A first principle study of pristine and BN-doped graphyne family

ORIGINAL RESEARCH

A first principle study of pristine and BN-doped graphyne family

Ngangbam Bedamani Singh • Barnali Bhattacharya •

Utpal Sarkar

Received: 12 November 2013 / Accepted: 5 May 2014

� Springer Science+Business Media New York 2014

Abstract Based on first principle calculation using gen-

eralized gradient approximation, we report electronic

properties of graphyne and its related structures (graph-

diyne, graphyne-3, graphyne-4). Boron and nitrogen atoms

are systematically substituted into the position of carbon

atom and the corresponding changes of the properties are

reported. All the structures are found to be direct band gap

semiconductors with band gap depending on the concen-

tration and position of the doping material. Our band

structure calculation clearly shows that the band gap can be

tuned by B–N doping and the spin-polarized calculation

depicts the nonmagnetic nature of these structures. The

possibility of modulating the band gap provides flexibility

for its use in nanoelectronic devices. Projected density of

state (PDOS) analysis shed insights on the bonding nature

of these novel materials, whereas from the view point of

Crystal Orbital Hamilton Population (–COHP) analysis, the

nature of chemical bonding between neighbouring atoms

and the orbital participating in bonding and antibonding

have been explored in details.

Keywords Graphyne � Stability � Electronic band gap �Density of states � –COHP analysis

Introduction

Carbon-based nano materials have attracted great attention

due to their unique properties and wide prospect for tech-

nological applications [1–14]. Different allotropes of car-

bon such as fullerene, carbon nanotube (CNT), graphene

have already enriched the future nano-electronics [1–3]. As

a result, so many works have already been done on nano-

tube, graphene and their derivatives having different car-

bon network [10–14]. Graphene, one of the most versatile

materials of recent days, has been in the focus because of

its exciting properties and potential use in technological

applications [3–5]. For the application of graphene in nano-

electronics, the band structure near the Dirac cones has to

be suitably controlled [4]. Graphyne, a new planar allo-

trope of carbon with hexagonal rings joined together by

acetylenic linkages (–C:C–) are also shown to possess

Dirac cones [15]. The planar structure of graphyne was first

predicted by Baughman et al. [16], and the presence of

acetylenic link provides an extra flexibility in modulation

of its structure. Other members of graphyne family can be

obtained by increasing the number of –C:C– links

between two hexagonal rings. Even though, the experi-

mental fabrication of graphyne cannot achieved so far,

graphdiyne (expanded graphynes having two acetylenic

lingkages) films and graphdiyne tubes have already been

synthesized [17, 18].

Unlike graphene, graphyne and its families have non-

zero band gap which is attributed to the presence of

acetylenic linkages [19] and this non-zero band gap prop-

erty may provide a golden opportunity to use them in

electronic device. As the band gap directly depends on the

chain length and the size of hexagon, by varying the length

of chain and size of hexagon one can modulate its band

gap. That is why graphyne is more flexible than graphene

Electronic supplementary material The online version of thisarticle (doi:10.1007/s11224-014-0440-4) contains supplementarymaterial, which is available to authorized users.

N. B. Singh � B. Bhattacharya � U. Sarkar (&)

Department of Physics, Assam University, Silchar 788011, India

e-mail: [email protected]

123

Struct Chem

DOI 10.1007/s11224-014-0440-4

http://dx.doi.org/10.1007/s11224-014-0440-4

and CNT. However, the first principle calculations [19]

have shown that graphyne and its related structures are

small band gap semiconductors which need to be widened

up in order to use in the electronic devices.

Chemical doping is one of the most common and

effective method for controlling the electronic properties of

graphene [20–22]. Hybrid boron carbon nitrogen (BNC)

structures obtained by doping B and N (BN) atoms into

carbon network and are expected to possess suitable band

gap property [23]. The doping with boron and nitrogen

affects the electronic conductivity and density of states of

graphene sheet and single-walled CNT [24]. BN doping

also changes the global and local reactivity parameters of

nanotube [25]. Nitrogen doping led to the appearance of a

true band gap in graphene electronic spectrum even for a

random distribution of the N dopants [22]. Therefore, we

can expect such widening of band gap and also interesting

changes in electronic properties due to doping on graphyne,

graphdiyne and other extended systems.

Recent investigation on the electronic and optical

properties of graphyne-like boron nitride sheet [26] reveals

their wide band gap and strong absorption behaviour in UV

region. In another theoretical investigation of boron–

nitrogen (B–N) substituted graphdiyne reveals that B–N

preferred to substitute sp-hybridized carbon at chain than

hexagon at low-doping rate, and at high-doping rate, it first

attack the hexagon before attacking chain [27].

