Study of Li Adsorption on Graphdiyne Using Hybrid DFT Calculations

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Study of Li Adsorption on Graphdiyne Using Hybrid DFT Calculations Jaewook Kim, Sungwoo Kang, Jaechang Lim, and Woo Youn Kim* Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea ABSTRACT: Promising applications of graphdiyne have often been initiated by theoretical predictions especially using DFT known as the most powerful first-principles electronic structure calculation method. However, there is no systematic study on the reliability of DFT for the prediction of the electronic properties of the graphdiyne. Here, we performed a study of Li adsorption on the graphdiyne using hybrid DFT with LC-ωPBE and compared the results with those of PBE, because accurate prediction of the Li adsorption is important for performance as a Li storage that was first theoretically suggested and then experimentally realized. Our results show that PBE overestimates the adsorption energy inside a pore and the barrier height at the transition state of in-plane diffusion compared to the those of LCωPBE. In particular, LC-ωPBE predicted almost barrier-less in-plane diffusion of Li on the graphdiyne because of the presence of both in-plane and out-of-plane π orbitals. Also, LC-ωPBE favors a high spin state due to the exact exchange energy when several Li atoms are adsorbed on the graphdiyne, whereas PBE favors a low spin state. Thus, the use of the hybrid DFT is critical for reliable predictions on the electronic properties of the graphdiyne. KEYWORDS: graphdiyne, lithium storage, energy storage, density functional theory, hybrid functional

1. INTRODUCTION Graphdiyne (GDY) has attracted much attention as a new 2D carbon allotrope consisting of sp- and sp2-hybridized carbons, since synthesis of large-scale GDYs became possible.1,2 It shows excellent conductivity and mechanical properties like graphene, while at the same time exhibiting semiconducting properties due to large pores formed with 6-alkyne bonds in contrast to the semimetallic graphene.3−9 For these reasons, the GDY has been actively studied for various applications such as energy storage,10−16 a catalyst,17−20 an optoelectronic device,21−23 and a permeable membrane.24−26 Along the recent trend in new materials research, application of the GDY has often been initiated by computational predictions and then realized in experiments. For example, the active study of the GDY for optoelectronic devices has been stimulated by the prediction of the natural band gap and high hole mobility of the GDY.27,28 Also, the feasibility of the GDY as a Li storage material has been proposed by density functional theory (DFT) calculations in 2012 and 2013 and proven by experiments in 2015.10−13 Therefore, accurate prediction of the GDY properties using valid computational methods is vital for successful applications. The GDY properties can be predicted by DFT which has been most widely used for electronic structure calculations because of its reasonable reliability and efficiency.29 Most previous DFT studies on the GDY under periodic boundary conditions adopted the generalized gradient approximation (GGA) such as PBE30 for the exchange-correlation functional.5,8,10,11,16,24,27,28,31−34 However, there is no systematic study on the reliability of the GGA method. In general, hybrid DFT methods made by including a fractional amount of exact exchange energy in GGA show better performance in many © XXXX American Chemical Society

aspects than GGA. A benchmark study on thermodynamic properties shows that the hybrid DFT is far more accurate than PBE; for example, the mean absolute errors (MAEs) of LCωPBE35 and B3LYP36 for the atomization energies of the G2 test set37 are 5.6 and 7.5 kcal/mol, respectively, whereas that of PBE is 17.9 kcal/mol. For the activation energies in the HTBH38/0438 and NHTBH38/0439 test sets, LC-ωPBE shows much smaller MAE (2.4 kcal/mol) than that of PBE (MAE = 10.7 kcal/mol).40,41 Given that a reaction rate varies exponentially with the activation energy, use of the hybrid DFT for activation energies is more critical than for adsorption energies. In particular, magnetic properties and band gaps are even more sensitive to the choice of appropriate hybrid functionals whose accuracy can be tuned by the amount of exact exchange.42 In fact, a few previous works used hybrid DFT methods for adsorption energy calculations, but they employed a small flake of GDY.19,20,43−47 That is because a computational load of the hybrid DFT is extremely high under periodic boundary conditions. Alternatively, namely the GGA+U48 method devised for strong on-site interactions can be utilized for periodic systems including transition metals, since it shows similar results with those of hybrid functionals.49,50 However, it Special Issue: Graphdiyne Materials: Preparation, Structure, and Function Received: March 1, 2018 Accepted: May 3, 2018

