Exploring the Interaction between Lithium ion and ... - ECS Transactions

ECS Transactions, 53 (10) 23-32 (2013) 10.1149/05310.0023ecst ©The Electrochemical Society

Exploring the Interaction between Lithium ion and Defective Graphene Surface using Dispersion corrected DFT Studies M. Vijayakumar*, Jianzhi Hu Pacific Northwest National Laboratory, Richland, WA 99352, USA * Corresponding Author: [email protected], Phone- (509)-371-6540 To analyze the lithium ion interaction with realistic graphene surfaces, we carried out dispersion corrected DFT-D3 studies on graphene with common point defects and chemisorbed oxygen containing functional groups along with defect free graphene surface. Our study reveals that, the interaction between lithium ion (Li+) and graphene is mainly through the delocalized π electron of pure graphene layer. However, the oxygen containing functional groups pose high adsorption energy for lithium ion due to the Li-O ionic bond formation. Similarly, the point defect groups interact with lithium ion through possible carbon dangling bonds and/or cation-π type interactions. Overall these defect sites render a preferential site for lithium ions compared with pure graphene layer. Based on these findings, the role of graphene surface defects in lithium battery performance were discussed. Introduction The interaction between charged surface (i.e. an electrode) and ionic species (i.e. an electrolyte) is the basic science that drives various energy storage systems ranging from lithium batteries to supercapacitors. Consequently, overall performance of such energy storage system heavily depends on chemical and physical properties of materials that constitute the interfacial region. Graphene, with a very high surface area (2675 m2/g) and high electronic conductivity, is a promising candidate for the electrode material for modern energy storage devices[1, 2]. Evidently, graphene is widely reported as suitable electrode material for high energy density lithium-ion battery technology [3, 4]. However, wide range of performance (i.e. final specific capacity varying from 1200 mAh/g to 180 mAh/g) is reported for graphene synthesized by various methods [5]. For example, specially prepared graphene sheets with high concentration of structural defects shows mixed performance as electrode materials for lithium battery [6, 7]. Similarly, the engineered surface modification of graphene such as nano-structural designs, doping and/or surface functionalization yields relatively higher performance [2] and many research efforts are ongoing to design optimal graphene surface for lithium battery applications. However, to rationally design these graphene materials, we need clear understanding of surface properties and its effect on final performances. The fickle performances of graphene based lithium batteries can be related to the purity and structural homogeneity of the graphene material which heavily depend on their synthesis method [5]. For example engineered graphene surfaces often lead to physical defects such as vacancy defects, Stone-Wales defect and chemisorbed defects such as oxygen containing functional groups are present in the surface [8]. These defects can alter graphene’s physical and chemical properties due to the defect associated changes in their structural and electronic environments and dominate the interaction between lithium ions

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ECS Transactions, 53 (10) 23-32 (2013)

and graphene surfaces [9]. Therefore, understanding the chemistry behind these graphene defects and their interaction with lithium can facilitate the efficient tailoring of graphene surface to have optimal performance in lithium battery [5]. In recent years, some attempts have been made to understand the interaction between lithium ions (Li+) and graphene surfaces [10-14]. However, most of these studies were mainly carried out using either with the assumption of pure graphene sheets and/or classical density functional theory (DFT) based methods [15-17]. These classical DFT methods primarily focus on covalent interaction, and perform poorly for the non-covalent interactions such as dispersion driven van der Waals interactions [18]. Ironically, the interaction between lithium ion and graphene can involve a large component of cation - π type dispersion interaction arising from aromatic nature of graphene [16]. Recently, S. Grimme et al. reported dispersion corrected density function method (DFT-D3) which can effectively include this dispersion driven van der Walls interactions into large molecules interactions [19]. Subsequently, this DFT-D3 calculation is gaining momentum as efficient method for calculating the molecule adsorption on graphene surfaces [20, 21]. Hence it is essential to study the realistic graphene surfaces (i.e. graphene with possible defects and functional groups) using modern DFT-D3 techniques for better understanding of Li+ - graphene interactions. In this letter, we attempted to explore the atomic scale interactions between defective graphene surfaces and Li+ through the dispersion corrected DFT-D3 analysis to explain the performance of graphene in lithium battery. Computational Methods Density functional theory (DFT) based calculations were carried out using the Amsterdam Density Functional (ADF-2012) package. The Becke (exchange) + LYP (correlation) based function with recent dispersion correction (DFT-D3) is employed for both geometry and NMR chemical shift calculations [22-25]. All the calculations were carried out using the TZ2P basis set (triple Z, double polarization function, all electron) with the Slater type functional implemented in the ADF program[26]. The graphene sheet is modeled using polycyclic aromatic hydrocarbons (PAH) compound C96H24 which has 37 hexagonal rings arranged with armchair edges and hydrogen termination. The fully optimized structure of C96H24 yields C-C and C-H bond length of 1.42 Å and 1.08 Å respectively which are in good agreement with literature reported values for graphene. However, this PAH system only represents finite graphene sheets and introducing a defect system within may have some boundary effects due to insufficient lattice extension around the defect site which could affect the electronic levels and density of states (DOS) calculations [27]. Nevertheless, the PAH system relieves huge computing load associated with infinite sheet models and offers reasonable model for graphene in computational studies [28-32]. Therefore, we proceed with PAH as graphene model but restricted ourselves to geometrical and energetic calculations to analyze the graphene-lithium ion interactions. For the graphene-lithium molecular structure, a single lithium ion is introduced near the center of the graphene model and optimized without any structural constraints and final geometries are verified with frequency calculation to ensure the proper energy minima. During the optimization process as well as in the final geometry the lithium molecule doesn’t interact with edges of the graphene model. The adsorption energy (∆Eobs) was determined as the difference between the binding energy of the graphene-lithium composite material and the sum of the binding energies of the graphene

