structure search, the accurate basis set of 3-21+G(d) was used for the refined structure optimization and vibrational frequency calculation for the isomers with low-lying energies. The absence of an imaginary frequency confirms that the predicted structures are stability.

First, we calculated the reaction voltage per solvent molecule, the formation energies were defined as

where G_{[MgxCly(DME/THF)n]^(2x−y)+} is the lowest energy of structure Mg_xCl_y(DME/THF)_n, E_MgCl2 and G_DME/THF are the energy of MgCl₂ and DME/THF molecule respectively. And G_Mg²⁺ is the energy of magnesium ion. All the energies involved in the calculation in eqn (1) are based on the solvent environment of 1,2-dimethoxy-ethane (DME) and 1,4-epoxybutane (THF). In addition, the implicit solvent method is used (ε = 7.2 (DME) and ε = 7.6 (THF)).

The Gibbs reaction free energy is defined as

ΔG = E_resultant − E_reactant (2)

where E_resultant is the energy of the resultant, E_reactant is the energy of the reactants.

The change in the driving force of the Gibbs reaction is defined as

Δ²G = ΔG_Rx − ΔG_Ry (3)

where ΔG_Rx and ΔG_Ry are the Gibbs free energies of the corresponding equation.³¹

HOMO–LUMO energy gap (E_g) was calculated as follows

E_g = E_LUMO − E_HOMO (4)

Among them, E_LUMO and E_HOMO are the energy levels of LUMO and HOMO, respectively.

3. Results and discussion

3.1 Effect of different anions within DME solvent on the de-solvation of Mg²⁺

Magnesium sulfur battery electrolyte solute anions are numerous, corresponding to the formation of different complexes, before the study of the exact complex mechanism need to determine the appropriate anion, which has practical significance to put into production in later stage, we have done research on several suitable anions, by adding anions in the solvent stable structures as shown in the Table below.

From the stable structure of [Mg(DME)₃]²⁺ without anion added in Table 1, it can be seen that the oxygen atom coordination number around Mg ion is 6. Table 1 shows the stable structures of adding one Cl⁻ ion (No. 2) and two Cl⁻ ions (No. 3). It can be seen that Cl atoms replace the position of oxygen atoms and form Mg–Cl bond, indicating that Cl⁻ can have a better de-solvation effect on Mg²⁺ at DME solvent, help to increase the solubility of Mg²⁺ and improve the performance of Mg–S battery. In the following, we will focus on the structures and formation process of Mg–Cl complexes of MgCl₂ salt solute in different electrolytes (DME, THF) according to Mg/Cl ratio.

Table 1 The different anions in DME solvent form stable structures with Mg²⁺, and the stable structure of Mg–Cl complexes in DME and THF solvents

No. 1	No. 2	No. 3	No. 4
[Mg(DME)3]^2+	[MgCl(DME)3]^+	MgCl2(DME)2	[Mg2(μ-Cl)2(DME)4]^2+
No. 5	No. 6	No. 7	No. 8
[Mg3(μ-Cl)4(DME)5]^2+	[Mg(THF)6]^2+	MgCl2(THF)4	[Mg2(μ-Cl3)(THF)6]^+

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3.2 Structures and formation process of MgCl₂ solute within DME solvent

The structure of different Mg–Cl complexes in DME solvent are shown in the Table 1. We first found the lowest energy stable complex structures through calculation, and the results are shown in the Table 1.

According to the Mg/Cl = 1 : 1, Mg/Cl = 1 : 1.3 and Mg/Cl = 1 : 2, the three structures can be obtained in Table 1. From the structures in Table 1, it seen that the mono-nuclear complex (No. 3) of Mg atom is composed of four Mg–O bonds and two Mg–Cl bonds, with a total coordination number of 6. It can be seen from the structures of bi-nuclear (No. 4) and tri-nuclear complex (No. 5) that two chlorine atoms are shared between the two magnesium atoms, and the remaining coordination are complemented by the oxygen atoms in the DME. The stable structures we found based on the DFT calculation are consistent with the structures in the previous literature.⁶

3.2.1 Formation path of Mg–Cl complexes within DME solution. In the above, we have obtained the lowest energy structure of mono-nuclear, bi-nuclear and tri-nuclear complexes, but the formation process and reaction mechanism of each complex are still not well understood. Therefore, we predict the reaction generation paths of several complexes, as shown in Table 2 below.

