two-dimensional icy water clusters between a pair of graphene- like molecules...

Two-Dimensional Icy Water Clusters Between a Pair of Graphene-Like Molecules or Graphene SheetsSeong Kyu Kim,*,† Wenzhou Chen,‡ Saeed Pourasad,‡ and Kwang S. Kim*,‡

†Department of Chemistry, Sungkyunkwan University, Suwon 16419, Korea‡Center for Superfunctional Materials, Department of Chemistry, Ulsan Institute of Science and Technology (UNIST), Ulsan 44919,Korea

*S Supporting Information

ABSTRACT: To understand the 2-dimensional (2D) struc-tural evolution of water molecules intercalated into a graphenebilayer, the geometries of water clusters up to tridecamerformed between a pair of graphene sheets or betweengraphene-like molecules (coronene and dodecabenzocoro-nene) are investigated. Due to their large sizes, the self-consistent-charge density-functional tight-binding (SCC-DFTB) method expanded into the third order andsupplemented with a Slater−Kirkwood dispersion term was used. In this way both hydrogen bonding and H−π/π−πinteractions are calculated in a balanced manner with the right magnitude of binding energies very close to the reference valuesbased on the most accurate ab initio results. It should be noted that conventional density functional theory (DFT) calculationsunderestimate the H−π/π−π interaction, while dispersion-corrected DFT calculations overestimate hydrogen bonding. Thelatter method is also employed for comparison and to confirm the reliability of the SCC-DFTB results. For (H2O)6, the fusedbitetragonal hexamer is nearly isoenergetic to the most stable planar hexagonal ring structure, and it is more frequently found. In(H2O)10 and (H2O)13 clusters, a tetragon is the most frequent geometry followed by a pentagon, while the hexagon is lessfrequent. These results certainly provide evidence of the recent planar tetragonal ice structure found inside a graphene bilayer(Nature 2015, 519, 443) which is in contrast to the well-known hexagonal pattern of the bulk ice. This structural change fromhexagonal to tetragonal network on the graphene surface is attributed mainly to the inherent nature of 2D water.

1. INTRODUCTION

Two-dimensional (2D) chemistry has been emerging throughnoncovalent adsorption on graphene1 or intercalation insidebilayer graphene.2 It is thus timely to study water structures in 2Dsystems since water is the most important substance in our life.As yet, such the 2D nature of water has rarely been studied. Veryrecently, it has been reported that ice water forms a 2Dcheckerboard pattern between a pair of graphene sheets.3 Thecheckerboard arrangement of water molecules should withstandsubstantial strain out of unusual hydrogen bonding structure.The understanding of such complex phenomena cannot be madesimply either by ab initio or DFT calculations or by empirical/semiempirical potential-based Monte Carlo or moleculardynamic (MD) simulations. For the logical understanding, it isnecessary to study the progressive change as the number of watermolecules increases.Icy water confined in a highly restricted environment shows

unique properties that are not observed in bulk ice. The confinedwater molecules can assemble into structures that are differentfrom their tetrahedral hydrogen bonding network of liquid or ice.When the confined environment is hydrophobic, they usuallyfollow the confined shape. For example, according to MDsimulations4 and X-ray diffraction studies,5 icy water formstubular structures inside carbon nanotubes with tetragonal tooctagonal cross sections depending on the tube diameter. When

confined by 2D substrates, a monolayer ice is likely to form a 2Dstructure.6 As already mentioned, icy water can form a 2Dcheckerboard pattern between a pair of graphene sheets.3 It isintriguing because water tends to favor hexagon structure in iceand liquid, and the pentagon structure is relatively stable in thegas phase, while the planar tetragon structure is strained. In thisregard, to understand the 2D icy water structure, a systematicstudy for water−water and water−substrate interactions isrequired with accurate calculations. However, high levelcalculations are limited to small systems. Calculations of largesystems are feasible only at low levels of theory. Here, theinformation from small systems may help to set up initialconditions for large systems. With these in mind, we have tried tofind the structures and interactions of water clusters between apair of graphene-like polyaromatic rings or a pair of graphenesheets.Two kinds of approaches are used to find the information on

water−graphene interactions. The first is to use graphene directlyas a substrate. In this case, a periodic cell of graphene substratemust be large enough to avoid interaction of water moleculesbetween neighboring cells. This involves a large number of atoms

Received: June 16, 2016Revised: July 31, 2016Published: August 3, 2016

Article

pubs.acs.org/JPCC

© 2016 American Chemical Society 19212 DOI: 10.1021/acs.jpcc.6b06076J. Phys. Chem. C 2016, 120, 19212−19224

pubs.acs.org/JPCC

http://dx.doi.org/10.1021/acs.jpcc.6b06076

in the calculation, and therefore, the level of calculation is ratherlimited. Limited studies7−10 based on density functional theory(DFT) have been performed on water clusters up to hexamer ona graphene monolayer. The second kind of approach is usingpolycyclic aromatic hydrocarbons as a model substrate, and then,the results from the study are extrapolated to that ofgraphene.11−19

Reported adsorption energies of a single water molecule ongraphene fall in a wide range (between 2.2 and 5.8 kcal/mol).11−19 Despite the large uncertainty in the reportedadsorption energy, the geometry of the adsorbed water isrelatively consistent frommethod to method. On the most stablegeometry, the water molecule stands upright with the twohydrogens pointed down toward the substrate plane, althoughthe geometry with the two hydrogens pointed up is only slightlyhigher in energy (by ∼0.5 kcal/mol). Compared to manycomputational works for water on graphene or its molecularmodels, the study of water between two layers of graphene or itsmolecular model is very rare. Ruuska and Pakkane20 used aHartree−Fock (HF) method for a single water molecule placedbetween a pair of coronene (Cor; C24H12) molecules. However,the water intercalation energy could not be correctly describeddue to the lack of electron correlation.In this article, we report the energies and geometries of

(H2O)1−6 clusters between a pair of coronene molecules,(H2O)n=1−6,10 clusters between a pair of dodecabenzocoronene(DBC; C54H18) molecules, and (H2O)n=10,13 species between apair of graphene sheets, with a hope that such information wouldprovide geometries of much larger water clusters inside a bilayergraphene.

2. METHODS

Since accurate ab initio calculations including coupled clusterwith single, double, and perturbative triple excitations (CCSD-(T)) are too time-consuming, the only feasible approach wouldbe to use DFT with dispersion correction. Even the hybrid

density functionals would not be feasible for this systematic studyinvolved in very large systems. What is more critical is thatdispersion-corrected DFT-D3 gives overbinding energies (asmuch as 20−30%) for water clusters. Therefore, here we exploit aself-consistent-charge density-functional tight-binding (SCC-DFTB) method21 which provides more realistic bindingenergies. The SCC-DFTB method is an approximation toDFT by expanding DFT energy expression to second or thirdorder terms. The interaction between atoms is then described byan effective damped Coulombic interaction between atomiccharges derived from the expansion. Since the speed ofcalculation is higher by 2−3 orders of magnitude than that ofDFT calculations using small to medium size basis sets and theaccuracies in describing molecular geometries are comparable tothe results of DFT or higher level calculations, the SCC-DFTB ishighly useful for large systems.As most density functionals describe dispersion interaction

poorly, additional terms with empirical fitting parameters areusually employed to reproduce the dispersion interaction. Theuse of empirical fitting parameters provides flexibilities to theSCC-DFTB method rather than lessens its reliabilities, as theparameters can be slightly adjustable to best describe the systemunder study. In our case, a Slater−Kirkwood atomic polarizablemodel was used with the parameters described by Elstner, Hobza,and co-workers,22 but a slightly larger (by 0.2 Å) covalent radiusfor C atom was used to provide better dispersion energies for thebenzene (Bz) dimer and Bz−water systems.In the standard SCC-DFTB method, the second order

expansion of the DFT energy is used, and this is sufficient formost covalently bound systems. However, it is insufficient forhydrogen bonding systems, which require the expansion up tothe third order.23 To be short, the major computation methodemployed in this work is referred to as SCC-DFTB-3D, where“3” represents the expansion up to the third order and “D”represents the Slater−Kirkwood type dispersion term. Thesefeatures are provided by a version 1.2 code of the DFTB+

