CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201301151
Mechanism of Dissolution of a Lithium Salt in an Electrolytic Solvent in a Lithium Ion Secondary Battery: A Direct Ab Initio Molecular Dynamics (AIMD) Study Hiroto Tachikawa*[a] The mechanism of dissolution of the Li + ion in an electrolytic solvent is investigated by the direct ab initio molecular dynamics (AIMD) method. Lithium fluoroborate (Li + BF4) and ethylene carbonate (EC) are examined as the origin of the Li + ion and the solvent molecule, respectively. This salt is widely utilized as the electrolyte in the lithium ion secondary battery. The binding of EC to the Li + moiety of the Li + BF4 salt is exothermic, and the binding energies at the CAM–B3LYP/6-311 + + G(d,p) level for n = 1, 2, 3, and 4, where n is the number of EC molecules binding to the Li + ion, (EC)n(Li+BF4), are calculated to be 91.5, 89.8, 87.2, and 84.0 kcal mol1 (per EC molecule), respectively. The intermolecular distances between Li + and the
F atom of BF4 are elongated: 1.773 (n = 0), 1.820 (n = 1), 1.974 (n = 2), 1.942 (n = 3), and 4.156 (n = 4). The atomic bond populations between Li + and the F atom for n = 0, 1, 2, 3, and 4 are 0.202, 0.186, 0.150, 0.038, and 0.0, respectively. These results indicate that the interaction of Li + with BF4 becomes weaker as the number of EC molecules is increased. The direct AIMD calculation for n = 4 shows that EC reacts spontaneously with (EC)3(Li+BF4) and the Li + ion is stripped from the salt. The following substitution reaction takes place: EC + (EC)3(Li+BF4)!(EC)4Li + (BF4). The reaction mechanism is discussed on the basis of the theoretical results.
1. Introduction Molecular interactions in the lithium ion secondary battery, for example, interactions between lithium and the solvent, the solvent and the graphite electrode, or lithium and the graphite electrode, strongly dominate the performance of the battery system.[1–4] Therefore, the elucidation of both the electronic states of the Li + ion and the process of its solvation in the electrolyte are important in the development of lithium secondary batteries with higher performances and longer lifetimes.[5, 6] The dissolution of the lithium ionic salt in the electrolyte is the initial process in the construction of the lithium ion secondary battery.[7–10] Lithium fluoroborate, Li + BF4 , and lithium hexafluorophosphate, Li + PF6 , are widely used lithium ionic salts.[11, 12] These salts are dissolved in the solvents, and the solvated Li + ion and the solvated counter anion are formed. Ethylene carbonate (EC), propylene carbonate (PC), and related molecules are usually utilized as solvents in the lithium ion secondary battery. The Li + ion is strongly bound to the BF4 ion by an ionic bond. Therefore, it is considered that a large amount of energy is necessary to dissociate the Li + ion from the Li + BF4 salt. However, it is known that the salt is easily dissolved in organic solvents (such as EC and PC). Although the salt dissolution process is important, its mechanism is not clearly understood. In order to elucidate the de[a] Dr. H. Tachikawa Division of Materials Chemistry Graduate School of Engineering Hokkaido University Sapporo 060-8628 (Japan) E-mail: [email protected]
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tails of the interaction of the lithium salt with the electrolyte, several theoretical works have been performed. Ganesh et al. calculated the change in the solvation structure of EC around the Li + ion using ab initio simulation.[13] They found that the LiPF6 salt is dissociated into Li + and PF6 in EC at 310 K. It was also shown that a solid-electrolyte interphase (SEI) is formed in the presence of an electrode.[14] In bulk solution, the Li + ion is solvated by a few EC molecules as the first solvation shell. Recent theoretical calculations have shown that the Li + ion is solvated by four EC molecules as the first solvation shell. The binding energy for the interaction of the Li + ion with four EC molecules is 35 kcal mol1 (per EC molecule).[15, 16] Thus, the static interaction between the Li + ion and EC molecules is well understood theoretically. However, the dynamic features of the solvation of the Li + ion, especially the dissolution mechanism of the BF4 electrolyte in EC are still unclear. In the present study, the dissociation process of Li + BF4 in EC solution and the solvation process of Li + by EC molecules were investigated by means of density functional theory (DFT) and direct ab initio molecular dynamics (AIMD) methods.
Experimental Section Method of Calculation First, we calculated the structures of Li + BF4 , the EC molecule, and the complex (EC)n(Li+BF4) (n = 0–4) at the CAM–B3LYP level of theory. The second-order Møller-Plesset perturbation (MP2), coupled cluster with single and double excitations (CCSD), and quadratic configuration interaction with single and double excitations (QCISD) methods were applied to the Li–(EC) 1:1 complex. ChemiChemPhysChem 2014, 15, 1604 – 1610
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cal structures of Li + BF4 and EC are given in Figure 1. All static ab initio calculations were carried out using the Gaussian 09 and GAMESS programs.[17, 18]
Figure 1. Chemical structures of lithium tetrafluoroborate (Li salt) and ethylene carbonate (EC).