Table 2 Reaction steps to form mono-nuclear, bi-nuclear, and tri-nuclear complexes in DME solutions

No.	Equation	ΔG (eV)	ΔGper DME
R1	MgCl2 + 2DME = MgCl2(DME)2	−8.62	−4.31
R2	Mg^2+ + MgCl2(DME)2 + 2DME = [Mg2(μ-Cl)2(DME)4]^2+	3.95	0.99
R3	MgCl2 + [Mg2(μ-Cl)2(DME)4]^2+ + DME = [Mg3(μ-Cl)4(DME)5]^2+	0.46	0.09
R4	Mg^2+ + MgCl2 + 4DME = [Mg2(μ-Cl)2(DME)4]^2+	−4.67	−1.17
R5	Mg^2+ + 2MgCl2 + 5DME = [Mg3(μ-Cl)4(DME)5]^2+	−4.21	−0.84

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We studied the reaction mechanism of Mg–Cl cationic ligands to form complexes in DME. The results of the free energy are calculated with the eqn (1), and the simulation show that the possible reactions between MgCl₂ and four DME molecules and the corresponding reaction free energy are shown in Fig. 1. One reaction pathway is that with the addition of MgCl₂, MgCl₂(DME)₂, [Mg₂(μ-Cl)₂(DME)₄]²⁺ and [Mg₃(μ-Cl)₄(DME)₅]²⁺ complexes gradually appear in the solution. The other is to form MgCl₂(DME)₂ complex in solution first, then react with Mg ion in solution to form [Mg₂(μ-Cl)₂(DME)₄]²⁺, and then continue to react with MgCl₂ salt to form [Mg₃(μ-Cl)₄(DME)₅]²⁺. As shown in step R₁, the reaction between MgCl₂ and DME produces the intermediate MgCl₂(DME)₂, where calculated free energy (ΔG) is −4.31 eV, and then MgCl₂ increases to produce [Mg₂(μ-Cl)₂(DME)₄]²⁺ complex, as shown in step R₄. The free energy of the process is −1.17 eV. MgCl₂ salt continues to increase the reaction to form the [Mg₃(μ-Cl)₄(DME)₅]²⁺ complex, which ΔG is −0.84 eV, as shown in step R₅. Others reaction method, such as R₂ and R₃, ΔG are all over 0 for [Mg₂(μ-Cl)₂(DME)₄]²⁺ and [Mg₃(μ-Cl)₄(DME)₅]²⁺, indicating that the reaction is difficult to occur. The reaction shown in R₁, R₄, and R₅ is more favorable. And mono-nuclear, bi-nuclear, and tri-nuclear complexes are formed directly in the electrolyte solution with the increase of MgCl₂ salt.

Fig. 1 Reaction pathways of Mg–Cl complexes in DME solvent.

3.2.2 The Mg–Cl complexes within DME solution in the process of discharge reaction. The positive electrode is a very important part of the Mg–S battery system, so we studied the reaction of the positive electrode of sulfur, according to the change of the valence of sulfur, we listed the following reaction equation, and calculated the corresponding reaction free energy ΔG.

All the calculation results in Table 3 are obtained under the conditions of DME solvation. As can be seen from Table 3, the magnesium polysulfide involved in the calculation are the structures energy optimized in the previous work,³² the ΔG of R₁₃ is under 0, which can be occurred spontaneously, while the free energy of the rest R₆–R₁₂ are over 0, As mentioned above, both [Mg₂(μ-Cl)₂(DME)₄]²⁺ and [Mg₃(μ-Cl)₄(DME)₅]²⁺ are directly formed in solution and do not undergo spontaneous transformation. If the reaction of R₆–R₁₂ are required, we assume that external forces may be needed to assist it, such as adding catalysts or additives.