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and lithium ion. The lithium chemical shift were calculated at fully optimized geometry and referenced with respect to hydrated Li+ i.e. [Li.(4H2O)]+.Cl-.6H2O which represents aqueous LiCl commonly used in Nuclear Magnetic Resonance (NMR) spectroscopy measurements. Results & Discussions Li+ at the defect free Graphene Surface: For the defect free graphene surface, lithium ion resides at ~1.82Å above the center of hexagonal ring (d⊥) with nearest C-Li bond length of ~2.32Å and exerts very minimal change (~0.01 Å) in their C-C bond environments. Figure 1 shows the lithium ion adsorption energy and Hirshfeld charge analysis calculated from DFT-D3 based method for graphene surface with different point defects along with defect free graphene surface (labeled as pure G). The calculated adsorption energy for the lithium ion near the defect free graphene is -2.27 eV which is in accordance with recent DFT based calculations [33]. It is interesting to note that the natural charge of lithium ion is reduced from 1.0e- to 0.5e- possibly due to the increase of electron density around the lithium ion. This could be due to ionic type bonding interaction where charge is transferred from carbons of nearby hexagonal ring to lithium ion. Interestingly, the net alteration in Hirshfeld charge of carbon atoms in that hexagonal ring (0.15e-) is smaller than the change in lithium charge (i.e. 0.5e-). This suggests that ionic type interaction is not the predominant interaction mechanism between lithium ion and defect free graphene surface. Hence, a likely mechanism would be cation-π type interaction where delocalized π electron cloud of sp2 type graphene is attracted towards lithium ion due to its π acceptor property [15]. Under this cation-π type interaction, the electron density around lithium ion is increased without significant changes in original electronic environments of graphene. This is evident by the minimal structural distortion observed in graphene 2D planar structure, where sp2 type orbitals are retained even after lithium ion interaction. This agrees with previous results that, lithium-graphene interaction doesn’t change the sp2 hybridization of defect free graphene [34]. Now, we can analyze the lithium ion-graphene interaction in presence of different point defects and functional group defects on graphene surfaces. Li+ near the Stone-Wales defect site The Stone-Wales (SW) defect arise due to right angle rotation of a C-C bond in the sp2 type carbon structures, and is experimentally observed in graphene [35]. Hence it is important to analyze graphene surface with these point defects in order to understand the lithium interaction mechanism with realistic graphene surfaces. At first, we separately optimized the graphene structure with single SW defect. The presence of this SW defect induces structural strain in the graphene surface and resulted in distribution of C-C bond length varying from 1.38Å at the five member ring to 1.47Å at hexagonal ring next to the defect site. However these bond length values are considerably smaller than sp3 type bonds (~1.53Å observed in diamond), which indicates that graphene with SW type defects are mainly sp2 in nature and agrees with recent ab initio calculations [36]. Nevertheless, slightly out of plane carbon atoms are found around the defect site which might be due to choice of PAH as our graphene model and/or presence of small amount of sp3 type bonds in the system[35]. Introduction of lithium near this SW defect site doesn’t impose any significant strain on the graphene structure, the C-C bond lengths near the Li+ increases by small amount (~0.03Å) but overall it remains well below the sp3 type bond lengths. This implies that Li+ - SW defect system do not suffer a transition from sp2to sp3 hybridization and it is