Being influenced by these findings, and also by the

successful synthesis of BN sheet and BN-doped graphene

[28, 29]; we have carried our study considering all possi-

bility of B–N substitution on graphyne and its related

structures. For the substitution, we first consider the

structures with carbon atom at hexagonal rings linked by

BN-chains. Next, the structures with BN-rings linked by

C-chains are considered and finally, all the carbon atoms

are substituted with BN atoms. Here, our result demon-

strates the change in electronic structure by B–N substi-

tution at different sites and the associated effects. The

projected density of state (PDOS) and Crystal Orbital

Hamilton Population (–COHP) analysis have been done to

determine the orbital responsible for energy states near

Fermi level and the nature of the chemical bonding by

exploring the orbitals participating in bonding and anti-

bonding states respectively.

Computational details

The spin-polarized density functional theory calculations

[30] have been performed with GGA and Perdew–Burke–

Ernzerhof (PBE) is used to treat the exchange correlation

part of density functional. The DZP basis set has been

employed and the norm-conserving Troullier–Martins

pseudopotentials [31] are used for the core–valence inter-

actions. We have done the structure relaxations by conju-

gate-gradient method as implemented in the siesta package

[32]. Relaxation was done until the forces on the atoms are

less or equal to 0.010 eV/A. The Brillouin zone was

sampled using 11 9 11 9 1 Monkhorst–Pack set of k

points. The mesh cut-off value was set at 300 Rydberg. To

avoid the interaction between two images, the vacuum

space of 15 A is used along z direction. To study the sta-

bility of the various configurations, the cohesive energy is

calculated as

Cohesive energy¼ E Systemð Þ� ½nE Cð ÞþmE Bð Þþ lE Nð Þ�nþmþ l

;

where E (System), E(C), E (B) and E (N) are energies for

the whole system, carbon, boron and nitrogen atoms,

respectively, and n, m, l are the number of carbon, boron

and nitrogen atoms present in the system, respectively.

Results and discussions

The optimized geometries along with their unit cells are

presented in Fig. 1. Figure 1a represents graphyne which

contains one acytelinc linkage (–C:C–) between two

adjacent carbon hexagons of graphene. The other pristine

member of graphyne family containing more acetylenic

linkages between the nearest neighbouring carbon hexagons

is presented in Fig. 1e–g, where graphdiyne, graphyne-3 and

graphyne-4 contain two, three and four acetylenic linkages,

respectively. The BNC derivatives of graphyne, i.e.

‘graphyne with BN at linear chain’ and ‘graphyne with BN at

hexagonal ring’ are shown in Fig. 1b–c, where the former is

composed of carbon hexagonal rings linked by BN chain and

the latter is composed of BN hexagons connected by carbon

chain. Figure 1d depicts ‘graphyne-like BN sheet’ where all

the carbon atoms of pristine graphyne are replaced by

alternative arrangement of boron and nitrogen. In general,

replacement of all carbon atoms along the chain between two

carbon hexagons of pristine graphyne family by alternative

arrangement of boron and nitrogen has been termed as

‘systems with BN at linear chain,’ while substitution of all

carbon atoms of carbon hexagons of pristine graphyne

family by boron and nitrogen give rise to ‘systems with BN at

hexagonal ring’. Finally, we have replaced all the carbon

atoms of pristine graphyne family by alternative arrange-

ment of boron and nitrogen to get ‘BN sheet’.

Lattice length of all the systems in the present study is

presented in Table 1. We observed that the cell length

changes not only on replacing the carbon atom by BN

atoms but also depend on the position of the BN atoms.

The observed behaviour is because of the formation of

different types of bonds at different sites, and also different

Struct Chem

123

atomic radii of carbon, boron and nitrogen atoms. Overall,

the lattice lengths are seen to increase when B, N atoms are

introduced and the BN sheet has maximum lattice cell

length. When B, N atoms are doped at the hexagon site, it

has minimum cell length compared to BN sheet.