Table 1. Binding Energies (kcal/mol) of Selected Clusters Calculated at Various Levels of Theorya

SCC-DFTB PBE-D3

3D 2D 3 TZVP (scaledd) TZVPP (scalede) ref values

(H2O)2 5.05 3.40 4.97 7.02 (4.91) 6.31 (5.05) 5.0,f 5.02g,h

(H2O)3 15.8 9.84 15.6 22.3 (15.6) 20.4 (16.3) 15.8f,i,j

(H2O)4 27.5 18.2 26.9 39.1 (27.4) 35.6 (28.5) 27.4,f 27.6j

(H2O)5 36.3 23.8 35.5 51.4 (36.0) 46.6 (37.3) 35.9,f 36.3j

(H2O)6, ring 44.8 29.1 43.8 63.2 (44.2) 56.9 (45.5) 44.3,f 44.9,j 45.2k

(H2O)6, book 45.9 30.2 44.8 65.1 (45.6) 59.2 (47.4) 45.4,f 45.6,j 46.1k

(H2O)6, bag 46.1 30.0 45.1 64.8 (45.4) 59.0 (47.2) 45.5k

(H2O)6, cage 47.0 30.6 45.9 66.1 (46.3) 60.3 (48.2) 45.9,f,j 46.5k

(H2O)6, prism 48.0 31.0 46.6 66.7 (46.7) 60.6 (48.5) 46.2,f 45.9,j 46.6k

Bz(H2O)1 2.90 1.79 2.17 5.19 (3.63) 4.55 (3.64) 3.34g,l

Bz−Bzb 3.17 3.21 0.19 2.90 (2.03) 2.88 (2.30) 2.7−2.8m

Cor−Corb 19.3 20.1 0.0 17.6 (12.3) 16.8 (13.4) 20.0 ± 7.3,n 20.0 ± 1.7o

Cor−Cor (6 Å)c 1.55 0.75 0.0 1.86 (1.30) 1.93 (1.54)aAll energies at the SCC-DFTB and PBE-D3 levels are given without corrections for zero point energy and basis set superposition error (BSSE).bParallel-displaced geometry. cCor−Cor (6 Å) denotes that two Cor molecules are separated by 6 Å, where the stacked or the parallel-displacedconformations do not show any significant difference in binding energy. dScaled binding energies in parentheses scaled by 0.7 toward the realisticvalues because of large overestimation. eScaled binding energies in parentheses scaled by 0.8. fCCSD(T)/CBS result from ref 31. gCCSD(T)/CBSresult from ref 32. hCCSD(T)/CBS result from ref 33. iMP2/CBS results from ref 34. jMP2/CBS result from ref 35. kMP2(FC)/HZ4P(2fg,2d)++result from ref 36. lCCSD(T)/CBS result from ref 37. mCCSD(T)/CBS result from refs 38−40. nSCS-MP2/pVDZ result calculated in this work(the middle value between BSSE uncorrected and corrected values, where the error bar denotes half the BSSE; see refs 28, 36, and 42 for thereliability of the middle value). oM06-2X/DIDZ result from ref 41 (the middle value between BSSE uncorrected and corrected values, where theerror bar denotes half the BSSE).

The Journal of Physical Chemistry C Article

DOI: 10.1021/acs.jpcc.6b06076J. Phys. Chem. C 2016, 120, 19212−19224

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quantum mechanical calculation package.24,25 DFT calculationswere carried out using the Turbomole program package (version6.4).26 All the geometrical structures of water clusters with andwithout rigid substrates were optimized using both SCC-DFTB-3D and the PBE-3D/TZVP methods independently.2.1. Background Study: (H2O)1−6, H2O−Benzene,

Benzene Dimer, and Coronene Dimer. The geometries ofwater clusters confined by a pair of graphenes or graphene-likemolecules are determined mostly by H−OH H-bondinginteraction in water clusters and by H−π interaction27 betweenwater and substrate, while the π−π interaction28 between thesubstrate pair contributes to a lesser extent. In Table 1, thebinding energies of (H2O)1−6, Bz(H2O)1, Bz dimer, and Cordimer calculated by the SCC-DFTB methods are compared withthose of the highest level ab initio calculations from the literatureand those of PBE29-D330 calculations which are commonly andwidely used in both physics and chemistry communities as one ofthe most representative dispersion-corrected DFT methods.Three values listed under columns of 3D, 2D, and 3 are,respectively, the binding energies from the SCC-DFTBcalculations with both the third order expansion and thedispersion term (3D), with the second order expansion andthe dispersion term (2D), and with the third order expansionterm without dispersion (3). It should be noted that PBE-D3overestimates the binding energies; thus, the energy values arescaled to obtain almost the right values calculated at the high levelof ab initio theory including nearly full electron correlation. Incontrast, the binding energies of water clusters calculated withSCC-DFTB-3D are almost same as the most accurate referencevalues within uncertainties of the reference methods. In waterclusters, the contribution of the dispersion is a small fraction. Incontrast, the expansion up to the third order is very important;without the third order expansion, the binding energies of waterclusters are underestimated as much as about 70%. In the bindingenergy of Bz(H2O)1 calculated by SCC-DFTB-3D, thedispersion term contributes about 25% to the total bindingenergy, which is also in good agreement with the referencevalues. In the Bz dimer and the Cor dimer, the dispersion term isdominant in the binding energy. The binding energy of the Bzdimer calculated by the SCC-DFTB-3D is larger by ∼10% thanthe reference value. However, this small overestimation hardlyinfluences the geometries of water clusters in the substrates ofthis work since the π−π interaction is very weak as theintersubstrate distance is far from their binding distance due tothe intercalated water clusters.From these results, SCC-DFTB-3D performs very well, in

close agreement with the best reference values since water−water, water−π, and π−π interactions are all in reasonableagreement with the reference values.31−41 The results are muchmore reliable than both the standard DFT (which givesreasonable values of water−water interactions but poor valuesfor water−π, and π−π interactions) and the standard DFT-D3(which gives overbinding energies for water−water interactionsdespite reasonable values for water−π, and π−π interactions). Asnoted in Table 1, the PBE-D3/TZVP and PBE-D3/TZVPPbinding energies need to be scaled by 0.7 and 0.8, respectively, soas to give the realistic magnitude of these water binding energies.Furthermore, their water−water and water−Bz binding energiesare much less reliable than the SCC-DFTB-3D results, whencompared with the accurate CCSD(T)/complete-basis-set-(CBS) results.2.2. Preparing Initial Geometries. The three substrates

employed in this study are a pair of Cor molecules, a pair of DBC

molecules, and a bilayer graphene. The structure of a single Cormolecule was fully optimized to be used as a molecular substrate.Another molecular substrate DBC is partially optimized with thecentral six C−C bond lengths fixed to 1.427 Å. A single layer ofgraphene consisting of 128 carbon atoms was constructed withall C−C bond lengths fixed to 1.427 Å in a periodic supercell of19.773 × 17.124 × (20 + dz) Å3, where dz is the interlayerseparation. The internal geometries of the three kinds ofsubstrates were then fixed in the next step calculations for theintercalated water systems.The general approach of computation is as follows. First, each