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similar to Li+ -defect free graphene system discussed previously. In the presence of the SW defect lithium ion resides at relatively longer distance (~3.01Å) from the nearest carbon atom. In addition, Li+ near SW defect site mostly retains its ionicity (i.e. cationic charge) owing to smaller effect of aromatic π electron cloud of graphene on lithium ion (see Fig.1b). Now this could be due to the decrease of aromaticity in graphene with SW defects, however the knowledge about the aromatic ring current in layered graphene is limited [20]. In addition, relatively lower Li+ adsorption energy (-1.82eV) ascertains that the cation - π interaction between lithium ion and graphene with SW defect is significantly lower than with pure graphene (see Fig.1a). Overall, SW defect site is not a preferential site and Li+ can be easily removed from this defect site owing to relatively smaller potential barrier.

Figure 1. a) Lithium ion adsorption energy on defect free graphene (pure G) and graphene with single vacancy (SV), double vacancy (DV) and stone-Wales defect (SW). b) Hirshfeld charge analysis of lithium and carbon (nearest to lithium ion) at defect free and point defect graphene surfaces. Both adsorption energy and charge analysis are carried out on fully relaxed structures using BLYP-D3 function and TZ2P basis set based geometry optimization (see text for details). Li+ near the single and double vacancy sites The missing atoms is simple form of defect generally encountered in crystalline materials and obviously such a single vacancy (SV) and double vacancy (DV) sites are experimentally observed in graphene [8]. Despite their high formation energy (~7.5eV) in graphene, the SV defect sites represent unique electronic environments which make it worthwhile to study its interaction with lithium ion. For example, SV defect site produces one carbon dangling bond along with fivemembered and nine-membered rings [37]. Typically, this SV defect in the graphene with distorted structure and dangling bond indicates the presence of sp3 type bonding. This formation of dangling bond represents the John-Teller distortion and associated out-ofplane displacement of carbon atom with an unpaired electron. Now, lithium ion is introduced near the SV defect site and specific interactions are analyzed by fully relaxed geometry optimization procedure. As expected lithium ion binds with the free carbon (i.e. carbon with dangling bond) and the effective C-Li bond length is 2.05Å. Such a short bond length is accompanied by significant variation in both carbon and lithium ion charges and represents predominantly ionic type C-Li bonding (see Fig.1b). In particular, the introduction of Li+ significantly increases the electron density at the nearest carbon which previously had dangling bond. This implies that, the unpaired electron is spatially localized on carbon atom which in turn exerts negative charge on Li+ ion in the C-Li bond. This is different from the cation - π interaction

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discussed earlier, where Li+ in feels the π electron cloud of nearest hexagonal ring system. This C-Li bond in the presence of SV defect is energetically favorable than the cation - π interaction due to its strong binding nature. In other words, Li+ entering graphene system with SV defect would strongly bind with dangling bond and lead to higher potential barrier for its removal from the SV defect site. In typical sp2 type carbon structure, double vacancy (DV) sites form due to merging of two nearby SV defects. The DV defect site produces two pentagon and one octagon structure (known as 585 defect structure) without any dangling bonds and energetically favorable than the single SV defect in the graphene[8]. The strain induced by DV defect site causes twisting of graphene sheet causes carbons at the opposite diagonal edges to move out of plane direction which hints the presence of at least some sp3 type bonding in the structure. The presence of sp3 type bonding is further corroborated by the longer C-C bond length (~1.56 Å) at the octagon structure of DV site, however remaining C-C bond lengths (~1.43Å) are similar to that of sp2 type bonding. Now, a lithium ion is introduced near this octagon site and fully optimized without any constraints. The Li+ resides at ~1.62Å above the center of octagon ring with nearest C-Li bond length of ~2.36Å and exerts minimal change (~0.02 Å) to their C-C bond environments. It is interesting to note that nearest C-Li bond length (~2.36Å), adsorption energy (-2.4eV) and changes in Hirshfeld charges for Li+ near DV site graphene is very similar to that of defect free graphene (see Fig.1). This indicates that cation - π interaction might be the major bonding interaction, despite the presence of sp3 type bonding in graphene with DV defect site. This means, Li+ can be easily removed from the DV site and offers a highly reversible lithium interaction site within the graphene. In addition, the Li+ distance from DV graphene plane (d⊥~1.62Å) is considerably smaller than for defect free graphene (d⊥~1.82Å), which supports the lithium diffusion through the DV defect site and accessing the adjacent graphene layer [12].