Detailed structures

For the sake of clarity, we denote different types of bonds

of pristine structures by assigning numbers as shown in

Fig. 2. Let us first consider the structure of graphyne,

Fig. 1 Geometric structure of optimized a graphyne, b graphyne with BN at linear chain, c graphyne with BN at hexagonal ring, d graphyne-like

BN sheet, e graphdiyne, f graphyne-3, g graphyne-4

Table 1 Lattice cell (in angstrom) of graphyne, graphdiyne, graphyne-3, graphyne-4 and their BN analogues

System Number of

acetylenic lingkages

in chain

Pristine

(Lattice

cell in A)

Systems with BN

at linear chain

(Lattice cell in A)

Systems with BN

at hexagonal ring

(Lattice cell in A)

BN sheet

(Lattice

cell in A)

Graphyne and its analogues 1 6.909 6.992 6.995 7.001

Graphydiyne and its analogues 2 9.502 9.589 9.589 9.620

Graphyne-3 and its analogues 3 12.095 12.207 12.183 12.233

Graphyne-4 and its analogues 4 14.681 14.827 14.772 14.860

Struct Chem

123

where the carbon atoms forming the hexagonal ring is sp2

hybridized, and these hexagons are joined by sp-hybridized

acetylenic linkages. In the present study, the C–C bond in

hexagonal rings of graphyne (bond 1) is found to be

1.427 A. This bond between two sp2 hybridized C atoms

has (r ? big p) character as in pristine graphene sheet and

lies in between single (*1.470 A) and double (*1.380 A)

bonds. px, py and s orbitals contribute to r bond, and the pbond is contributed by pz orbitals. Hence, the p conjugation

feature of graphene still remains in the hexagons. The bond

between the hexagonal ring and C-chain (bond 2 and 4) is

1.412 A, which is shorter than single r bond (*1.470 A),

implying the presence of p bonding between them. This

bond between sp2 and sp-hybridized C atoms is contributed

by px, py and s orbitals. The C–C bond between two sp-

hybridized C atoms (bond 3) in the chain is observed to be

1.232 A, close to the triple bond (*1.210 A), indicating

that a triple bond is formed in between them. These two sp-

hybridized C atoms are (r ? 2p) bonded, where px, py and

s orbitals contribute to r bond and one of the p bond, while

the other p bond is contributed by px and py orbitals. The

distance between two nearest hexagonal rings is 6.909 A.

When BN are placed at the linear chain positions of

graphyne as presented in Fig. 1b, the bond between two C

atoms in the hexagonal ring (bond 1) increases to 1.445 A,

and the bond between sp2 hybridized C atom and boron (or

nitrogen) is 1.516 A (or 1.335 A). The carbon– nitrogen

(C–N) bond is much shorter than the C–B bond due to the

different atomic radii of BN. The C–B bond is mainly

contributed by the pz orbitals of C and B atoms (and dis-

cussed in –COHP analysis below). The bond between BN

atoms, in the linear chain (bond 3) is 1.264 A, which has a

triple bond type of character.

On putting BN atoms at the hexagonal rings, while the C

atoms remain at the linear chain positions as shown in

Fig. 1c, we observed that the B–N bond (bond 1) is

1.461 A, which is slightly higher than the calculated values

of 1.452 A in the pristine BN sheet [33, 34]. The bond

between C and B atom (bond 2) is 1.494 A, while C and N

atom (bond 4) is 1.346 A. The C–C bond in the linear chain

(bond 3) retains its triple bond characteristics with the bond

length being 1.231 A.

Next, we consider the structure of the graphyne-like BN

sheet which consists of BN hexagons and linear BN chain

units as seen in Fig. 1d. Such system consists of mixed

type of hybridization (sp2 ? sp). The B–N bond in the

hexagons (bond 1) is found to be 1.466 A, which is larger

than the pristine BN sheet bond length of 1.452 A [33, 34].

The B–N bond at the middle of the linear chain (bond 3) is

1.271 A and has triple bond characteristics. The B–N bond

between B atom at hexagon and N atom at linear chain

(bond 2) is observed to be 1.395 A, whereas the bond

between N atom at hexagon and B atom at linear chain

(bond 4) is 1.399 A (slightly higher than bond 2). This

slight difference in the bond lengths of bond 2 and bond 4

arises due to the different neighbouring environments of B

and N atoms. In case of bond 2, B atom is bonded with

three N atoms (two at hexagons and one at chain), whereas

in bond 4, B atom is bonded with only two N atoms (one at

linear chain and another at hexagon). An approximate

character of single and double bond alternations is

observed in the linear BN chain.