A

DOI: 10.1021/acsami.8b03482 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

where EGDY, ELi, atom, and Etotal denote the energies of the GDY flake, a Li atom, and the adsorbed system, respectively. To make sure that Eads of the flake is quantitatively comparable to that of the corresponding bulk system, we investigated the convergence of Eads for a single Li atom as increasing the flake size from a single triangular unit (GDY-1tri) to a seven triangular units (GDY-7tri) as depicted in Figure 1. Eads of PBE

would not be appropriate for GDY systems with no transition metals. In this work, we investigated the effect of the hybrid DFT on the prediction of the electronic properties of GDY. Specifically, we studied the adsorption energy of Li on the GDY as a candidate for a Li storage, which is one of the most promising applications of the GDY. We compared the results of LC-ωPBE with those of PBE. LC-ωPBE as a well-known long-range corrected hybrid functional is known to provide more accurate thermodynamic and activation energies than those of B3LYP as a de facto standard hybrid method in chemistry. In addition, accelerated hybrid calculations are feasible with LC-ωPBE by employing an approximation known as the 2-gau method.41 We proposed a new approach of the hybrid DFT based on a local exact exchange potential method and showed that LC-ωPBE modified by our new approach together with the 2-gau method is just about twice slower than PBE in a grid-based DFT code, enabling us to apply it to large systems.51 Thus, we were able to employ a sufficiently large GDY flake to give converged adsorption energy comparable to that of a periodic system. Our study shows that LC-ωPBE and PBE give considerably different adsorption properties of Li on the GDY, implying that the use of the hybrid DFT is critical for reliable predictions on the electronic properties of the GDY.

2. COMPUTATIONAL METHODS To determine an appropriate size of the GDY flake, we checked out the Li adsorption energy convergence with respect to the flake size. The flake geometry should be the same as that of the periodic system for comparison to the bulk value. The bulk geometries of the GDY with and without Li were obtained from periodic calculations with PBE augmented by the D3 dispersion correction52 with the BeckeJohnson damping53 as implemented in VASP 5.4;54 as already known, structural change by the D3 correction was negligible.10 We used the energy cutoff of 400 eV and the k-points of 7 × 7 × 1. In both GDY and Li-adsorbed GDY (GDY+Li), the unit cell was set to a = b = 9.465 Å, c = 20 Å, α = β = 90°, and γ = 60°. Then, the optimized GDY structure was cut into a flake, and the resulting dangling bonds were capped with hydrogen atoms. The flake size was increased by repeating the unit cell geometry. The actual adsorption energy on the GDY flake was calculated using our in-house grid-based code, ACE-Molecule,51,55−58 for direct comparison with the results of VASP, because ACE-Molecule also employs the projector augmented wave (PAW)59 method for core electrons like VASP. In addition, it supports an accelerated LC-ωPBE method for the efficient hybrid DFT calculation of large GDY flakes. To achieve the accuracy of 0.1 eV (∼3 kcal/mol) for the adsorption energy, the grid spacing was set to 0.45 Bohr, which corresponds to the kinetic energy cutoff of ∼663 eV in a plane-wave code like VASP. The simulation box was made by superimposing all of the atom-center spheres with the radius of 5.5 Å determined by the total energy convergence test. For diffusion study, the transition state of the in-plane diffusion of Li was obtained by using the TS optimization method as implemented in GAUSSIAN0960 with PBE/631+G(d). Then, the activation energy on the given geometry was calculated by ACE-Molecule using the same simulation setting with that of the adsorption energy. All orbital figures were drawn with the isovalue of 0.02.

Figure 1. Structure of the Li-adsorbed GDY flake with various sizes and the corresponding adsorption energies with PBE/LC-ωPBE. Each structure corresponds to (a) single triangular unit, (b) two triangular units, (c) four triangular units, and (d) seven triangular units.

almost converged at the size of GDY-4tri, whereas LC-ωPBE converged at the size of GDY-7tri. In the case of PBE, we also performed a periodic calculation on the gamma point for a single Li adsorbed supercell of 3 × 3 × 1 with the plane-wave cutoff of 400 eV. For comparison between the bulk and the flake, we imposed the doublet spin state for the periodic system. The Li adsorption energy of the bulk system was 2.24 eV, which is somewhat higher than the converged value of the flake (1.82 eV). We noted that the adsorption energy of GDY2tri from GAUSSIAN09 with PBE/cc-pVTZ (aug-cc-pVTZ for Li) (1.68 eV) was even lower than that of ACE-Molecule. These differences are probably due to the difference between the methods used for core electrons in each package; GAUSSIAN09 treated all electrons explicitly, ACE-Molecule used the PAW setup files provided by GPAW,61 while VASP adopted its own files. We note that for all the flake sizes, the Eads of LC-ωPBE was significantly lower than that of PBE. To understand such a tendency, we examined the electronic mechanism of Li adsorption to the GDY flake. We analyzed the orbitals of the Li atom, GDY-1tri, and GDY-1tri+Li. The 2s orbital energy of Li was 2 eV higher than the highest occupied molecular orbital (HOMO) energy of GDY-1tri for both PBE and LC-ωPBE. In contrast, the lowest unoccupied molecular orbital (LUMO) energy of GDY-1tri was very close to the 2s orbital energy of Li. Therefore, the 2s orbital of Li forms a bond with the LUMO of GDY by sharing the single valence electron of Li, resulting in the electron transfer from Li to GDY. The LUMO of GDY is

