Density Functional Theory Modeling-Assisted Investigation of

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Article Cite This: J. Phys. Chem. C 2018, 122, 10675−10681

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Density Functional Theory Modeling-Assisted Investigation of Thermodynamics and Redox Properties of Boron-Doped Corannulenes for Cathodes in Lithium-Ion Batteries Jiwoong Kang,†,‡ Ki Chul Kim,*,§ and Seung Soon Jang*,†,∥,⊥ †

Computational NanoBio Technology Laboratory, School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245, United States ‡ School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States § Department of Chemical Engineering, Konkuk University, Seoul 05029, Republic of Korea ∥ Institute for Electronics and Nanotechnology, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ⊥ Parker H. Petit Institute for Bioengineering and Bioscience, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ABSTRACT: Understanding thermodynamics and reduction potentials of boron-doped corannulenes (BDCs) can provide meaningful insight to establish strategies for designing doping processes of organic materials applicable to cathodes in lithium-ion batteries (LIBs). In this study, a comprehensive set of BDC models is prepared to investigate the effect of the number and geometric position of doped boron atoms on the thermodynamic stability and redox properties of the corannulene. Our investigation enables us to evaluate their potential as organic cathode materials in LIBs. In this study, it is found that the first and second boron atoms can be exclusively doped in thermodynamically stable positions. Corannulene derivatives doped by the boron atom show enhanced reduction potentials ranged from 2.41 to 5.05 V vs Li/Li+ as compared with the pristine corannulene (0.9 V vs Li/Li+). A higher level of structural heterogeneity created by another boron atom does not guarantee a higher reduction potential (3.03 and 2.51 V vs Li/Li+ for probability-averaged reduction potentials of 1- and 2-boron-doped corannulenes, respectively). Reduction potential is strongly correlated with the spin state as well as the structural and electronic properties. The doped boron atoms play a critical role in improving the stability of the Li-binding thermodynamics, showing their positive impact on the enhancement of the charge capacity.

1. INTRODUCTION Recently, lithium-ion batteries (LIBs) have been utilized as main power sources for electric vehicles due to their high charge and energy densities.1−3 However, a couple of shortcomings have to be overcome for wide range of applications of the LIBs. Specifically, the relatively low power density arising from the slow diffusion of Li ions through the entire battery system during the charge and discharge processes is a primary issue to be addressed.3−7 To improve ionic diffusion, significant efforts have been made by introducing organic molecules for fast surface redox reactions.8−16 For example, Gall et al. studied the specific charge capacity and cycling stability of poly(2,5-dihydroxy-1,4-benzoquinone-3,6methylene) as an organic cathode material in LIBs.8 They reported that the polymerized cathode material achieved moderately good performance. Likewise, Liu et al. employed the density functional theory (DFT) method to investigate the potential of carbon nanotubes coated by self-polymerized dopamines as organic cathode materials in LIBs,15 reporting that the surface redox activity of the carbonyl group in the dopamines could be consistently sustained at high cell voltages during the discharge process, suggesting that the organic materials could be ideal candidates for the next generation © 2018 American Chemical Society

cathode materials in LIBs. All these studies have contributed to develop molecules that could enhance the ionic diffusion without losing charge and energy densities. However, despite such significant efforts, it should be noted that only a limited number of molecules has been explored, and thereby comprehensive understanding of the molecular structure− electrochemical property relationship has not been accomplished. Corannulene is an organic molecule consisting of five benzene rings around cyclopentane ring, as shown in Figure 1. The molecule has a unique structural characteristic with curved carbon lattices, in which the existence of the highly overlapped π orbitals is expected to provide a highly attractive Li-binding environment.17−19 A couple of studies have been explored to unravel the structural and electronic properties of the molecule.18,20−23 For example, Baldridge and Siegel reported that the convex face of the corannulene would have a considerably different environment in the electron density as compared with its concave face, provoking dipole moment to Received: January 24, 2018 Revised: April 29, 2018 Published: May 2, 2018 10675