The bond lengths of graphyne and its derivatives are

represented in Fig. 3. In case of graphdiyne, the bond length

in the hexagon (bond 1) is found to be 1.432 A, which lies in

between typical single and double C–C bonds. The bond at

the centre of the linear chain (bond 4) is found to be 1.349 A,

which is basically the bond length for single C–C bond in

diacetylene (*1.380 A). The bond joining the carbon atoms

at the hexagon and at the chain (bonds 2 and 6) is 1.402 A,

shorter than the typical single C–C bond, while the bonds 3

and 5 are found to be 1.242 A, which is nearly equal to the

triple bond length (*1.210 A). Thus, we observed an

approximate alternation of triple and single bonds in the

linear chain of graphdiyne and also in its BN analogues (see

Fig. 3b). Similar behaviour of bond alternations is also

observed in graphyne-3 (Fig. 3c) and graphyne-4 (Fig. 3d)

and in their BN analogues. The C–C bond in the hexagon

Fig. 2 Bond types of a graphyne and its analogues, b graphdiyne and its analogues, c graphyne-3 and its analogues, d graphyne-4 and its

analogues

Struct Chem

123

(bond 1) is same (1.432 A) for graphdiyne, graphyne-3 and

graphyne-4, which clearly signify that increasing the number

of atoms in the linear chain has negligible effects to the atoms

at the hexagons for these systems. This constant bond length

behaviour of bond 1, on increasing the number of atoms in

the chain positions, is also true when BN atoms are placed in

graphdiyne, graphyne-3 and graphyne-4 and can be seen

from Fig. 3b, c and d.

Bandstructure

We have presented the spin-resolved bandstructure of

graphyne family and observed that all the structures are

direct band gap semiconductors. No splitting of band

structure for spin up and spin down has been observed in

their band structure.

Our calculation of valence band maximum (VBM) and

conduction band minimum (CBM) of graphyne (repre-

sented in Fig. 4a) reveals that both VBM and CBM are

located at M point in the hexagonal brillouin zone and the

gap is 0.454 eV, consistent with the results of other GGA–

PBE calculation [35]. The bandstructure for graphdiyne is

presented in Fig. 4b, depicts that graphdiyne is direct band

gap semiconductor with a gap of 0.485 eV. The CBM and

VBM are located at the gamma (C) point of the brillouin

zone. We see that graphdiyne has higher band gap compare

to graphyne. The bandstructure of graphyne-3 and graph-

yne-4, as shown in Fig. 4c, d, respectively, depicts that

they are also direct band gap semiconductor with band gap

of 0.566 eV located at M point and 0.542 eV located at Cpoint of the brillouin zone, respectively. So the band gap

location is characterized by the number of acetylenic

linkages present between two neighbouring benzene rings.

Next, we calculate the bandstructures by introducing BN

atoms at the linear chain positions, at the hexagonal posi-

tions and at linear chain, as well as in hexagonal positions

and are presented in Fig. 4e, f and g, respectively. The

bandstructure of graphyne with BN atoms at linear chain

site (Fig. 4e) indicates that both VBM and CBM are at the

M point and the band gap is 1.392 eV, which is much

greater than that of graphyne. But the placement of BN

atoms at the hexagons of graphyne increased the band gap

to 2.502 eV, with VBM and CBM at M point, as shown in

Fig. 4f. However, the bandstructure for graphyne-like BN

sheet given in Fig. 4g, reveals that VBM and CBM are

located at M point of the brillouin zone with a wide band

Fig. 3 Bond lengths of a graphyne and its analogues, b graphdiyne and its analogues, c graphyne-3 and its analogues, d graphyne-4 and its

analogues

Struct Chem

123

gap of 4.110 eV. The band gaps for pristine graphyne

systems (one to four acetylenic linkages along linear chain)

and BN-substituted graphyne systems (one to four BN

linkages along linear chain) are presented in Fig. 5a.

We see that the band gap for graphyne, graphydiyne,

graphyne-3 and graphyne-4 is increased when BN atoms

are placed in the system. When all the carbon atoms are

replaced by BN, i.e. BN sheet, the gap becomes very large

(4.110, 3.759, 3.609, 3.416 eV for graphyne, graphydiyne,

graphyne-3 and graphyne-4-like BN sheets, respectively).

Hence, by changing the length of the carbon atom chain

and also by introducing BN, the band gap in such systems

can be tuned. This property might be useful in electronics

and semiconductor industry.

Fig. 4 Bandstructure of a graphyne, b graphdiyne, c graphyne-3, d graphyne-4, e graphyne with BN at linear chain, f graphyne with BN at

hexagonal ring, g graphyne-like BN sheet

Struct Chem

123

Cohesive energy

Since more negative cohesive energy signifies greater sta-

bility of the system, it is clear from Fig. 5b that the pristine

systems are more stable than their BN analogues. The BN

sheet has more negative cohesive energy than the systems

where BN placed at linear or hexagonal position. The

stability of the pristine systems is in the order of graph-

yne [ graphdiyne [ graphyne-3 [ graphyne-4, and the

stability on placing BN atoms is in the order of pris-

tine [ BN sheet [ BN at linear chain [ BN at hexagons,

as depicted in Fig. 5b. It is also clear from Fig. 5b that

cohesive energy tends to attain a saturation value when

number of acetylenic linkage in the linear chain increases.

