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Theoretical Study of the Solvation Effect on the Reductive Reaction of Vinylene Carbonate in the Electrolyte Solution of Lithium Ion Batteries Kento Kasahara,† Hiroshi Nakano,†,‡ and Hirofumi Sato*,†,‡ †

Department of Molecular Engineering, Kyoto University, Nishikyo-ku, Kyoto 615-8510, Japan Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Nishikyo-ku, Kyoto 615-8520, Japan

‡

S Supporting Information *

ABSTRACT: Carbon monoxide generation reaction of vinylene carbonate (VC) in the electrolyte solution of lithium ion batteries (ethylene carbonate (EC) and 1.0 M LiClO4/EC) is studied using the RISM-SCF-SEDD method, a hybrid methodology of statistical mechanics for molecular liquids and quantum chemistry. The analytical treatment of the solvent and lithium salt enables us to treat the complicated composition of the solution such as the concentration of the salt which is difficult for the methods based on the molecular dynamics (MD) simulation. The free energy profile and solvation structure are discussed in order to clarify the effect of the solvent, especially lithium salt on the reaction. The lithium salt strongly stabilizes the system due to the electrostatic interaction compared with the system in which the salt does not exist. The effect of the salt is especially important for considering the ionization process of VC.

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INTRODUCTION

Li-ion secondary battery (LIB)1 is one of the most used batteries in terms of cycle life, energy density, power density, and charge rate. Basically, the Li-ion battery system consists of a graphite electrode, an organic electrolyte, and a transition metal oxide electrode. When Li ions migrate from cathode to anode, the batteries are charged, and the discharge occurs in the opposite direction. A mixture of alkyl carbonates such as ethylene carbonate (EC), propylene carbonate (PC), and lithium salts has been employed as a typical electrolyte solution of LIBs. Over the past few decades, many researchers have been interested in the chemical reactions in the electrolytes of LIBs. It is known that the reductive decomposition of the solvent during the first several cycles triggers the formation of a passivating film often called as solid electrolytes interphase (SEI). SEI film suppresses the extreme reductive decomposition, improving the safety, power, capability, and cycle life of LIBs. In order to improve the properties of SEI film, small amounts of compounds are added to the electrolytes. Vinylene carbonate (VC) is a typical electrolyte additive of LIBs, promoting the formation of the fairly thin SEI that considerably improves the performance of LIBs.1−5 The molecualar structures of EC and VC are given in Figure 1. Many theoretical researches have been carried out on the chemical reactions of electrolytes and additives.6−16 Undoubtedly, the solvation effect is a key to understand the reactions in the electrolyte solutions of LIBs. In the reduction processes, the © XXXX American Chemical Society

Figure 1. Molecular structures of vinylene carbonate (VC) and ethylene carbonate (EC).

reaction intermediates are anionic species and there exists strong electrostatic interaction between the reaction species and solvents. Possible reaction pathways for the solvent molecules-Li+ clusters have been proposed by means of polarizable continuum model (PCM)17 in the electrolyte solutions.6−8,10 Over the past few years, some researchers have employed ab initio molecular dynamics (AIMD) such as Car−Parrinello molecular dynamics (CPMD),18 treating solvent molecules explicitly with density functional theory.11−16 Recently, Ushirogata et al. investigated the effect of VC on the two electron reduction of EC with CPMD by calculating the free energy profiles of the reduction processes for EC and VC. Their results suggest that VC reacts with EC anion radical to Received: March 27, 2017 Revised: April 28, 2017

A

DOI: 10.1021/acs.jpcb.7b02864 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B suppress the two electron reduction of EC.16 In reality, however, the compositions of the electrolyte solutions used in LIB are generally complicated. The concentration of lithium salts is considerably small compared with the solvent molecules such as 1.0 M LiClO4/EC. In spite of the small amount of lithium salt, it is expected that the electrostatic field produced by Li+ around the reactant molecule is expected to be strong. Hence, the explicit treatment of a large number of the solvent molecules is required to express the concentration of lithium salt. In the present study, we employ reference interaction site model self-consistent field (RISM-SCF) with spatial electron density distribution (SEDD)19−21 to elucidate the solvation effects on the reaction in LIBs. RISM-SCF-SEDD method is a hybrid methodology of quantum chemistry and statistical mechanics for molecular liquids. Thanks to the inherent nature of RISM theory, solvation free energy can be computed in an analytical fashion, together with molecular level information on solvent distribution. It should be also emphasized that an infinite number of solvent molecules is treated and the complicated composition of solution can be expressed easily. We focused on the solvation effects on the CO generation reaction of VC in 1.0 M LiClO4/EC solution from the microscopic point of view. The free energy profiles along the reaction is calculated by means of RISM-SCF-SEDD combined with CCSD, a highly sophisticated electronic structure theory.