In the direct AIMD calculations[19–25] the potential energy and its gradient were calculated at the CAM–B3LYP/6-311 + + G(d,p) level for the reaction systems and used without basis set superposition error (BSSE) corrections in the trajectory calculation. The equation of motion was solved by the velocity Verlet algorithm with a time step of 0.25 fs. The drifts of total energies were less than 0.05 kcal mol1 in all trajectories. No symmetry restrictions were applied to the calculation of the energy gradients. The positions of EC around (EC)3(Li+BF4) used in the direct AIMD calculations were selected as follows. First, the positions of EC around (EC)3(Li+BF4) were randomly generated, then the energy difference between each generated geometry and the most stable position of the EC molecule was calculated. Five geometries possessing energy differences of lower than 2.0 kcal mol1 were selected. The initial internal vibrational energy of the (EC)3(Li+BF4) complex and the velocity of EC were set to zero. In order to elucidate the effects of the surrounding solvents on the reaction dynamics, a quantum mechanics combined with molecular mechanics (QM/MM) approach was used for the direct AIMD calculations. The first layer (higher layer), which was composed of (EC)3(Li+BF4) complexes that participate directly in the reaction process, was calculated at the B3LYP/6-31G(d) level, and the environmental solvent molecules (the second layer) were calculated by the PM3 method. Twenty solvent EC molecules were examined as the environmental solvent molecules.
1.773 . The binding energy of the Li + ion to the BF4 ion was calculated to be 144.9 kcal mol1. This energy is in good agreement with the previously reported value (141.7 kcal mol1 at the G2MP2/6-31 + G(d) level).[26] The natural population analysis (NPA) showed that the charge on the Li + ion is + 0.93, which indicates that 7 % of the positive charge is transferred to the BF4 ion after binding. For comparison, the structure and electronic states of Li + BF4 were also calculated at the CCSD/6-311 + + G(d,p) level. The results are given in Table 1. The binding energy was calculated to be 142.7 kcal mol1, which is in good agreement with the value obtained in the CAM–B3LYP calculation (144.9 kcal mol1). The NPA charge of Li + ion was + 0.95. The Li +F distance was 1.791 . The agreement between the two levels of theory indicates that the CAM–B3LYP functional can be expected to give reasonable energetics and structures for the Li + BF4 system. The structures of Li + BF4 solvated by EC are also given in Figure 2. For n = 1, one EC molecule solvates the Li + ion of the
Table 1. Binding energies, Ebind [kcal mol1], NPA atomic charges, and bond distances [] for Li + (BF4). The basis set used was 6-311 + + G(d,p).
1
Ebind [kcal mol ] NPA charge Li B F F’ Distance r(LiF) []
CAM–B3LYP
CCSD
144.9
142.7
+ 0.93 + 1.33 0.62 0.52
+ 0.95 + 1.48 0.65 0.56
1.773
1.791
2. Results and Discussion 2.1. Solvation Structures The structure of the lithium salt (lithium tetrafluoroborate; Li + BF4) is given in Figure 2. The structure was fully optimized at the CAM–B3LYP/6-311 + + G(d,p) level. Two of the fluorine atoms of the salt interact equivalently with the Li + ion. The bond distance between the Li + ion and the F atom was calculated to be
Figure 2. Optimized geometries of Li + BF4 and solvated Li + BF4 , (EC)n(Li+BF4) (n = 0 = 3), calculated at the CAM– B3LYP/6-311 + + G(d,p) level. The geometrical parameters obtained from the CAM–B3LYP/6-311G(d,p) calculation are given in parentheses.
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CHEMPHYSCHEM ARTICLES salt. The C=O carbonyl oxygen of EC interacts with the Li + ion, and two of the fluorine atoms of the BF4 anion are oriented towards the Li + ion from the opposite direction. The solvation distance (OLi + distance) is 1.836 . It was found that the Li +F distance is significantly elongated on interaction with EC molecules (1.773 for n = 0 and 1.820 for n = 1). For n = 2, the solvation structure around the Li + ion has a tetrahedral structure, in which two C=O carbonyl groups and two fluorine atoms interact with the Li + ion. The solvation distance, r(OLi), is 1.974 , which is 0.154 longer than that in the structure for n = 1. In the case of n = 3, the solvation structure is significantly changed: only one fluorine atom interacts with the Li + ion and three C=O carbonyl groups are oriented towards the Li + ion. Figure 2 (n = 3) shows the optimized structure of (EC)3(Li+BF4). The backbones of the EC molecules are illustrated with the tube model for clarity. The solvation distance was calculated to be 1.945 . Figure 3 shows the optimized structure of the solvated salt for n = 4. The solvation structure for n = 4 is drastically changed: the r(LiF) distance is significantly elongated [r(LiF) = 4.156 ], which indicates that the BF4 ion is dissociated from Li + . Four EC molecules are bound to the Li + ion, and the solvation shell is completed for n = 4.
www.chemphyschem.org dependent on the solvation number (n). The LiF bond distances, r(LiF), in the Li + BF4 salt, are plotted in Figure 4 A as a function of the number of EC molecules (n). In the case of n = 0 (free salt), the LiF bond distance is 1.773 . The bond distances in n = 1, 2, and 3 were calculated to be r(LiF) = 1.820, 1.974, and 1.942 , respectively. The LiF bond distance in Li + BF4 is significantly elongated on increased solvation of EC around Li + , although the distance becomes almost constant in n = 2 and 3.
Figure 4. A) Lithium-fluorine atomic distance, r(LiF), plotted as a function of the number of EC molecules (n). B) Lithium-fluorine atomic bond populations, P(LiF).
2.3. Bond Population Figure 3. Optimized geometry of (EC)n(Li+BF4) (n = 4) calculated at the CAM–B3LYP/6-311 + + G(d,p) level. The geometrical parameters obtained from the CAM–B3LYP/6-311G(d,p) calculation are given in parentheses.