3. RESULTS AND DISCUSSION 3.1. Li Adsorption Energy. We first compared the adsorption energies of Li on the GDY flake obtained with PBE and LC-ωPBE. The adsorption energy (Eads) was calculated as follows. Eads = −(Etotal − EGDY − E Li,atom) B


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Figure 2. Orbital energy diagram of the Li-adsorbed GDY flake and the corresponding orbitals. All results were obtained with PBE.

made of π orbitals perpendicular to the GDY plane, and hence it is delocalized across the GDY flake. The resulting singly occupied molecular orbital (SOMO) of the GDY+Li maintained the original shape of the LUMO of the free GDY flake. Unlike graphene, the GDY has additional π-bonding orbitals parallel to the GDY plane which comes from acetylenic chains. Li after giving its electron to the LUMO of the GDY attracts electrons in the in-plane π-bonding orbitals, leading to substantial distortion of those orbitals as shown in Figure 2. As a result, the energy levels of the corresponding orbitals dropped down by a few eV (Figure 2). As discussed above, the Li adsorption caused the electron transfer from the localized 2s orbital of Li to the delocalized out-of-plane π orbital of the GDY flake. This explains the reason why PBE overestimates the adsorption energy compared to that of LC-ωPBE. In general, PBE favors a delocalized state of the electron density due to the so-called self-interaction error. Such a spurious repulsion becomes weaker as the electron moves from the localized 2s to the delocalized π orbital, resulting in the overestimation of Eads. In contrast, the exact exchange energy included in hybrid functionals like LCωPBE alleviates the spurious self-interaction error, giving rise to the smaller adsorption energy than that of PBE. Our analysis provides an orbital-based insight about the most preferred Li adsorption site; the Li cation is strongly stabilized by the electron-rich in-plane π orbitals of two adjacent acetylenic chains simultaneously, whereas Li on the out-ofplane is stabilized by only one π orbital. The previous calculation with PBE under a periodic boundary condition showed that the in-plane position is the most preferred adsorption site of Li.10,11 Unfortunately, one cannot perform periodic calculations with LC-ωPBE at present. Instead, we expect that PBE and LC-ωPBE will give similar electronic structures including the π orbitals except for energy gaps, considering the fact that various calculations using LDA, PBE, HSE,62 and G0W063 for a pristine GDY gave similar electronic structures but with different band gaps.3,6,9 Therefore, the adsorption mechanism due to the π orbitals and thus the energetically preferred adsorption site would be the same for PBE and LC-ωPBE. 3.2. Effect of Defects on the Li Adsorption. For the practical use of GDY as a Li storage, it is important to consider the effect of various defects. In fact, the GDY is known to have a low concentration of defects.2 A previous report shows that the electronic structure of the GDY does not change significantly due to carbon vacancies except for the band gap change from 0.43 to 0.37 eV.8 Since the Li adsorption is

affected by the LUMO energy level, it is expected that the carbon vacancies may increase the adsorption energy a little bit due to the smaller band gap. The in-plane diffusion barrier will not change much, because both the in-plane and out-of-plane π orbitals remain intact in the presence of the vacancies. Therefore, overall behavior would be similar in the presence of a small number of the vacancies. However, an aging process of the GDY naturally increases oxygenic and nitrogenic defects.32 The chemisorption of such atoms needs sp2 or sp3 hybridized carbon atoms, giving rise to breaking up the sp hybridization of the GDY frontier orbitals. As a result, it is expected that the adsorption mechanism of Li would be different around such defect sites. 3.3. Transition State Energy of in-Plane Diffusion of Li. To investigate the effect of the hybrid DFT on the in-plane diffusion rate of Li for energy storage application, we compared the energy barrier of LC-ωPBE at the transition state along an in-plane diffusion path across an acetylenic chain with that of PBE. The GDY-2tri was used as a model system. To mimic a periodic calculation using the nudged elastic band method in the literature,10 we changed only the angle between Li and the in-plane vector while maintaining the other geometric factors as shown in Figure 3(a). Then, we investigated the change in the Li adsorption energy according to the angle (θ). The barrier height of PBE (0.53 eV) was close to that of periodic