Figure 2. a) Lithium ion adsorption energy on defect free graphene (pure G) and graphene with hydroxyl group (OH), carboxyl group (COOH) and epoxy group (>O). b) Hirshfeld charge analysis of oxygen both before (filled bars) and after lithium (sliced bars) interaction along with lithium (crossed bars) at graphene surfaces with functional defect groups. Both adsorption energy and charge analysis are carried out on fully relaxed structures using BLYP-D3 function and TZ2P basis set based geometry optimization (see text for details).

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Li+ near the surface functional groups The oxygen containing functional groups such as epoxy (>O), carboxyl (COOH) and hydroxyl groups (OH) are common surface defect groups observed in graphene surfaces. In particular, the cost effective chemical synthesis methods often lead to the formation of oxygen-containing functional defect groups on graphene surfaces [38, 39]. Hence it is necessary to study graphene surfaces that include these functional groups to explore the realistic graphene- Li+ interactions. The adsorption of these functional groups leads to increase in C-C bond lengths (~1.50 Å) and forms sp3 type bonding through oxygenated aliphatic region near the adsorption site [40]. Consequently, the carbon atoms near the adsorption site are slightly moved out of plane towards the oxygen group and forms slight disorder in the planar graphene structure. Now a lithium ion is separately introduced near each of these functional groups and fully optimized without any constraints. Figure 2 shows the lithium ion adsorption energy and Hirshfeld charge analysis calculated from DFT-D3 based method for graphene surface with different oxygen containing functional groups. It is interesting to note that the adsorption energies for Li+ near these functional groups is about 2 – 4 times higher than that of defect free graphene. Also with oxygen containing functional groups on graphene surface, lithium tends to bind with the oxygen rather than the carbon on graphene surface. Apparently, the Hirshfeld charge analysis of oxygen shows significant increase in negative charge density at the oxygen atom due to its interaction with Li+. In particular, Li+ is able to remove the OH group from the graphene surface and forms LiOH type bonding well above the graphene surface (d⊥~2.92Å). In this case, the graphene surface goes back to its original sp2 type bonding with 2D planar structure and C-C bond length of 1.42Å. Similarly, upon interaction with Li+, the epoxy group changes it’s near equilateral triangular structure (bond ~1.50Å & angle~60º) to the single C-O bond (1.42Å) structure. This interaction simultaneously increases the negative charge in the oxygen which indicates the formation of O-Li ionic type bond (1.68Å). Such a strong ionic bond leads to high Li+ adsorption energy (-8.4eV) for graphene with epoxy functional group. Therefore we can infer that epoxy group site is preferential site for Li+ and its strong interaction with epoxy group means it would be harder to remove lithium from this site. On the other hand, interaction of Li+ with the carboxyl group doesn’t exert any significant strain on either graphene or carboxyl group structure (≤0.03Å). Similarly the observed charge on double bonded oxygen atom in the carboxyl group shows no significant changes even though it remains closer (~1.83Å) to Li+. This indicates that there is no significant binding between carboxyl group and the Li+, whereas the cation-π interaction is still dominant interaction in this environment. Interestingly the Li+ adsorption energy (-5.6eV) under carboxyl group is relatively smaller compared with other oxygen containing functional groups probably due to the absence of Li-O ionic type bonding (Fig.3a). However, the Li+ adsorption energy is still significantly higher than the pristine graphene and graphene with point defects (Fig.1a). Overall, we can deduce that oxygen containing groups on graphene surface has significantly higher adsorption energy and can act as trapping center for lithium ion subsequently make it harder for reversible intercalation process.