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ρmulti

ωmulti

α ,γ

(4)

(5)

where Esolute is the free energy of the solute molecule which includes the thermal correction calculated by electronic structure theory. The electronic structure of the solute and solvation structure are obtained in a self-consistent manner. Because of the reasonable computational time to calculate Δμ, we can employ sophisticated electronic structure theory such as coupled-cluster. It should be noted that the RISM-SCF-SEDD method has been proved to be a powerful tool to obtain free energy profiles along reaction coordinates in solutions.28−32

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COMPUTATIONAL DETAILS In a quantum chemical aspect, the cc-pVDZ basis set is adopted for hydrogen atom, and diffuse functions are added to carbon and oxygen atoms (aug-cc-pVDZ). The geometries are optimized in the gas phase using DFT (UB3LYP) method. The optimization is also performed in EC with PCM. The dielectric constant used in the PCM calculation is ϵ = 89.78.10 All the energies are then evaluated with ROCCSD method. The RISM integral equation is solved with Kovalenko−Hirata closure.25 The thermal corrections to free energy in the solutions with RISM-SCF-SEDD method are evaluated with the frequency analysis33 in EC obtained from PCM method. The temperature (T) is set to 323.15 K. The potential parameters for the solute and solvents are taken from literatures34−36 and shown in Table 1. Geometry optimizations and frequency analysis are performed by Gaussian0937 program package. The CCSD calculations with PCM are performed by Gaussian09, the calculation in the gas phase and in the solutions (RISM-SCFSEDD) are performed by GAMESS38 program package modified by us.

(1)

Here, “*” denotes convolution integral. h and c are matrices of total and direct correlation functions, respectively. ρ is the matrix of the number density of the solvent, and ω is the matrix of the intramolecular correlation functions, describing the geometries of solvent molecules. Since the equation contains two unknown functions (h and c), it is solved by combining an additional relation called as a closure. In the present study, we employed Kovalenko−Hirata (KH) closure.25 The solvation free energy Δμ is readily computed using h and c as follows

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RESULTS AND DISCUSSION Reaction Profile of VC. The CO generation pathway from VC for each species is shown in Figure 2. In the gas phase, the neutral species (1) has a planar structure and is almost unchanged even after the ionization (1′) and both 1 and 1′ have C2v symmetries. From 1′ to 2, the bondings around C1 are changed from planar to tetrahedral via the transition state (TS1′2), corresponding to the change of out-of-plane angle O1− O2−O3−C1 (0.00° (1′) → 13.00° (TS1′2) → 24.05° (2)). Then, the bond C1−O3 becomes elongated, and the lengths for 2, TS23, and 3 are 1.57, 1.72, and 2.91 Å, respectively. The bond breaking in C3−O3 bond is reported, but some studies have proved that C1−O3 bond dissociation is preferable to C3−O3

∫ dr [cαγ(r)− 12 hαγ 2(r)Θ(−hαγ (r))

1 + hαγ (r )cαγ(r )] 2

⎡ ωEC 0 0 ⎤ ⎢ ⎥ 0 ⎥ = ⎢ 0 ωLi+ ⎢ ⎥ 0 ωClO4− ⎦ ⎣ 0

( = Esolute + Δμ

In this section, we describe a brief summary of the RISM-SCFSEDD method. This method provides the electronic structure of a solute with the solvation effect being taken into account in a self-consistent manner. The solvation structure is obtained as radial distribution functions (RDFs). The RISM equation is written as follows:22−24

Δμ = −kBT ∑ ργ

(3)

where ρi and ωi are the number density and intramolecular correlation function for species i (i=EC, Li+, ClO4−). As mentioned above, RISM-SCF-SEDD is a hybrid method of quantum chemistry and RISM theory. In this method, total free energy of the system is defined as