The binding energies of EC to Li + BF4 for n = 1, 2, 3, and 4 were calculated to be 91.5, 89.8, 87.2, and 84.0 kcal mol1 (per EC) at the CAM–B3LYP/6-311 + + G(d,p) level, respectively. The atomic charges of (EC)3(Li+BF4) were calculated using the NPA method. The molecular charges on (EC)3(Li+BF4) were found to be + 0.22, + 0.71, and 0.93, respectively. This result indicates that the interaction between Li + and BF4 is fully ionic. 2.2. Bond Distances The structure of the Li + BF4 salt was thus drastically changed by solvation by EC, and the magnitude of the deformation is 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
In order to elucidate the effects of the solvent molecules on the bonding nature between the Li and F atoms of the Li + BF4 salt, the bond population was analyzed, and the results are given in Figure 4 B. The bond populations of LiF for n = 0, 1, and 2 were 0.203, 0.186, and 0.150, respectively, which indicates that the LiF bond becomes weaker on solvation of the Li + ion. In the case of n = 3, the population shows the smallest value and is close to zero (0.038). This result suggests that the Li + ion is very weakly bound to BF4 in the case of n = 3. The Li + ion of the salt may be stripped off by solvation. 2.4. Potential Energy Surface The potential energy surface (PES) for the reaction of EC with (EC)3(Li+BF4) was calculated at the CAM–B3LYP/6-31G(d) level. The result is plotted in Figure 5 as functions of R1 = r(OLi) and R2 = r(LiB), where R1 and R2 denote the distance between Li + ChemPhysChem 2014, 15, 1604 – 1610
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Figure 6. Sample trajectory obtained by direct AIMD calculation. A) Potential energy of the system plotted as a function of time (in fs). B) Intermolecular distances (R1 and R2).
Figure 5. Potential energy surface (PES) for the reaction of EC with (EC)3(Li+BF4), plotted as functions of R1 and R2. Contours are drawn at each 2 kcal mol1. The calculation was performed at the CAM–B3LYP/6-311G(d,p) level.
and EC, and that between Li + and BF4 , respectively. The potential minimum was found at R1 = 2.00 and R2 = 2.40 ; this corresponds to a reaction intermediate complex composed of EC(Li+BF4)(EC)3. This complex is E(RC) = 38 kcal mol1 more stable in energy than the reactant [EC + (EC)3(Li+BF4); R1 = 4.00 and R2 = 2.40 ], and is also 5 kcal mol1 more stable than the product region (PD) on the PES. The shape of the PES indicates that the potential energy is open for the product region. 2.5. AIMD Calculation The collision dynamics of EC with solvation system, (EC)3(Li+BF4), that is, the reaction between EC and (EC)3(Li+BF4), was investigated by the direct AIMD method. A total of twenty trajectories was run from several initial configurations. All trajectories followed similar routes and gave the same product. A typical trajectory obtained from the direct AIMD calculation is given in Figure 6. The sample trajectory was started from R1 = 4.00 and R2 = 1.95 , and the initial momentum vectors of the atoms were assumed to be zero at time zero. The structures of (EC)3(Li+BF4) and EC at time zero were fixed at the optimized values obtained at the B3LYP/6-311G(d,p) level. The zero level 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
of the potential energy corresponds to the total energy of the initial separation between EC and (EC)3(Li+BF4) at time zero (point a). It was found that the reaction proceeds spontaneously without activation energy. The time evolution of the potential energy (Figure 6 A) shows that the energy of the system decreases gradually as EC approaches (EC)3(Li+BF4), and reaches the energy minimum at 415 fs (point b). After the minimum, the energy vibrates rapidly in the range (7)–(3) kcal mol1. The time evolution of the interatomic distances (R1 and R2) are plotted in Figure 6 B. The distance between EC and the salt, R1, decreases gradually and reaches the minimum value (1.80 ) at 415 fs (complex formation). This trajectory predicts that EC approaches the (EC)3(Li+BF4) reagent spontaneously. The distance between the Li + ion and the BF4 ion, R2, increases gradually from 1.95 to 2.35 from 0–320 fs, and then suddenly further to 3.10 from 320–400 fs. From 0 to 415 fs (point b) the distances R1 and R2 are changed from 4.00 to 1.80 (R1) and 1.95 to 3.20 (R2), respectively. At 710 fs (point c), distances R1 and R2 were 2.65 and 3.56 , respectively. This change indicates that bond exchange takes place by collision of EC with the salt. However, full dissociation of BF4 from the system did not occur, and BF4 remained in the system (R1 = 2.65 and R2 = 4.00 ). We also found that the approach of EC to Li + and the dissociation of Li + from Li + BF4 took place without an activation barrier, which indicates that the dissolution of the Li + ion from the Li + BF4 salt takes place spontaneously in EC solution. 2.6. Snapshots of the Solvation Process Snapshots of the reaction system are illustrated in Figure 7. The initial separation of this trajectory (R1) was 4.0 at time ChemPhysChem 2014, 15, 1604 – 1610
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www.chemphyschem.org 2.8. Effects of Environmental Solvent Molecules on the Reaction Dynamics
In order to elucidate the effects of surrounding solvents on the reaction dynamics, direct AIMD– QM/MM calculations were performed on the reaction system surrounded by environmental solvent molecules. Snapshots after the reaction are given in Figure 9. The higher layer, which is composed of (EC)3(Li+BF4) and participates directly in the reaction process, was calculated at the B3LYP/6-31G(d) level, whereas the environmental solvent molecules (the second layer) were represented by the PM3 method. At time zero, the EC molecule was located at the initial separation (R1 = 3.60 ), and the distance between Li + and the B atom of BF4 was R2 = 1.955 , which represents the optimized Figure 7. Snapshots of the reaction of EC with (EC)3(Li+BF4) obtained by direct AIMD calculation. This snapshot geometry. After starting the recorresponds to potential energy surface shown in Figure 5. action, the EC reactant gradually approached Li + BF4 , and inversion of the umbrella mode of the Li + moiety occurred after 158 fs. The EC molecule further zero. The distance between Li + and the B atom in BF4 (R2) was 1.95 , which corresponds to that of the optimized approached (EC)3(Li+BF4), and BF4 left the Li + ion (c). geometry. At 228 fs, the distances were R1 = 1.883 and R2 = 3.000 , After starting the reaction, the reactant EC approached the which indicates that the dissociation took place after the reacLi + BF4 and the collision complex was formed at 415 fs. The tion of EC. EC molecule continues to gradually approach (EC)3(Li+BF4), The time evolution of the potential energy and bond distanand the distance between the BF4 ion and Li + is slightly inces (R1 and R2) are given in Figure 10. The potential energy of creased (c). However, the dissociation of BF4 is not complete, the system decreases gradually as a result of the approach of and the ion vibrates in the space defined by three EC EC to (EC)3(Li+BF4). The magnitude of the energy change in molecules (d).
