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Materials Today Communications

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Effect of the bond polarity on interlayer interactions in B–C–N layeredmaterials: A dispersion-corrected density functional study

Nan Liua, Xiaoguang Luob, Xiaohong Yuanc, Kun Luoa,d, Julong Hea, Dongli Yua,*,Yuanchun Zhaoa,*a State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, 066004, ChinabDepartment of Electronics, College of Electronic Information and Optical Engineering, Nankai University, Tianjin, 300071, Chinac Center for High Pressure Science and Technology Advanced Research, Beijing, 100094, ChinadHebei Key Laboratory of Microstructural Material Physics, School of Science, Yanshan University, Qinhuangdao, 066004, China

A R T I C L E I N F O

Keywords:B–C–N layered materialsDensity functional theoryDispersion correctionsBond polarityInterlayer interactions

A B S T R A C T

The interlayer interactions in nonpolar graphite and other BeCeN layered materials involving polar covalentbonds (h-BN, g-C3N4, graphite-like BC3 and BC2N) have been investigated by dispersion-corrected densityfunctional calculations. Lattice parameters, bulk moduli and interlayer binding energies of these layered ma-terials have been calculated using different dispersion correction schemes for comparison. Charge density dif-ference plots have also been presented to elucidate the charge transfer behaviors along the nonpolar/polarcovalent bonds as well as in the interlayer region. At first, graphite and h-BN were examined as benchmarks; theformer contains planar graphene layers regardless of the interlayer binding, while the monolayers in the latterexhibit an asymmetric charge distribution along the BeN polar bonds, leading to a slightly puckered featureinduced by the interlayer interaction. Similar geometric deviations have also been observed in other layeredstructures involving CeN and/or BeC polar bonds, but with distinct characteristics directly related to theirspecific interlayer stacking situations. By contrast, all of the isolated monolayers free from interlayer bindingshow a pristine planar feature in despite of the polar covalent bonds involved. Our theoretical findings furtheraddress the necessity of considering the electron-density variations induced by specific bonding environments inpolar BeCeN layered materials, which can be properly described by the Tkatchenko-Scheffler correction.

1. Introduction

Boron (B), carbon (C), and nitrogen (N) locate at the neighboringpositions in the second row of the periodic table of elements. Their sp2-hybridized bonds inherently construct well-defined two-dimensional(2D) frameworks, constituting an important family among the layeredmaterials [1–3]. BeCeN layered materials involve a rich diversity ofbonding states, including intralayer nonpolar/polar covalent bonds andweak interlayer van der Waals (vdW) interactions. Their electronicstructures can be effectively tailored by designing binary or trinarysystems with different stoichiometries [4]. As a consequence, BeCeNlayered materials exhibit impressive mechanical, optical, electrical, andelectrochemical properties, which make them playing the central rolein a wide range of applications, including solid-state lubrication, energystorage, photo/electrocatalysis, microelectronics, and biomedicine[5–9]. They are also the promising precursors for the synthesis of cor-responding superhard phases by high-pressure and high-temperature

technique [10,11].Among the BeCeN layered materials, both graphite and hexagonal

boron nitride (h-BN) have been extensively investigated; however, thesynthesis of other bulk BeCeN layered materials are still under ex-ploration [12–15]. The strong covalent bonding in a layered system canbe well described by density functional theory (DFT) [16,17], however,it failed to represent the weak interlayer vdW interactions within thelocal or semilocal exchange-correlation (XC) functionals [18,19].Random phase approximation (RPA) [20,21] and quantum Monte Carlo(QMC) calculations [22,23] have achieved success in describing thelong-range dispersive forces within chemical accuracy, however, bothof them require very high computational cost and are unsuitable forlarge-scale calculations. Consequently, different semi-empirical or evennonempirical methods have been proposed to correct the missing dis-persion terms from the DFT energies with a reasonable compromisebetween the precision and the computational cost [24–28]. These so-called dispersion-corrected DFT (DFT-D) approaches have produced

https://doi.org/10.1016/j.mtcomm.2019.100781Received 26 September 2019; Received in revised form 17 November 2019; Accepted 17 November 2019

⁎ Corresponding authors.E-mail addresses: ydl@ysu.edu.cn (D. Yu), yzhao56@ysu.edu.cn (Y. Zhao).

Materials Today Communications 22 (2020) 100781

Available online 21 November 20192352-4928/ © 2019 Elsevier Ltd. All rights reserved.

T

improved results for predicting the total energies, equilibrium latticeconstants, as well as interlayer binding energies of various layeredperiodic systems.

Note that B, C, and N possess different electronegativities, and thusthe bonding states in various BeCeN layered configurations exhibitvery different characteristics. For example, the homonuclear sp2 CeCbonds in graphene are nonpolar, and the unpaired pz electrons aresufficiently delocalized to form a collective π system with the semi-metallic feature [29]; the πz band further splits in graphite originatedfrom the interlayer interaction, endowing it an excellent conductivity[30]. Nevertheless, the BeN bonds in h-BN are highly polar, thus the πelectrons tend to localize around the N atoms, making the material aninsulator [31]. Very interestingly, these two materials possess almostsame interlayer distances (d0) and interlayer binding energies (Ebind).Hod [32] reported that the interlayer electrostatic interactions in h-BNcould be elegantly cancelled out by the kinetic energy term, and theresidual potential is responsible to set the AA’ stacking mode as theoptimal configuration but has a marginal effect on the interlayerbinding. The Tkatchenko-Scheffler (TS) correction predicts a nearlyidentical d0 of ∼3.33 Å and very similar Ebind for graphite and h-BN[32,33], however, other DFT-D approaches provide distinct d0 and Ebindvalues that in contrast to the experimental data [34]. Furthermore,other BeCeN layered materials may involve polar BeC and/or CeNcovalent bonds, both of them should have different features from theBeN bond. Are these materials expected to have similar d0 and Ebindvalues to those of graphite and h-BN? Does the bond polarity have anyeffect on the interlayer interactions in various BeCeN layered mate-rials?