water cluster (H2O)n (n = 1−6) on the surface of a single Cor wasoptimized. Here, the initial geometry of each water cluster onCor was taken from its known geometry in an isolatedstate.36,41,43 All initial geometries of water clusters werepositioned approximately at the center of the Cor plane. Planarring structures for n = 3−6 were positioned with the ring planeparallel to the Cor plane. Each nonplanar structure for n = 6, suchas book, bag, cage, and prism configurations,43 was positionedwith two or three different tumbling orientations and two lateralspinning orientations with respect to the Cor plane. Second, theother Cor was placed above each optimized (H2O)1−6/Corgeometry, and then the water cluster between the Cor pair wasoptimized. The two Cor molecules were stacked with the Cor−Cor distance (dz) set to 20 Å initially, and then, the distance wasreduced gradually. The geometry of water cluster optimized ateach dz was used as an initial geometry for optimization at a nextdecremented dz. As the energy of the cluster approaches aminimum, the decrement of dz was reduced to as much as 0.1 Å.The M06-2X/DIDZ41 calculations show that the parallel-

displaced Cor dimer (displaced by 1.75 Å with the interlayerdistance of 3.32 Å) is more stable than the exactly stackedsandwiched Cor dimer (with the interlayer distance of 3.66 Å).However, at the separation distance of 6 Å, we find that bothstacked and parallel-displaced structures have almost the samebinding energies, and so the orientation is not important. Asimilar trend is also found for the SCC-DFTB-3D method whichshows the binding energies of 19.3 kcal/mol for the parallel-displaced Cor dimer (3.3 Å) and 1.6 kcal/mol for the Cor−Cor(6 Å) conformer. When any water clusters in this study areinserted into the Cor pair, the binding energy between two Cormolecules at dz = 6.0 Å is almost the same (within 0.07 kcal/mol)regardless of their stacking orientations. This trend also holds forthe DBC pair and the bilayer graphene. Since such stackingorientations do not affect the binding energies significantly, thewater structures could change the stacking conformation in favorof their maximal interactions with two Cor molecules, which,however, turn out to be insignificant. Overall, the energydifference depending on the stacking types could be minimal.Nevertheless, we calculated the stacking cases and displacedstacking cases, and the intermediate conformations between thetwo are also studied; the maximum binding energies are reportedhere.Third, a pair of DBC molecules were used as the substrate to

adopt a larger size (H2O)10 as well as (H2O)1−6. (H2O)10 waschosen because a bihexagonal configuration, like naphthalene,can be formed. As configurations of various water clusters arediverse, we will use the following notation. The ring type isdenoted as 3 for triangle, t for tetragon, p for pentagon, and h forhexagon. The cross(es) ( × ) separates the ring types betweensuccessive rows. When similar configurations are to bedistinguished, additional italic letters, a, b, and so forth, areattached at the end. We will use the notation throughout for all



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fused ring configurations in this study. The configurations andthe notations of (H2O)3−6,10,13 clusters are schematicallyrepresented in Figure 1.

An initial geometry of the bihexagonal (hh) configuration wascreated under the following guideline; 11 hydrogen bonds areneeded to form a bihexagon, and at a stable geometry theremaining 4 and 5 OH bonds point alternatively toward the topand bottom DBC molecules, respectively. Four checkerboardconfigurations that consisted of four fused tetragonal rings arepossible for (H2O)10. They are ttt × t-a, ttt × t-b, tt × tt, tttt, asshown in Figure 1. The following guideline is applied to prepareinitial geometries for the checkerboard configurations; 13hydrogen bonds are needed to keep the structure, and theremaining 3 and 4 OH bonds are arranged to point toward thetop and bottom DBC molecules, respectively.Configurations can also be created with combinations of fused

triangular, tetragonal, and pentagonal rings. Initial geometries ofsuch kinds of structures were found with a simulated annealingmethod.44 These structures (tt × tp, pt × p, tpp, tht-a. tht-b, h ×tp) are depicted in Figure 1. A series of MD simulations werecarried out starting at 400 K and ending at 0 K in order toovercome conformational barriers followed by gradual cooling toreach a low energy regime. Annealing was done with Nose−Hoover thermostat and 0.5 fs time step. During the simulation,we used the TIP4P model for water. A pair of DBC moleculeswith the interlayer separation varied between 6.0 and 7.0 Å wasused as a substrate to find six stable configurations of (H2O)10.Fourth, to adopt (H2O)13 clusters, as well as (H2O)10 clusters

mentioned above, a bilayer graphene was used as a substrate.This size of the water clusters was chosen because a trihexagonalconfiguration (hh × h) can be formed. Seven checkerboardconfigurations, which consist of six fused tetragonal rings, werealso prepared for (H2O)13. Configurations consisting of acombination of multiple kinds of rings are also possible. Initialgeometries in such configurations were prepared by thesimulated annealing method.

3. RESULTS3.1. (H2O)1−6 on Graphene-like Surface. In our optimized

geometry of (H2O)1 on graphene-like surface, the two hydrogenspoint down (d) toward the substrate plane, consistent with mostresults in the literature; this geometry will be denoted as “dd”.The geometries of (H2O)2−6 on the Cor surface optimized withthe SCC-DFTB-3D are shown in Figure 2. The geometries on

other graphene-like surfaces are qualitatively independent of thesubstrate studied in this work. The geometry of the lowest energywater dimer shows C2v point group symmetry with the principalaxis along theH-bond. All three non-H-bonding hydrogens pointdown toward the Cor surface. One dangling OH of the H-bonddonating water molecule makes 14.3° from the surface normaland the two dangling OH’s of the H-bond accepting watermolecule make 62.3° from the surface normal. We call thisstructure “dHdd”, which is ∼0.4 kcal/mol more stable than thestructure “uHdd” with the first dangling hydrogen (Hd) pointingupward (u), where “H” denotes a H-bonded hydrogen. Thegeometries of (H2O)3−5 take on planar ring structures, formingan equilateral triangle, a square, and a regular pentagon,respectively, consistent with the results in the literature.10,17

The geometries of water hexamer on graphene-like surfacetake on complicated features as the isolated water hexamer mayexist in five different isoenergetic geometries: cyclic ring, book,bag, cage, and prism. Lin et al. have studied, with the SCC-DFTB-D method, the geometry changes of the water hexamersas they are adsorbed onto the graphene-like surface.17 Our resultsrecognize the following facts which are consistent with theirdiscussion points. (i) In all kinds of water hexamers, geometrychange upon adsorption is rather small. The negligible geometrychange includes the orientation of dangling OH’s with respect tothe skeleton of water cluster. As a result, the number of danglingOH bonds pointing toward the substrate surface is a major factorto determine relative stability of the corresponding hexamer. (ii)

Figure 1. Schematic representation of the hydrogen bonding networkconfigurations of 2D water clusters in this study.

Figure 2. Top view of Cor(H2O)2−6 optimized at the SCC-DFTB-3Dlevel. For Cor(H2O)6, only the structures with the lowest energy at eachnonplanar configuration (ring, book, bag, cage, prism) are displayed.Hydrogen bonds between water molecules are shown with green dottedlines.