RISM-SCF-SEDD METHOD

ρ hρ = ω*c*ω + ω*c*ρ hρ

⎡ ρEC 0 0 ⎤ ⎢ ⎥ 0 ⎥ = ⎢ 0 ρLi+ ⎢ ⎥ 0 ρClO − ⎥⎦ ⎢⎣ 0 4

(2)

where kB and T are Boltzmann constant and temperature and Θ is the Heaviside step function, respectively. Since Δμ can be formally decomposed into the contribution from each solute site denoted as α, we can easily recognize the solute sites that largely contribute to the stabilization of the system. The RISM equation can treat multicomponent solutions by extending the ρ and ω matrices as follows:26,27 B

DOI: 10.1021/acs.jpcb.7b02864 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B Table 1. Lennard-Jones Parameters (σ/Å, ϵ/kcal mol−1) and Point Charges (q/|e|) for Vinylene Carbonate (VC), Ethylene Carbonate and LiClO4a molecule VC34

EC35

LiClO435,36

a

atom

σ

ϵ

q

C1 C2,C3 O1 O2,O3 H1, H2 Ce1 Ce2 Oe1 Oe2 He Li+ Cl O

3.750 3.550 2.960 3.000 2.420 3.750 3.500 2.960 3.000 2.500 1.460 3.470 2.960

0.105 0.076 0.210 0.170 0.030 0.105 0.066 0.210 0.170 0.030 0.191 0.265 0.210

b b b b b 1.0996 0.0330 −0.6452 −0.4684 0.1041 1.0000 1.0812 −0.5203

The labels of atoms are defined in Figure 1. determined through RISM-SCF-SEDD procedure.

b

Figure 3. Free energy changes along the CO generation pathway in the gas phase, EC, and 1.0 M LiClO4/EC solutions.

Self-consistently

kcal mol−1), corresponding to C3−O3 and C2−O2 bond dissociations. After CO generation (4), the system becomes considerably stabilized and the free energy change from 1′ to 4 is −49.56 kcal mol−1. In EC (RISM-SCF-SEDD), the profiles are drastically changed. All the intermediate species are stabilized compared with the gas phase. In the case of C1−O3 bond breaking process (2 → 3), the activation barrier height is 4.55 kcal mol−1 and higher compared with the gas phase (1.03 kcal mol−1). The activation barrier of C1−O2 bond breaking process (2.42 kcal mol−1) is also increased from that of the gas phase. Since the highest barrier in the gas phase corresponding to the distortion process of CO3 plane does not exist in EC, the reaction is preferable in EC, although the barriers of the bond breaking processes become higher. In 1.0 M LiClO4/EC, each species is further stabilized compared with that in EC. The profile is similar to that in EC. However, by adding ions, the highest barrier located at TS23 is 8.53 kcal mol−1, which is higher than that in EC. Hence, the lithium salt suppresses the CO generation after the ionization. The CPMD study by Ushirogata et al. also shows the increase of the height in the case of VC−-Li+ cluster in EC solution.16 It is not trivial to evaluate the energy change from 1 to 1′ (gas phase) and 2 (solution). If VC is assumed to receive an excess electron (e−) from the graphite electrode, the energy of the electron is roughly approximated as the work function of the graphite electrode with a minus sign, −ϕ = −106 kcal mol−1.39 The free energy difference between 1′ and 1 + e− is 129 kcal mol−1 in the gas phase, suggesting that the ionization hardly occurs in the gas phase. The difference between 2 and 1 + e− greatly decreases to 77 kcal mol−1 in EC and 42 kcal mol−1 in 1.0 M LiClO4/EC. The energy change from 1 to 2 is still large even though the presence of the lithium salt. However, since the charge voltage of LIBs is 4.2 V,40 it would be possible that the reaction proceeds during the charging process in 1.0 M LiClO4/EC. The present result is consistent with the experimental observation that the reaction proceeds only in the presence of the applied voltage (charging process).5 Therefore, the presence of EC and the lithium salt is essential for the CO generation reaction. It is worthwhile to compare the results of RISM-SCF-SEDD method and PCM method. It seems that the profile obtained from PCM method is similar to that from RISM-SCF-SEDD method (in EC). The barriers related to the bond breaking

Figure 2. CO generation pathway of VC in the gas phase and in EC solution (PCM). Species 4 is defined as the sum of products at infinite separation. The geometrical parameters which change largely during the reaction are underlined.

