Density Functional Theory Study on Structural and Energetic

Article pubs.acs.org/JPCC

Density Functional Theory Study on Structural and Energetic Characteristics of Graphite Intercalation Compounds Ken Tasaki* Mitsubishi Chemical USA, Inc., 410 Palos Verdes Boulevard, Redondo Beach, California 90277, United States ABSTRACT: The structures and energetics of a number of graphite intercalation compounds (GICs) having a relatively wide range of chemistry have been investigated by density functional theory calculations with the van der Waals correction using the dispersion correction method within the framework of generalized gradient approximation. The GICs studied included potassium-intercalated graphite (KCn), lithium-intercalated graphite (LiCn), lithium solvated by dimethyl sulfone (DMSO)-intercalated graphite (Li(DMSO)4Cn), lithium solvated by dibuthoxy ethane (DBE)-intercalated graphite (Li(DBE)2Cn), perchlorate (ClO4)-intercalated graphite (ClO4Cn), and hexafluorophosphate (PF 6 )-intercalated graphite (PF 6 C n ). Our calculations show reasonable agreement with experimental data for the interlayer distances of the GICs. A correlation between the size of the intercalate and the interlayer distance of the GIC has been observed. Our study has also predicted that all the GICs studied here are energetically stable except for Li(DBE)2Cn, consistent with experimental observations. Our results have suggested that there is a strong correlation between the intercalation energy and the electron transfer between the intercalate and graphite. On the basis of our results, we propose that the ionization potential or the electron affinity of the intercalate, along with the size of the intercalate, is a good measure for the stability of the resulting GIC in general.

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INTRODUCTION Although a graphite intercalation compound (GIC) was first reported in 1841 for a sulfate-intercalated GIC,1 it was not until the 1940s that X-ray diffraction analyses identified the stage indexes of a number of GICs,2 which was followed by a surge of interest in GICs in the 1970s after their ability to control a wide range of physical properties through the guest materials was recognized.3−5 Of a variety of intercalation compounds, GICs are of particular interest because of their relatively high degree of structural ordering, responsible for the staging which gives rise to different characteristics for a given guest material. The interest in GICs continues to date in a wide range of applications ranging from catalysts and superconducting materials to energy storage electrodes.6−11 A large volume of experimental data have also prompted a number of theoretical studies on GICs.12−22 Our interest in GICs is as active electrode materials for energy storage. Graphite has been extensively used as the anode active materials for commercial lithium-ion batteries, although it has also been examined as the cathode in so-called dual cells.23−28 It has been reported that when graphite is used as the anodeactive material, the solvent molecules cointercalate into graphite along with the lithium ion, forming what is called a ternary GIC, during the first charge cycle.29,30 Intercalations of anions such as perchlorate (ClO4−) or hexaflorophosphate (PF6−) into graphite have also been reported.26,27,31−34 Yet, the energetics of these GICs are not well understood. For example, it is known that dimethylsulfoxide (DMSO), a well-known solvent for lithium, cointercalates into graphite along with a lithium ion, while 1,2-dibutoxyethane (DBE), another solvent for lithium, does not.30,35 We have chosen lithium, lithium solvated by © 2013 American Chemical Society

DMSO (Li(DMSO)4), lithium solvated by DBE (Li(DBE)2), potassium, ClO4, and PF6 as the intercalate into graphite. In this report, we apply density functional theory (DFT) calculations to these GICs to gain insight into their structural and energetic characteristics in order to examine the nature of the GIC formations.

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CALCULATIONS The GICs examined in this study included lithium intercalated graphite (LiCn=6,12), potassium-intercalated graphite (KCn), Li(DMSO)4-intercalated graphite (Li(DMSO)4Cn), Li(DBE)2intercalated graphite (Li(DBE)2Cn), perchlorate-intercalated graphite (ClO4Cn), and hexaflorophosphate-intercalated graphite (PF6Cn). KCn has been well characterized and its thermodynamic data are available for comparison.36 In order to examine the energetics of intercalation into graphite, we assumed the following processes for the solvated lithium: Li+(S)m + e → Li(S)m

(1)

Li(S)m + Cn → Li(S)m − l Cn + l × S

(2)

for potassium:

36

K metal − e → K+

(3)

K+ + e → K

(4)

Received: September 29, 2013 Revised: December 20, 2013 Published: December 24, 2013 1443

dx.doi.org/10.1021/jp409700q | J. Phys. Chem. C 2014, 118, 1443−1450

The Journal of Physical Chemistry C

Article

Table 1. Structural Parameters of LixC6a

this work calcd. exp.