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The ring hexamer adsorbs with little geometry change as long asthe hexagon plane in the initial geometry is oriented moreparallel to the substrate surface. It converts to the book hexamerwhen the hexagon plane in the initial geometry is oriented moreparallel to the surface normal. (iii) The optimized book hexameron a graphene-like surface has either open or flipped geometry.The energy difference of the two geometries is almost negligible,and the unfolding angle of the book in the adsorbed state is largerthan in the isolated state.The root-mean-square deviation (RMSD)45 of each calculated

water cluster geometry with substrates from the correspondingpristine water cluster geometry is reported in Table 2 for(H2O)1−6 on the three graphene-like surfaces by using theKabsch algorithm46 to superimpose the two geometries. TheRMSD values for n = 1 and for the planar ring geometries of n =3−5, 6 (ring) are less than 0.2 Å. The RMSD value of n = 2 isrelatively high as the Hd’s point to different directions from theisolated dimer in the cases of Cor and DBC, but not high in thecase of graphene. It arises because the Cor and DBC cases shownonuniform potentials on the molecular surface due to edge Hatoms, while the graphene surface shows almost flat uniformpotential surface. The RMSD values for nonplanar hexamers(book, bag, cage) are somewhat high due to their facile structure,while that of the rigid nonplanar prism hexamer is small.Binding energies of (H2O)1−6 on the three graphene-like

surfaces are also summarized in Table 2. Overall, the bindingenergies on DBC or graphene are slightly larger than those onCor, as the H−π interaction increases with the larger substrate.The binding energies of (H2O)2−6 are larger than those reportedby Karapetian et al.,9 Leenaerts et al.,10 or Lin et al.17 (Lin et al.’svalues are not listed in Table 2 because the substrates aredifferent). This is probably because their calculation methodsunderestimate the H-bond interactions in water clusters. In thecase of water hexamer, the bag, the cage, and the prism structuresare not 2D structures, but they are no longer more stable than ornearly isoenergetic to the global minimum energy structure ofeither ring or book shape.3.2. Cor/(H2O)1−6/Cor. Interaction energies of (H2O)1,2 as a

function of Cor−Cor distance (dz) are plotted in Figure 3. Twokinds of interaction energies are defined as follows.

= − × − ×E E E n E21 total sub water (1)

= − −E E E2 1 sub sub (2)

Here Etotal, Esub, Ewater, and Esub-sub are the total electronic energy,the electronic energy of the substrate, the electronic energy of asingle water, and electronic energy of the substrate pair at a givenlayer displacement (dx, dy, dz), respectively. Figure 3 displays theenergy curves for a sandwiched substrate pair, i.e., (dx, dy) = (0,0). Both E1 and E2 curves resemble typical molecular interactioncurves; as dz is reduced, the energy decreases slowly to theminimum and then increases rapidly due to the hard wallrepulsion.As an H2O monomer is pressured by reducing dz, the E2

minimum is reached when dz = 5.9 Å. Until this point, thegeometry of H2Omonomer is little changed from that on a singleCor in which the water molecule stands upright whilemaintaining C2v symmetry (“dd” geometry, Figure 4a). Thisstructure is maintained until dz is shortened to that (5.5 Å) of theE1 minimum. From this point, H2O is optimized with the upperCor displaced along x or y directions, each time by 0.1 Å and upto±0.5 Å. In either direction, the energy increases; therefore, theexactly stacked Cor pair provides an optimal environment tostabilize the H2O monomer. As dz is further shortened, the twowater hydrogens slowly turn to point horizontally (Figure 4b).We also tried to optimize an initial geometry in which two

hydrogens point in opposite directions: one toward bottom Cor,and the other toward top Cor when the two Cor molecules areseparated by 9.0 Å. However, this “ud” geometry does not staystable at the center of the Cor ring. H2O is moved to the Cor edge

Table 2. Binding Energies and RMSD Values of (H2O)1‑6 on a Single Layer of Graphene-like Substrate (Cor, DBC, Graphene),Optimized with the SCC-DFTB-3D and PBE-D3/TZVP Methodsa

binding energy (kcal/mol)a RMSD (Å)

Cor DBC graphene Cor DBC graphene

(H2O)1 3.00 [5.41 (3.79)], {2.4−5.2}c 2.75 [5.67 (3.97)], {2.6−5.3}d 2.52 {2.2−5.8}e 0.004 [0.006] 0.004 [0.006] 0.004(H2O)2 8.29 [16.2 (11.3)] 9.49 [16.0 (11.2)] 9.76 {10.3f, 5.5g} 0.60 [0.36] 0.54 [0.36] 0.04(H2O)3 20.3 [32.4 (22.7)] 22.1 [33.1 (23.2)] 22.0 {19.6f, 16.4g} 0.18 [0.05] 0.16 [0.04] 0.13(H2O)4 32.8 [49.8 (34.9)] 35.0 [51.0 (35.7)] 35.2 {31.7f, 29.5g} 0.09 [0.04] 0.17 [0.07] 0.11(H2O)5 43.5 [63.6 (44.5)] 45.8 [65.5 (45.9)] 45.9 {41.7f, 39.2g} 0.20 [0.05] 0.20 [0.13] 0.16

(H2O)6, ringb 52.8 [78.5 (55.0)] 55.6 [80.7 (56.5)] 56.0 {50.8}f 0.11 [0.03] 0.27 [0.13] 0.20

(H2O)6, bookb 53.8 [77.6 (54.3)] 56.3 [79.4 (55.6)] 56.5, {51.4}f 0.35 [1.30] 0.48 [0.12] 0.44

(H2O)6, bagb 53.1 [78.5 (55.0)] 55.8 [79.8 (55.9)] 55.3 0.69 [0.33] 0.76 [0.77] 0.49

(H2O)6, cageb 52.8 [76.6 (53.6)] 54.9 [77.6 (54.3)] 55.0 {48.3}f 0.53 [0.28] 0.48 [0.09] 0.27

(H2O)6, prismb 53.3 [76.7 (53.7)] 55.8 [78.5 (55.0)] 56.2 {50.9}f 0.16 [0.11] 0.13 [0.09] 0.13

aThe binding energy is defined as the energy sum of all fragments (n × Ewater + Esub) minus the total energy. The PBE-D3 values are in brackets inwhich the scaled values are in parentheses (scale factor = 0.7). The reference values are in braces. RMSD denotes the deviation in water geometryfrom the pristine water cluster. bThe value is shown only for the lowest energy orientation. cReferences 11−14. dReferences 11, 12, 14, 19.eReferences12, 16. fDang−Chang model potential II of ref 9. gPBE/PAW calculation of ref 10.

Figure 3. Interaction energy as a function of the Cor−-Cor distance (dz)for (H2O)1,2 between a pair of sandwiched Cor molecules, optimizedwith the SCC-DFTB-3D method. In the (H2O)2 case, the plots are forthe dHdd conformer as the initial geometry.



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when dz is reduced to 8.5 Å. As dz is further reduced, theoptimized H2O is placed farther from the edge while the overallenergy keeps decreasing. At a fixed dz, the energy of H2O at theedge of the Cor pair is always lower than that of the intercalatedH2O. This arises because the energy of Cor dimer plus the energyof H2O is lower than the energy of Cor/H2O/Cor where H2O isintercalated. Namely, the state of intercalation is a local minimumwhich can be generated from a well-defined precursor state.When the “ud” geometry was optimized inside the DBC pair orthe graphene pair, it converted to “dd” geometry.The geometry of (H2O)2 varies in a more complicated fashion

as dz is decreased. When the “dHdd” conformer of Cor(H2O)2 ispressured by the top Cor, the adsorbed geometry in Figure 2 isqualitatively maintained until dz reaches 9.0 Å. Then, at shorterdz, the H-bond accepting water is lifted as its dangling OH ispulled by the top Cor. During this process, the whole H2O dimermoves to the edge of the Cor plane (Figure 5a). As dz is reducedto 7.0 Å, the lifted H2O comes back to the same height as theother H2O. In this way, the geometry of the E1 minimum isreached when dz = 5.6 Å. At this stage, the Hd of the H-bonddonating water points sideways, and the two Hd’s of the H-bondaccepting water point upward and downward. Upon furtheroptimization of the structure by displacing the top Cor along thex and y directions, the two water molecules are translated slightlywith a somewhat large change in the pointing directions of thethree Hd’s. The final optimized geometry is found at (dx, dy, dz) =(−0.4, −0.3, 5.6) Å (Figure 5b). This geometry will be denotedas “hHud” even though the directions are intermediate betweenhorizontal and up/down.When the “uHdd” conformer of Cor(H2O)2 is pressured by

the top Cor, the geometry change undergoes a different route. Inthis case, the H-bond donating water is lifted as its Hd is pulled bythe top Cor when dz is between 7.0 and 9.0 Å. In fact, the energiesof these geometries in this range of dz’s are lower by 0.1−1.4kcal/mol than the corresponding geometries optimized from the“dHdd” conformer. Then, at shorter dz’s, the optimized geometryfrom the “uHdd” conformer is merged into the geometry fromthe “dHdd” conformer with the reflection symmetry. At the PBE-