Figure 3. (a) Structure of the GDY-2tri+Li for in-plane diffusion study. (b) Out-of-plane and in-plane π MOs of the free GDY flake. (c) Change in the out-of-plane and in-plane π MOs of the GDY-2tri+Li with respect to the Li position. C


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ACS Applied Materials & Interfaces calculations with PBE (0.75 eV)10 and with B8864+LYP65 (0.52 eV).11 However, LC-ωPBE gave considerably lower barrier height (0.33 eV). Like in the stable adsorption case, the electron in the 2s orbital of Li was transferred to the delocalized out-of-plane π orbital of the GDY, resulting in the SOMO having a similar shape with the LUMO of the free GDY flake (Figure 3c). The lower barrier height of LC-ωPBE can be explained for the same reason as the lower adsorption energy of LC-ωPBE. To further elucidate the origin of such a low energy barrier, we examined the change in the shapes of the SOMO and the π orbital of the GDY-Li complex with respect to the Li position. On the minimum energy position (θ = 0°), the Li ion made by the electron transfer was stabilized by the distortion of the inplane π orbital (the bottom figure in the first column in Figure 3c). On the transition state (θ = 0°), the Li ion is on top of the triple bond of two carbon atoms and thus interacts mainly with the out-of-plane π orbital. In this case, there would be no stabilization effect by the in-plane π orbital (the bottom figure in the rightmost column in Figure 3c). Instead, the out-of-plane π orbital was distorted by the attraction from the Li ion to stabilize the complex. On the position in-between the minimum energy and transition state (θ = 45°), the Li ion interacts with both the in-plane and out-of-plane π orbitals in part, and thus the energy difference from the other two states becomes small. Consequently, the small energy barrier is due to the presence of both the in-plane and out-of-plane π orbitals forming the triple bond between carbons. Therefore, Li can be stabilized by either in-plane or out-of-plane π orbitals at any angle around the triple bond. To examine the local structural relaxation effect on the barrier height at the transition state, we performed the TS optimization while maintaining the GDY framework with fixed positions of all side atoms. Figure 4 shows the result. We used

structural relaxation during the diffusion gave rise to the barrierless in-plane diffusion of Li, which is a unique feature of GDY due to the presence of sp-hybridized orbitals not being in other 2D carbon allotropes such as graphene. 3.4. Spin State. We investigated the effect of the hybrid DFT on the spin state of the Li-adsorbed GDY flake. To consider the fully charged state that has been computationally discovered, we supposed that three Li atoms occupied the 18carbon cavity of GDY. For the sake of computational efficiency, we used the GDY-2tri with six Li atoms. The GDY-2tri+6Li complex can have four possible spin states: singlet, triplet, quintet, and septet. Table 1 shows the relative energy of the Table 1. Relative Energy of the GDY-2tri+6Li Complex at Various Spin States with Respect to the Lowest Energy State (units in eV) singlet triplet quintet septet

PBE

LC-ωPBE

0.26 0.00 0.25 1.18

0.58 0.73 0.00 0.37

complex for each state with respect to the lowest energy state. PBE favors the triplet state, while LC-ωPBE has the quintet as the lowest energy state. It is well-known that hybrid functionals favor high spin states because of the Pauli Exclusion principle implied in the exact exchange energy, whereas pure functionals having no exact exchange term favor low spin states. The results in Table 1 also follow the aforementioned trend. 3.5. Practical aspects. To investigate the effect of the hybrid DFT on GDY-based Li-ion battery performance, we roughly estimated the open circuit voltage (OCV), storage capacity, and Li ion mobility using the results of PBE and LCωPBE. The OCV can be deduced directly from the adsorption energy of Li with the following formula. VOC = (Eads − E Li,coh)/e

where Eads is the adsorption energy per adsorbed Li atom, ELi,coh is the cohesive energy of the bulk Li with the body-centered cubic unit cell, and e is the electric charge of an electron. We used the converged adsorption energies of Li given in Figure 1 and the experimental value of 1.63 eV for ELi,coh.66 The PBE result predicted a positive OCV value (0.19 V), which is consistent to that of the previous periodic calculations (0.1−0.5 V for LixC6 case with x from 0.43 to 11.1816). The reason for the significantly lower OCV value in our calculation is due to the use of the experimental cohesive energy (ELi,coh of PBE = 1.53 eV67) and the GDY flake. Not so surprisingly, LC-ωPBE gave a negative OCV value (−0.86 V) due to the substantially lower adsorption energy than that of PBE. It is known that the OCV should be in the range of 0−2 V to be qualified as an anode material when the bulk Li is used as a reference electrode.16 However, the negative OCV value of LC-ωPBE does not mean that the GDY is not qualified as an anode. The negative value comes from the crude approximation used here. For more accurate estimation of the OCV, one has to consider the entropy contribution of Li to the adsorption free energy. The entropy of Li will be increased from that of the bulk by the Li adsorption. Another important factor is to consider a multilayer GDY. It is expected that the adsorption energy of Li will be larger in a multilayer than in a single layer. In fact, the experiment of Huang et al. showed that in addition