Table 3 Reaction equation for the formation of magnesium polysulfides and tri-nuclear complex within DME solution by bi-nuclear complex and sulfur anion

No.	Equation	ΔG (eV)	ΔGper S
R6	S8^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS8 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	1.86	0.23
R7	S7^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS7 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	1.82	0.26
R8	S6^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS6 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	1.67	0.28
R9	S5^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS5 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	1.55	0.31
R10	S4^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS4 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	1.29	0.32
R11	S3^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS3 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	0.80	0.27
R12	S2^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS2 + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	0.11	0.05
R13	S^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ = MgS + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME	−1.49	−1.49

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MgS	MgS2	MgS3	MgS4	MgS5	MgS6	MgS7	MgS8

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3.2.3 Effect of Mg–Cl complexes on S-reduction process within DME solution. As shown in Table 4, the positive anion of sulfur initially exists in solution in the form of S₈²⁻, and reacts with the bi-nuclear complex [Mg₂(μ-Cl)₂(DME)₄]²⁺ in the first step to form the tri-nuclear complex [Mg₃(μ-Cl)₄(DME)₅]²⁺ and S₆²⁻ anion. In the second step, the S₆²⁻ anion continues to react with the bi-nuclear complex [Mg₂(μ-Cl)₂(DME)₄]²⁺ to form the tri-nuclear complex [Mg₃(μ-Cl)₄(DME)₅]²⁺ and S₄²⁻ anion. In the third step, the S₄²⁻ anion continues to react with the bi-nuclear complex [Mg₂(μ-Cl)₂(DME)₄]²⁺ to form the tri-nuclear complex [Mg₃(μ-Cl)₄(DME)₅]²⁺ and S₂²⁻anion. The fourth step S₂²⁻ anion continues to react with the bi-nuclear complex [Mg₂(μ-Cl)₂(DME)₄]²⁺ to form the tri-nuclear complex [Mg₃(μ-Cl)₄(DME)₅]²⁺ and S²⁻ anion. Tables 5–7 show the decomposition of complexes involved in the S-reduction reaction.

Table 4 Reaction of bi-nuclear to tri-nuclear complexes during S-reduction within DME solution

No.	Equation	ΔG (eV)	ΔGper S
R14	3S8^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = 3S6^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + MgS6	−5.57	−0.23
R15	2S6^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = 2S4^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + MgS4	−5.18	−0.43
R16	S4^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = S2^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + MgS2	−4.13	−1.03
R17	S2^2− + 2[Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = S^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + MgS	−3.01	−1.50

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Table 5 Reaction of bi-nuclear to mono-nuclear complexes during S-reduction within DME solution

No.	Equation	ΔG (eV)	ΔGper S
R18	3S8^2− + [Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = 3S6^2− + MgCl2(DME)2 + 2DME + MgS6	−14.64	−0.61
R19	2S6^2− + [Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = 2S4^2− + MgCl2(DME)2 + 2DME + MgS4	−14.26	−1.19
R20	S4^2− + [Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = S2^2− + MgCl2(DME)2 + 2DME + MgS2	−13.20	−3.30
R21	S2^2− + [Mg2(μ-Cl)2(DME)4]^2+ + 2e^− = S^2− + MgCl2(DME)2 + 2DME + MgS	−12.08	−6.04

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Table 6 Reaction of tri-nuclear to mono-nuclear complexes during S-reduction within DME solution

No.	Equation	ΔG (eV)	ΔGper S
R22	3S8^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 2e^− = 3S6^2− + 2MgCl2(DME)2 + DME + MgS6	−23.71	−0.99
R23	2S6^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 2e^− = 2S4^2− + 2MgCl2(DME)2 + DME + MgS4	−23.33	−1.94
R24	S4^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 2e^− = S2^2− + 2MgCl2(DME)2 + DME + MgS2	−22.27	−5.57
R25	S2^2− + [Mg3(μ-Cl)4(DME)5]^2+ + 2e^− = S^2− + 2MgCl2(DME)2 + DME + MgS	−21.15	−10.58

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Table 7 Reaction of tri-nuclear to bi-nuclear complexes during S-reduction within DME solution

No.	Equation	ΔG (eV)	ΔGper S
R26	3S8^2− + Mg^2+ + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + 2e^− = 4S6^2− + 2[Mg2(μ-Cl)2(DME)4]^2+	−12.36	−0.52
R27	2S6^2− + Mg^2+ + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + 2e^− = 3S4^2− + 2[Mg2(μ-Cl)2(DME)4]^2+	−11.60	−0.97
R28	S4^2− + Mg^2+ + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + 2e^− = 2S2^2− + 2[Mg2(μ-Cl)2(DME)4]^2+	−9.36	−2.34
R29	S2^2− + Mg^2+ + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + 2e^− = 2S^2− + 2[Mg2(μ-Cl)2(DME)4]^2+	−6.64	−3.32