D3/TZVP level, the water dimer tends to stay more toward thecentral part of Cor.Interaction energy curves for (H2O)3−5 upon changing

interlayer distance dz behave similarly to the case of (H2O)1−2.For these sizes of water clusters, the ring structures are known tobe stable not only in the isolated phase but also on the graphenesurface.10,17 Initially as a planar structure centered on the bottomCor at dz = 20 Å, all the ring clusters undergo rather a biggeometry change when dz is in the range between 7 and 9 Å. Inthe case of a water trimer, one water molecule whose Hd ispointing up is pulled toward the top Cor at dz = 9 Å and returns toits planar position at dz = 7 Å. In the case of a water tetramer, twowater molecules whose Hd’s are pointing up are pulled towardthe top Cor at dz = 9 Å and return to their planar position at dz = 7Å. When dz is reduced to that (6.2 ± 0.5 Å) of the energyminimum, the geometry (in terms of O atoms) is a perfectsquare. The water tetramer undergoes the geometry change inthe following fashion: planar square (>9 Å)→ bent square (7−9Å) → planar square (6−7 Å) → planar rectangle (5−6 Å). Awater pentamer behaves similarly. It undergoes the geometrychange in the following fashion: planar pentagon (>9 Å) →puckered pentagon (7−9 Å)→ planar regular pentagon (6−7 Å)→ slightly distorted pentagon (<6 Å).The interaction energy curves and the geometric changes for

water hexamers behave in different patterns depending on theinitial configuration. The ring structure of a water hexamerchanges in a similar pattern to the cases of (H2O)3−5: planarhexagon (>9 Å) → armchair form (7−9 Å) → planar hexagon(<7 Å). In the case of the almost 2D-like book hexamer, thetransformation is smooth, and no kink appears in the interactionenergy curve with respect to the separation distance dz of twoCor molecules. However, other nonplanar water hexamers atinitial geometries undergo big geometry changes for dz between7.5 and 8.5 Å. In this range, parts of the water molecules arepulled up, and a transformation from nonplanar to planargeometries occurs, which gives a kink in the curve plot ofinteraction energy versus dz. Details of all these transformationsare shown in Supporting Information.

Figure 4. Geometry of H2O monomer between a pair of Cor moleculesoptimized with the SCC-DFTB-3D method: (a) lowest energy state at(dx, dy, dz) = (0.0, 0.0, 5.5) Å, (b) overcompressed state at (dx, dy, dz) =(0.0, 0.0, 5.0) Å. In the top view of each case, the top Cor is removed fora clearer view.

Figure 5. Geometry of (H2O)2 between a pair of Cor moleculesoptimized with the SCC-DFTB-3D method: (a) geometry at (dx, dy, dz)= (0.0, 0.0, 7.5) Å, (b) final optimized state at (dx, dy, dz) = (−0.4, −0.3,5.6) Å. The top Cor and the bottom Cor are shown with blue and blackwires, respectively.



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The geometries of the water trimer to hexamer between theCor pair at their energy minima are shown in Figure 6. Even if the

initial geometries are very different, the geometries of thenonplanar hexamers take on a few configurations like Figure 6eor Figure 6f at their energy minima, as long as they are confinedbetween the Cor pair. The configuration in Figure 6e is a fusedbitetragon (tt) in which 7 H-bonds keep the structure and theremaining 3 + 2 Hd’s point up and down. Each tetragon is notexactly a square but a rhomboid. Several different lateralorientations in tt configuration in the Cor plane were obtainedfrom initial nonplanar hexamer geometries with different Horientations. The energy difference among them is less than 0.5kcal/mol as long as upward and downward Hd’s are 3 + 2 or 2 + 3.Of 20 initial structures of nonplanar (book, bag, cage, prism)

water hexamers in various orientations on the Cor surface, 15structures including overlapped or symmetric ones wereoptimized into the tt configuration, three structures failed tostay inside the Cor pair, and two structures turned to the p3configuration as shown in Figure 6f. In the p3 configuration, 7 H-bonds keep the structure, and the remaining 3 + 2 Hd’s point upand down, as in the tt configuration. There should be astabilization effect in forming the pentagonal ring structure of theH-bonding network over forming the tetragonal ring structure,but the stabilization is likely to be canceled out by thedestabilization effect to form a triangular ring structure in theH-bonding network in which one of the H-bonding interactionsappears to be much weaker than others.The geometries and binding energies of (H2O)1−6 between the

Cor pair are in Table 3. Particularly interesting is a comparison ofthe binding energies of the water hexamers in differentconfigurations. The lowest energy structure of the water hexamerhas a tt configuration. However, the binding energy of the ringhexamer is only ∼0.3 kcal/mol higher than that of the lowestenergy structure in tt configuration. On the other hand, the ring

hexamer is more stable than the tt configuration when optimizedwith the PBE-D3 method. The structure in the p3 configurationis less stable by 1.6 kcal/mol than the one in the tt configurationat the SCC-DFTB-3D level and by 2.1 kcal/mol than the one inthe ring configuration at the scaled PBE-D3/TZVP level.

3.3. DBC/(H2O)1−6/DBC. Structures of (H2O)1−6 clustersbetween a pair of DBC molecules are not much different fromthose between the Cor pair except there is a slight difference inthe water dimer which is optimized into an “hHdd” geometry onthe central part of DBC at the SCC-DFTB-D3 level and an“hHud” geometry at the PBE-D3/TZVP level. The bindingenergies and the layer displacements are summarized in Table 4.The ring hexamer is 0.5 and 2.1 kcal/mol more stable than the tthexamer at the SCC-DFTB-3D and scaled PBE-D3/TZVP

Figure 6. Top views of water trimer (a), water tetramer (b), waterpentamer (c), water hexamer in hexagonal ring configuration (d), waterhexamer in tt configuration (e), and water hexamer in p3 configuration(f), which were optimized with the SCC-DFTB-D3 method. The topCor and the bottom Cor are shown with blue and black wires,respectively. The stacking displacement (dx, dy, dz) for each case isshown on top.

