Long range corrected-wPBE based analysis of the H₂O adsorption on magnetic BC₃ nanosheets

Abstract

Density functional theory based methods were used for the analysis of the interaction between BC₃ (a graphene nanosheet doped with boron), pristine and with point defects (vacancies of carbon – V_C and boron – V_B), and the H₂O molecule. The Perdew–Burke–Ernzerhof (LC-wPBE) functional, which includes long range corrections, combined with the 6-31G(d) basis sets developed by Pople et al. was used. The results from the structural and electronic relaxation indicate that the BC₃ nanosheets, pristine and with V_C and V_B defects, present magnetic properties. For the neutral case, they have magnetic moments of 2, 4, and 3 bohr magnetons (μ_B). Roughly, BC₃ and BC₃/V_B present metallic character but BC₃/V_C exhibits semiconductor behavior. Adsorption of the H₂O molecule on the pristine BC₃ and BC₃/V_C nanolayers is mainly governed by van der Waals forces, yielding adsorption energies of −0.45 and −0.21 eV, respectively. In the BC₃–H₂O and BC₃/V_B–H₂O systems, the water molecule is oriented in a parallel manner to the BC₃ mesh, presenting equilibrium distances of 1.79 and 2.45 Å, respectively. This type of functionalization may produce changes in the hybridization of such bi-dimensional structures. Remarkably, in the BC₃/V_C–H₂O system, the water molecule is dissociated into hydroxyl and hydrogen moieties. Structural stability is achieved in the three systems (as was confirmed by vibrational analysis) and the magnetic properties are also preserved, or even enhanced. On BC₃–H₂O (pristine, and with V_C and V_B vacancies), the following was found: an increase in the polarity, low chemical reactivity and low values for the work function. Thus, BC₃–H₂O, BC₃/V_C–H₂O and BC₃/V_B–H₂O may be used for the transportation of pharmaceuticals, in optoelectronics and in the design of magnetic devices.

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1. Introduction

Few years ago, in 2004, a graphene mono-layer of atomic thickness was isolated. This was one of the most interesting allotropic forms of carbon. It has been found that this type of nanosheet has a diversity of properties and technological applications.¹ Indeed, graphene is one of the most studied systems during the last decade. This monolayer of carbon atoms presents a structural pattern of hexagonal symmetry, and from an electronics point of view, it shows semiconductor behavior.² These findings have produced an increase in the number of studies for these types of two-dimensional systems; as indicated by the number of synthesis up to 2014, about 170 different and novel bi-dimensional nanostructures have been reported.^3,4

Substitutional doping of graphene frequently involves boron as a means for the modification of its electronic properties.⁵ The effects of different concentrations of boron, including defects, have been broadly studied. It has been found that for higher levels of boron doping, the BC₃ stoichiometry is feasible.

Indeed, the experimentally synthesized BC₃ sheet^6–9 is one of such widely studied 2D nanostructures, shown in Fig. 1. This system presents an hexagonal symmetry, a graphene structure decorated with boron atoms, presenting a B–C bond length of 1.55 Å, sp²-hybridization, and semiconductor behavior with a gap of 0.54 eV (as indicated by theoretical calculations performed by the local density approximation LDA).¹⁰ Likewise, it has been found that the 1D tubular structure of BC₃ shows metallic behavior because the gap is reduced considerably: from 0.54 eV (BC₃-2D) to 0.2 eV (BC₃-1D).¹¹ Thus, the electronic properties of BC₃ sheets have been studied extensively, but its ability for the adsorption of molecular species has been less broadly addressed. The goal of the present study is the study of the structural and electronic properties for the absorption of a H₂O molecule on a BC₃ sheet, both pristine and with point defects. Such a study has not been carried out before, to the best of our knowledge. The most feasible BC₃ dot for such adsorption will be inspected.

Fig. 1 Structure of a BC₃ nanosheet with a C₄₀B₁₄H₁₈ chemical composition.

This study may be important for biological applications where some low dimensional nanostructures (2D), analogous to those constituted by boron nitride, embedded in aqueous media have been investigated.¹² The reported findings indicate a considerable reduction of the toxic effects, suggesting that this type of structure may be feasible for the transportation of pharmaceutical compounds.¹³ Along this marked direction, the first step of our investigation is to address the interaction of the pristine BC₃ nanostructure with a water molecule. The second part is to analyze the effects produced by the introduction of point defects, either by carbon (V_C) or boron (V_B) vacancies, in the BC₃ nanosheet. The structural and electronic changes produced by the adsorbed H₂O molecule on the BC₃/V_C and BC₃/V_B layers have also been studied. This has accomplished with the aid of density functional theory (DFT) based-methods that accurately describe covalent interactions. Moreover, recently developed functionals describing long range (non-covalent) weak interactions are employed because they are needed for an accurate determination of the structural and electronic properties of the functionalized BC₃ mono-layer. Our results provide insight on the application of the BC₃ nanosheets in biomedicine, optoelectronics, and magnetic devices.