DOI: 10.1021/acs.jpcc.8b00827 J. Phys. Chem. C 2018, 122, 10675−10681

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The Journal of Physical Chemistry C

design promising cathodes based on organic molecules, such as corannulene. In this study, we aim at establishing an appropriate borondoping strategy for better redox properties of the corannulene for positive electrodes in LIBs. To achieve this goal, we systematically generated a comprehensive set of boron-doped corannulene (BDC) models with various number of boron atoms and their geometric positions. It is assumed that lithium ions can reach the redox-active sites of individual corannulene molecule fixed by binders in positive electrode. It is worthwhile to note that electrons travel through the external circuit toward the molecules in the positive electrode during the discharge process as long as the positive electrode has higher reduction potential compared to negative electrode (Li). Also, note that the corannulene derivatives can be chemically bound onto conductive carbon materials, such as graphenes and carbon nanotubes, which would be a strategy to use the corannulene derivatives in cathodes by preventing the molecular dissolution. Polymerization is another strategy to resolve this issue. Liu et al. demonstrated the high cycling stability with self-polymerized dopamines, which were spontaneously coated on the surfaces of few-walled carbon nanotubes, indicating the successful incorporation of organic molecules in cathodes.15,30 Here, we focus on determining the reduction potential of corannulene derivatives as a function of the number of borons and their positions by employing the DFT method that has been used in our previous studies, in which all the technical details were reported.15,31−34 The predicted redox properties were further correlated with their electronic properties including the electron affinity, the highest occupied molecular orbital (HOMO), and the lowest unoccupied molecular orbital (LUMO). Our investigation was finally extended to understand how corannulene binds with Li atoms during the discharge process.

Figure 1. Structures of the boron-doped corannulene (BDC) molecules as well as pristine corannulene. Molecules are labeled in a format of BDCn-m where n represents the number of boron atoms and m is the case number. The gray, white, and pink colors depict carbon, hydrogen, and boron, respectively. The molecules in the blue boxes represent the most stable positions for boron atoms in the 1- and 2boron-doped cases, respectively.

this polycyclic aromatic hydrocarbon.20 Various computational studies on binding strengths of transition-metal ions with the corannulene have been performed.18,21 Dunbar employed the DFT method to investigate the binding properties of seven metal cations, namely three alkali metal cations (Li+, Na+, and K+) and four transition-metal cations (Ti+, Cr+, Ni+, and Cu+), with the corannulene. They reported that lithium cation would stably bind to corannulene with a binding energy of 43.3 kcal/ mol.21 Nonetheless, to date, corannulene has not been considered to be utilized for the cathode in LIBs. It is therefore worthwhile to evaluate the potential of the molecule and its modified ones as cathode materials. On the other hand, doping materials with boron has been regarded as one of the promising approaches to improve their performance.24−29 For instance, Feng et al. investigated the potential of boron-doped lithium trivanadate (LiV3O8) as cathode materials and verified that the doping process enhanced the charge capacity and cyclic stability of the LiV3O8. They inferred that the doped boron atoms could improve the electrochemical performance of the LiV3O8 cathode by promoting the deintercalation and intercalation thermodynamics of lithium during the charge and discharge processes, respectively.24 Veluchamy et al. synthesized boronsubstituted manganese spinels to investigate their physical and electrochemical characteristics for cathode materials in lithiumion batteries. They reported that the synthesis through solution route enhanced the charge capacity and cyclability.29 All these imply that boron-doping approach might be a good strategy to

2. COMPUTATIONAL METHOD All of the DFT calculations to predict the thermodynamics and redox properties of the BDC models were performed using the Jaguar software35 with the PBE036 functional and the 631+G(d,p) basis set.37 The restricted open shell calculations were performed in this study. It is to be noted that our test calculations on a given set of molecules based on both the restricted and unrestricted open shell approaches validated the reliability of the restricted open shell approach. The reduction potential of a corannulene derivative with respect to Li/Li+ (E0wrt Li) was computed by ⎞ ⎛ ΔGred(S , sol) 0 Ewrt + E H⎟ − E Li Li (V) = − ⎜ nF ⎠ ⎝