Table 3. Binding Energies (BEs, kcal/mol) of (H2O)1−6between the Cor Pair at the Layer Displacement (dx, dy, dz, Å),Optimized with the SCC-DFTB-3D Methoda

n geometry dx, dy, dz BE δBE

1 dd 0.0, 0.0, 5.5 6.0 0.0[0.0, 0.0, 6.0] [9.1(6.4)] [0.0, 0.0]

2 hHud[uHhd]

−0.4, −0.3, 5.6[0.7, −0.1, 6.3]

14.9[22.0(15.4)]

0.19[0.19(0.13)]

3 3 0.9, −1.4, 6.1[0.3, 0.4, 6.5]

27.5[40.3(28.2)]

0.21[0.15(0.11)]

4 t 0.0, −0.8, 6.2[0.0, 0.5, 6.6]

42.0[61.1(42.8)]

0.15[0.30(0.21)]

5 p −0.4, −0.5, 6.3[−0.4, 0.0, 6.5]

53.4[78.0(54.6)]

0.08[0.06(0.04)]

6 h 0.0, 0.0, 6.5 64.5 0.0[0.0, 0.0, 6.7] [94.2(65.9)] [0.0(0.0)]

6 tt 0.0, 0.0, 6.5[−0.3, −0.6, 6.8]

64.8[91.9(64.3)]

0.0[0.20(0.14)]

6 p3 0.4, 0.0, 6.4[0.2, −0.5, 6.6]

63.2[89.8(62.9)]

0.04[0.16(0.11)]

aAlso optimized with the PBE-D3/TZVP method whose values andscaled values (scale factor = 0.7) are in brackets. Also listed are theenergy differences (δBEs, kcal/mol) between (dx, dy, dz) and (0, 0, dz).

Table 4. Binding Energies (BEs, kcal/mol) of (H2O)1−6between the DBC Pair at the Layer Displacement (dx, dy, dz,Å), Optimized with the SCC-DFTB-3D Methoda

n geometry dx, dy, dz BE δBE

1 dd 0.0, −0.3, 4.9 12.2 0.01[0.0, 0.0, 5.8] [14.1(9.9)] [0.0(0.0)]

2 uHdd[hHud]

−0.1, 0.0, 5.4[0.1, 0.0, 6.0]

19.3[26.9(18.8)]

0.001[0.008(0.005)]

3 3 0.1, 0.0, 5.6[0.1, 0.0, 6.2]

32.7[45.6(31.9)]

0.001[0.02(0.02)]

4 t 0.0, 0.0, 5.8 47.1 0.0[−1.2, 0.0, 6.3] [66.3(46.4)] [0.43(0.30)]

5 p −0.1, 0.2, 5.8[−0.3, 0.0, 6.3]

59.5[84.3(59.0)]

0.02[0.01(0.008)]

6 h 0.0, −0.1, 5.8 70.9 0.09[0.0, 0.0, 6.4] [101.3(70.9)] [0.0(0.0)]

6 tt 0.1, 0.5, 5.8[0.0, 0.3, 6.5]

70.4[98.3(68.8)]

0.10[0.08(0.06)]

6 p3 0.0, 0.0, 5.9 69.5 0.0[−0.3, −0.1, 6.5] [96.5(67.6)] [0.03(0.02)]

aAlso optimized with the PBE-D3/TZVP method whose values andscaled values (scale factor = 0.7) are in brackets. Also listed are theenergy differences (δBEs, kcal/mol) between (dx, dy, dz) and (0, 0, dz)geometries.



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levels, respectively. Therefore, we conclude that the ring (h)structure is the most stable, followed by the tt structure for thewater hexamer.3.4. DBC/(H2O)10/DBC. Nine lowest energy structures of

(H2O)10 between a pair of DBCmolecules are shown in Figure 7.The binding energies and the layer displacements at energyminima are shown in Table 5. The geometry in hh configuration

was optimized from the bihexagonal initial geometry, and thegeometries in ttt×t-a and tt×tt configurations were optimizedfrom the initial geometries of the checkerboard pattern. Theother six geometries were optimized from the initial geometriesprovided by the simulated annealing method.As a whole, the geometry change from the initial to the

optimized one is found to be insignificant, which implies thatlateral movements of water molecules are small. The biggestdeviation from such a trend is found in the checkerboardconfigurations. One checkboard configuration ttt×t-b (L-shaped) as an initial geometry merged into ttt×t-a (T-shaped).The other checkboard configuration tttt (I-shaped) as a staringgeometry was not confined in the DBC pair.

The configuration change as water molecules are pressured bythe substrate pair may be related to unstable water moleculeswhich donate two H-bonds to keep the fused ring structure. Thiskind of water molecule lacks interaction with the substrate and islikely to trigger lateral movement of neighboring watermolecules. As all the (H2O)10 configurations have such unstablewater molecules, as many as the number of fused rings minusone, all their fused rings appear a little distorted from the regularones to some extent. The only exception is in the hhconfiguration where the number of unstable water molecule isone and therefore the bihexagon geometry is well-retained. Incontrast, the geometries in the checkerboard configuration havethree unstable water molecules, so a larger change from eachinitial geometry is induced.

3.5. Graphene/(H2O)10/Graphene. Nine lowest energygeometries of (H2O)10 clusters between a pair of graphenesheets, when optimized with the SCC-DFTB-3D method, areshown in Figure 8. Their binding energies and the layerdisplacements are in Table 6. Because of the larger substrate size,(H2O)10 clusters are compressed more, which brings slightinstability into water clusters. A few Hd’s do not point up ordown. This induces slight distortions in some ring geometries, sothat ring geometries deviate more from the regular onescompared to the case for a smaller DBC substrate. In comparingbinding energies of (H2O)10 in the graphene pair to those in theDBC pair, a few changes in their ordering are found. In bothcases, ttt×t-a and tt×tp are the two most stable configurationsfollowed by pt×p and tpp.

3.6. Graphene/(H2O)13/Graphene. The 11 lowest energygeometries of (H2O)13 clusters between a pair of graphenesheets, which were optimized with the SCC-DFTB-3D method,are shown in Figure 9. Their binding energies and the layerdisplacements are in Table 7. tt×ttt×p is the lowest energyconfiguration. However, five other configurations, tpp×t×t,ttp×ttt, pp3×tp, tt×tt×h, and ttt×tpt are almost isoenergeticwithin 1.1 kcal/mol. In fact, tt×ttt×p and ttt×tpt were optimizedfrom geometries in checkerboard configurations. In suchconfigurations, one of the unstable waters at a corner tetragonwas specially mobile and induced the rearrangement into apentagonal ring. Another checkerboard configuration tt×ttt×t isslightly deformed from the checkerboard pattern at the initialgeometry and turned into tt×ttt×t3, whose binding energy is 2.2kcal/mol less than that of tt×ttt×p. The trihexagonal

Figure 7. Low energy geometries of (H2O)10 clusters between a pair of DBCmolecules, optimized with the SCC-DFTB-3Dmethod. The top DBC andthe bottom DBC are shown with blue and black wires, respectively.

Table 5. Binding Energies (BEs, kcal/mol) of (H2O)10between the DBC Pair at the Layer Displacement (dx, dy, dz,Å), Optimized with the SCC-DFTB-3D Methoda

geometry dx, dy, dz BE δBE

tt×tp 0.0, 0.6, 6.2 [6.7] 119.4 [165.1(115.6)] 0.05ttt×t-a 0.0, −0.5, 6.1 [6.6] 119.4 [163.5(114.5)] 0.07pt×p 0.0, −0.3, 6.1 [6.6] 118.0 [163.9(114.7)] 0.04tpp 0.4, 0.9, 6.2 [6.7] 116.7 [165.4(115.8)] 0.19tht-b −1.6, −0.2, 6.3 [6.6] 116.1 [164.2(114.9)] 0.21hh 0.3, 0.9, 6.2 [6.6] 116.0 [166.1(116.3)] 0.41h×tp −0.3, −0.3, 6.1 [6.6] 115.2 [163.7(114.6)] 0.06tht-a −0.3, 0.3, 6.2 [6.7] 115.0 [162.8(114.0)] 0.03tt×ttb 0.6, −1.8, 6.2 [−] 113.1 [−] 0.86

aAlso optimized with the PBE-D3/TZVP method whose values andscaled values (scale factor = 0.7) are in brackets. Also listed are theenergy differences (δBEs, kcal/mol) between (dx, dy, dz) and (0, 0, dz).For the PBE-D3/TZVP method, the optimization along the x and ydisplacement was not done, and only the results for optimized dz arereported. bThe tt×tt configurations were not stable at the PBE-D3/TZVP level.