2. Simulation models and methods

First principles spin-unrestricted DFT total energy calculations were performed to study the interaction of the BC₃ nanosheet, having a chemical composition of C₄₀B₁₄H₁₈, with a water molecule (H₂O). The chosen BC₃ layer presents dimensions of x = 1.49 nm and y = 1.39 nm. This model is distinguished by having one boron atom for each hexagon, of carbon atoms, as shown in Fig. 1. Full structural and electronic optimization of pristine BC₃ indicates that triplet and quintet spin states are degenerate, as shown in Table 1. Likewise, for a smaller BC₃ dot, C₁₈B₆H₁₂, it was found that a triplet state was the one of lowest energy. That is, a triplet emerges as the most favorable state for the BC₃ layer. The size of the chosen system was validated by also obtaining the average cohesive energy of various structures, as those reported in ref. 14, resulting in 6.53 eV per atom.¹⁴

Table 1 Determination of the HOMO–LUMO gap for the BC₃ nanosheet. Several methods are used, some of which include dispersion corrections

HOMO–LUMO gap (in eV)	Reference/functional
a Ref. 10.b Becke A. D. (1993) J. Chem. Phys. 98: 5648–5652.c Hamprecht A., Cohen A., Tozer D. J., Handy N. C. (1998) J. Chem. Phys. 109: 6264–6271; Boese D., Doltsinis N. L., Handy N. C., Sprik M. (2000) J. Chem. Phys. 112: 1670–1678.d Heyd J., Scuseria G. (2004) J. Chem. Phys. 121: 1187–1192; Heyd J., Scuseria G. E. (2004) J. Chem. Phys. 120: 7274–7280.e Yanai T., Tew D., Handy N. (2004) Chem. Phys. Lett. 393: 51–57.f Chai J. D., Head-Gordon M. (2008) Phys. Chem. Chem. Phys. 10: 6615–6620.g Ref. 19.
0.54	LDA^a
Hybrid functionals
0.73	B3LYP^b
0.14	HCTH^c
Functionals with dispersion corrections
0.37	HSEh1PBE^d
0.39	CAM-B3LYP^e
0.41	wB97XD^f
0.44 for M = 1	LC-wPBE^g
0.45 for M = 3[6-31G(d) and 6-311g(d)]
1.52 for M = 5

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In the first step of this study, the generalized gradient approximation (GGA) was used as proposed in the functional developed by Hamprecht–Cohen–Tozer–Handy (HCTH).¹⁵ Previous studies in our group have demonstrated that this approach is an appropriate level of theory for an accurate description of the structural and electronic properties of low dimensional structures of nitrides.^16,17 Orbital basis sets of DNP quality (double polarization with one p orbital for the hydrogen and one d orbital for the B, C, and O atoms)¹⁸ were used. Such basis sets are contained in the quantum chemistry software DMol³.¹⁹ Thus, using all-electron calculations performed with the HCTH/DNP method, the optimized geometries for the BC₃ systems were determined according to the criterion of minimal energy. Furthermore, in a second step, the HCTH/DNP optimized BC₃ and BC₃–H₂O structures (with and without V_C and V_B defects) were re-optimized using several functionals, without and with dispersion corrections. The results, reported in Table 1, indicate that the LC-wPBE functional (a long range-corrected version of wPBE)²⁰ is the level of theory that most accurately describes the HOMO–LUMO gap, as compared to the reported value by Ni et al. of 0.54 eV.²¹ In addition, the LC-wPBE approach is accurate for a broad range of molecular properties, particularly in the description of processes involving long-range charge transfer. As will be shown, this is the case for the adsorption of the H₂O molecule on the BC₃ and BC₃/V_B layers, where despite the small adsorption energy values, significant charge transfers were observed. The LC-wPBE functional is available in the quantum chemistry software GAUSSIAN-09.²² Orbital basis sets of 6-31G(d) quality were employed; they are quite similar to the DNP functions. The multiplicity (M = 2S + 1, where S is the total spin) for the neutral systems (charge Q = 0) was determined for the low-lying states of pristine BC₃, BC₃/V_C and BC₃/V_B. The spin states were found to be triplet (M = 3), quintuplet (M = 5) and quartet (M = 4), respectively. Such multiplicities are preserved for the functionalized BC₃–H₂O (M = 3) and BC₃/V_C–H₂O (M = 5) layers, and it is reduced in BC₃/V_B–H₂O (M = 2), as shown in Table 2.