To answer these questions, we chose five representative BeCeNlayered materials, including graphite and h-BN, to perform DFT-D cal-culations. Dispersion correction schemes based on pairwise interatomicpotentials proposed by Ortmann et al. (OBS) [25], Grimme (D2) [26],and Tkatchenko et al. (TS) [27] were employed to calculate theirstructural and energetic properties for a comparative study. We furthercalculated the expected geometric deviations between the covalentlybonded atom pairs while perpendicular to the 2D layers, which werefound to be very small and closely related to both of the bond polarityand the interlayer interactions. Although some advanced dispersioncorrections have been developed recently, such as the widely usedGrimme-D3 [28] and the TS correction with self-consistent screening(TS+ SCS) [35], the derived dispersion coefficients are too sophisti-cated to conduct an in-depth comparison. Therefore, we only present abrief discussion based on the previously reported D3/TS+ SCS resultsfor graphite and h-BN, and no substantial improvements have beenachieved in comparison to those calculated by D2 and TS, respectively;because the dispersive terms can be well parameterized by interatomicpair potentials in the layered systems only containing light elements ofB, C, and N.

2. Methodology

In this section, we start with a brief introduction to address thedifferences of the employed DFT-D approaches, and then present thecomputational details applied in this work.

2.1. Dispersion correction schemes based on pairwise interatomic potentials

In general, the DFT-D total energy (EDFT-D) is expressed as:

= +− −E E E ,D DFTDFT KS disp (1)

where EKS-DFT is the standard Kohn-Sham DFT energy, and Edisp is thedispersion terms calculated by different correction schemes. In thiswork, the selected dispersion corrections only consider the pairwiseinteratomic interactions induced by the quantum fluctuations of theelectron density (n=6), and thus the general form of Edisp is:

∑= −≠

E sCR

f R12

( ),dispA B

AB

AB AB6

6dmp

(2)

where C AB6 is the dispersion coefficient for atom pair AB, RAB is their

internuclear distance, s is a global scaling factor related to the XCfunctional to be corrected, and fdmp is a damping function to scale thesingularity at small RAB as well as the double-counting effects of elec-tron correlations at intermediate distances.

In the OBS scheme [25], the C AB6 coefficients were derived from

London’s original description of the dispersion energy, in which theexperimental data of atomic ionization potentials (I) and dipole polar-izabilities (α) were directly used. The damping function has the form of

= − − +f e1 ,dmpλ R r r[ /( )]AB

A B ncov cov (3)

where r Acov and r B

cov are the covalent radii of the interacting two atoms,and the two constants, n and λ, were empirically determined to be 8 and7.5×10−4 for PW91, respectively.

In Grimme’s D2 scheme [26], the C AB6 coefficients were represented

as the geometric mean of the specific values of the considered atompair:

=C C C ,AB A B6 6 6 (4)

where =C NI α0.05ApA A

6 , the atomic ionization potentials Ip and staticdipole polarizabilities α were obtained from DFT calculations with N =10 for elements in the second raw of the periodic table. The proposeddamping function is in the form of

=+ − −

fe

11

,dmp d R R( / 1)ABAB

0 (5)

where R AB0 is the sum of the atomic vdW radii, and the two constants of

d and s are 20 and 0.75 for PBE, respectively.In the TS scheme [27], the basic expression is almost the same as in

Grimme’s D2, while the C AB6 coefficients and vdW radii R AB

0 were de-rived from the ground-state electron density of a molecule or solid andthe reference data of the free atoms. The C AB

6 coefficients have the formof

=⎛⎝

+ ⎞⎠

CC C

C C

2,AB

AA BB

αα

AA αα

BB6

6 6

6 6B

A

A

B0

0

0

0 (6)

where =C V V C( / )AA A A AA free6 eff free

26

, , the static polarizabilities=α V V α( / )A A A A

0 eff free free, and V V/A Aeff free is the ratio between the effective

atomic volume determined from the Hirshfeld partitioning of the cal-culated all-electron density according to the specific bonding environ-ment and the volume of the noninteracting free atom. The dampingfunction has the form of

=+ − −

fe

11

,d R sRdamp ( / 1)AB

AB0 (7)

where = +R R RAB A B0 0 0 , and the atomic vdW radius

=R V V R( / )A A A A0 eff free

1/3free. The parameters of d and s were determined to

be 20 and 0.94 for PBE, respectively.