2.7. Effects of the Initial Configurations of EC(Li+BF4)(EC)3 on the Reaction Dynamics The collision of EC with (EC)3(Li+BF4) occurs from several configurations. In order to study their effects, geometrical configurations of EC relative to (EC)3(Li+BF4) were randomly generated around the optimized structure, and five dynamics calculations were run from these selected points. The geometries were selected so that the energy differences from the optimized geometry were lower than 2.0 kcal mol1. The results of direct ab initio MD calculations from the five geometrical configurations are given in Figure 8. All trajectories gave the same product. 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 8. Initial configuration dependence on the reaction paths.
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www.chemphyschem.org of six trajectories were run from selected points, and similar results were obtained in all cases. Thus, it was found that the approach of EC to Li + and the dissociation of Li + from Li + BF4 both take place without activation barrier in the gas phase and in solution. This indicates that the dissolution of the Li + ion from the Li + BF4 salt takes place spontaneously in EC solution without activation energy.
3. Conclusions The mechanism of the dissolution of the Li + ion in EC solvent was investigated by direct AIMD methods. Lithium fluoroborate Figure 9. Snapshots of the reaction of EC with (EC)3(Li+BF4) obtained by the direct AIMD method combined with (Li + BF4) was examined as the a QM/MM calculation. origin of the Li + ion. The salt is widely utilized as the electrolyte of the lithium ion secondary battery. The EC molecule binds to the Li + moiety of the Li + BF4 salt. This binding process is exothermic. The intermolecular distances between Li + and the F atom of BF4 were elongated by solvation. These results indicate that the interaction of Li + with BF4 becomes weaker as the number of EC molecules increases. The (EC)3(Li+BF4) complex was formed if n = 3. The AIMD calculation for n = 4 showed that EC reacts with (EC)3(Li+BF4) and the Li + ion is stripped from the salt. The following substitution reaction takes place [Eq. (1)]: EC þ ðECÞ3 ðLiþ BF4 Þ ! ðECÞ4 Liþ ðBF4 Þ
ð1Þ
Acknowledgements The author acknowledges partial support from a Grant-in-Aid for Scientific Research (C) from the Japan Society for the Promotion of Science (JSPS) (Grant Number 24550001). This work was partially supported by a Grant-in-Aid for Scientific Research on Innovation Areas “Evolution of Molecules in Space” (Grant Number 2510800413).
Figure 10. Time evolution of the reaction system of the reaction of EC with (EC)3(Li+BF4) obtained by the direct AIMD method combined with a QM/ MM calculation.
solution is larger than that in the gas phase. This is due to the fact that solvent reorientation (twelve molecules) takes place during the reaction. Bond alternation occurs at 170 fs. This time scale is slightly faster than in the gas phase. This change is caused by the excess energy of solvent reorientation. A total 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Keywords: ab inito calculations · density functional calculations · lithium batteries · lithium fluoroborate salts · solvent dissociation [1] J.-Q. Huang, X.-F. Liu, Q. Zhang, C.-M. Chen, M.-Q. Zhao, S.-M. Zhang, W. Zhu, W.-Z. Qian, F. Wei, Nano Energy 2013, 2, 314 – 321. [2] O. Borodin, G. V. Zhuang, P. N. Ross, K. Xu, J. Phys. Chem. C 2013, 117, 7433 – 7444. [3] G. Kucinskis, G. Bajars, J. Kleperis, J. Power Sources 2013, 240, 66 – 79. [4] S. S. Zhang, J. Read, J. Power Sources 2011, 196, 2867 – 2870. [5] H. Usui, M. Shimizu, H. Sakaguchi, J. Power Sources 2013, 235, 29 – 35. [6] E. G. Leggesse, J.-C. Jiang, J. Phys. Chem. A 2012, 116, 11025 – 11033.