Table 2 Relative energies for the spin states of the BC₃, BC₃/V_C, BC₃–H₂O and BC₃/V_C–H₂O systems at the LC-wPBE/6-31G(d) level of theory. The multiplicity is defined as 2S + 1, where S is the total spin

Multiplicity	Relative energy (eV)
BC3 pristine
M = 1	3.78
M = 3	0.0
M = 5	1.36 × 10^−2
BC3/VC
M = 1	3.94
M = 3	7.09 × 10^−3
M = 5	0.0
M = 7	2.72
BC3–H2O
M = 1	3.79
M = 3	0.0
M = 5	1.26 × 10^−2
BC3/VC–H2O
M = 1	3.61
M = 3	1.75
M = 5	0.0
M = 7	1.56
BC3/VB
M = 2	0.74
M = 4	0.0
M = 6	7.63 × 10^−2
BC3/VB–H2O
M = 2	0.0
M = 4	1.34 × 10^−3

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7 candidate structures were considered for the interaction of the BC₃ layer with the H₂O molecule. They are shown in Fig. 2. Their relative energies are indicated in Table 3. In the first reaction profile, the water molecule is perpendicularly oriented through one of the oxygen atoms to the central hexagon. In the second geometry, the H₂O molecule is located in a parallel way over the central hexagon. The third candidate accounts for a perpendicular orientation of the H₂O molecule through the hydrogen atoms towards the central hexagon. In the fourth one, H₂O is perpendicularly oriented through one of the hydrogen atoms to one boron site. For the fifth reaction pathway, the H₂O molecule is perpendicularly oriented through one of the hydrogen atoms towards one of the carbon sites of the BC₃ network. In the sixth geometry, the water molecule interacts perpendicularly via a hydrogen atom with the central hexagon. Finally, in the seventh candidate, the water molecule is directed in a parallel fashion to a boron site of the central hexagon. The vacancies of carbon and boron atoms are located near the site (of the BC₃ mesh) where the interaction (of minimal energy) with the H₂O molecule occurs. An initial BC₃–H₂O distance of 2 Å was used for all candidates.

Fig. 2 Candidate geometries for the interaction of the BC₃ nanosheet with a water molecule. The orientation of H₂O towards the BC₃ optimized structure at the HCTH/DNP level of theory is shown.

Table 3 Total energy difference (meV) for the BC₃ nanosheet–H₂O configurations. The reference energy corresponds to the lowest energy state

Geometries	Relative energies
(1) The oxygen atom is oriented perpendicularly to the central hexagon	3.88
(2) Parallel towards the central hexagon	0.0
(3) Perpendicular through a H atom to the central hexagon	3.08
(4) Perpendicularly oriented by an H atom on a B atom	47.09
(5) Perpendicularly oriented by a H atom on a C site	15.79
(6) Perpendicularly oriented by a H atom to the hexagon center	7.69
(7) Parallel orientation through a H atom to the B site	34.79

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The computed quantum descriptors²³ are as follows: the electronic gap was considered as the energetic difference of the frontier orbitals—HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital). The interaction energy of the adsorbed water molecule on the BC₃ (BC₃/V_C and BC₃/V_B) monolayer is defined as follows: E_ad = E[BC₃(BC₃/V_C or BC₃/V_B)–H₂O] − E[BC₃(BC₃/V_C or BC₃/V_B)] + E[H₂O]. The chemical potential (μ) is obtained as the arithmetic average value: (HOMO + LUMO)/2. According to the definition of the free electrons gas, it is equal to the Fermi level (E_f), which is considered as the center of the gap energy. On the other hand, the work function (WF) accounts for the minimum energy required to remove an electron from the inside of a bulk solid to the outside. WF is defined more precisely as the energy difference between the state in which an electron has been removed to a point sufficiently far outside the surface so that the image force is negligible and the state in which the electron is in the bulk solid.^24,25 In this study, we will approximate WF as the energy needed to move an electron from the Fermi energy level into the vacuum. Thus, the work function will be estimated as the energy difference between the vacuum level (LUMO orbital) and the Fermi level (chemical potential). The work function is important for the design of optoelectronic devices. Finally, molecular electrostatics potential surfaces (MEPs) are estimated as described in the literature;²⁶ the MEP allows one to locate the regions of high electron density, mainly defining the most favorable site for the H₂O absorption. It is also usually associated with the lone pair of the more electronegative atom.

3. Results and discussion

3.1. BC₃ (pristine and V_C) nanosheets

The structural and electronic relaxation procedure of the pristine BC₃ nanosheet allows the identification of the low-lying state, a triplet (M = 3) providing structural stability. Effectively, the vibrational analysis for this state, shown in Fig. 3a, indicates the appearance of real frequencies. They define the infrared (IR) spectrum for the pristine BC₃ nanosheet. The spectrum clearly reveals vibrational bands at 1288.8 and 1458.1 cm⁻¹, which are assigned to “scissor” vibrational modes of the hexagons of carbon atoms. On the other hand, the equilibrium BC₃ structure preserves its geometrical parameters: the obtained values for the C–C (1.41 Å) and B–C (1.57 Å) bond distances are similar to those reported in the literature. Some geometrical regularity is also observed because the C–C–C and C–B–C bond angles are equal to 120.0°.