Density of states

For an understanding of the contribution of each constitu-

ent, we have presented spin resolved PDOSs along with

total density of states. Our spin-polarized calculation shows

that the pristine graphyne family and their BN analogues

are nonmagnetic, and the density of states for both spin are

symmetric. For the sake of simplicity, here we have dis-

cussed the density of states for up spin only.

The density of states for pristine graphyne is depicted in

Fig. 6a, the region above -2.000 eV and below the Fermi

level (Fig. 6a (ii)) in the valence band (VB) is mainly

contributed by pz orbitals, and the region between -3.000

and -1.600 eV is dominated by px, py and pz orbitals,

though pz contribution is less than that of px and py. It is

clear from the Fig. 6a (iii) that in the valence band, the

energy levels from -1.400 eV to the Fermi energy are

equally contributed by C atoms at linear chain, as well as at

the C atoms at hexagons. But the contribution from atoms

at linear chain becomes dominant in the range -3.500 to

-1.500 eV (Fig. 6a (iii)). In the conduction band (CB),

energy levels up to 3.300 eV above the Fermi level is

contributed more or less equally by both, C atoms in

hexagonal ring position and C atoms at linear chain posi-

tion, while above 3.300 eV, the main contribution comes

from atoms in linear chain position. The main contribution

in the CB up to 3.400 eV, comes from pz orbital of C

atoms; and the region between 3.400 and 5.200 eV, px, py

and pz orbitals are contributing, sometimes pz is contrib-

uting more than px and py or vice versa (Fig. 6a (ii)).

The density of states for graphdiyne, seen in Fig. 6b (ii),

depicts that near the Fermi energy (-1.100 to 1.700 eV),

the energy states are contributed by the pz orbitals. The s,

px and py orbitals do not make any substantial contributions

to the energy states around the Fermi energy. In the region

between -2.000 and -1.500 eV of the VB, the major

contribution is coming from px and py orbitals, while s-

orbital contribution is negligible. But in the CB, the region

from 2.300 to 3.000 eV, the energy states are contributed

by px, py and pz orbitals, however, pz contribution is less

than the other two orbitals. The contribution from atoms at

the linear chain is more than from that of atoms at hexa-

gons and is evident from Fig. 6b (iii). When we compare

graphyne and graphdiyne, we see that the contribution from

the linear chain atoms is more than from that of atoms at

hexagons (Fig. 6a (iii), b (iii)) and it is expected since the

number of atoms in linear chain is greater than that of

hexagons, in case of graphdyine, while they are equal for

graphyne.

The density of states for graphyne-3 and graphyne-4 is

presented in Fig. 6c, d, respectively. In the VB and CB

region of graphyne-3 and graphyne-4, we observed that s,

px, py and pz orbitals are contributing in the same fashion as

Fig. 5 a Band gaps of graphyne, graphdiyne, graphyne-3, graphyne-4 and their BN-doped structural analogues. b Cohesive energies of

graphyne, graphdiyne, graphyne-3, graphyne-4 and their BN-doped structural analogues

Struct Chem

123

they do for graphyne and graphdiyne. The only difference

is that the contribution of px and py orbitals starts con-

tributing at energy levels closer to Fermi level compared to

that of graphyne and graphdiyne. As observed in case of

graphyne and graphdiyne, the contributions of s, px and py

orbitals near the Fermi energy (-0.800 to 1.500 eV for

graphyne-3 and -0.600 to 1.100 eV for graphyne-4) is

negligible and only pz orbital is contributing in graphyne-3

and graphyne-4.

In Fig. 6e, f and g, we represent the total and partial

density of states when graphyne is doped by BN atoms at

the linear chain site, at the hexagonal position and

Fig. 6 Total and partial DOS of a graphyne, b graphdiyne, c graphyne-3, d graphyne-4, e graphyne with BN at linear chain, f graphyne with BN

at hexagonal ring, g graphyne-like BN sheet

Struct Chem

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throughout the system, respectively. The contribution of

carbon, nitrogen and boron atom is presented in Figs. 6e

(ii), (iii) and (iv). From Fig. 6e (ii), it is clear that for

carbon atom the pz orbital is basically contributing in the

valance band, as well as in CB. In case of nitrogen and

boron atom, all the p-orbitals are contributing (Fig. 6e (iii)

and (iv)) in the valence and conduction band. However,

p-orbitals contribution in the VB is more than that of the

CB in case of nitrogen, whereas, opposite effect has been

seen in case of boron. For all three atoms, the pz orbital first

start to contribute to the energy levels in both side of the

Fermi level compared to other orbitals.