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3.3 Structures and formation process of MgCl₂ solute within THF solvent

According to the Mg/Cl ratios of 1 : 0, 1 : 1.5 and 1 : 2, the relevant THF complex structures in Table 1 are obtained. It can be seen that [Mg(THF)₆]²⁺ (No. 6) is composed of one Mg ion and six THF molecules. THF are symmetrically distributed around Mg ion, and the total coordination number of Mg ion is 6. In addition, the THF pairs cross vertically in space, which can helps the structure remain stable. MgCl₂(THF)₄ (No. 7) consists of one magnesium atom and two chlorine atoms to form a mono-nuclear complex with Mg coordination number of 6, [Mg₂(μ-Cl)₃(THF)₆]⁺ (No. 8) shares three chlorine atoms between two magnesium atoms, and the remaining magnesium atoms are complemented by three oxygen atoms in the THF molecules to form a bi-nuclear complex. (This structure is consistent with that reported in earlier literature²²). The chlorine atoms replace the oxygen atoms well and significantly enhance the de-solvation of the magnesium atoms. Moreover, the three structures in Table 1 are highly symmetrical.

3.3.1 Formation path of Mg–Cl complexes within THF solution. According to the calculation results in Table 8, the bi-nuclear complex [Mg₂(μ-Cl)₃(THF)₆]⁺ in THF solution is directly formed under the condition of high salt concentration, as shown in R₃₂, and the reaction free energy is −2.78 eV. When the salt concentration is not that high, mono-nuclear complex [MgCl₂(THF)₄] is formed at first, which ΔG is −2.25 eV, as shown in R₃₀. Then it continues to react with MgCl₂ to form a bi-nuclear complex [Mg₂(μ-Cl)₃(THF)₆]⁺, as shown in R₃₁.

Table 8 Reaction steps to form mono-nuclear and bi-nuclear complexes within THF solution

No.	Equation	ΔG (eV)	ΔGper THF
R30	MgCl2 + 4THF = MgCl2(THF)4	−9.02	−2.25
R31	Mg^2+ + 3MgCl2(THF)4 = 2[Mg2(μ-Cl)3(THF)6]^+	−6.32	−0.53
R32	Mg^2+ + 3MgCl2 + 12THF = 2[Mg2(μ-Cl)3(THF)6]^+	−33.37	−2.78

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3.3.2 The Mg–Cl complexes within THF solution in the process of discharge reaction. The calculated results of all the above steps are obtained under the condition of THF solvation. It can be seen from Table 9 that the free energies of R₃₃–R₄₀ are all under 0, indicating that all the reactions of the above steps can be occurred spontaneously.

Table 9 Reaction equation for the formation of magnesium polysulfides and bi-nuclear complex within THF solution by mono-nuclear complex and sulfur anion

No.	Equation	ΔG (eV)	ΔGper S
R33	S8^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS8 + 2[Mg2(μ-Cl)3(THF)6]^+	−9.44	−1.18
R34	S7^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS7 + 2[Mg2(μ-Cl)3(THF)6]^+	−9.46	−1.35
R35	S6^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS6 + 2[Mg2(μ-Cl)3(THF)6]^+	−9.61	−1.60
R36	S5^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS5 + 2[Mg2(μ-Cl)3(THF)6]^+	−9.73	−1.95
R37	S4^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS4 + 2[Mg2(μ-Cl)3(THF)6]^+	−10.00	−2.50
R38	S3^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS3 + 2[Mg2(μ-Cl)3(THF)6]^+	−10.48	−3.49
R39	S2^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS2 + 2[Mg2(μ-Cl)3(THF)6]^+	−11.17	−5.59
R40	S^2− + 2Mg^2+ + 3[MgCl2(THF)4] = MgS + 2[Mg2(μ-Cl)3(THF)6]^+	−12.76	−12.76

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3.3.3 Effect of Mg–Cl complexes on S-reduction process within THF solution. It can be seen from Table 10, that the conversion of the mono-nuclear complex to the bi-nuclear complex in THF solution can occur spontaneously in the S-reduction reaction. The free energy of R₄₁–R₄₄ are all under 0, ΔG_{per S} of R₄₁ is −0.71 eV, R₄₂ is −1.38 eV, R₄₃ is −3.87 eV, R₄₄ is −7.19 eV. It indicates that R₄₁–R₄₄ reaction are more and more easily to occur. Table 11 shows the decomposition of complexes involved in the S-reduction reaction.