(1)

where n is the number of electrons in moles and F is Faraday constant. EH and ELi represent the reduction potentials of the absolute hydrogen electrode and the lithium electrode, respectively (EH = 4.44 V and ELi = −3.05 V). ΔGred(S, sol) represents the Gibbs free-energy change for the reduction of the corannulene derivative in solution. Because ΔGred(S, sol) cannot be calculated directly, ΔGred(S, sol) is indirectly estimated using the following equation ΔGred(S , sol) = [−ΔGsolv (S)] + [ΔGred(S , gas)] + [ΔGsolv (S −)] 10676

(2)

DOI: 10.1021/acs.jpcc.8b00827 J. Phys. Chem. C 2018, 122, 10675−10681

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The Journal of Physical Chemistry C Table 1. Calculated Reduction Potentials and Boltzman Distributions for the Molecules Illustrated in Figure 1a molecules

reduction potential (V vs Li/Li+)

pristine corannulene BDC1-1 BDC1-2 BDC1-3

0.90 3.03 3.32 2.90

BDC2-1 BDC2-2 BDC2-3 BDC2-4 BDC2-5 BDC2-6 BDC2-7 BDC2-8 BDC2-9 BDC2-10 BDC2-11 BDC2-12 BDC2-13 BDC2-14 BDC2-15 BDC2-16 BDC2-17 BDC2-18 BDC2-19 BDC2-20 BDC2-21 BDC2-22 BDC2-23 BDC2-24 BDC2-25 BDC2-26

2.77 3.09 3.07 3.41 2.96 3.16 3.35 3.00 3.16 2.95 3.01 3.10 3.18 2.51 3.08 3.00 2.97 5.05 2.41 2.92 3.14 2.56 3.08 2.93 2.58 2.54

Boltzman distribution (%)

probability-averaged reduction potential (V vs Li/Li+)

HOMO (eV)

LUMO (eV)

HOMO−LUMO gap (eV)

electron affinity (kcal/mol)

0.9 3.03

−6.50 −6.27 −6.22 −5.75

−1.81 −1.87 −1.72 −1.77

4.69 4.40 4.49 3.98

−14.99 −61.67 −69.90 −61.24

2.51

−6.08 −6.25 −6.10 −6.30 −6.30 −6.31 −6.21 −6.35 −6.31 −6.47 −6.34 −6.10 −6.20 −6.67 −5.74 −5.92 −6.03 −5.92 −6.39 −6.45 −6.13 −6.07 −5.67 −6.04 −6.01 −6.07

−3.23 −1.91 −3.99 −1.77 −1.80 −1.90 −1.66 −3.94 −1.90 −3.89 −1.85 −3.99 −3.80 −3.33 −3.95 −3.90 −3.86 −1.83 −3.40 −3.85 −4.21 −3.53 −3.89 −3.85 −3.46 −3.56

2.85 6.34 2.11 4.53 4.50 4.41 4.56 2.41 4.41 2.58 4.49 2.11 2.40 3.34 1.78 2.01 2.17 4.08 2.99 2.60 1.93 2.54 1.78 2.18 2.55 2.51

−58.75 −64.51 −65.22 −72.79 −64.07 −68.12 −72.07 −64.56 −68.24 −63.20 −64.35 −65.67 −67.59 −49.99 −66.91 −64.33 −64.47 −66.07 −50.57 −61.53 −68.81 −54.03 −65.14 −63.24 −54.26 −55.46

100 100

0.43

99.57

a

The weight-averaged reduction potential for each set with a given number of doped boron atoms is listed in the fourth column. Their electronic properties, namely HOMO and LUMO energy levels, as well as electron affinity are listed for each molecule.