Figure 4. Transition state geometry for the Li in-plane diffusion on the GDY flake: (a) top view, (b) side view along the arrow in panel a, and (c) tilted-side view.

the same geometry at the transition state obtained from PBE for LC-ωPBE calculation. At the transition state, the Li atom pushed underlying carbon atoms in the acetylenic chain. Thus, the angle between the three carbon atoms was changed from 180° to 155.2° as shown in Figure 4c. As a result, the 2p orbitals of the carbon atoms forming the out-of-plane π bond directed along the Li atom. Electrons in those orbitals were attracted by the Li ion left after the electron transfer, giving rise to the considerable stabilization of the transition state. The resulting energy barrier of PBE at the transition state was 0.13 eV, while that of LC-ωPBE was very close to zero. Thus, the D



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to the surface contribution, the interlayer insertion and extraction of Li in the multilayer GDY are important to make a high capacity Li storage.13 Therefore, the negative OCV value predicted by LC-ωPBE can be likely compensated by both the larger adsorption energy in the multilayer GDY and the positive entropy contribution, which may result in an overall positive value in the range of 0−2 V. Apparently, the OCV value of PBE will further increase by the same reason. The lower adsorption and OCV value of LC-ωPBE will lead to a lower Li storage capacity than predicted by PBE. In fact, Sun et al. estimated the reversible Li capacity as 744 mAh/g through periodic calculations with PBE on a monolayer GDY.10 However, experimental values using GDY films of 10.9 and 22.1 μm thickness were significantly lower as 520 and 285 mAh/g, respectively,13 than the predicted value. Considering the intercalation effect and the entropy contribution, it is suspicious that PBE strongly overestimates the Li storage capacity. Quantitative comparison between theoretical and experimental values may not be possible due to the lack of information on the intercalation effect and entropy contribution. However, the trend of LC-ωPBE that predicts a lower OCV value and a lower storage capacity than those of PBE supports the experimental results. Similarly, the same trend of LC-ωPBE on the barrier height affects the Li ion mobility and diffusion dynamics which are critical for fast charging and discharging rates. The almost barrierless in-plane diffusion of Li predicted by LC-ωPBE implies high battery rate performance as was reported in experiments.13 It should be noted that these arguments are not based on quantitative analysis. Therefore, further works should be followed for more concrete study using hybrid functionals.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jaewook Kim: 0000-0002-7209-1939 Woo Youn Kim: 0000-0001-7152-2111 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Basic Science Research Programs (NRF-2015R1A1A1A05001480) funded by the Korea government [MSIP] and by KISTI supercomputing center through the strategic support program (KSC-2017-C3-0034).

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REFERENCES

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4. CONCLUSION We investigated the effect of hybrid DFT on the Li adsorption and diffusion on graphdiyne (GDY) through a comparative study with PBE known as a standard approach to material research. The results show that LC-ωPBE predicts substantially smaller adsorption energy and almost zero barrier height for inplane diffusion. The barrier-less diffusion was due to the presence of both in-plane and out-of-plane π orbitals forming the triple bond between carbons in an acetylenic chain. The Li cation on the GDY can be stabilized by strong interaction with either in-plane or out-of-plane π orbitals at any position along the diffusion path, resulting in little energy change. That is a unique feature of 2D carbon allotropes with acetylenic chains. When several Li atoms occupied the GDY pores, LC-ωPBE favored a higher spin state because the exact exchange interaction in the hybrid functional stabilizes parallel spins. Our study shows that the use of hybrid DFT is vital for reliable predictions on the electronic properties of new materials such as GDY. Nonetheless, it is seldom used in the computational study of bulk materials, since hybrid DFT calculations are very demanding for periodic systems. There have been continuous efforts for the development of faster hybrid methods.68−70 We have also developed a new hybrid approach based on a local exact exchange potential for that purpose, but it does not work for periodic systems at present.51 We are planning to extend it for periodic calculations in the near future. We believe that such a fast hybrid method will further promote successful applications of GDY through more reliable predictions. E


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Study of Li Adsorption on Graphdiyne Using Hybrid DFT Calculations

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