Table 10 Reaction of mono-nuclear to bi-nuclear complexes within THF solution during S-reduction

No.	Equation	ΔG (eV)	ΔGper S
R41	3S8^2− + 2Mg^2+ + 3[MgCl2(THF)4] + 2e^− = 3S6^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + MgS6	−16.96	−0.71
R42	2S6^2− + 2Mg^2+ + 3[MgCl2(THF)4] + 2e^− = 2S4^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + MgS4	−16.53	−1.38
R43	S4^2− + 2Mg^2+ + 3[MgCl2(THF)4] + 2e^− = S2^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + MgS2	−15.50	−3.87
R44	S2^2− + 2Mg^2+ + 3[MgCl2(THF)4] + 2e^− = S^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + MgS	−14.38	−7.19

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Table 11 Reaction of bi-nuclear to mono-nuclear complexes during S-reduction within THF solution

No.	Equation	ΔG (eV)	ΔGper S
R45	3S8^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + 2e^− = 3S6^2− + 3[MgCl2(THF)4] + MgS6	−4.31	−0.18
R46	2S6^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + 2e^− = 2S4^2− + 3[MgCl2(THF)4] + MgS4	−3.88	−0.32
R47	S4^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + 2e^− = S2^2− + 3[MgCl2(THF)4] + MgS2	−2.85	−0.71
R48	S2^2− + 2[Mg2(μ-Cl)3(THF)6]^+ + 2e^− = S^2− + 3[MgCl2(THF)4] + MgS	−1.73	−0.87

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3.4 Properties of Mg–Cl complexes within DME and THF solvents

For complexes of [Mg(DME)₃]²⁺, [MgCl(DME)₃]⁺, MgCl₂(DME)₂, [Mg₂(μ-Cl₂)(DME)₄]²⁺ and [Mg₃(μ-Cl₄)(DME)₅]²⁺ formed in DME, and complexes of [Mg(THF)₆]²⁺, MgCl₂(THF)₄ and [Mg₂(μ-Cl₃)(THF)₆]⁺ formed within THF solvent, we calculated the length of Mg–O bond and the bond angle of∠O–Mg–O of the complexes, as shown in Fig. 2(a), we also calculated the LUMO–HOMO value of these complexes and the energy gap value of the complexes, as shown in Fig. 2(b).

Fig. 2 (a) The length of Mg–O bond and the bond angle of ∠O–Mg–O of Mg–Cl complexes within DME and THF solvents (b) HOMO–LUMO energy-level and Energy gap of Mg–Cl complexes within DME and THF solvents.

Fig. 2(a) shows the length of Mg–O bond of the complexes. [Mg(DME)₃]²⁺ without chloride atoms are 2.07 Å. With the addition of Cl ions, the length of Mg–O bond first shorts to 2.06 Å, and then the length of Mg–O bond are maintained at 2.07 Å. It means that the Mg–O bond length of Mg–Cl complexes in DME solvent is relatively stable. The length of Mg–O bond of the complexes in THF solution decrease with the increase of Cl ions. We also statistic the angle between O–Mg–O in different complexes in DME and THF solutions. It can be seen that the bond angle of ∠O–Mg–O of Mg–Cl complexes in DME are maintained at about 79°, while the bond angle of THF complexes are slightly larger. In addition, we calculated the length of Mg–Cl bond in Mg–Cl complexes of DME and THF, and found that the bond lengths were concentrated between 2.4 Å and 2.6 Å, which are consistent with the data in the early literature.³³ The length of Mg–Cl bond of MgCl₂ salt remains at 2.26 Å, and the formation of complexes make the length of Mg–Cl bond become longer, the difference was about 0.2 Å. The bond angle between Cl–Mg–Cl of complexes in both DME and THF solvents are all about 84°. Fig. 2(b) statistics the HOMO–LUMO values of Mg–Cl complexes in DME and THF solvents. LUMO energy also represents the ability to acquire electrons. Therefore, a lower LUMO energy means a higher electron affinity, and the ability to accept electrons also enhanced. It can be seen from Fig. 2(b) that [Mg(DME)₃]²⁺ has the lowest LUMO energy, indicating that [Mg(DME)₃]²⁺ is the most easily oxidized compound, and it is easy to obtain electrons from the anode during discharge. A reduction in the total energy gap between HOMO and LUMO improves electrical conductivity, which speeds up electron transport.³⁴ The results of the energy gap are calculated with the formula (4). It can be seen from Fig. 2(b) that the energy gap of [Mg(DME)₃]²⁺ (8.42 eV) and [Mg(THF)₆]²⁺ (8.45 eV) complexes are the highest, and the energy gap decreases after the addition of Cl ions, which means that the addition of Cl⁻ improves the conductivity of each complex in the electrolyte. Finally, the energy gap value of the Mg–Cl complexes remained stable between 6.7 and 8.0 eV.