bond dissociation because O2−C2−C3−O3 forms a conjugation unit, maintaining C3−O3 bond.9,16 After completing the breaking of C1−O3, the bond C1−O2 becomes elongated via TS34 (1.34 and 1.38 Å for 3 and TS34), and finally, CO is continuously dissociated to the separated products (4). In EC, the reaction pathway is similar to that in the gas phase except for the process immediately after the ionization. The planar structure such as 1′ is not stable in the solution, and the optimization from 1 provides the structure corresponding to 2. The structural change from 2 to 4 is almost the same as that in the gas phase. Since this tendency is also shown in EC and 1.0 M LiClO4/EC solutions with RISM-SCF-SEDD, the result indicates that the solvation effect does not change the electronic character of VC significantly. However, it should be noted that the solvation effect is not trivial for evaluating the free energy profile as discussed in the next section. Free Energy Profile. Figure 3 shows the free energy profiles of the reaction in the gas phase, in EC, and in 1.0 M LiClO4/EC solutions, respectively. To clarify the solvation effects, the free energy for each species is displayed with respect to that for the neutral species 1. In the gas phase, the barrier is located at TS1′2, corresponding to the distortion of CO3 plane. This is the highest barrier in all the processes (6.92 kcal mol−1), higher than that at TS23 (1.03 kcal mol−1) and at TS34 (1.20 C

DOI: 10.1021/acs.jpcb.7b02864 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

strong stabilization of 2 by Li+ makes the activation barrier in the entire reaction higher as shown in Figure 3. From eq 2, Δμ can be formally decomposed into the contribution from each VC site i, Δμi. the contributions are defined as,

processes with PCM and RISM-SCF-SEDD methods are very close to each other, although the energy change from 1 to 2 with PCM is −37.73 kcal mol−1 which is more stable by 9.10 kcal mol−1. As compared to the profile computed from RISMSCF-SEDD method (in 1.0 M LiClO4/EC), the relative free energy for each species is unstable. The difference can be mainly attributed to the effect of the lithium salt that PCM does not consider. The present result indicates that the lithium salt should be treated explicitly to evaluate the free energy profile including the ionization process. Solvation Effects. Solvation Free Energy. The solvation free energies Δμ along the reaction pathway in EC and in 1.0 M LiClO4/EC obtained from RISM-SCF-SEDD method are shown in Figure 4. For both the solutions, the intermediate

ΔμC H = ΔμC + ΔμC + ΔμH + ΔμH 2

2

2

3

1

ΔμCO = ΔμC + ΔμO + ΔμO + ΔμO 3

1

1

2

3

2

(6) (7)

Figure 5. Decomposed solvation free energies ΔμC2H2 and ΔμCO3 along the CO generation pathway in EC and 1.0 M LiClO4/EC solutions.

Figure 4. Solvation free energies along the CO generation pathway in EC and 1.0 M LiClO4/EC solutions.

Figure 5 shows the changes in ΔμCO3 and ΔμC2H2 along the reaction pathway. We first focus on the changes from 1 to TS34. For neutral species 1, both ΔμC2H2 and ΔμCO3 hardly affect the stabilization of the system. The change in ΔμC2H2 is almost flat in both the solutions. From the viewpoint of the electrostatic potential (ESP) charges computed by a grid-based method (CHELPG),42 the charge of C2H2 group is almost zero from 2 to TS34, and hence, the electrostatic interaction between the group and solvents is very weak. This is the reason why C2H2 group hardly contributes to the stabilization. On the other hand, ΔμCO3 drastically changes immediately after the ionization (2). The value of the intermediate species is negatively large, especially in 1.0 M LiClO4/EC, and the profile is similar to that of Δμ (Figure 4). Therefore, ΔμCO3 mainly determines the stabilization effect due to the solvation. Since CO3 group always possesses −1 |e| charge during the reaction, the strong interaction between the group and solvents occurs and the profile is affected by the presence of lithium salt. As for 4, the situation is different. ΔμC2H2 and ΔμCO3 become positively and negatively large from TS34. VC anion is decomposed into CO (neutral) and C2H2O2 (anion) and the two oxygen atoms (O2 and O3) in C2H2O2 are negatively charged. Hence, the attractive interaction between the oxygen atoms and solvents occur. On the other hand, since C2H2 group has positive charge, the repulsive interaction between the group and solvents occurs. Solvation Structure of Li+. The RDFs of Li+ around O1, O2, O3, and C1 at 2, 3, and 4 are shown in Figure 6. The