2.2. Computational details

DFT calculations were performed by using the Cambridge series oftotal-energy package (CASTEP) code [36]. The ultrasoft pseudopoten-tial [37] was used to describe the interaction of valence electrons. TheXC potentials were considered by the generalized gradient approx-imation (GGA) functionals of Perdew and Wang (PW91) [38] orPerdew-Bruke-Ernzerhof (PBE) [39] without or with vdW corrections,in which the OBS method was employed to correct PW91, and the D2and TS schemes were applied for PBE. Results calculated by localdensity approximation (LDA) functional [40] were also presented forreferences. After a series of convergence tests, the plan-wave cutoffenergy was set to 520 eV, and the first Brillouin zone was sampled using

N. Liu, et al. Materials Today Communications 22 (2020) 100781

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the Monkhorst-Pack grid [41] with a k-spacing of 2π × 0.04 Å−1 for allthe structures. The Pulay density mixing scheme [42] was employed forthe energy minimization process. All the atomic positions and latticeparameters were fully relaxed by using the BFGS algorithm [43], duringwhich the convergence threshold was set to 5×10-6 eV/atom for en-ergy, 0.01 eV/Å for maximum residual force, and 5×10-4 Å for max-imum displacement.

The interlayer binding energies of the selected B–C–N layered ma-terials were calculated by the equation [44]:

=−

EE nE

N,bind

tot layer

(8)

where Etot is the total energy obtained by DFT(-D) calculations, n is thelayer number (for all the structures in this study, n=2) and N is thetotal atom number in the unit cell, and the energy of an isolatedmonolayer (Elayer) was calculated using corresponding functionals byputting the monolayer into the middle of a unit cell with the constantc=20Å.

3. Results and discussion

The equilibrium lattice parameters, bulk moduli (B0), and interlayerbinding energies (Ebind) of the selected BeCeN layered materials werecalculated by using different DFT-D approaches, and the obtained re-sults have been discussed by comparing the determined C6 coefficientsof the applied dispersion corrections. Additional calculations werecarried out by using the optB88-vdW functional [45] at the vdW-DFlevel for reference, and the results have been summarized in Table S1.To investigate the interlayer charge transfer behaviors in these non-polar/polar layered systems, charge density difference contours havealso been plotted for comparison. Subsequently, we have calculated therelative geometric deviations between the covalently bonded atomsalong the interlayer direction, which intrinsically demonstrates the ef-fect of bond polarity on the interlayer interactions in the selectedBeCeN layered materials.

We first took graphite and h-BN as benchmarks, the reported D3/TS+ SCS results and experimental data have also been included fordiscussion. Then, the investigation has been extended to other re-presentative B–C–N layered systems: g-C3N4, graphite-like BC3 andBC2N.

3.1. Graphite and h-BN

Graphite with the AB stacking mode and h-BN with the AA’ modehave been chosen for DFT-D calculations, which are known to be theirground-state phases [32], respectively. Both of the unit cells share asame space group of P63/mmc (No. 194). In the former the graphenelayers are shifted with respect to each other, and half of the carbonatoms in one layer locate at the hexagonal centers of the other; while inthe latter the BN monolayers are geometrically overlapped, but with thepositively charged B atoms in one layer residing on the top of the ne-gatively charged N atoms in the adjacent layers.

3.1.1. Lattice parametersThe calculated and experimental equilibrium lattice parameters of

graphite and h-BN are summarized in Table 1. The obtained results arein good agreement with that reported in previous works[30,32–34,52–55]. Compared with the experimental data [46,50], bothPW91 and PBE reproduce accurate parameters a for graphite, while forh-BN the calculated values exhibit a small relative error within +0.28%. As expected, the DFT-D approaches generate slightly shrunk values.Both of PW91-OBS and PBE-TS provide very similar parameter a with arelative error of −0.32 % for graphite while an excellent agreementwith the experimental data of h-BN. The D2 correction to PBE is rela-tively gentle for covalent bonding, and thus the obtained relative errorsare −0.16 % for graphite and +0.16 % for h-BN, respectively.

As for the lattice parameter c, the DFT-D approaches provide sub-stantial improvements over the corresponding DFT results. PBE-TSpredicts very reasonable c values, and the relative errors with respect tothe experimental data are only −0.52 % for graphite and +0.20 % forh-BN, respectively. PW91-OBS shows a moderate performance with therelative errors of −0.66 % for graphite and −2.12 % for h-BN.However, PBE-D2 overestimates the interlayer interactions and therelative errors are found to be−4.28 % for graphite and−7.42 % for h-BN, respectively.

Note that B, C, and N are all light elements. Even by simply con-sidering the interatomic dipole-dipole potentials of C6R−6, the involvedfactors can be well parameterized to provide reasonable estimates onthe equilibrium lattice parameters, especially for PBE-TS. The reportedresults based on D3 and TS+ SCS corrections [30,33,34] are also listedin Table 1, both of them are fairly good, but have no significant im-provements compared with that calculated by the D2 and TS schemes.The D3 version amends the interlayer overbinding tendency of D2, andthe calculated parameters c show positive relative errors of +3.85 %for graphite and +3.20 % for h-BN, respectively.

3.1.2. Bulk modulus and interlayer binding energyThe key energetic properties of B0 and Ebind have also been calcu-

lated and compared. Since no experimental Ebind is available for h-BN,the theoretical value of 39meV/atom obtained by the high-level RPAcalculation [56] is taken as the reference.