Figure 6f (ii), (iii) and (iv) show the contribution of

individual atoms to the density of states when BN atoms

Fig. 6 continued

Struct Chem

123

are doped at the hexagonal positions of graphyne. We

observed that all the p orbitals of C atoms (Fig. 6f (ii))

contribute both in the valance and conduction band. This

feature was not seen when BN atoms are situated at linear

chain site of graphyne, in which only pz orbitals of C atoms

contribute mainly to both the bands (Fig. 6e (ii)). The N

atoms contribution is mainly coming from pz orbitals with a

small part coming from px and py orbitals in the VB as can

be seen from Fig. 6f (iii). For B atoms, shown in Fig. 6f

(iv), the contribution of pz orbitals is again much larger as

compared to other orbitals.

For graphyne like BN sheet, energy levels near the

Fermi level of VB come from the p-orbitals of the N atoms

(Fig. 6g (ii)) and near the Fermi level of CB come from the

p-orbitals of the B atoms (Fig. 6g (iii)). In both situations

pz orbital start contributing first and its contribution is

higher than others. Major contribution in the valence region

comes from N atoms but for conduction region, major

contribution is from B atoms. The significant contribution

of N atoms in the VB comes from those atoms which are at

the linear chain site, while atoms at the hexagons con-

tribute very less (Fig. 6g (iv)). As far as the contribution of

B atoms in the CB near the Fermi level is considered,

contributions of both the B atoms at the linear chain and

hexagon sites are nearly equal (Fig. 6g (iv)).

–COHP analysis

In order to partition the band structure energy in terms of

orbital pair contribution and have a clear vision about

chemical bonding, we have considered the –COHP analy-

ses which illustrate pair wise interaction of occupied

(bonding) and unoccupied (antibonding) band. The –COHP

analyses gives an idea about the participating orbital pair,

Fig. 7 –COHP analysis of pristine a graphyne, b graphdiyne, c graphyne-3, d graphyne-4

Struct Chem

123

where the positive value represents the bonding state and

negative value, the antibonding states.

The –COHP analysis for pristine graphyne, graphdiyne,

graphyne-3, graphyne-4 are demonstrated in Fig. 7a, b, c

and d, respectively. The states below the Fermi level (VB)

and above the Fermi level (CB) contain bonding (occupied)

states close to Fermi energy due to the contribution of

p-orbital (Fig. 7a (i)). More specifically the pz orbital of

carbon gives the clear insight (Fig. 7a (ii)) about the strong

p-bond hybridization. In the case of pristine graphyne, we

consider the carbon–carbon (C–C) interaction in chain

(Fig. 7a (i)), and found that the first bonding states appears

at -0.256 eV below and 0.266 eV above the Fermi level.

Similar result was found when a carbon atom in ring

Table 2 Nature of chemical bonding in pristine graphyne, graphdiyne, graphyne-3, graphyne-4

System 1st Energy state

at valence band

(near EF))

Nature of

chemical

bonding

1st Energy state

at conduction

band (near EF)

Nature of

chemical

bonding

Participating

orbital

Difference between

first energy states

at VB and CB

Graphyne -0.256 Bonding 0.266 Bonding pz–pz 0.522

Graphdiyne -0.352 Bonding 0.352 Bonding pz–pz 0.704

Graphyne-3 -0.293 Bonding 0.274 Bonding pz–pz 0.567


Fig. 8 –COHP analysis of a B–N interaction in graphyne with BN at chain, b B–C interaction in graphyne with BN at chain, c C–C interaction

in graphyne with BN at chain, d C–N interaction in graphyne with BN at chain

Struct Chem

123

interacts with a neighbouring carbon atom in chain or with

the carbon atoms in the ring. Figure 7a (ii) states that pz has

dominant bonding contribution near the Fermi level, on

both side, and the other orbital pairs contribute in bonding

at much lower energy (see Fig. S1a in the supplementary

material). Hence pz orbital is responsible for strong p-bond

hybridization; strongly bind at the energy -0.256 and

0.266 eV (Fig. 7a (ii) inset). Similar type of bonding

interaction has been observed in pristine graphdiyne,

graphyne-3 and graphyne-4 and is depicted in Fig. 7b, c

and d. Only difference is that when the chain size increases

the bonding contribution of the px–px, py–py s–s orbital

pairs appear near the Fermi energy than graphyne (see Fig.

S1 in the supplementary material). Table 2 represents the

relative position of the bonding states.