species are considerably stabilized due to the solvation except for the neutral species 1. It is interesting to note that the changes of Δμ in both the solutions are very similar to each other, although the absolute value in 1.0 M LiClO4 is quite larger. It is confirmed from the RDFs for EC and Li+ that the VC sites to which Li+ strongly coordinates are also coordinated with the positively charged EC sites. Therefore, a plausible cause is that the positively charged sites in the solvent molecules mainly determine the Δμ. In both of the solutions, Δμ of 2 is the lowest and increases as the reaction proceeds until the generation of CO (4). The final product 4 is stabilized compared with 3 and TS34 in EC and TS23, 3, and TS34 in 1.0 M LiClO4/EC. To understand the change in Δμ, the dipole moment (DM) for each species is examined.41 The DMs for 2, TS23, 3, TS34, and 4 in EC are 7.55, 5.20, 4.48, 4.33, and 4.61 D, respectively. The tendency of change in DM is the same as that in Δμ. The same behavior is also found in the case of 1.0 M LiClO4/EC solution, although each species is more polarized. Hence, the large value of DM for 2 causes the stabilization due to the interaction between the DM of 2 and solvents. The difference between the Δμ in EC and that in 1.0 M LiClO4/EC, ΔΔμ is illustrated in Figure 4. The values of 2 and 4 are −35.29 and −34.36 kcal mol−1, respectively, and larger than those of the other species that are around −30 kcal mol−1. Since the RDFs of ClO4− show small peaks compared with that of Li+ (see Figures S1 and S2 in the Supporting Information), the stabilization is attributed to the strong solvation by Li+. The D

DOI: 10.1021/acs.jpcb.7b02864 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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charges of those sites make the peaks higher due to the attractive electrostatic interaction. The RDF around C1 site shows the comparatively large peak at 2 and 3, though the site is positively charged. The peak corresponds to the Li+ which solvate O1 site. Since 3 has the positive charge on the site compared with 2, 3 is destabilized as shown in Figure 4 because of the repulsive interaction. The situation that large negative and positive charges are adjacent to each other corresponds to the decrease in the DM. Similar behavior is found in TS23 and TS34. After the generation of CO (4), since the charges on O1 and C1 sites which belong to CO are almost zero, the peaks of the RDFs (O1−Li+ and C1−Li+) are very small. Thus, these sites hardly contribute to the stabilization of the system. Instead, the O2 (O3) site has large negative charge and the RDF shows the strong peak. The C2 (C3) site adjacent to O2 (O3) site has positive charge (0.3136 |e|). However, the charge is smaller than that on C1 site for 3, and hence, the repulsive interaction is not strong. This is the reason why 4 is stabilized compared with 3.

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CONCLUSION In the present study, we investigated the solvation effect on the CO generation reaction of VC in the electrolyte solutions of LIBs by means of RISM-SCF-SEDD method. The free energy profile as well as the solvation structure were discussed in EC and in 1.0 M LiClO4 to reveal the effect of the lithium salt. In the solutions, the intermediate species are strongly stabilized due to the solvation, especially in the presence of lithium salt. The presence of lithium salt is important when the ionization process of VC is considered. From the RDFs of Li+ around VC, the preferable configuration of Li+ changes as the reaction proceeds and the position of Li+ cannot be determined uniquely at each species. The present result indicates that the explicit treatment of Li+ is essential to investigate the reaction in electrolyte solutions of LIBs.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b02864. The radial distribution function (RDF) of ClO4− around VC (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(H.S.) E-mail: [email protected]. ORCID

Hirofumi Sato: 0000-0001-6266-9058 Notes

Figure 6. Radial distribution functions (RDFs) for O1−Li+(red), O2− Li+(blue), O3−Li+(green), and C1−Li+(orange) at (a) 2, (b) 3, and (c) 4. q means the ESP charge for each site.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS K.K. expresses thanks for the Grant-in Aid for JSPS Fellows. The work was financially supported in part by a Grant-in-Aid for Scientific Research (C) (25410011). A part of this work was performed under a management of “Elements Strategy Initiative for Catalysts & Batteries (ESICB)”. Theoretical computations were partly performed using Research Center for Computational Science, Okazaki, Japan. All of them were supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) Japan.

distribution of Li+ greatly changes along the reaction pathway. Li+ solvates O1 at 2, O2 and O3 at 3, and O2 (O3) site at 4. Furthermore, the several sites are solvated by Li+ at the same time. Thus, treating a lot of configurations of Li+ is essential to evaluate the solvation free energy appropriately. The heights of the first peaks for three oxygen sites for each species correlate with the negative charges of those site. Increased negative E

DOI: 10.1021/acs.jpcb.7b02864 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcb.7b02864 J. Phys. Chem. B XXXX, XXX, XXX−XXX