DFT calculations based on PW91 and PBE predict almost no inter-layer binding, and thus yield extremely small B0 and Ebind values. In theOBS scheme, the damping function was directly parameterized basedon graphite, hence the computed B0, representing the equilibriumcurvature of the total energy dependent on the volume, are in goodagreement with the experimental data. However, the C6 coefficientswere derived from the original London’s formula with a tendency tooverestimate the vdW interactions, and thus the calculated Ebind are2.06 and 2.57 times larger than the reference values of graphite and h-BN, respectively.

PBE-D2 predicts a reasonable B0 of 40.9 GPa for graphite, but for h-BN the calculated value shows a large relative error of +54.32 % to theexperimental one. Interestingly, PBE-TS yields diametrical results: thecomputed B0 of graphite is much larger than that by PBE-D2 and theexperimental data, while the resulted relative error for h-BN is only+2.97 %. We suggest this contrary on B0 values could be attributed to

Table 1Bulk properties of graphite and h-BN: equilibrium lattice constants, bulkmodulus B0, and interlayer binding energy Ebind calculated using different ap-proaches as well as the experimental data.

Layeredmaterial

Approach a (Å) c (Å) B0 (GPa) −Ebind(meV/atom)

Refs.

Graphite LDA 2.439 6.630 28.7 26.54 This workPW91 2.461 9.581 0.6 3.01 This workPBE 2.462 8.864 0.5 2.20 This workPW91-OBS 2.454 6.663 39.5 90.58 This workPBE-D2 2.458 6.420 40.9 59.72 This workPBE-TS 2.454 6.672 57.7 85.07 This workPBE-D3 2.464 6.965 23.8 47.30 [30]PBE-TS+ SCS 2.461 6.633 40.5 53.76 [30]EXPERIMENT 2.462 6.707 34−42 44 [46,47,48,49]

h-BN LDA 2.485 6.483 27.4 28.11 This workPW91 2.509 9.191 1.0 2.75 This workPBE 2.510 8.497 1.6 2.13 This workPW91-OBS 2.502 6.520 37.0 100.14 This workPBE-D2 2.507 6.167 57.1 78.77 This workPBE-TS 2.503 6.674 38.1 87.33 This workPBE-D3 6.796 48.31 [34]PBE-TS+ SCS 2.50 6.67 34 73 [33]Experiment 2.503 6.661 37 [50,51]

N. Liu, et al. Materials Today Communications 22 (2020) 100781

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the nonpolar/polar bonding environments in graphite and h-BN, whichcan be properly described by the C6 coefficients determined in the TSscheme. In the D2 scheme, the ratio of C C/CC BN

6 6 was found to be 0.89[26], while that in the TS scheme was 1.02 [32]. Meanwhile, both theD2 and TS corrections to PBE still overestimate the interlayer bindingenergies of graphite and h-BN, but to some extent better than PW91-OBS. Since the TS scheme gives similar C6 coefficients in graphite and h-BN, it yields very close Ebind values for these two materials [32,33], asshow in Table 1.

Compared to D2, the D3 scheme covers all the chemically relevantelements (Z=1–94) and provides a greatly improved description formetallic and heavier elements but similar results for the light ones suchas B, C, and N [28]. The calculated Ebind of graphite agrees well with theexperimental value, while the B0 becomes too small. For h-BN, thepredicted Ebind still exhibits a large relative error of +23.87 % to theRPA reference data.

Compared to the TS scheme, the TS+ SCS version takes the self-consistent screening effect into account [35], which produces improvedB0 and Ebind for graphite. However, this additional electrodynamic re-sponse contribution seems to be less effective for the C6 coefficients inh-BN, probably due to the polarity of the heteronuclear BeN bond. As aresult, the computed B0 and Ebind of h-BN are decreased by 10.76 % and16.41 % with respect to TS, much smaller than those in graphite de-creased by 29.81 % for B0 and 36.80 % for Ebind, respectively. For h-BN,the B0 calculated by PBE-TS+ SCS shows a relative error of−8.11 % tothe experimental value, and the obtained Ebind is still 1.87 times largerthan the RPA reference data.

3.1.3. Bond polarity and interlayer bindingThe interlayer binding plays a crucial role in bulk layered materials,

which could be very different between nonpolar and polar systems. Thecharge transfer behaviors in graphite and h-BN have been investigatedby plotting the charge density difference contours along two adjacentlayers based on the PBE-TS results. As shown in the left panel of Fig. 1,the C− C bonds in graphite show a nonpolar feature, and the corre-sponding contours are symmetrically distributed between the bonded Catoms. By contrast, the charge accumulation along the polar B−Nbonds in h-BN exhibits a highly asymmetric distribution: the contourssurrounding B atoms correspond to a pronounced electron loss, cou-pling with the negatively charged regions surrounding N centers [57].As indicated by the arrows between the two panels, the polarity ofB−N bond promotes the charge depletion surrounding B centers ex-tending toward the interlayer region, which is very different from the

nonpolar case in graphite. The AA’ stacking mode offers an appropriateinterlayer stacking between the oppositely charged B and N atoms, andthe extended contours are well complementary for this optimal inter-layer binding. It should be noted that other functionals also providedalmost same charge transfer behaviors no matter without or with vdWcorrections, indicating that the observed interlayer charge-transfer ex-tension in h-BN is intrinsically related to its bond polarity.