Since we still have not exactly understood whether the presence of complexes accelerate or slow down the S-reduction process, we took the S-reduction reaction process without complexes as the basic reaction formula and explored the properties of the complexes under the solvents of DME and THF respectively. We plotted Fig. 3 with the data from Tables 12 and 13. As shown in Fig. 3(a), sulfur spontaneously changes from S₈²⁻ to S²⁻ during the discharge process. The final product of Mg–S battery, MgS, is a solid, and accelerating the formation of the last step of the reaction product cannot extend the electrochemical performance of the battery, and improving the battery performance. In the process of charging reaction, the reaction product is transformed from solid MgS to MgS₈. According to Fig. 3(a), the bi-nuclear to tri-nuclear complex is a synthetic reaction, which is exactly the opposite of the decomposition of bi-nuclear into mono-nuclear, tri-nuclear into bi-nuclear, and tri-nuclear into mono-nuclear. According to Fig. 3(b), mono-nuclear complex to bi-nuclear complex is a synthesis reaction, and bi-nuclear to mono-nuclear complex is a decomposition reaction, and their step diagrams are just distributed on both sides of the original S-reduction reaction. We calculated with the eqn (2) and (3) in the above. From the data, it can be seen that the decomposition of Δ²G of tri-nuclear into mono-nuclear in the DME complex is the largest, which changes from the original S-reduction of 0.41, 1.45 and 1.76 eV to 0.96, 3.62 and 5.01 eV, indicating that the driving force of the decomposition of tri-nuclear into mono-nuclear is the largest. The complexes in DME [Mg₂(μ-Cl)₂(DME)₄]²⁺ and [Mg₃(μ-Cl)₄(DME)₅]²⁺, Mg/Cl are 1 : 1 and 1 : 1.3, respectively, while the complexes in THF, MgCl₂(THF)₄ and [Mg₂(μ-Cl)₃(THF)₆]⁺, Mg/Cl are 1 : 2 and 1 : 1.5 respectively, indicating that DME solvent is suitable for low Mg/Cl ratio, and THF solvent is suitable for high Mg/Cl ratio. In contrast, the Mg/Cl ratio in DME is lower, while the Mg/Cl ratio in THF is higher. If the two solvents are mixed, then the Mg/Cl ratio of the electrolyte can be kept constant.

Fig. 3 Reactions of Mg–Cl complexes in (a) DME solvents and (b) THF solvents in S-reduction.

Table 12 Reaction steps of Mg–Cl complexes within DME solution during S-reduction

No.	Equation	ΔG (eV)	ΔGper S
R49	2[Mg2(μ-Cl)2(DME)4]^2+ = [Mg3(μ-Cl)4(DME)5]^2+ + 3DME + Mg^2+	5.13	—
R50	[Mg2(μ-Cl)2(DME)4]^2+ = MgCl2(DME)2 + 2DME + Mg^2+	−3.95	—
R51	[Mg3(μ-Cl)4(DME)5]^2+ = 2MgCl2(DME)2 + DME + Mg^2+	−13.02	—
R52	Mg^2+ + [Mg3(μ-Cl)4(DME)5]^2+ + 3DME = 2[Mg2(μ-Cl)2(DME)4]^2+	−5.13	—
R53	Mg^2+ + 3S8^2− + 2e^− = 3S6^2− + MgS6	−10.69	−0.45
R54	Mg^2+ + 2S6^2− + 2e^− = 2S4^2− + MgS4	−10.31	−0.86
R55	Mg^2+ + S4^2− + 2e^− = S2^2− + MgS2	−9.25	−2.31
R56	Mg^2+ + S2^2− + 2e^− = S^2− + MgS	−8.14	−4.07