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CHEMPHYSCHEM ARTICLES [7] S.-D. Han, J. L. Allen, E. Jnsson, P. Johansson, D. W. McOwen, P. D. Boyle, W. A. Henderson, J. Phys. Chem. C 2013, 117, 5521 – 5531. [8] J.-W. Park, K. Yamauchi, E. Takashima, N. Tachikawa, K. Ueno, K. Dokko, M. Watanabe, J. Phys. Chem. C 2013, 117, 4431 – 4440. [9] A. von Wald Cresce, O. Borodin, K. Xu, J. Phys. Chem. C 2012, 116, 26111 – 26117. [10] C. M. Burba, R. Frech, J. Phys. Chem. B 2005, 109, 15161 – 15164. [11] J. T. Lee, N. Nitta, J. Benson, A. Magasinski, T. F. Fuller, G. Yushin, Carbon 2013, 52, 388 – 397. [12] R. Younesi, M. Hahlin, F. Bjorefors, P. Johansson, K. Edstrom, Chem. Mater. 2013, 25, 77 – 84. [13] P. Ganesh, D. Jiang, P. R. C. Kent, J. Phys. Chem. B 2011, 115, 3085 – 3090. [14] K. Tasaki, J. Phys. Chem. B 2005, 109, 2920 – 2933. [15] M. D. Bhatt, M. Cho, K. Cho, J. Solid State Electrochem. 2012, 16, 435 – 441. [16] M. D. Bhatt, M. Cho, K. Cho, Appl. Surf. Sci. 2010, 257, 1463 – 1468. [17] Gaussian 03 (Revision B.04), M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G.
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Received: December 4, 2013 Published online on March 11, 2014
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Mechanism of Dissolution of a Lithium Salt in an Electrolytic Solvent in a Lithium Ion Secondary Battery: A Direct Ab Initio Molecular Dynamics (AIMD) Study Hiroto Tachikawa*[a] The mechanism of dissolution of the Li + ion in an electrolytic solvent is investigated by the direct ab initio molecular dynamics (AIMD) method. Lithium fluoroborate (Li + BF4) and ethylene carbonate (EC) are examined as the origin of the Li + ion and the solvent molecule, respectively. This salt is widely utilized as the electrolyte in the lithium ion secondary battery. The binding of EC to the Li + moiety of the Li + BF4 salt is exothermic, and the binding energies at the CAM–B3LYP/6-311 + + G(d,p) level for n = 1, 2, 3, and 4, where n is the number of EC molecules binding to the Li + ion, (EC)n(Li+BF4), are calculated to be 91.5, 89.8, 87.2, and 84.0 kcal mol1 (per EC molecule), respectively. The intermolecular distances between Li + and the
F atom of BF4 are elongated: 1.773 (n = 0), 1.820 (n = 1), 1.974 (n = 2), 1.942 (n = 3), and 4.156 (n = 4). The atomic bond populations between Li + and the F atom for n = 0, 1, 2, 3, and 4 are 0.202, 0.186, 0.150, 0.038, and 0.0, respectively. These results indicate that the interaction of Li + with BF4 becomes weaker as the number of EC molecules is increased. The direct AIMD calculation for n = 4 shows that EC reacts spontaneously with (EC)3(Li+BF4) and the Li + ion is stripped from the salt. The following substitution reaction takes place: EC + (EC)3(Li+BF4)!(EC)4Li + (BF4). The reaction mechanism is discussed on the basis of the theoretical results.
1. Introduction Molecular interactions in the lithium ion secondary battery, for example, interactions between lithium and the solvent, the solvent and the graphite electrode, or lithium and the graphite electrode, strongly dominate the performance of the battery system.[1–4] Therefore, the elucidation of both the electronic states of the Li + ion and the process of its solvation in the electrolyte are important in the development of lithium secondary batteries with higher performances and longer lifetimes.[5, 6] The dissolution of the lithium ionic salt in the electrolyte is the initial process in the construction of the lithium ion secondary battery.[7–10] Lithium fluoroborate, Li + BF4 , and lithium hexafluorophosphate, Li + PF6 , are widely used lithium ionic salts.[11, 12] These salts are dissolved in the solvents, and the solvated Li + ion and the solvated counter anion are formed. Ethylene carbonate (EC), propylene carbonate (PC), and related molecules are usually utilized as solvents in the lithium ion secondary battery. The Li + ion is strongly bound to the BF4 ion by an ionic bond. Therefore, it is considered that a large amount of energy is necessary to dissociate the Li + ion from the Li + BF4 salt. However, it is known that the salt is easily dissolved in organic solvents (such as EC and PC). Although the salt dissolution process is important, its mechanism is not clearly understood. In order to elucidate the de[a] Dr. H. Tachikawa Division of Materials Chemistry Graduate School of Engineering Hokkaido University Sapporo 060-8628 (Japan) E-mail: [email protected]
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tails of the interaction of the lithium salt with the electrolyte, several theoretical works have been performed. Ganesh et al. calculated the change in the solvation structure of EC around the Li + ion using ab initio simulation.[13] They found that the LiPF6 salt is dissociated into Li + and PF6 in EC at 310 K. It was also shown that a solid-electrolyte interphase (SEI) is formed in the presence of an electrode.[14] In bulk solution, the Li + ion is solvated by a few EC molecules as the first solvation shell. Recent theoretical calculations have shown that the Li + ion is solvated by four EC molecules as the first solvation shell. The binding energy for the interaction of the Li + ion with four EC molecules is 35 kcal mol1 (per EC molecule).[15, 16] Thus, the static interaction between the Li + ion and EC molecules is well understood theoretically. However, the dynamic features of the solvation of the Li + ion, especially the dissolution mechanism of the BF4 electrolyte in EC are still unclear. In the present study, the dissociation process of Li + BF4 in EC solution and the solvation process of Li + by EC molecules were investigated by means of density functional theory (DFT) and direct ab initio molecular dynamics (AIMD) methods.