The oppositely charged atomic centers in B−N bonds couplingwith the interlayer interaction may induce a small geometric deviation,which makes the BN monolayers in h-BN slightly puckered. Therefore,we further performed structural optimization by using different ap-proaches for both graphite and h-BN, and their high crystallographicsymmetry was cancelled (i.e., to make P1) for a full relaxation. Notethat for DFT calculations based on GGA-type functionals the latticeparameters c were fixed at their experimental values. The relativegeometric deviation (DAB) between covalently bonded atoms A and Balong c axis is defined as:

= × −D c cd

100 | | %,ABA B

0 (9)

where d0 is the equilibrium interlayer distance (for PW91 and PBE, d0= dexp), cA and cB are the z coordinates of the corresponding bondedatoms, respectively. As shown in Fig. 2, the calculated DCC in graphite iszero for all the applied functionals, indicating that the interlayerbinding indeed has no influence on the planar nature of graphenelayers. Nevertheless, even DFT calculations can yield very small DBN inh-BN, and the corresponding DFT-D approaches generate notably in-creased values. The C6 coefficients in D2 were derived from DFT cal-culations, and thus the calculated DBN is much larger than that by themore empirical OBS scheme. In the TS scheme, however, the C6 coef-ficients strongly depend on the specific bonding environments, whichfurther enlarge the corresponding DBN. In addition, we have calculatedthe DBN in an isolated BN monolayer, which was found to be zero for allthe employed functionals.

The last but not the least, the PBE-TS functional predicts very si-milar d0 and Ebind for graphite and h-BN that in line with the experi-mental data (see Table 1). In this scheme, the C BB

6 (C NN6 ) coefficient is

larger (smaller) than C CC6 , and the determined C BN

6 is opportunely“balanced” thus very similar to C CC

6 [27,32]. This charge-distributioncomplementation between the interlayer B and N atoms, with respect tothe isoelectronic C− C system, should be the secret responsible for thesimilarity of interlayer interactions in graphite and h-BN. However, theinterlayer binding in other BeCeN layered materials involving BeC

Fig. 1. Charge density difference plots of graphite and h-BN along the (110) plane calculated by PBE-TS. The color scale is in eV/Å3.

N. Liu, et al. Materials Today Communications 22 (2020) 100781

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and/or CeN polar bonds could be different; therefore, in the next sec-tion we extend our investigation to other three representative BeCeNlayered structures.

3.2. g-C3N4, graphite-like BC3 and BC2N

Crystal structures of the selected B–C–N layered structures areshown in Fig. 3. The well-known g-C3N4 structure [58] has a hexagonalunit cell with P m6 2 symmetry (No. 187). Graphite-like BC3 with the ABstacking mode is more stable than its AA stacking counterpart [59], abig orthorhombic unit cell is determined with a space group of Cmcm(No. 63), but for simplicity its hexagonal primitive cell is directly pre-sented in this study. The selected BC2N structure is the lowest-energyone in the layered BC2N allotropes examined by Pan et al. [60], and theAB stacking mode also results in an orthorhombic unit cell exhibitingPmma symmetry (No. 51). Note that all of these three layered materialsshow semiconductor characters, which have attracted great attention asmetal-free photo/electrocatalysts [7,61–63] and electrode materials forion batteries [59,64].

3.2.1. Lattice parameters and energetic propertiesThe calculated equilibrium lattice parameters, B0, Ebind, and the

reported experimental data of the selected BeCeN layered structureshave been summarized in Table 2. The calculated results by different

approaches show a similar tendency to those in graphite and h-BN. Forthe lattice parameter a (a and b for BC2N), PW91 and PBE yield veryclose values, which are expected to be reasonable. By considering thelong-range dispersion terms, the DFT-D functionals yield slightly de-creased values, which are comparable with the optB88-vdW results(Table S1). The lattice parameters a (b) produced by PBE-D2 are largerthan those by PW91-OBS and PBE-TS, indicating its weaker correctionto the intralayer covalent bonds. The experimental lattice parametersexhibit relatively larger deviations with respect to the correspondingtheoretical values, probably because most of the synthesized sampleswere in form of poorly crystalline phases [65–70].

Both of PW91-OBS and PBE-D2 predict that BC3 has the smallest c inthe selected three structures; however, that determined by PBE-TS is the

Fig. 2. Relative geometric deviations between the covalently bonded atomsalong c axis in graphite and h-BN calculated by different functionals.

Fig. 3. Crystal structures of the selected BeCeN layeredstructures of g-C3N4, graphite-like BC3 and BC2N. All thestructures contain two consecutive layers with the AB stackingmode. In the top-view panels, the upper (lower) layer struc-tures are indicated by smaller (larger) balls and thinner(thicker) sticks representing the corresponding atoms and sp2

covalent bonds, to show the stacking sequences clearly.

Table 2Bulk properties of the selected B–C–N layered structures: equilibrium latticeconstants, bulk modulus B0, and interlayer binding energy Ebind calculatedusing different approaches as well as the experimental data.