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Table 13 Reaction steps of Mg–Cl complexes within THF solution during S-reduction

No.	Equation	ΔG (eV)	ΔGper S
R31	Mg^2+ + 3[MgCl2(THF)4] = 2[Mg2(μ-Cl)3(THF)6]^+	−6.32	—
R57	2[Mg2(μ-Cl)3(THF)6]^+ = 3[MgCl2(THF)4] + Mg^2+	6.32	—
R58	Mg^2+ + 3S8^2− + 2e^− = 3S6^2− + MgS6	−10.64	−0.44
R59	Mg^2+ + 2S6^2− + 2e^− = 2S4^2− + MgS4	−10.21	−0.85
R60	Mg^2+ + S4^2− + 2e^− = S2^2− + MgS2	−9.17	−2.29
R61	Mg^2+ + S2^2− + 2e^− = S^2− + MgS	−8.06	−4.03

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4. Conclusions

In this paper, we studied the complexes formed by ring THF and chain DME solvents in the battery and the reaction process of the complexes in the battery, and explored the role of the solute salt anion additive in the battery discharge process. It was found that MgCl₂, as an ideal anionic salt additive, can form mono-nuclear complex MgCl₂(DME)₂, bi-nuclear complex [Mg₂(μ-Cl)₂(DME)₄]²⁺ and tri-nuclear complex [Mg₃(μ-Cl)₄(DME)₅]²⁺ in DME solvent. These three kinds of complexes mono-nuclear, bi-nuclear, and tri-nuclear are directly formed in solution in turn. The bi-nuclear complex [Mg₂(μ-Cl)₃(THF)₆]⁺ in THF solution is directly formed under the condition of high salt concentration, when the salt concentration is lower, the mono-nuclear complex [MgCl₂(THF)₄] is formed at first, and then continues to react with MgCl₂ to form the bi-nuclear complex [Mg₂(μ-Cl)₃(THF)₆]⁺. By comparing HOMO–LUMO and energy gap values of Mg–Cl complexes in different solvents, it was found that [Mg(DME)₃]²⁺ had the lowest LUMO value, so it was the most easily oxidized compound. The energy gap values of the complexes decreased after the addition of Cl⁻, indicating that the addition of Cl⁻ increased the conductivity of each complex in the electrolyte. According the data, the synthetic reaction is exactly the opposite of the decomposition. And the decomposition of Δ²G of tri-nuclear into mono-nuclear in the DME complex is the largest, indicating that the driving force of the decomposition of tri-nuclear into mono-nuclear is the largest. According to the different ratios of Mg/Cl in the complexes involved in S-reduction, the Mg/Cl in the complex cations [Mg₂(μ-Cl)₂(DME)₄]²⁺ and [Mg₃(μ-Cl)₄(DME)₅]²⁺ in DME are 1 : 1 and 1 : 1.3, respectively. The Mg/Cl of the complex cations MgCl₂(THF)₄ and [Mg₂(μ-Cl)₃(THF)₆]⁺ in THF are 1 : 2 and 1 : 1.5, respectively. So we speculated that DME had better performance as an electrolyte solvent in battery when the Mg/Cl ratio was low, and THF had better performance as an electrolyte solvent in battery when the Mg/Cl ratio was high. The reaction of magnesium ions in the electrolyte is very complicated, this paper mainly considers the possibility of Mg–Cl complex participating in the S-reduction reaction, which has certain limitations. In addition, although the solubility of a single MgCl₂ salt in DME is very small, it is difficult to be applied in practice, but relevant literature shows that the addition of MgCl₂ greatly improves the electrochemical performance of Mg(TFSI)₂/DME electrolyte solutions,⁶ and MgCl₂ is a key component in these solutions, and the auxiliary role of TFSI anion will also be considered in future work. Overall, this study represents a significant step forward in understanding the impact of complexes on Mg–S battery performance and paves the way for further optimization.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

JBW was supported by the National Natural Science Foundation of China (No. 11047164), the National Key Laboratory of Infrared Detection Technologies (No. IRDT-23-S01), the Shanghai College Foundation for Excellent Young Teachers of China (No. gjd10023) and the Academic Program of Shanghai Municipal Education Commission (No. 11XK11 and 2011X34).

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