Here, ΔGsolv(S) and ΔGsolv(S−), respectively, account for the solvation free energies for the molecules in neutral and anion states, whereas ΔGred(S, gas) represents the Gibbs free-energy change for the reduction of the molecule in gas phase. A dielectric constant, 16.14, was used for calculation of ΔGsolv(S) and ΔGsolv(S−) corresponding to the mixed solvent consisting of ethylene carbonate and dimethyl carbonate in 3:7 v/v ratio. It is to be noted that our previous studies on various organic materials, including quinones, dopamines, ketones, and graphenes, have consistently presented the reliability of our computational approach with its conditions, such as DFT functional, basis set, implicit model, and so on, demonstrating accurate prediction of reduction potential with an uncertainty of ∼0.3 V with respect to Li/Li+.15,31−34 For a set of M molecules with a given number of doped boron atoms, Boltzmann distributions of the molecules defined by the probability of molecule, i, pi = Fi/∑M i Fi, were calculated to assess their relative thermodynamic stabilities. The Boltzmann factor, Fi = exp(−Ei/kT), was utilized to evaluate the Boltzmann distribution. Here, E is the Gibbs free energy, k represents Boltzmann constant, and T is the room temperature (298.15 K). The probability-averaged reduction potential ) for a set of the nonidentical M molecules (Eprobability‑averaged wrt Li with a given number of doped boron atoms was computed by using

M probability ‐ averaged Ewrt Li

(V) =

∑ (pi × n × Ei0

wrt Li

i=1

) (3)

Here, n represents the number of degeneracy for a corannulene derivative. For instance, the number of degeneracy (or the number of identical configurations) for BDC2-14 in Figure 1 would be five. In general, experimental cyclic voltammetry measurements provide all redox peaks that correspond to boron-doped constituents in cathodes. However, because the contribution from the major species seems to be dominant, according to Table 1, it is expected that the experimental cyclic voltammetry measurements would present only peak from such major species. Further, it is worthwhile to report such a probability-averaged reduction potential owing to the following reasons: (1) the probability-averaged reduction potential will assist us to understand the correlation of the reduction potential with the number of doped boron atoms; (2) this concept will allow us to rapidly evaluate the contribution of each structural configuration to the averaged reduction potential and construct a promising design strategy. The free-energy variations associated with the Li binding to the molecules were predicted by ΔG b = G(Q + Li) − (GQ + G Li) 10677

(4) DOI: 10.1021/acs.jpcc.8b00827 J. Phys. Chem. C 2018, 122, 10675−10681

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The Journal of Physical Chemistry C Here, GQ+Li, GQ, and GLi represent the Gibbs free energies for a molecule binding with Li atom, the molecule, and Li atom, respectively. To predict the corresponding free-energy variations in electrolyte solutions, we employed the same approach as the one described above for the prediction of the reduction potential.

3. RESULTS AND DISCUSSION 3.1. Thermodynamic Probabilities for Configurations of Boron-Doped Corannulenes. The thermodynamics and redox properties of organic molecules rely on their electronic properties. In principle, electronic properties can be tuned by incorporating the functionality of the organic molecules, as described in our previous studies.15,31−34 For example, an electron-withdrawing carbonyl moiety incorporated into an organic molecule is expected to increase its reduction potential. Doping is another possible approach to modify its redox properties. We therefore investigated boron-doped corannulene molecules to characterize how the reduction potential of the corannulene is affected by the positions and numbers of doped boron atoms. As shown in Figure 1, the pristine corannulene was doped with 1 or 2-boron atoms. Three distinctive geometric positions were considered for doping the pristine corannulene molecule with 1 boron atom, whereas 26 irreducible positions were possible to place 2 boron atoms into the molecule. Each of the 29 BDC molecules was labeled as “BDCn-m” where n and m depict the number of boron atoms and case number, respectively. For example, BDC1-1, BDC1-2, and BDC1-3, in Figure 1, depict all of the possible derivatives generated by doping 1 boron atom into the corannulene. From the energy difference among these three derivatives, shown in Figure 2, it is found that BDC1-1 has lower free energy in solution at least by 8.53 kcal/mol than the other two derivatives. Such a large energy deviation leads to an exclusive presence of BDC1-1 (see Table 1). Likewise, total 26 derivatives can be possibly generated by doping 2 boron atoms into the corannulene, and the top four cases with the lowest free energies in solution are depicted in Figure 2. The case of BDC2-14 is predicted to have lower free energy in solution at least by 3.23 kcal/mol than the other cases. Such an energy difference still enables BDC2-14 to be exclusively present (99.57%) (see Table 1). All these emphasize that the most probable configuration for each group of molecules with a given number of doped boron atoms exists exclusively against the other configurations. 3.2. Redox Properties of BDCs. Geometric positions of boron atoms doping the corannulene can be tuned to manipulate not only the thermodynamic stability (see Section 3.1) but also redox properties. Hence, we attempted to identify optimal position of boron atoms to improve reduction potential. To understand the effect of the number and geometric position of the doped boron atoms on the reduction potential of the corannulene, we calculated the reduction potentials for the pristine corannulene and all of the 29 BDCs, as listed in Table 1. As a result, it is found that the boron-doped corannulene has enhanced electron affinity, which enhances the reduction potential. However, increasing the number of the doped boron atoms does not guarantee the enhancement of the reduction potential. Specifically, among the three 1 borondoped models with reduction potentials ranged from 2.90 to 3.32 V vs Li/Li+, the most stable model, namely BDC1-1, where an outermost carbon atom is substituted by a boron atom, shows the reduction potential of 3.03 V vs Li/Li+. On the