Layered material Approach a (Å) b (Å) c (Å) B0 (GPa) −Ebind(meV/atom)

g-C3N4 LDA 4.736 6.121 35.4 35.16PW91 4.790 8.223 1.9 4.97PBE 4.791 7.883 3.4 4.07PW91-OBS 4.778 6.506 27.5 67.07PBE-D2 4.782 6.160 38.3 57.92PBE-TS 4.776 6.458 43.1 69.48Experiment[65]

5.042 6.576

BC3 (primitive cell) LDA 5.113 6.416 25.0 27.75PW91 5.157 10.276 0.5 2.22PBE 5.160 9.481 0.4 1.52PW91-OBS 5.140 6.480 33.7 98.86PBE-D2 5.154 6.135 45.9 68.58PBE-TS 5.145 6.679 45.3 89.19Experiment[66]

4.948 6.874

BC2N LDA 2.455 4.310 6.424 31.6 32.06PW91 2.478 4.351 9.252 1.0 2.66PBE 2.480 4.353 8.563 1.3 2.09PW91-OBS 2.471 4.337 6.532 38.3 97.28PBE-D2 2.475 4.343 6.217 50.7 72.29PBE-TS 2.472 4.338 6.553 52.9 91.99Experiment[67]a

2.486 4.363 6.637

a A hexagonal unit cell of BC2N was reported in ref. 67, which only con-sidered the crystallographic geometry but overlooked the different kinds of B,C, and N atoms; herein the hexagonal unit cell was converted into the morereasonable orthorhombic one.

N. Liu, et al. Materials Today Communications 22 (2020) 100781

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largest one, which is interestingly in line with the PW91 and PBE re-sults. With respect to these two GGA-type XC functionals, the weakinterlayer interactions are dominated by the short (or middle)-rangeKohn− Sham contributions, in which the charge transfers between thepolar BeC and/or CeN covalent bonds can be accurately described.These bond polarity-induced electron-density variations are furtherconsidered in the TS correction for interlayer binding, and thus theobtained interlayer distances could be more reasonable for these polarlayered systems. This can be further confirmed by the experimentaldata and the results calculated by the optB88-vdW functional at thevdW-DF level (Table S1), both of them reveal that BC3 has the largestlattice parameter c in these three layered materials. PBE-TS predicts alattice parameter c of 6.679 Å for BC3 that is almost the same as gra-phite and h-BN, whereas those are notably smaller for g-C3N4 (6.458 Å)and BC2N (6.553 Å). Our results suggest that the interlayer binding inthese selected BeCeN layered materials could be affected by the ef-fective atomic volumes and the specific bond polarities, which could setan equilibrium d0 deviating from 3.3 Å observed in graphite and h-BN.In addition, bulk graphitic carbon nitride materials have been widelystudied as a visible light-responsive photocatalyst [61,71,72], a d0 inrange of 3.22− 3.26 Å has been reported, which is comparable with thepredicted value of g-C3N4 by PBE-TS.

The D2 and TS corrections to PBE yield quite close B0 for eachstructure, unlike the big differences between the computed B0 of gra-phite and h-BN. Both of the involved BeC and CeN bonds are less polarthan the BeN bond, therefore, for the TS scheme the contribution ofelectron-density variations on the C6 coefficients in these three struc-tures will be not as large as that in h-BN. Nevertheless, the B0 valuescalculated by PW91-OBS are remarkably small for each structure, in-dicating that the more empirical OBS correction may be too scabrous topresent a rational prediction for complex BeCeN layered materials.

Another question is whether the selected layered materials havecomparable Ebind to graphite and h-BN. For graphite-like BC3 and BC2N,PBE-TS provides a positive answer: the resulted Ebind are −89.19meV/atom for BC3 and −91.99meV/atom for BC2N, which are very close tothose of graphite (−85.07meV/atom) and h-BN (−87.33meV/atom).PW91-OBS also yields comparable Ebind results but more negative. Bycontrast, PBE-D2 predicts a notable difference on Ebind for BC3 andBC2N; the latter involves additional CeN bonds and has an Ebind 1.10times larger than BC3, while this ratio is smaller than the correspondingone (1.32) between the highly polar h-BN and nonpolar graphite. Anexception is the computed Ebind of g-C3N4, each of the DFT-D ap-proaches predicts a much smaller value than the other two structures.As shown in the left panel of Fig. 3, to achieve the C3N4 stoichiometricratio the C atoms are selectively removed from the monolayer [58],leaving periodic hole structures that will make the interlayer bindingweaker.

3.2.2. Charge transfer and relative geometric deviationAs mentioned above, charge transfer behavior along a covalent

bond is dominated by the short (or middle)-range XC interactions;therefore, the charge density difference plots of the selected BeCeNstructures calculated by different DFT functionals, without or with vdWcorrections, are almost the same. However, when we calculated the DAB

values by using different DFT-D approaches, only PBE-TS predictedreasonable results. DAB values calculated by PBE are also presented asbelow for comparison, during which the lattice parameter c of eachstructure was fixed at that determined by PBE-TS.