Then, we report –COHP analysis by putting B–N at

chain and observed that four considerable interaction lies

between boron–nitrogen (B–N), boron–carbon (B–C),

carbon–carbon (C–C) and carbon–nitrogen (C–N). In B–N

interaction of graphyne, the most notable feature is the

bonding states near the Fermi level appears at -0.623 eV

due to the contribution of pz orbital of boron and nitrogen,

whereas the antibonding states are found at 0.82412 eV,

contributed by the pz orbital pair of both boron and nitrogen

(Fig. 8a). For B–C, N–C interaction, the antibonding state

appears at -0.623 eV (Fig. 8a, b), while the bonding states

appears at 0.824 eV (Fig. 8a, b). The C–C interaction is

always contributed by bonding states near the Fermi level.

Table 3 tabulates the nature of chemical bonding for

graphdiyne, graphyne-3 and graphyne-4 with BN at chain.

It has been observed that the presence of BN atoms in chain

sweeps the energy states (bonding and antibonding) away

from Fermi level as we go from graphyne to graphyne-4

which results an increasing trend for difference between

first energy states at VB and CB with order graph-

yne \ graphdiyne \ graphyne-3 \ graphyne-4.

The –COHP analysis of graphyne family with B–N at

ring has a remarkable feature that the difference between

first energy states at VB and CB (band gap) shows a

decreasing trend with increase in chain size. Another

important observation for graphyne is that the presence of

B–N at ring shifts the bonding and antibonding states away

from the Fermi level (in both CB and VB) than graphyne

with B–N at chain site and increase the band gap. In case of

graphdiyne with B–N at ring site, the first energy state

moves away in VB and comes nearer in CB than graph-

diyne with B–N at chain site which results negligible

increase in band gap. However, for graphyne-3 and

graphyne-4, the energy state is more close to Fermi level

(in both CB and VB) in comparison to B–N at chain site

showing the opposite trend for bandgap which are in good

agreement with the result depicted in Fig. 5a.

In case of B–N (Fig. 9a), B–C (Fig. 9b), and C–N

(Fig. 9c) interaction of graphyne, the first bonding (occu-

pied) state appears at -1.538, 0.954 and 0.954 eV,

respectively, whereas the antibonding (unoccupied) states

Table 3 Nature of chemical bonding in graphyne, graphdiyne, graphyne-3 and graphyne-4 with BN at linear chain

Interaction System 1st Energy state

at valence band

(near EF))

Nature of

chemical

bonding

1st Energy state

at conduction

band (near EF)

Nature of

chemical

bonding

Participating orbital Difference between

first energy states

at VB and CB

B–C Graphyne -0.623 Antibonding 0.824 Bonding pz–pz 1.447




B–N Graphyne -0.623 Bonding 0.824 Antibonding pz–pz 1.447


Graphyne-3 -1.114 Antibonding 1.177 Bonding pz–pz 2.290

Graphyne-4 -1.174 Bonding 1.238 Bonding px–px,py–py in

valence

band and pz–pz

in conduction band.

2.410

C–C Graphyne -0.623 Bonding 0.824 Bonding pz–pz 1.447




N–C Graphyne -0.623 Antibonding 0.824 Antibonding pz–pz 1.447


Graphyne-3 -1.145 Antibonding 1.207 Antibonding pz–pz 2.351

Graphyne-4 -1.264 Antibonding 1.267 Antibonding pz–pz 2.531

Struct Chem

123

are found at 0.954, -1.538 and -1.538 eV (Fig. 9c), near

the Fermi level. But in C–C (Fig. 9d) interaction, both VB

and CB comprises bonding state near the Fermi level at

-1.538 and 1.040 eV. Table 4 shows the nature of bonding

and the responsible orbital of graphdiyne, graphyne-3 and

graphyne-4.

Figure 10 depicts that all these three interaction contains

the bonding state far away from Fermi level at -2.753 and

at 1.378 eV thus results a high increase in band gap. Same

type of observation has been seen (see Figs. S2, S3 and S4

in the supplementary material) in case of graphdiyne,

graphyne-3 and graphyne-4-like BN sheet containing

bonding states at VB and CB, except for graphyne-4-like

BN sheet in the CB of B–N interaction where it shows

antibonding state near the Fermi level, and is depicted in

Table S1(in the supplementary data). Only exception is that

the px and py orbitals are also participating in bonding

along with pz orbital near the Fermi level for graphdiyne,

graphyne-3 and graphyne-4-like BN sheet which is absent

in case of graphyne-like BN sheet. It is important to note

that the difference between first energy states at VB and

CB shows similar decreasing trend with increase in chain

size (presented in Table S1 in the supplementary data), as

obtained in graphyne family with BN at ring site, which is

in good agreement with the result obtained in band struc-

ture analysis.