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configuration hh×h preserved the regular hexagon rings well, butits binding energy is not particularly large.3.7. Many-Body Interactions. Interaction energy of water

clusters (ΔEw) can be divided into many-body contributions,while the contribution of substrate is excluded. For example,ΔEwof a water tetramer is a sum of deformation energy (Edef) ofindividual monomers, and two-body (E(2)), three-body (E(3)),and four-body (E(4)) interaction energies. The exact formulationof these terms is found in the literature.43,47,48 Many-bodyinteraction energies of water tetramers extracted from thesubstrates of this study are summarized as an exemplary case inTable 8 (tables for the water dimer and trimer cases are inSupporting Information). This shows that the water−waterinteraction energies are hardly decreased by the presence ofsubstrates. Thus, the water structures intercalated inside bilayergraphene are likely determined by the nature of 2D water insteadof the substrate effect. Furthermore, the potential surface of thewater−graphene interaction is almost uniform (which does notdepend on the location of atomic sites of graphene at the sameseparation distance from the graphene surface); the water−graphene interaction does not play a role in governing theintercalated 2D water structure.The ΔEw values of water tetramer in the substrate states are

higher by 0.14−0.27 kcal/mol than that of the pristine state; here,destabilization is attributed from the 2-body and 3-body terms,while stabilization arises in the 4-body term. The deformationenergy is slightly higher in the intercalated state than on thesingle substrate surface.

4. DISCUSSIONInserting water into a dimer of a graphene-like molecule or adouble layer of graphene is an unfavorable process. For example,the interaction energy for Cor/H2O/Cor is −12.2 kcal/mol atthe minimum, and the corresponding Esub-sub is −2.5 kcal/mol.Sum of these energies is smaller in magnitude than theinteraction energy of the Cor dimer (−18.8 kcal/mol). Thisimplies that forming Cor/H2O/Cor from the Cor dimer is anunfavorable process. This situation would be unchanged when aDBC dimer or a bilayer graphene is a substrate.Therefore, water clusters between a pair of Cor molecules,

DBC molecules, or graphene sheets are in a metastable statewhich can be formed via a narrow channel of preparation. Theymay be formed by first forming an adsorbed state on the surfaceof bottom substrate, followed by covering with the top substrate.In this respect, the method in this work to study the geometriesof (H2O)1−6 clusters at gradually reducing interlayer distancesseems sensible. The geometry transformation of (H2O)1−6described in this work must be close to a real scenario. In thecase of (H2O)2−5, the small size water cluster sits on the substratesurface with the internal geometry close to that in the isolatedstate. Then, as the second substrate approaches from the top, afew water molecules are pulled toward the top substrate when theinterlayer distance is in the range 7−9 Å, followed by beingsettled down into a 2D geometry (defined as positions of Oatoms) at a shorter interlayer distance. Once the 2D geometry isformed, the pointing directions of Hd atoms are restrained uponfurther changing the interlayer displacement.In the case of the water hexamer, a distribution of different

structures adsorbed on the substrate surface is possible due totheir similar energies. They should undergo rather a big geometrychange at the interlayer distance of about 7.5−8.5 Å; we will callthis situation the “transient state”. The transient state determinesthe geometry of water cluster when it is settled down at shorterinterlayer distance. Only when the settled geometry is close to ahexagonal ring the final geometry is a hexagonal ring. Othergeometries result in tt or p3 configurations, with the former onebeing dominant.The geometries of nonplanar (H2O)10 and (H2O)13 were not

able to be searched from the adsorbed geometries on a singlesubstrate surface. On the basis of the results from smaller sizedwater clusters, a nonplanar transient state would be a precursorfor the settled configuration. As the configuration is little changedwhen the interlayer distance is less than 7 Å, the settledconfiguration becomes the final configuration.

Figure 8. Low energy configurations of (H2O)10 clusters between a pair of graphene sheets, optimized with the SCC-DFTB-3D method. The top andbottom graphene sheets are shown with blue and black wires, respectively. Only the part of the graphene substrate around each water cluster is shown.

Table 6. Binding Energies (BEs, kcal/mol) of (H2O)10between the Graphene Pair at the Layer Displacement (dx, dy,dz, Å), Optimized with the SCC-DFTB-3D Methoda


ttt×t-a 0.2, −0.7, 5.7 120.1 0.2tt×tp 0.1, −0.3, 5.8 119.8 0.1pt×p −0.2, 0.0, 5.7 119.2 0.02tpp −0.1, −0.2, 5.8 118.5 0.3hh 0.0, 0.0, 5.7 118.5 0.0tt×tt3 0.0, 0.1, 5.6 117.3 0.01tht-b −0.1, 0.0, 5.8 117.0 0.1h×tp −0.1, 0.1, 5.7 116.5 0.02tht-a 0.5, 0.0, 5.7 116.6 0.05

aAlso listed are the energy differences (δBEs, kcal/mol) of geometriesbetween (dx, dy, dz) and (0, 0, dz).



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As the size of water clusters becomes larger, the transient stategeometry may take a less restricted shape, which would result instatistical weights in the compositions of fused ring geometries inthe settled configuration. By a count of all the configurations in(H2O)10 and (H2O)13, the tetragonal ring is most frequent,followed by the pentagon, while the hexagonal ring is very rare.As the size of water clusters becomes larger, the portion oftetragonal rings in the settled state tends to increase, and that ofhexagonal rings decreases. The large portion of the tetragonalrings would help form a rigid structure.Though graphene has the hexagonal structure, the water

clusters adsorbed on graphene do not show high adsorptionenergies. Furthermore, the potential energy surface of a watermolecule interacting with graphene is nearly flat, and so the

hexagonal rings of graphene cannot play a significant role indetermining the adsorbed water structures. On the other hand,the strong water−water binding energies determine the adsorbedwater cluster structures as the 3D network needs to be changedto a 2D network on/inside graphene layers. Thus, this structuralchange from a hexagonal (in 3D)49,50 to a tetragonal (in 2D)network arises mainly from the inherent 2D water nature. It isinteresting to compare the above case with small water clusters infree space, where the geometrical factor is important in formingwater networks because the water networks inherit from thenature of water−water interaction itself. For the water hexamer,the cage and book structures form tetragonal networks, while theprism structure is composed of tetragonal and triangularnetworks, the bag structure is composed of pentagonal andtetragonal networks, and the ring structure has a hexagonalnetwork.44 On the other hand, the water 20-mer cluster51 in freespace or the magic dodecahedral water 20-mer cluster52−55

encapsulating a small cation such as Cs+ or NH4+ favors the

pentagonal networks due to the geometric curvature.

5. CONCLUSION

Geometries of water clusters, (H2O)n (n = 1−6, 10, 13), formedbetween a pair of graphene sheets or between graphene-likemolecules (coronene and dodecabenzocoronene), were studiedwith the SCC-DFTB method expanded into the third order andsupplemented with the Slater−Kirkwood dispersion term. Thismethod describes both H-bonding and H−π/π−π interactionaccurately in a comparison with reference data reported frommost accurate ab initio studies. In contrast, conventional DFTcalculations seriously underestimate the H−π/π−π interaction,while DFT-D calculations seriously overestimate the H-bonding.We also reported the DFT-D results (scaled PBE-D3/TZVPbinding energies) for the check-up of the SCC-DFTB results.

Figure 9. Low energy configurations of (H2O)13 clusters between a pair of graphene sheets, optimized with the SCC-DFTB-3D method.