Experimental Section Method of Calculation First, we calculated the structures of Li + BF4 , the EC molecule, and the complex (EC)n(Li+BF4) (n = 0–4) at the CAM–B3LYP level of theory. The second-order Møller-Plesset perturbation (MP2), coupled cluster with single and double excitations (CCSD), and quadratic configuration interaction with single and double excitations (QCISD) methods were applied to the Li–(EC) 1:1 complex. ChemiChemPhysChem 2014, 15, 1604 – 1610
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cal structures of Li + BF4 and EC are given in Figure 1. All static ab initio calculations were carried out using the Gaussian 09 and GAMESS programs.[17, 18]
Figure 1. Chemical structures of lithium tetrafluoroborate (Li salt) and ethylene carbonate (EC).
In the direct AIMD calculations[19–25] the potential energy and its gradient were calculated at the CAM–B3LYP/6-311 + + G(d,p) level for the reaction systems and used without basis set superposition error (BSSE) corrections in the trajectory calculation. The equation of motion was solved by the velocity Verlet algorithm with a time step of 0.25 fs. The drifts of total energies were less than 0.05 kcal mol1 in all trajectories. No symmetry restrictions were applied to the calculation of the energy gradients. The positions of EC around (EC)3(Li+BF4) used in the direct AIMD calculations were selected as follows. First, the positions of EC around (EC)3(Li+BF4) were randomly generated, then the energy difference between each generated geometry and the most stable position of the EC molecule was calculated. Five geometries possessing energy differences of lower than 2.0 kcal mol1 were selected. The initial internal vibrational energy of the (EC)3(Li+BF4) complex and the velocity of EC were set to zero. In order to elucidate the effects of the surrounding solvents on the reaction dynamics, a quantum mechanics combined with molecular mechanics (QM/MM) approach was used for the direct AIMD calculations. The first layer (higher layer), which was composed of (EC)3(Li+BF4) complexes that participate directly in the reaction process, was calculated at the B3LYP/6-31G(d) level, and the environmental solvent molecules (the second layer) were calculated by the PM3 method. Twenty solvent EC molecules were examined as the environmental solvent molecules.
1.773 . The binding energy of the Li + ion to the BF4 ion was calculated to be 144.9 kcal mol1. This energy is in good agreement with the previously reported value (141.7 kcal mol1 at the G2MP2/6-31 + G(d) level).[26] The natural population analysis (NPA) showed that the charge on the Li + ion is + 0.93, which indicates that 7 % of the positive charge is transferred to the BF4 ion after binding. For comparison, the structure and electronic states of Li + BF4 were also calculated at the CCSD/6-311 + + G(d,p) level. The results are given in Table 1. The binding energy was calculated to be 142.7 kcal mol1, which is in good agreement with the value obtained in the CAM–B3LYP calculation (144.9 kcal mol1). The NPA charge of Li + ion was + 0.95. The Li +F distance was 1.791 . The agreement between the two levels of theory indicates that the CAM–B3LYP functional can be expected to give reasonable energetics and structures for the Li + BF4 system. The structures of Li + BF4 solvated by EC are also given in Figure 2. For n = 1, one EC molecule solvates the Li + ion of the
Table 1. Binding energies, Ebind [kcal mol1], NPA atomic charges, and bond distances [] for Li + (BF4). The basis set used was 6-311 + + G(d,p).
1
Ebind [kcal mol ] NPA charge Li B F F’ Distance r(LiF) []
CAM–B3LYP
CCSD
144.9
142.7
+ 0.93 + 1.33 0.62 0.52
+ 0.95 + 1.48 0.65 0.56
1.773
1.791
2. Results and Discussion 2.1. Solvation Structures The structure of the lithium salt (lithium tetrafluoroborate; Li + BF4) is given in Figure 2. The structure was fully optimized at the CAM–B3LYP/6-311 + + G(d,p) level. Two of the fluorine atoms of the salt interact equivalently with the Li + ion. The bond distance between the Li + ion and the F atom was calculated to be
Figure 2. Optimized geometries of Li + BF4 and solvated Li + BF4 , (EC)n(Li+BF4) (n = 0 = 3), calculated at the CAM– B3LYP/6-311 + + G(d,p) level. The geometrical parameters obtained from the CAM–B3LYP/6-311G(d,p) calculation are given in parentheses.
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CHEMPHYSCHEM ARTICLES salt. The C=O carbonyl oxygen of EC interacts with the Li + ion, and two of the fluorine atoms of the BF4 anion are oriented towards the Li + ion from the opposite direction. The solvation distance (OLi + distance) is 1.836 . It was found that the Li +F distance is significantly elongated on interaction with EC molecules (1.773 for n = 0 and 1.820 for n = 1). For n = 2, the solvation structure around the Li + ion has a tetrahedral structure, in which two C=O carbonyl groups and two fluorine atoms interact with the Li + ion. The solvation distance, r(OLi), is 1.974 , which is 0.154 longer than that in the structure for n = 1. In the case of n = 3, the solvation structure is significantly changed: only one fluorine atom interacts with the Li + ion and three C=O carbonyl groups are oriented towards the Li + ion. Figure 2 (n = 3) shows the optimized structure of (EC)3(Li+BF4). The backbones of the EC molecules are illustrated with the tube model for clarity. The solvation distance was calculated to be 1.945 . Figure 3 shows the optimized structure of the solvated salt for n = 4. The solvation structure for n = 4 is drastically changed: the r(LiF) distance is significantly elongated [r(LiF) = 4.156 ], which indicates that the BF4 ion is dissociated from Li + . Four EC molecules are bound to the Li + ion, and the solvation shell is completed for n = 4.
www.chemphyschem.org dependent on the solvation number (n). The LiF bond distances, r(LiF), in the Li + BF4 salt, are plotted in Figure 4 A as a function of the number of EC molecules (n). In the case of n = 0 (free salt), the LiF bond distance is 1.773 . The bond distances in n = 1, 2, and 3 were calculated to be r(LiF) = 1.820, 1.974, and 1.942 , respectively. The LiF bond distance in Li + BF4 is significantly elongated on increased solvation of EC around Li + , although the distance becomes almost constant in n = 2 and 3.