Fig. 4 shows the corresponding charge density difference plots andDAB values of g-C3N4. Due to the removed 1/4 C atoms from themonolayer, the involved N atoms exhibit two different coordinationstates: those in the C3N3 triazine ring are denoted as NR, while thebridging atoms with N–3C coordination are indicated by NB. Chargetransfers along the C–NB and C–NR covalent bonds are shown inFig. 4(a) and 4(b), respectively. The charge accumulation along a CeNbond is partial to the N center, revealing its polarity. Compared to the

NR site, the charge accumulation surrounding the NB center shows aseparated distribution, offering it a large degree of freedom. It shouldbe noted that the stacking features of the consecutive two layers arevery different: in the upper layer the NB–3C motif resides on the holewhile the triazine ring locates upon the NB–3C motif in the adjacentlayer, and vice versa for the lower layer. As a result, the computed DAB

values are also different for these two layers. As shown in Fig. 4(c), inthe upper layer the DCNR values are found to be very small due to therigidity of the triazine ring; by adding the vdW correction the PBE-TSfunctional attempts to enhance the ring planarity further, leading to adecreased value in comparison to that by PBE. Meanwhile, the calcu-lated DCNB corresponds to the NB–3C motif suspended between the holesin the adjacent layers, and thus the PBE-TS value is remarkably in-creased with respect to that by PBE. In the lower layer, the obtainedDCNR (DCNB) are larger (smaller) than those in the upper, and the PBE-TSfunctional yields enlarged deviations for both of C–NR and C–NB bonds.

The BC3 monolayer has a complete honeycomb lattice similar tographene, with the bond lengths of 1.42 Å for CeC and 1.55 Å for BeC[73]. This difference leads to a slight shift between the AB-stackinglayers along the BeC direction and the parallel CeC bonds exhibit anotable displacement, as shown in the middle panel of Fig. 3. Thislattice rearrangement makes the interlayer interaction much morecomplicated than as expected. Charge density difference plots in dif-ferent planes are shown in Fig. 5(a–c), to demonstrate the chargetransfer behaviors along the BeC and CeC bonds as well as in the in-terlayer region. In order to identify the distinct stacking situations, theinvolved B and C atoms are numbered specifically, as represented inFig. 5(d). Charge accumulation along each polar B− C bond exhibits anasymmetric distribution, while that along the C− C bond is nearly thesame as in graphite. The charge transfer from B to C further enhancesthe electron-deficiency nature of B atom, therefore, the charge deple-tion surrounding a B center is substantially extended (Fig. 5(a) and (c)).In particular, the outmost contour surrounding the B2 site, which lo-cates at the center of a B2C4 hexagonal ring in the adjacent layer, evenspan the whole interlayer region (Fig. 5(a)). The calculated DAB for BeCand CeC bonds with various stacking situations are summarized inFig. 5(e). PBE yields largerDB C1 1, DC C1 3, DB C2 2 and DC C2 3 ranged from0.006 % to 0.008 % but much smaller values for the others, which couldoriginate from the polarity of BeC bonds and the interlayer displace-ment between the C3 atoms, as shown in Fig. 5(b). By taking the dis-persion terms into account, however, the DAB values calculated by PBE-TS exhibit remarkable differences, highlighting the effects of specificstacking configurations on the interlayer interaction. As shown inFig. 5(a), the B1 sites reside on C2 of the other layer, while the B2 siteslocate at the hexagonal centers; and vice versa for the C1 and C2 sites.The outmost contour surrounding B1 links with that of the covalentlybonded C1 but is separated from the adjacent layer, whereas for the B2

sites it is just on the contrary. Compared with the DAB values calculatedby PBE, the DB C1 1 derived by PBE-TS shows a significant decrease, ac-companying with remarkably enlarged DB C1 3 and DC C1 3; by contrast, thecomputed DB C2 2 and DB C2 3 show notable increases, whereas the en-hancement effect of TS correction on DC C2 3 is relatively small. Finally,the resulted DC C3 3 is larger than the PBE value, probably due to thepronounced dispersion contribution from the electron-density varia-tions induced by the notable lattice displacement.

Unlike g-C3N4 and BC3 merely involving CeN or BeC polar bonds,the graphite-like BC2N is isoelectronic to graphite and h-BN. As shownin Fig. 6(a), charge depletion surrounding the B centers shows a re-markable extension, and the outmost contour directly links with eachother between the interlayer overlapped B atoms. It is interesting tonote that the charge distribution along the CeC bonds is also obviouslyasymmetric, probably due to the charge extraction/depletion of each Catom from/to the concurrently bonded B or N atoms, which are shownin Fig. 6(b) and (c), respectively. The calculated DAB values are shownin Fig. 6(d), for each bond PBE-TS predicts an enlarged DAB comparedto PBE, and the variation tendency of the DAB values with respect to

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different bonds is consistent for these two functionals. Due to theasymmetric charge distribution along the CeC bonds, the calculatedDCC are small but nonzero; and the isoelectronic BeN bond generatesmoderated DBN values, which are comparable to those in h-BN as shownin Fig. 2. The obtained DCN are the largest for all the covalent bonds inBC2N, suggesting the DAB is not only dependent on the bond polarity,but also related to the effective radii of the bonded atoms.

3.3. Additional discussion on DAB

For all the selected BeCeN layered structures, the calculated DAB

show a good reproducibility and distinct characteristics. These devia-tions are closely related to the bond polarity, which induces an asym-metric charge distribution and then affects the interlayer interactions;therefore, even the pristine DFT functionals (including LDA) generateprimary DAB values, which will be further corrected by the corre-sponding DFT-D approaches. Except the DCNB obtained in g-C3N4, otherDAB values in all the selected structures are within 0.015 %, and thusscarcely influence their crystallographic symmetries. On the contrary,

these small geometric deviations can be confined by the crystal-lographic symmetries, without cancelling them the stacking layers willretain planar after structural optimization. We have also checked theisolated monolayers free from interlayer binding, and all of the ob-tained DAB were found to be zero.