Table 7. Binding Energies (BEs, kcal/mol) of (H2O)13between the Graphene Pair at the Layer Displacement (dx, dy,dz, Å), Optimized with the SCC-DFTB-3D Methoda


tt×ttt×p 0.0, −0.1, 5.8 151.9 0.01tpp×t×t 0.0, 0.0, 5.9 151.7 0.0ttp×ttt −0.3, −0.3, 5.8 151.6 0.1pp3×tp −0.3, 0.3, 5.8 151.5 0.1tt×tt×h 0.1, 0.1, 5.8 150.9 0.02ttt×tpt −0.2, 0.0, 5.9 150.8 0.02tpp×p3 0.1, −0.1, 5.8 150.5 0.02tt×ttt×t 0.4, 0.0, 5.8 149.7 0.02hh×h 0.1, 0.2, 5.9 148.5 0.09p3t×pp 0.1, −0.7, 5.8 148.4 0.4tt×ttt×t3 0.0, 0.0, 5.8 148.3 0.0

aAlso listed are the energy differences (δBEs, kcal/mol) between (dx,dy, dz) and (0, 0, dz).



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Water clusters between a pair of the graphene-like moleculesor graphene sheets are in a metastable state since their bindingenergy is lower than the sum of binding energies of the substratedimer and the water molecules. The metastable intercalated statemust be formed through a narrow channel from a precursor state.The most probable precursor in experimental situations wouldbe an adsorbed state on a substrate surface. The formationchannel involves a transient state at the interlayer distancebetween 7 and 9 Å, where a rather big geometry change from theprecursor state is induced.When the size of water cluster is as small as n = 1−5, the

geometry change in the transient state is small. Therefore, thefinal geometries of the small sized water clusters are not muchdifferent from that of the adsorbed state on the substrate surface.This trend also holds when the ring configuration of the waterhexamer is a planar ring. However, for nonplanar water clustersfor n≥ 6, the structure of the transient state is very different fromthat of the precursor state. The water hexamer in a bitetragonconfiguration, whose energy is nearly isoenergetic to that of thering hexamer, is formed in such a way.In (H2O)10 and (H2O)13 clusters, various fused geometries

composed of triangle, tetragon, pentagon, and hexagon arecompeting. The tetragon is the most frequent geometry followedby the pentagon, while the hexagon is much less frequent. Whenthe size of water clusters gets larger, the transient state becomesmore uncharacteristic, and the distribution of fused ringgeometries would be determined statistically. Tetragonstructures are dominating in the configurations of much largersized water clusters. This result is consistent with the recentplanar tetragonal ice structure observed inside a graphene bilayer,in contrast to the hexagonal structure of the bulk ice.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.jpcc.6b06076.

Details of structures and energies of (H2O)1−6 clustersbetween a pair of coronenes during optimizations, andmany-body interactions of water clusters extracted fromthe substrates of this study (PDF)

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected]. Phone: +82-31-290-7069 (S.K.K.).

*E-mail: [email protected]. Phone: +82-52-217-5410 (K.S.K.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This work was supported by KISTI (KSC-2015-C3-059, KSC-2015-C3-061, KSC-2015-C1-046) and NRF (2010-0025285).

■ REFERENCES(1) Georgakilas, V.; Otyepka, M.; Bourlinos, A. B.; Chandra, V.; Kim,N.; Kemp, K. C.; Hobza, P.; Zboril, R.; Kim, K. S. Functionalization ofGraphene: Covalent and Non-Covalent Approaches, Derivatives andApplication. Chem. Rev. 2012, 112, 6156−6214.(2) Kim, N.; Kim, K. S.; Jung, N.; Brus, L.; Kim, P. Synthesis andElectrical Characterization of Magnetic Bilayer Graphene Intercalate.Nano Lett. 2011, 11, 860−865.(3) Algara-Siller, G.; Lehtinen, O.; Wang, F. C.; Nair, R. R.; Kaiser, U.;Wu, H. A.; Geim, A. K.; Grigorieva, I. V. Square Ice in GrapheneNanocapillaries. Nature 2015, 519, 443−445.(4) Koga, K.; Gao, G. T.; Tanaka, H.; Zeng, X. C. Formation ofOrdered Ice Nanotubes Inside Carbon Nanotubes. Nature 2001, 412,802−805.(5) Maniwa, Y.; Kataura, H.; Abe, M.; Udaka, A.; Suzuki, S.; Achiba, Y.;Kira, H.; Matsuda, K.; Kadowaki, H.; Okabe, Y. Ordered Water insideCarbon Nanotubes: Formation of Pentagonal to Octagonal Ice-nanotubes. Chem. Phys. Lett. 2005, 401, 534−538.(6) Zangi, R.; Mark, A. E. Monolayer Ice. Phys. Rev. Lett. 2003, 91,025502.(7) Cortes, E. R.; Solís, L. F. M.; Arellano, J. S. Interaction of a WaterMolecule with a Graphene Layer. Rev. Mex. Fisica S 2013, 59, 118−125.(8) Sanfelix, P. C.; Holloway, S.; Kolasinski, K. W.; Darling, G. R. TheStructure of Water on the (0001) Surface of Graphite. Surf. Sci. 2003,532−535, 166−172.(9) Karapetian, K.; Jordan, K. D. Properties of Water Clusters on aGraphite Sheet. In Water in Confined Geometries; Devin, J. P., Buch, V.,Eds.; Springer-Verlag: New York, 2003; Chapter 6.(10) Leenaerts, O.; Partoens, B.; Peeters, F. M. Water on Graphene:Hydrophobicity and Dipole Moment using Density Functional Theory.Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 235440.(11) Feller, D.; Jordan, K. D. Estimating the Strength of the Water/Single-Layer Graphite Interaction. J. Phys. Chem. A 2000, 104, 9971−9975.(12) Sudiarta, I. W.; Geldart, D. J. W. Interaction Energy of a WaterMolecule with a Single-Layer Graphitic Surface Modeled by Hydrogen-and Fluorine-Terminated Clusters. J. Phys. Chem. A 2006, 110, 10501−10506.

Table 8. Many-Body Interaction Energies (in kcal/mol) of Water Tetramers with Various Substrates, Calculated with the SCC-DFTB-3D Method

substrate ΔEw Edef E(2) E(3) E(4)

pristine −27.47 [−27.37 (−27.60)]a 1.51 −22.52 {−18.56}b −5.91 {−6.23}b −0.54 {−0.54}b

Cor −27.25 1.59 −22.45 −5.85 −0.54DBC −27.22 1.53 −22.39 −5.83 −0.53graphene −27.34 1.58 −22.47 −5.70 −0.74(Cor)2 −27.20 1.72 −22.48 −5.88 −0.56(DBC)2 −27.30 1.62 −22.49 −5.88 −0.64(graphene)2 −27.24 1.64 −22.46 −5.81 −0.61

aCCSD(T) (and MP2 in parentheses) complete basis set limit value based on the extrapolation scheme using aug-cc-pVTZ and aug-cc-pVQZ (andaug-cc-pVQZ and aug-cc-pV5Z), respectively. bMP2/aug-cc-pVDZ results for n-body interactions (ref 48). The MP2/aug-cc-pVDZ total interactionenergy is −25.33 kcal/mol which is underestimated by over 2 kcal/mol. This MP2 2-body interaction is underestimated because the BSSE correctedMP2/aug-cc-pVDZ interaction energy for the water dimer is underestimated by 0.58 kcal/mol compared with the CCSD(T)/CBS value. This leadsto the underestimation of as much as ∼2.3 kcal/mol for the 2-body interaction for the water tetramer. All these results based on the total interactionenergy and many-body interactions clearly show the remarkable success of the SCC-DFTB-3D method in very close agreement with the CCSD(T)/CBS values.



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two-dimensional icy water clusters between a pair of graphene- like molecules...

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