3.30 3.35d

calcd. exp.

this work 35.53 35.1d

x=0

x=1

1/2 cb, Å

1/2 cb, Å ref 21

ref 22

this work

ref 20

ref 21

ref 22

3.25

ref 20

3.30

3.35c

3.70

3.547

3.76

Vg × 103, Å3 ref 20 34.175

51.38

3.71 3.706e,f Vg × 103, Å3 this work 58.26 59.5f

ref 20 59.07

56.51

ref 21

ref 21

a The cells used for calculations are shown in Figure 1. bThe interlayer distance. cThe interlayer distance was fixed at this value. dRef 55. eRefs 56 and 57. fRef 58. gThe unit cell volume.

Figure 1. The stacking structures of (a) graphite (AB) and (b) fully lithiated graphite (AA) predicted by PBE/DNP calculations using the Grimme correction. The lithium atoms are shown by balls, while the graphite carbons are represented by sticks.

K + Cn → KCn A− − e → A

(6)

process of intercalation; rather, the two-step process was useful for the calculations, and it still seems a reasonable assumption. Then, the intercalation energy, ΔEinter, was calculated by the following equation:

A + Cn → ACn

(7)

ΔE inter[Li(S)m − l Cn] = E[Li(S)m − l Cn] + l × E[S] − E[Cn]

(5)

and for the anion,

− E[Li(S)m ]

where Li(S)m‑lCn represents the GIC where S is the solvent solvating the lithium ion (S = EC, DMSO, and DBE), Kmetal is potassium metal, A− is the anion (A = ClO4 and PF6), and Cn is graphite, n being the number of graphite carbon atoms per the intercalate. The values for m and l were both 4 for LiCn=6,12; 4 and 0 for Li(DMSO)4Cn; 2 and 0 for Li(DBE)2Cn, respectively. While the ternary GIC of Li(EC)4 is known to undergo spontaneous reduction decompositions inside graphite during the first charge cycle, that of Li(DMSO)4 has been identified by X-ray diffraction.35 The lithium solvation numbers of 4.1−4.3 and 4.2 were reported for 1 M LiClO4 in EC and 1 M LiN(SO2CF3)2 in DMSO, respectively.37,38 For DBE, we used 2 as the solvation number since one DBE molecule has two solvation sites: the ether oxygen atoms. No solvation number for DBE has been reported. Li+(S)m and Li(S)m in eqs 1 and 2 refer to the lithium solvation in bulk solution and near the anode graphite surface, respectively. Likewise, A− and A in eqs 3 and 4 are the anion in bulk solution and the neutralized anion near the cathode graphite surface, respectively. The underlining assumption is that the potassium cation, the positively charged solvated lithium or the anion is first reduced or oxidized on the graphite surface, respectively, depending on whether graphite is used as the anode or the cathode, prior to the interaction into graphite, or as it intercalates into graphite during the charge cycle. This may not necessarily reflect the actual physical

ΔE inter[KCn] = E[KCn] − E[Cn] − E[K metal]/i

ΔE inter[ACn ] = E[ACn ] − E[Cn] − E[A]

(8) (9) (10)

where E is the SCF energy of the system inside the brackets, and i is the number of potassium atoms in a cell for potassium metal. The value of 16 was used as the value of i after confirming that further increase in the number of potassium atoms in a cell did not alter the value of E[Kmeal]/i by calculations. E[Kmetal] was calculated using the crystal structure of potassium.39 The value of n depended on the size of the intercalate so that any of the atoms of the intercalate molecule were outside the van der Waals radius of the atoms of its imaginary molecule in neighboring cells. For example, the shortest distance between DBE, the largest molecule in this study, and its image in the neighboring cells was more than 2.5 Å which was the distance between the hydrogen atom of the methyl group and that of the next neighbor image of the DBE molecule. Some of the GICs involve a strong binding between the intercalate and graphite such as LiCn=6,12 and KCn. Application of basis set superposition error (BSSE) using schemes such as the counterpoise correction method40 to systems like these may not be valid. Hence, no BSSE was corrected to all the systems 1444