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Figure 3. The Li+ chemical shift calculated from fully relaxed structures with different graphene surfaces using BLYP-D3 functional and TZ2P all electron basis set. The chemical shifts are referenced to aqueous lithium cation with same level of theory (see text for details). Understanding Li+ - π interaction in Graphene Our study reveals that Li+ - π interaction is dominant in many environments of graphene, may be except for the SV defect and epoxy functional group. The cation - π type interaction is a non-covalent and mostly electrostatic interaction between a cation such as Li+ and the planar surface of an aromatic π donor system such as graphene. Therefore to clearly understand the Li+ - π type interaction we need to analyze the delocalized π electron cloud of graphene with surface defects. Unfortunately the effect of surface defect on delocalized π electron cloud i.e. aromatic ring current of graphene is not well studied [41]. The chemical shift analysis is the simple and efficient probe to analyze the aromatic ring current effect [42]. Recently we reported the efficiency of chemical shift on probing the effect of defects on aromatic ring current using ionic liquid immobilized on defective graphene material {my article Ref}. The aromatic ring chemical shielding (ARCS) theory [43], relates the chemical shift of an atom to the radius of the aromatic ring current loop and the perpendicular distance of atom from the loop center. In essence, the calculated chemical shift at optimized Li+ can give information about the nature of delocalized π electron cloud of individual graphene surfaces. However, it should be noted that the chemical shift also depend on the perpendicular distance (d⊥) between Li+ and graphene surfaces which is again determined by the level of Li+ - π interaction. Overall, the chemical shift calculation is still effective method to understand Li+ - π interaction, because it can be verified by experimental 6/7Li NMR spectroscopy method. Figure 3 shows the calculated Li+ chemical shift on different graphene surfaces using DFT-D3 methods. According to ARCS theory, the chemical shift of an atom is expected to shift towards higher field (i.e. towards lower frequency) or towards lower field (i.e. towards higher frequency) depend on its position with respect to ring current shielding field or de-shielding field respectively. Such a chemical shifts were commonly observed in aromatic and anti-aromatic compounds and explained on the basis of anisotropic magnetic susceptibility arising from ring current [44]. It is interesting to note

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that the SV and DV point defects induces significant shift in 6/7Li chemical shift towards higher frequency. This could be due to possibilities that the preferential Li+ site near the SV and DV point defects lies on de-shielding field of the graphene aromatic current which can result in chemical shift towards higher frequency. It should be noted that the DFT calculated chemical shifts reported here represents only the diamagnetic and magnetic anisotropic term (due to aromatic ring current). In reality, the experimental chemical shift might contain paramagnetic induced chemical shift due to the possible magnetic moment arising from defective graphene. For example, recent research works suggests that vacancy defects in graphene's lattice can carry magnetic moment, which can lead to parmagnetic induced NMR chemical shift [46-48]. However, to exactly define the parmagnetic chemical shift arising from defective aromatic carbon, we need more details about the aromatic ring current and magnetism on defective graphene which are still matter of debate and active research topic [45]. On the other hand, the SW defect group and oxygen containing defect groups registers chemical shift towards lower frequency indicating the possible shielding effect from the graphene aromatic ring current. The calculated chemical shifts under these environments shows similar values except for the epoxy group site, which shows minimal shift towards lower frequency (see Fig.3). This indicates that for all the chemisorbed defect sites (except for epoxy defect site), the Li+ - π interaction is the dominant factor deciding Li+ reversible intercalation properties. Overall this study reveals that the Li+ interaction with delocalized π electron of aromatic graphene and possible chemical bonding with oxygen containing surface groups can greatly affect lithium cycling properties of graphene based electrodes. Hence, it is essential to explore more deeply into the defect induced electrical and chemical properties of graphene in order to design an optimal graphene based electrode materials. Conclusion We carried out dispersion corrected DFT studies to understand the nature of Li+ interaction with graphene containing common surface defects. It is clear that, Li+ interacts profoundly with the delocalized π orbital electron cloud of pure graphene layers. For defective graphene, the single vacancy type defect group can also interact with Li+ through its chemical binding with carbon dangling bonds. Similarly the oxygen containing functional groups mainly interacts by forming Li-O ionic bond. In either case, the Li+ adsorption energy is higher for the defective sites indicating the possible resistance for reversible lithium intercalation with defective graphene. With this understanding, we attempted to hypothesize the reasons behind the fickle graphene performances reported in the literature. The graphene with significant oxygen containing functional groups (which are often synthesized through aqueous/solvent based chemical methods) can yield a poor performance due to the formation Li+ trapping center at the functional group sites. In other words, graphene with higher concentration of chemisorbed functional groups could result in capacity fading due to loss of Li+ at these trapping centers. However, graphene with significant vacancy type defects (which are often synthesized by exfoliation or high temperature methods) might improve the cycling performance, mainly due to the possibilities of Li+ passing through the vacancy centers (such as double vacancy). As we seen in our DFT study and previous studies, Li+ stays relatively closer to graphene with double vacancy defective site and might initiate Li+ diffusion through the defects (i.e. perpendicular to surface basal plane) and thereby gain