The small DAB values could be hardly identified by experimentalmeasurements, however, they are well associated with the nonuniformcharge distribution induced by the intralayer polar bonds and highlysensitive to the specific stacking situations. This fine electronic effectcould further facilitate the adsorption of exotic atoms (ions) and che-mical species on the surface of BeCeN layered materials or even otherpolar systems, which could be crucial to provide new insights into someelegant physical/chemical processes, especially in photo/electro-catalysis [7,61–63] and drug delivery [74,75].

It also should be noted that all of the employed DFT-D approachesprovide reasonable DBN in h-BN as shown in Fig. 2, probably becausethe charge distribution is well complementary between the interlayeradjacent B and N centers. For the other three structures, however, bothPW91-OBS and PBE-D2 yield abnormal results, the former predicts

Fig. 4. Charge density difference plots of g-C3N4 along (a) the (110) plane and (b) the (-210) plane calculated by PBE-TS, in which the unit cell has been downshifted0.25 primitive vectors along the c axis to show two stacking layers inside. The color scale is in eV/Å3. (c) Relative geometric deviations between the covalentlybonded atoms along c axis of the structure.

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much larger DAB than PW91, while the latter generates decreased va-lues than PBE. These results are consistent with the calculated Ebindlisted in Table 2, as the OBS (D2) correction provides the largest(smallest) Ebind for each structure. Our findings address the necessity ofconsidering the electron-density variations of specifically bonded atomsto calculate these geometric deviations, which can be properly de-scribed by the TS scheme.

4. Conclusions

In conclusion, we have investigated the interlayer interactions innonpolar graphite and representative BeCeN layered materials invol-ving polar covalent bonds. By considering the electron-density varia-tions related to specific bonding environments, the TS correction pre-sents a reasonable description on the dispersive potentials, especiallyfor the polar layered systems. PBE-TS predicts almost identical inter-layer distances around 3.3 Å for graphite, h-BN, and graphite-like BC3,while those of g-C3N4 and BC2N are found to be smaller. The calculated

Fig. 5. Charge density difference plots of graphite-like BC3 along the (110) planes showing (a) the BeC bonds and (b) the CeC bonds, and (c) the (-210) planecalculated by PBE-TS. The color scale is in eV/Å3. (d) A BC3 monolayer showing the nomination of the specific B and C atoms. (e) Relative geometric deviationsbetween the covalently bonded atoms along c axis of the structure.

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interlayer binding energies of these BeCeN layered materials are quiteclose, ranging from −85.07 to −91.99meV/atom; expect a notablesmaller value of g-C3N4 (−69.48meV/atom), probably due to the in-complete honeycomb lattice in the C3N4 monolayers. According to theexperimental or high-level RPA data of graphite and h-BN, however, thecalculated interlayer binding energies by PBE-TS could be still toolarge.

We further demonstrate the symmetric charge distribution along theC− C bonds in graphite, and thus the stacking graphene layers exhibita pristine planar feature. By contrast, the polar B−N bonds in h-BNinduce an asymmetric charge distribution, and the interlayer bindingpromotes a geometric deviation between the covalently bonded atompairs, making the BN monolayer slightly puckered. This geometric de-viation can be derived from DFT calculations and further enlarged bytaking the long-range dispersive terms into account. As for otherBeCeN layered structures, the involved B−N and/or C−N polarbonds can generate similar geometrical deviations but with distinctcharacteristics, which are related to the nonuniform charge distributionas well as the specific stacking situations. This fine electronic effect,arising from the intralayer bond polarity and the interlayer interactionsboth, could play a crucial role in some subtle physical/chemical pro-cesses.

CRediT authorship contribution statement

Nan Liu: Data curation, Formal analysis, Investigation,Methodology, Validation, Visualization, Writing - original draft.Xiaoguang Luo: Conceptualization, Formal analysis, Investigation,Writing - review & editing. Xiaohong Yuan: Data curation, Formalanalysis, Investigation, Methodology, Validation, Visualization. KunLuo: Conceptualization, Formal analysis, Investigation, Validation.Julong He: Conceptualization, Formal analysis, Investigation,Methodology, Resources, Validation. Dongli Yu: Conceptualization,Formal analysis, Funding acquisition, Investigation, Resources,Supervision, Validation, Writing - review & editing. Yuanchun Zhao:Conceptualization, Formal analysis, Funding acquisition, Investigation,Methodology, Project administration, Resources, Supervision,Validation, Visualization, Writing - original draft, Writing - review &editing.

Declaration of Competing Interest

The authors declared that they have no conflicts of interest to thiswork.

Acknowledgement

This work was supported by the National Natural Science

Fig. 6. Charge density difference plots of graphite-like BC2N along (a) the (130) plane, the (100) planes showing (b) the BeC bonds and (c) the CeN bonds calculatedby PBE-TS. The color scale is in eV/Å3. (d) Relative geometric deviations between the covalently bonded atoms along c axis of the structure.

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Foundation of China under Grant No. 51772261and No.51572235.

Appendix A. Supplementary data

Supplementary material related to this article can be found, in theonline version, at doi:https://doi.org/10.1016/j.mtcomm.2019.100781.

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