Figure 4. A) Lithium-fluorine atomic distance, r(LiF), plotted as a function of the number of EC molecules (n). B) Lithium-fluorine atomic bond populations, P(LiF).
2.3. Bond Population Figure 3. Optimized geometry of (EC)n(Li+BF4) (n = 4) calculated at the CAM–B3LYP/6-311 + + G(d,p) level. The geometrical parameters obtained from the CAM–B3LYP/6-311G(d,p) calculation are given in parentheses.
The binding energies of EC to Li + BF4 for n = 1, 2, 3, and 4 were calculated to be 91.5, 89.8, 87.2, and 84.0 kcal mol1 (per EC) at the CAM–B3LYP/6-311 + + G(d,p) level, respectively. The atomic charges of (EC)3(Li+BF4) were calculated using the NPA method. The molecular charges on (EC)3(Li+BF4) were found to be + 0.22, + 0.71, and 0.93, respectively. This result indicates that the interaction between Li + and BF4 is fully ionic. 2.2. Bond Distances The structure of the Li + BF4 salt was thus drastically changed by solvation by EC, and the magnitude of the deformation is 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
In order to elucidate the effects of the solvent molecules on the bonding nature between the Li and F atoms of the Li + BF4 salt, the bond population was analyzed, and the results are given in Figure 4 B. The bond populations of LiF for n = 0, 1, and 2 were 0.203, 0.186, and 0.150, respectively, which indicates that the LiF bond becomes weaker on solvation of the Li + ion. In the case of n = 3, the population shows the smallest value and is close to zero (0.038). This result suggests that the Li + ion is very weakly bound to BF4 in the case of n = 3. The Li + ion of the salt may be stripped off by solvation. 2.4. Potential Energy Surface The potential energy surface (PES) for the reaction of EC with (EC)3(Li+BF4) was calculated at the CAM–B3LYP/6-31G(d) level. The result is plotted in Figure 5 as functions of R1 = r(OLi) and R2 = r(LiB), where R1 and R2 denote the distance between Li + ChemPhysChem 2014, 15, 1604 – 1610
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Figure 6. Sample trajectory obtained by direct AIMD calculation. A) Potential energy of the system plotted as a function of time (in fs). B) Intermolecular distances (R1 and R2).
Figure 5. Potential energy surface (PES) for the reaction of EC with (EC)3(Li+BF4), plotted as functions of R1 and R2. Contours are drawn at each 2 kcal mol1. The calculation was performed at the CAM–B3LYP/6-311G(d,p) level.
and EC, and that between Li + and BF4 , respectively. The potential minimum was found at R1 = 2.00 and R2 = 2.40 ; this corresponds to a reaction intermediate complex composed of EC(Li+BF4)(EC)3. This complex is E(RC) = 38 kcal mol1 more stable in energy than the reactant [EC + (EC)3(Li+BF4); R1 = 4.00 and R2 = 2.40 ], and is also 5 kcal mol1 more stable than the product region (PD) on the PES. The shape of the PES indicates that the potential energy is open for the product region. 2.5. AIMD Calculation The collision dynamics of EC with solvation system, (EC)3(Li+BF4), that is, the reaction between EC and (EC)3(Li+BF4), was investigated by the direct AIMD method. A total of twenty trajectories was run from several initial configurations. All trajectories followed similar routes and gave the same product. A typical trajectory obtained from the direct AIMD calculation is given in Figure 6. The sample trajectory was started from R1 = 4.00 and R2 = 1.95 , and the initial momentum vectors of the atoms were assumed to be zero at time zero. The structures of (EC)3(Li+BF4) and EC at time zero were fixed at the optimized values obtained at the B3LYP/6-311G(d,p) level. The zero level 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
of the potential energy corresponds to the total energy of the initial separation between EC and (EC)3(Li+BF4) at time zero (point a). It was found that the reaction proceeds spontaneously without activation energy. The time evolution of the potential energy (Figure 6 A) shows that the energy of the system decreases gradually as EC approaches (EC)3(Li+BF4), and reaches the energy minimum at 415 fs (point b). After the minimum, the energy vibrates rapidly in the range (7)–(3) kcal mol1. The time evolution of the interatomic distances (R1 and R2) are plotted in Figure 6 B. The distance between EC and the salt, R1, decreases gradually and reaches the minimum value (1.80 ) at 415 fs (complex formation). This trajectory predicts that EC approaches the (EC)3(Li+BF4) reagent spontaneously. The distance between the Li + ion and the BF4 ion, R2, increases gradually from 1.95 to 2.35 from 0–320 fs, and then suddenly further to 3.10 from 320–400 fs. From 0 to 415 fs (point b) the distances R1 and R2 are changed from 4.00 to 1.80 (R1) and 1.95 to 3.20 (R2), respectively. At 710 fs (point c), distances R1 and R2 were 2.65 and 3.56 , respectively. This change indicates that bond exchange takes place by collision of EC with the salt. However, full dissociation of BF4 from the system did not occur, and BF4 remained in the system (R1 = 2.65 and R2 = 4.00 ). We also found that the approach of EC to Li + and the dissociation of Li + from Li + BF4 took place without an activation barrier, which indicates that the dissolution of the Li + ion from the Li + BF4 salt takes place spontaneously in EC solution. 2.6. Snapshots of the Solvation Process Snapshots of the reaction system are illustrated in Figure 7. The initial separation of this trajectory (R1) was 4.0 at time ChemPhysChem 2014, 15, 1604 – 1610