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within the framework of the generalized gradient approximation (GGA).47 The numerical basis sets were used, as opposed to Gaussian-type basis sets, and had one atomic orbital (AO) for each occupied atomic orbital, the second sets of valence AOs, d-functions for non-hydrogen atoms, and p-functions on hydrogen atoms, which is to be referred to as the doublenumerical polarization or DNP.48 For the dispersion corrections to the Kohn−Sham DFT, we adopted the Grimme’s correction.49 The combination of PBE and DNP, to be referred to as PBE/DNP, was chosen as a compromise between the accuracy and the practicality of computation. The PBE functional was also used for the Grimme’s correction.49 For the numerical integration of wave functions, the atom centered grids were used, including approximately 2000 grid points for each atom with the real space cutoff distance of 5.0 Å. Also, Self-Consistent-Field (SCF) convergence criterion was set to the root-mean-square change in the electronic density to be less than 1 × 10−6 a.u. The geometry optimization was carried out using the delocalized internal coordinates. The convergence criteria applied for geometry optimization were 1 × 10−5 a.u. for energy, 0.02 au nm−1 for force, and 5 × 10−4 nm for displacement. A spin-unrestricted approach was applied with all electrons being considered explicitly. Stationary points were characterized as minima by verifying the absence of any imaginary frequencies for all geometry optimizations.

Figure 2. The interlayer potential energy per atom in a cell as a function of the c/2 parameter of a graphite unit cell obtained from PBE/DNP calculations: (a) with and (b) without the Grimme correction.

studied to maintain the uniformity. Interactions for a series of molecules, including Li and Li+ with polyaromatic hydrocarbons have been reported without BSEE.41 Periodic boundary conditions were applied to the GICs and graphite. The COSMO model42 was adopted to estimate the solvation energy of the solvated lithium (Li(EC)4, Li(DMSO)4 and Li(DBE)2), EC, ClO4 in propylene carbonate (PC), or PF6 in the mixed solvents consisting of EC and diethyl carbonate (DEC) in the (EC/DEC = 33:67) volume ratio. The dielectric constants were 89.6, 47.0, 7.1, 64.4, 2.83 for EC, DMSO, DBE, PC, and DEC, respectively.43 The mixed solvents of EC and DEC had the volume average dielectric constant of 31.45.44 The optimized structure in each solvent was used for the intercalate prior to optimization of each GIC. For the construction of the GIC, the intercalate was first inserted between two graphene layers in a cell by expanding the layers to accommodate it. This layout corresponds to stage 2 of GICs, with the exception of LiC6, which represents stage 1. Then, the c parameter of the cell was incrementally adjusted while geometry optimization was performed at the fixed c parameter, and this procedure was repeated until the energy minimum was found. Then, a full optimization was performed, relaxing all the parameters. This stepwise procedure was taken to increase the possibility of locating the global minimum, given many variables to optimize. The charge of the system inside the bracket in eqs 8−10 was all maintained to be neutral. This is required by the use of periodic boundary conditions for the GICs and graphite and also by the assumption made for the intercalate prior to intercalation described above. The DFT calculations have been performed, using the Perdew− Burke−Ernzerhof (PBE) exchange-correlation functional45,46

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RESULTS AND DISCUSSION It is known that weak interactions such as van der Waals interactions, the important force for graphite, are poorly described by DFT calculations, especially with the GGA framework.50 Various approaches have been proposed for corrections of the London dispersion interactions in the DFT formalism.49−54 Here, we adopt the dispersion correction method in which the correction of R−6 (the dispersion) term is made through parametrization developed by Grimme, et al.49 Since graphite was not included in the parametrization of the dispersion term in the Grimme correction, we first tested its validity by applying to the structures of graphite and fully lithiated graphite. Table 1 lists the interlayer distance, c/2, and the cell volume for both graphite and fully lithiated graphite, along with the experimental data and the calculated results from previous reports.20−22 Our results with the Grimme correction show reasonable agreement with the experimental data.55−58 It has been reported that the interlayer distance of graphite is not reproduced by GGA in the combination with local density approximation.21 As a result, the interlayer distance was often fixed in previous studies.22 Figure 1 illustrates the stacking structures for graphite and Li3C18 predicted by PBE/DNP calculations using the Grimme