From the above analysis of the orbital participating to

the bonding and antibonding in graphyne and graphyne

with B–N, it is clear that all the bonding and antibonding

states near the Fermi level are arises due to the dominant

contribution of pz–pz pair of the neighbouring atoms. The

states contributed by other orbital pair px–px, py–py, s–s, are

negligible near Fermi energy and arise at much lower or

much higher energy, far away from the Fermi level. When

we go from graphyne to graphyne-4, with the increasing

chain size, the bonding contribution of the px–px, py–py,

s–s orbital pair appears near the Fermi energy seen (see

Fig. S1 in the supplementary material). The –COHP ana-

lysis clearly manifest that doping with B–N shifts the

energy states away from the Fermi level. This is due to the

enhancement of bonding discrepancy between B and N

atom.

Fig. 9 –COHP analysis of a B–N interaction in graphyne with BN at hexagonal ring, b B–C interaction in graphyne with BN at hexagonal ring,

c N–C interaction in graphyne with BN at hexagonal ring, d C–C interaction in graphyne with BN at hexagonal ring

Struct Chem

123

Conclusions

Using density functional theory, we have studied the geo-

metric structure and electronic properties of graphyne,

graphdiyne, graphyne-3 and graphyne-4 by systematically

doping boron and nitrogen atoms. Our spin-polarized cal-

culation reveals that all the structures are nonmagnetic in

nature. The stability of these systems is in the order of

graphyne [ graphdiyne [ graphyne-3 [ graphyne-4 for

pristine systems and on substituting BN atoms on these

systems, it becomes pristine system [ BN sheet [ BN at

linear chain [ BN at hexagons. We have obtained

beautiful bond alternation behaviour in the linear chain for

all these systems. All the structures are found to be direct

band gap semiconductors with band gap depending on the

position and concentration of the doping material. In

pristine systems, the contribution to the energy levels near

the Fermi energy from the linear chain atoms is more than

that of atoms at hexagons except for graphyne where the

atoms at linear chain sites and hexagonal rings contribute

equally. Most of the contribution for these systems comes

from the pz orbitals. However, the contribution of px and py

orbitals of graphyne-3 and graphyne-4 starts at energy

levels closer to Fermi level compared to that of graphyne

Table 4 Nature of chemical bonding in graphyne, graphdiyne, graphyne-3 and graphyne-4 with BN at hexagonal ring

Interaction System 1st Energy

state at valence

band (near EF))

Nature of

chemical

bonding

1st Energy state

at conduction

band (near EF)

Nature of

chemical

bonding

Participating

orbital

Difference between

first energy states

at VB and CB

B–C Graphyne -1.538 Antibonding 0.954 Bonding pz–pz 2.492




B–N Graphyne -1.538 Bonding 0.954 Antibonding pz–pz 2.492


Graphyne-3 -0.866 Bonding 0.882 Antibonding pz–pz 1.748


C–C Graphyne -1.538 Bonding 0.954 Bonding pz–pz 2.492




N–C Graphyne -1.538 Antibonding 0.954 Bonding pz–pz 2.492




Fig. 10 –COHP analysis of a B–N interaction in graphyne-like BN sheet, b B–B interaction in graphyne-like BN sheet, c N–N interaction in

graphyne-like BN sheet

Struct Chem

123

and graphdiyne. When BN atoms are substituted, the

nitrogen atom p-orbitals contribution in the VB is more

than that of the CB where as opposite effect has been seen

in case of boron. The contribution of N atoms in the VB is

more for those atoms which are placed at the linear chain

site compared to the atoms placed at the hexagonal ring.

The –COHP analysis confirms the presence of p bond

hybridization in the pristine systems due to pz orbitals. In

most of the cases, except graphdiyne-like BN sheet,

graphyne-3-like BN sheet and graphyne-4-like BN sheet,

all the bonding and antibonding states near the Fermi level

are arises due to the pair wise contribution of pz orbital of

neighbouring atoms. But the increasing chain length (when

we move from graphyne to graphyne-4) activates the

contribution of s, px, py orbitals near the the Fermi level.

The doping with BN sweeps the energy states (bonding and

antibonding) away from Fermi level. The difference

between first energy states at VB and CB increases with the

chain size when BN atoms are at chain, but opposite trend

have been observed for BN at ring or BN-like sheets.

Acknowledgments Dr U. Sarkar would like to acknowledge the

support from Prof Paul W Ayers, Department of Chemistry,

McMaster University, Canada, in various ways and SHARCNET

Canada for providing computational facilities for this research work.

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Documents

A first principle study of pristine and BN-doped graphyne family