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maximum access to the wide surface area of graphene layers. We like to emphasize that these hypothesis are based on our preliminary DFT studies and needs validation through vigorous experimental analysis. In addition, even though this study tries to explore the role of graphene surface defects, it is still unclear about what is the optimal concentration and combination of defects which can give desired lithium battery performance. Obviously, more detailed computational and experimental studies are required to fully understand the Li+ interaction with graphene defects and subsequently tailor the graphene based electrode materials. Acknowledgements We thank Drs. J. Liu, G.L. Graff, B. Schwenzer and S. Thevuthasan for their support and fruitful discussions. We acknowledge the funding by Pacific Northwest National Laboratory (PNNL) under the LDRD program. PNNL is a multiprogram laboratory operated by Battelle Memorial Institute for the Department of Energy (DOE) under Contract DE-AC05-76RL01830. The DFT computation work was carried out at EMSL (www.emsl.pnl.gov), a national scientific user facility sponsored by the DOE’s Office of Biological and Environmental Research. References [1] M. Pumera, Energy & Environmental Science, 4 (2011) 668-674. [2] Y. Sun, Q. Wu, G. Shi, Energy & Environmental Science, 4 (2011) 1113-1132. [3] E. Yoo, J. Kim, E. Hosono, H.-s. Zhou, T. Kudo, I. Honma, Nano Letters, 8 (2008) 2277-2282. [4] R. Mukherjee, A.V. Thomas, A. Krishnamurthy, N. Koratkar, ACS Nano, (2012). [5] O.A. Vargas C, A. Caballero, J. Morales, Nanoscale, 4 (2012) 2083-2092. [6] X. Zhao, C.M. Hayner, M.C. Kung, H.H. Kung, ACS Nano, 5 (2011) 8739-8749. [7] D. Pan, S. Wang, B. Zhao, M. Wu, H. Zhang, Y. Wang, Z. Jiao, Chemistry of Materials, 21 (2009) 3136-3142. [8] F. Banhart, J. Kotakoski, A.V. Krasheninnikov, ACS Nano, 5 (2010) 26-41. [9] A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K.S. Novoselov, C. Casiraghi, Nano Letters, 12 (2012) 3925-3930. [10] E. Lee, K.A. Persson, Nano Letters, 12 (2012) 4624-4628. [11] M. Khantha, N.A. Cordero, L.M. Molina, J.A. Alonso, L.A. Girifalco, Physical Review B, 70 (2004) 125422. [12] X. Fan, W.T. Zheng, J.-L. Kuo, ACS Applied Materials & Interfaces, 4 (2012) 24322438. [13] F. Yao, F. Güneş, H.Q. Ta, S.M. Lee, S.J. Chae, K.Y. Sheem, C.S. Cojocaru, S.S. Xie, Y.H. Lee, Journal of the American Chemical Society, 134 (2012) 8646-8654. [14] E. Pollak, B. Geng, K.-J. Jeon, I.T. Lucas, T.J. Richardson, F. Wang, R. Kostecki, Nano Letters, 10 (2010) 3386-3388. [15] F. Valencia, A.H. Romero, F. Ancilotto, P.L. Silvestrelli, The Journal of Physical Chemistry B, 110 (2006) 14832-14841. [16] D. Krepel, O. Hod, Surface Science, 605 (2011) 1633-1642. [17] C. Uthaisar, V. Barone, J.E. Peralta, Journal of Applied Physics, 106 (2009) 113715. [18] S. Grimme, Journal of Computational Chemistry, 25 (2004) 1463-1473. [19] S. Grimme, J. Antony, S. Ehrlich, H. Krieg, The Journal of Chemical Physics, 132 (2010) 154104. [20] S. Panigrahi, A. Bhattacharya, S. Banerjee, D. Bhattacharyya, The Journal of Physical Chemistry C, 116 (2012) 4374-4379.

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