Table 2. Optimized Cell Parameters (a, b, c), Intercalation Energies (ΔEinter), and Interlayer Distances (ld) for GICsa GIC

a, Å

b, Å

c, Å

ΔEinter, kcal mol−1

ld, Å

K3C36 Li3C36 Li(DMSO)4C64 Li(DBE)2C110 ClO4C18 PF6C18

7.43 7.40 9.84 12.31 7.39 5.06

7.43 7.40 9.84 12.31 7.39 4.95

8.49 7.01 13.31 11.02 10.10 10.97

−23.7 (−27.08b) −31.1 −15.6 7.3 −13.3 −28.7

5.38 (5.41c) 3.71 (3.7d) 10.11 (11.6e) 12.10 6.96 (5.27f) 7.7 (7.9g)

a The values in the parentheses are the experimental data. ΔE is expressed as the energy difference per one intercalate in the cell. The interlayer distance is the distance between the two graphene layers between which the intercalate is present. All of the GICs are at stage 2. bFor KC10.36 cRef 2. d Ref 55. eRef 30. fRef 34. gRef 27.

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Figure 4. The interlayer distances, ld, of GICs as a function of the molecular volumes of the corresponding intercalates. The molecular volumes were calculated based on the Connolly surface, listed in Table 3. The triangles represent the data for ClO4C18 and PF6C18, while the circles are for the rest of the GICs.

Table 3. Molecular Volume of Each Intercalatea volume, Å3 a

K

Li

Li(DMSO)4

Li(DBE)2

ClO4

PF6

86.1

22.2

322.2

448.5

56.4

74.3

Calculated based on the Connolly surface of each intercalate.

potential energy (ΔEvdw) was then obtained by the following equation: ΔEvdw (r ) = E(r ) − E(∞)

(11)

where E(r) and E(∞) are the SCF energy of the cell at the c/2 parameter of r and at infinity, respectively. Little change in the energy was seen beyond r = 10 Å; thus, E(∞) was replaced by E(10 Å). Figure 2 plots the interlayer potential energy as a function of the c/2 parameter of a graphite unit cell obtained from PBE/DNP calculations with and without the Grimme correction. While the potential energy calculated without the Grimme correction shows a negligible potential well, which is consistent with previous reports,21,22 the potential well of 1.59 kcal mol−1 atom−1 was predicted with the correction. The experimental data range from 0.8 to 1.2 kcal mol−1 atom−1.59−61 Dappe et al. have calculated the van der Waals energy between two graphene sheets through a combination of the DFT approach and the perturbation theory.62 Their result, 1.4−1.7 kcal mol−1 atom−1, is close to our result. With the structural and energetic characteristics of graphite reasonably reproduced, next, we applied the same DFT scheme to the GICs under study. Table 2 summarizes the results, along with some experimental data where available. The all GICs listed in Table 2 are at stage 2. Figure 3 shows the optimized structures of GICs (Figure 3a−f) and of the lithium solvations by EC, DMSO, and DBE (Figure 3g−h). The interlayer distances for K3C36, Li3C36, and PF6C18 show excellent agreement with the experimental data. The interlayer distance originally reported for PF6C18, 4.6 Å,26 was later found to be longer, 7.9 Å.27 Our calculations actually support the corrected result. However, the calculated interlayer distance for Li(DMSO)4C64 is underestimated by a little over 1 Å, whereas that for ClO4C18 is overestimated by about 1 Å. Clearly, the difference in the nature of interactions between the intercalate and graphite is at work, and there is a limit to the approach to apply the same functional and basis set to the wide range of chemistry examined in this study. Still, the overall agreement is reasonable. No data are available for the interlayer distance of Li(DBE)2C110. The largest interlayer distance is reported for

Figure 3. The optimized structures of the GICs and the solvation structures: (a) K3C36, (b) Li3C36, (c) Li(DMSO)4C64, (d) Li(DBE)2C110, (e) ClO4C18, (f) PF6C18, (g) Li(EC)4, (h) Li(DMSO)4, and (i) Li(DBE)2. The cross section perpendicular to the graphene layers are shown for the GICs.

correction. They show the well-known AB and AA stacking structures in Figures 1a and 2b, respectively. The potential energy was calculated by optimizing the atomic positions in a unit cell having two graphene layers while keeping the cell parameters fixed at each point. Both a and b cell parameters, taken from the crystallographic data,55 were kept constant throughout the calculations. The interlayer stacking 1446



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Table 4. Hirshfeld Charges (qI) of the GICs charge