Figure 2. Free-energy differences in solution for molecules from the most stable molecule for each case: (a) BDC1 and (b) BDC2. Probability of each molecule was calculated based on their Boltzmann factors for (a) 1 boron case and (b) 2 boron case. In (b), only four molecules with the lowest free energies in solution are shown among the 26 BDC2 molecules. Emin denotes the free energy in solution for the most stable molecule.

other hand, the most stable 2 boron-doped model, namely BDC2-14, exhibits 2.51 V vs Li/Li+. It is to be noted that BDC2-14 has the second boron atom at the nearest outermost position (Figure 1). This indicates that the reduction potential of the molecule relies not only on the doping process but also on other factors such as the geometric position of the dopant. Considering that the reduction potential of BDC1-1 is higher than that of BDC2-14, it is notable that an increase in the level of structural heterogeneity of a BDC molecule by boron atoms does not necessarily entail an improvement of the reduction potential of the molecule, suggesting that dopant concentrations should be carefully tuned for applications. Nonetheless, a general consensus is that the boron-doped corannulenes (2.41−5.05 V vs Li/Li+) show high reduction potentials as compared to the pristine corannulene (0.90 V vs Li/Li+). Another observation from Table 1 is that probabilityaveraged reduction potentials for 1- and 2-boron-doped corannulenes are nearly the same as the reduction potentials 10678

DOI: 10.1021/acs.jpcc.8b00827 J. Phys. Chem. C 2018, 122, 10675−10681

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The Journal of Physical Chemistry C for the most stable cases owing to their exclusive probabilities, as shown in Figure 2. This allows us to estimate a reduction potential for a cathode that contains both 1- and 2-borondoped corannulene derivatives. For instance, it is expected that the reduction potential from a cathode containing both 1- and 2-boron-doped corannulenes in 1:1 molar ratio is 2.77 V vs Li/ Li+, which is calculated by the following way 2.77 V = 0.5 × 3.03 V (BDC1) + 0.5 × 2.51 V (BDC2) (5)

It is to be noted that this value is comparable with anthraquinone-2,6-dicarboxylic acid.34 A probability-averaged reduction potential from a mixture of 1- and 2-boron-doped corannulenes would be ranged from 2.51 to 3.03 V vs Li/Li+ depending on the molar ratio. The probability-averaged reduction potential of the mixture is increased up to 3.03 V vs Li/Li+ as a function of the molar ratio for a family of 1 boron-doped corannulenes in the mixture. Therefore, the reduction potential of the battery can be tuned by harnessing the molar ratio between 1- and 2-boron-doped corannulenes. To further understand the redox properties of the borondoped corannulene derivatives, we investigated correlations of their reduction potentials with their electronic properties, such as electron affinity, highest occupied molecular orbital (HOMO) energy level, and lowest unoccupied molecular orbital (LUMO) energy level. Figure 3 shows correlations of the reduction potential with the electronic properties for all of the molecules studied here. As expected, the reduction potential exhibits a strong correlation with the electron affinity, suggesting that a more negative electron affinity leads to a higher reduction potential. Such a linear correlation is reasonable because a molecule with a high electron affinity is preferential for receiving electrons, and similar observations have been reported elsewhere.15,31−34 In contrast, the other electronic properties, such as the LUMO and HOMO, exhibit poor correlations with the reduction potential, as shown in Figure 3b−d. In particular, the poor correlation between the reduction potential and LUMO is abnormal in the sense that numerous studies have reported strong correlations between them for various materials. For example, our previous studies showed strong linear correlations between the calculated reduction potentials of various organic materials, such as graphene oxides and quinone derivatives, and their LUMO.32−34 The predicted poor correlation between the calculated reduction potential and LUMO was scrutinized to understand its reason. Our additional analysis highlights that the correlation can be also affected by the spin states of the molecules. More specifically, all of the molecules, including the pristine corannulene and BDCs, can be categorized into either open shell (spin multiplicity ≥ 2) or closed shell (spin multiplicity = 1) depending on their spin states. Indeed, Figure 3c shows that a molecular reduction potential is highly dependent on its spin state. Aforementioned observations on redox properties of corannulene derivatives provide an insight on the potential of corannulene derivatives as cathodes at fully charged state. However, the characteristics of the corannulene derivatives associated with Li during the discharge process should be unveiled to understand the electrochemical behavior of the molecules as cathodes in lithium-ion batteries. Hence, we investigated the Li-binding characteristics on redox-active sites available for corannulene derivatives. Figure 4 shows the