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www.chemphyschem.org 2.8. Effects of Environmental Solvent Molecules on the Reaction Dynamics
In order to elucidate the effects of surrounding solvents on the reaction dynamics, direct AIMD– QM/MM calculations were performed on the reaction system surrounded by environmental solvent molecules. Snapshots after the reaction are given in Figure 9. The higher layer, which is composed of (EC)3(Li+BF4) and participates directly in the reaction process, was calculated at the B3LYP/6-31G(d) level, whereas the environmental solvent molecules (the second layer) were represented by the PM3 method. At time zero, the EC molecule was located at the initial separation (R1 = 3.60 ), and the distance between Li + and the B atom of BF4 was R2 = 1.955 , which represents the optimized Figure 7. Snapshots of the reaction of EC with (EC)3(Li+BF4) obtained by direct AIMD calculation. This snapshot geometry. After starting the recorresponds to potential energy surface shown in Figure 5. action, the EC reactant gradually approached Li + BF4 , and inversion of the umbrella mode of the Li + moiety occurred after 158 fs. The EC molecule further zero. The distance between Li + and the B atom in BF4 (R2) was 1.95 , which corresponds to that of the optimized approached (EC)3(Li+BF4), and BF4 left the Li + ion (c). geometry. At 228 fs, the distances were R1 = 1.883 and R2 = 3.000 , After starting the reaction, the reactant EC approached the which indicates that the dissociation took place after the reacLi + BF4 and the collision complex was formed at 415 fs. The tion of EC. EC molecule continues to gradually approach (EC)3(Li+BF4), The time evolution of the potential energy and bond distanand the distance between the BF4 ion and Li + is slightly inces (R1 and R2) are given in Figure 10. The potential energy of creased (c). However, the dissociation of BF4 is not complete, the system decreases gradually as a result of the approach of and the ion vibrates in the space defined by three EC EC to (EC)3(Li+BF4). The magnitude of the energy change in molecules (d).
2.7. Effects of the Initial Configurations of EC(Li+BF4)(EC)3 on the Reaction Dynamics The collision of EC with (EC)3(Li+BF4) occurs from several configurations. In order to study their effects, geometrical configurations of EC relative to (EC)3(Li+BF4) were randomly generated around the optimized structure, and five dynamics calculations were run from these selected points. The geometries were selected so that the energy differences from the optimized geometry were lower than 2.0 kcal mol1. The results of direct ab initio MD calculations from the five geometrical configurations are given in Figure 8. All trajectories gave the same product. 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 8. Initial configuration dependence on the reaction paths.
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www.chemphyschem.org of six trajectories were run from selected points, and similar results were obtained in all cases. Thus, it was found that the approach of EC to Li + and the dissociation of Li + from Li + BF4 both take place without activation barrier in the gas phase and in solution. This indicates that the dissolution of the Li + ion from the Li + BF4 salt takes place spontaneously in EC solution without activation energy.
3. Conclusions The mechanism of the dissolution of the Li + ion in EC solvent was investigated by direct AIMD methods. Lithium fluoroborate Figure 9. Snapshots of the reaction of EC with (EC)3(Li+BF4) obtained by the direct AIMD method combined with (Li + BF4) was examined as the a QM/MM calculation. origin of the Li + ion. The salt is widely utilized as the electrolyte of the lithium ion secondary battery. The EC molecule binds to the Li + moiety of the Li + BF4 salt. This binding process is exothermic. The intermolecular distances between Li + and the F atom of BF4 were elongated by solvation. These results indicate that the interaction of Li + with BF4 becomes weaker as the number of EC molecules increases. The (EC)3(Li+BF4) complex was formed if n = 3. The AIMD calculation for n = 4 showed that EC reacts with (EC)3(Li+BF4) and the Li + ion is stripped from the salt. The following substitution reaction takes place [Eq. (1)]: EC þ ðECÞ3 ðLiþ BF4 Þ ! ðECÞ4 Liþ ðBF4 Þ
ð1Þ
Acknowledgements The author acknowledges partial support from a Grant-in-Aid for Scientific Research (C) from the Japan Society for the Promotion of Science (JSPS) (Grant Number 24550001). This work was partially supported by a Grant-in-Aid for Scientific Research on Innovation Areas “Evolution of Molecules in Space” (Grant Number 2510800413).
Figure 10. Time evolution of the reaction system of the reaction of EC with (EC)3(Li+BF4) obtained by the direct AIMD method combined with a QM/ MM calculation.
solution is larger than that in the gas phase. This is due to the fact that solvent reorientation (twelve molecules) takes place during the reaction. Bond alternation occurs at 170 fs. This time scale is slightly faster than in the gas phase. This change is caused by the excess energy of solvent reorientation. A total 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Received: December 4, 2013 Published online on March 11, 2014
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