K3C36

Li3C36

Li(DMSO)4C64

Li(DBE)2C110

ClO4C18

PF6C18

qIa -qI/nNIb

1.30 −0.012

1.84 −0.017

−1.73 0.027

−0.55 0.005

−0.45 0.025

−0.72 0.040

a The charge of the intercalate: K3 for K3C36 and Li3 for Li3C26. bThe averaged charge of the graphite carbon divided by the number of the intercalate in the cell: n is the number of graphite carbon atoms, and NI is the number of intercalate in the cell.

and the solvation energy, using different models, thus, each introducing different degrees of errors, some of which can cancel one another or only accumulate. The theory used, PBE/ DNP, is also not necessarily highly accurate. Thus, our results should be considered only qualitative. Still, it is tempting to make sense of our results from simple characteristics of the GIC. For example, the intercalation energy tends to decrease negatively as the interlayer distance expands, although that is not always the case, as is seen for Li(DMSO)4C64 and PF6C18. Then, we examined the electronic characteristics of the GICs through the Hirshfeld atomic charges.65 The electrostatic potential fitting is difficult to apply to a system under periodic boundary conditions. Table 4 lists the results obtained from PBE/DNP calculations for each GIC. qI is the charge of the intercalate obtained from the Hirshfeld atomic charge. For K3C36 and Li3C36, the subscript I of qI represents three potassium and lithium atoms, as in qK3 and qLi3, respectively. Since the total charge of the system is zero, the charge of the graphene layers in the cell is −qI. Then, the averaged atomic charge of a graphite carbon per an intercalate is −qI/nNI, where n and NI are the number of graphite carbons and the number of the intercalates in the cell, respectively. Since the atomic charge of graphite without the intercalate should be neutral, the deviation of the graphite carbon atomic charge from zero reflects the net electron transfer between graphite and the intercalate upon the GIC formation: when it is positive, the electron transfers from graphite to the intercalate, and the negative charge suggests the transfer in the opposite direction. Figure 5 plots the intercalation energy of the GIC against its −qI/nNI. The plots suggest that the more electron transfer occurs, the more stable the GIC becomes. The strong electron transfer has also been reported for the LiC6 system.21 Although the Hirshfeld analysis tends to yield too small dipole moments,66 it is defined relative to the deformation density; thus, it may be more relevant to describe the difference in the electron transfer. Figure 5 reveals that when I = K3 and Li3, the value of −qI/nNI is negative, while that for the other intercalates has a positive charge. It is inferred that the cationic K and Li atoms tend to supply electrons to graphite, whereas the anionic PF6 and ClO4 groups withdraw electrons from graphite, given their high ionization potentials and electron affinities, respectively. For the solvated lithium GIC, such as Li(DMSO)4C64 and Li(DBE)2C110, the solvent molecules with electron withdrawing groups such as the SO group or the ether oxygen atoms have a propensity to pull electron from graphite. Table 5 lists the ionization potentials or the electron affinities of the intercalate studied here. They were calculated at the

Figure 5. The intercalation energy, ΔEinter, plotted against the value of −qI/nNI for each GIC, where qI is the charge of the intercalate, n is the number of the graphite carbons, and NI is the number of the intercalates in the cell.

Li(DMSO)4C64, 10.11 Å. This is illustrated in Figure 3c,h: the bulky lithium solvation by four DMSO molecules expands the graphene layers considerably. Since DBE has two solvation sites, the two oxygen atoms, the solvation of a lithium ion can be sufficiently solvated by two DBE molecules, as is shown in Figure 3i. Figure 4 plots the relationship between the interlayer distance of each GIC and the molecular volume of the corresponding intercalate. The molecular volume of the intercalate was calculated, based on the Connolly surface63−65 shown in Table 3. The graphite interlayer tends to expand as the molecular volume of the intercalate increases in general. It is of interest to observe that there is a linear relationship for the cation-based intercalate, although the number of data is too small to draw any conclusion. As to the intercalation energy, our results show a negative energy for all of the GICs except for Li(DBE)2C110. In fact, the cointercalation of DBE-solvated lithium into graphite was not observed in an earlier report.30 In addition, the intercalation energy for K3C36 shows fairly good agreement with the experimental data.36 It should also be noted, however, that the experimental data are given as the enthalpy, while our results represent the internal energy. As to LiCn, Persson et al. have reported −0.3 kcal mol−1/6C ∼ −0.4 kcal mol−1/6C for the intercalation energy for Li0.3−0.5C6 at stage 2.22 Our result for Li3C36 corresponds to −1.8 kcal mol−1/6C. The different functionals and approaches used in both studies make a direct comparison difficult. It is also important to note that our results include inevitable uncertainties. The intercalation energy consists of multiple components, such as the interaction between the intercalate and graphite, that between the graphene layers,