Figure 3. Correlations of the calculated reduction potentials with the electronic properties: (a) electron affinity; (b) HOMO energy; (c) LUMO energy; (d) HOMO−LUMO gap. 10679

DOI: 10.1021/acs.jpcc.8b00827 J. Phys. Chem. C 2018, 122, 10675−10681

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The Journal of Physical Chemistry C

their spin states as well as their structural and electronic properties; (2) the boron atoms incorporated into the pristine corannulene enhance the reduction potential; (3) the reduction potential does not have strong correlation with the density of doped boron atoms; (4) the boron-doping increases the Libinding energy of corannulene, implying that charge capacity could be improved accordingly in LIBs. It is expected that these conclusions would assist us to provide meaningful borondoping strategies, to design desirable organic cathode materials.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (K.C.K.). *E-mail: [email protected] (S.S.J.). ORCID

Ki Chul Kim: 0000-0002-9359-9811 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge that J.K. was supported by President Undergraduate Research Award (PURA) of Georgia Institute of Technology. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2017R1A4A1014806).

Figure 4. Structures of corannulene derivatives associated with one Li on various binding positions: (a) on pentagon of pristine system (concave face); (b) on pentagon of pristine system (convex face); (c) on hexagon of pristine system (convex face); (d) on boron-doped hexagon of BDC1-1 (concave face); (e) on boron-doped hexagon of BDC2-14 (concave face). The gray, white, pink, and purple colors depict carbon, hydrogen, boron, and lithium, respectively.

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REFERENCES

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strongest Li-binding sites and their Li-binding free energies for the pristine corannulene and 1- and 2-boron-doped cases with the most probable state. It is found that the pristine corannulene has multiple sites with comparable Li-binding strengths ranged from −16 to −18 kcal/mol. On the other hand, the incorporation of the boron atoms into the corannulene strengthens the Li binding of corannulene, leading to the single-site formation with binding energies of −73.12 and −54.98 kcal/mol for 1- and 2-boron-doping, respectively. Such significant increase in the binding energy implies that the boron doping could improve the charge capacity of the pristine corannulene. It is also noteworthy that Li atoms prefer to be positioned near the doped boron atoms on the concave faces of the molecules.

4. CONCLUSIONS In this study, we computationally investigated the thermodynamics and electrochemical properties of a comprehensive set of boron-doped corannulenes (BDCs) to evaluate their reduction potential as cathodes in lithium-ion batteries. The BDCs with various numbers and geometric positions of doped boron atoms were compared to understand the effect of the structural and electronic variations on the thermodynamic stability and electrochemical properties of the corannulene. It was observed that the first and second boron atoms were dominantly doped in outermost positions of corannulene. Our analysis further led to the following conclusions: (1) the reduction potentials of corannulene derivatives strongly rely on 10680

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The Journal of Physical Chemistry C

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DOI: 10.1021/acs.jpcc.8b00827 J. Phys. Chem. C 2018, 122, 10675−10681