Table 5. Ionization Potentials (IP) or Electron Affinities (EA) of the Intercalates IP,a eV EA,b eV a

K

Li

Li(DMSO)4

Li(DBE)2

98.87

136.72

55.68

59.05

ClO4

PF6

−96.80

−100.30

The energy required to remove an electron from the intercalate. bThe energy released when an electron is added to the intercalate. 1447



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Figure 6. The isosurface of the deformation density for Li3C36 having three interlayer distances: (a) 3.7 Å, (b) 7.4 Å, and (c) 11.1 Å.

PBE/DNP level. Our results suggest that the intercalation energy of the GIC depends on the ionization potential or the electron affinity of the intercalate. Although the intercalation energy is a function of many variables, the electronic interaction between the intercalate and graphite seems to play an important role in the stability of GICs. Since the electron transfer seems one of the drivers for GIC formations, we examined the deformation density of each GIC by the following equation: Δρ(r ) = ρGIC (r ) −

∑ ρi (r) i

(12)

where ρGIC(r) and ρi(r) are the charge density of the GIC at the point r and the charge density of atom i at the same point when all the atoms in the system are isolated, respectively. Then, the difference, Δρ(r), reflects the degree to which the electron transfer occurs in the GIC. For example, when Δρ(r) is zero, no electron transfer should take place among the atoms in the system. The calculations were performed at the PBE/DNP level. Figure 6 displays the isosurface of the deformation density for Li3C36 having three different interlayer distances. At the interlayer distance of 3.7 Å (Figure 6a), Li3C36 has continuous isosurfaces across the cross section perpendicular to the graphene layers, having a large contact area between the lithium atoms and the graphite carbon atoms, suggesting significant electron transfers between the lithium atoms and the graphene layers. At 7.4 Å (Figure 6b), however, the contact of the isosurface between the lithium atoms and the graphene layers is lost. Instead, the overlap among the lithium atoms only remains. At 11.1 Å (Figure 6c), the empty space between the lithium atoms and the graphene layers only widens without any isosurface contact, isolating the lithium atoms further. Figure 7 shows the isosurfaces for the rest of the GICs, illustrating different degrees of the electron transfer for the GICs. For example, the isosurface of K3C36 runs from the top of the graphene layer to the bottom layer straight through the potassium atoms (Figure 7a). Li(DMSO)4C64 has clear isosurface contact areas between Li(DMSO)4 and the graphene layers (Figure 7b), while some of the contacts with the graphene layers are lost for Li(DBE)2C110 (Figure 7c). As to ClO4C18 (Figure 7d) and PF6C18 (Figure 7e), the electron flows from the graphene layers to the intercalate. This is represented by the intercalate contacting the thin layer of isosurface which is a part of the graphene carbon atoms.

Figure 7. The isosurface of the deformation density for each GIC: (a) K3C36, (b) Li(DMSO)4C64, (c) Li(DBE)2C110, (d) ClO4C18, and (e) PF6C18.

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CONCLUSIONS The structural and energetic characterizations of a number of GICs with differences in chemistry have been examined by DFT calculations including the van der Waals correction. Our results show reasonable agreement with experimental data for the interlayer distances of GICs studied here. A correlation between the size of the intercalate and the interlayer distance has been clearly observed, though other factors such as the 1448



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interaction between the intercalate and graphite are certainly at work. Our study has also predicted that all the GICs studied here have negative intercalation energies except for Li(DBE)2Cn. Our results are consistent with experimental observations.30 Our calculations have also suggested that there is a strong correlation between the intercalation energy and the electron transfer between the intercalate and graphite. On the basis of our results, we propose that the ionization potential or the electron affinity of the intercalate, along with the size of the intercalate, can be a good measure for the stability of the resulting GIC in general. Our observations in this study warrant further study to gain better understanding of the complex nature of GICs in general.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (310) 373-4196; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author thanks Dr. Alexander Goldberg of Shrödinger for valuable discussions.

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REFERENCES

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