Fig. 3 Calculated infrared spectra for the pristine (a) BC₃ structure, (b) BC₃–H₂O, (c) BC₃/V_C–H₂O, and (d) BC₃/V_B–H₂O.

The inclusion of carbon vacancies (V_C, Fig. 4a) on the BC₃ network produces a quintet ground state and promotes the appearance of Stone–Wales defects,²⁷ which do not appear for the boron vacancies (V_B, Fig. 4b). Thus, pyrene-type structures are formed in a pentagon–hexagon–hexagon–pentagon, 5–6–6–5, geometrical pattern. In particular, in the BC₃/V_C layer, 2 adjacent hexagons of 2B4C composition and 2 pentagons are generated, one of carbon atoms (5C) and the other of 2B3C composition. These features produce considerable deviation from planarity of the BC₃/V_C sheet, being indicated by the angles: 26.2° by the Z axis and 19.0° by the X axis. Thus, an increase in the magnetic moment: from 2 μ_B, for BC₃, to 4 μ_B for BC₃/V_C renders significant structural changes on BC₃, as is shown by its curvature.

Fig. 4 Optimized structure for (a) BC₃ monolayer and (b) BC₃/V_B nanostructure. The appearance of Stone–Wales type defects for BC₃/Vc has been presented.

Note that the magnetic moment of the BC₃ layer originated from the unpaired electrons occupying the HOMO and HOMO−1 levels, as shown in Fig. 5a and b. Such plots reveal significant signatures from carbon atoms lying at the periphery of the BC₃ dot. As seen in Fig. 5c, d and 5e, f, the magnetic moment is more localized in the BC₃/V_C and BC₃/V_B nanosheets, having important contributions around the Stone–Wales region in the former.

Fig. 5 HOMO and HOMO−1 orbitals for (a and b) pristine BC₃, (c and d) BC₃/Vc, and (e and f) BC₃/VB.

Other geometrical parameters of BC₃/V_C, the C–C and B–C equilibrium distances, present variations within 1.35–1.51 Å and 1.55–1.64 Å. Results are shown in Table 4.

Table 4 Bond length (Å), HOMO–LUMO gap (eV), Fermi energy (eV), dipole moment (Debye), work function (eV) for BC₃, BC₃/Vc, BC₃–H₂O, and BC₃/Vc–H₂O, and adsorption energy (eV)

System	Bond length		HOMO–LUMO gap	Energy Fermi level (Ef)	Dipole moment	Work function	Adsorption energy
	C–C	B–C
a This work.
BC3	1.41	1.55	0.54 (ref. 10)
	1.42	1.55	0.66 (ref. 10)	−5.07		1.33
			0.52 (ref. 24)
			0.19–0.54 (ref. 29)
	1.43 (ref. 10 and 40)	1.49
	1.42	1.56
Ref. 30	1.43	1.49	2.67
Ref. 31			2.65
Ref. 41	1.41	1.57	0.14
Pristine BC3^a	1.41	1.57	0.45	−8.63	0.06	6.19
BC3–H2O^a	1.35–1.51	1.55–1.64	0.43	−8.51	3.35	0.10	−0.45
BC3/VC^a	1.36–1.44	1.52–1.63	1.15	−8.88	1.54	0.58
BC3/VC–H2O^a	1.30–1.45	1.51–1.58	1.08	−8.89	1.28	0.54	−2.11
BC3/VB^a	1.30–1.45	1.51–1.58	0.49	−8.63	5.43	0.25
BC3/VB–H2O^a	1.30–1.45	1.51–1.58	0.17	−8.43	7.24	0.09	−0.21

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On the electronic side, the pristine BC₃ structures and those with carbon vacancies possessing gaps of 0.45 and 1.15 eV (see Tables 1 and 4), present semi-metallic and semiconductor behaviors, respectively. Small gaps were also found for BC₃–H₂O (0.43 eV), BC₃/V_B (0.49 eV) and BC₃/V_B–H₂O (0.17 eV). The gaps were estimated through the difference of energies between the frontier HOMO and LUMO orbitals, evaluated with the LC-wPBE/6-31g(d) method, which is the one that more closely reproduces the theoretical value for the pristine structure, as reported by Tomanek et al., at the LDA level of theory.^10,21 The reduction in the gap may produce an improvement of the electric conductivity of these nanosheets. The proper estimation of the electrical conductivity certainly requires band theory calculations. Nevertheless, it is possible to see this behavior qualitatively through the expression σ = α exp(−E_g/kT), where E_g = HOMO–LUMO gap, “k” is the Boltzmann constant and “T” is the temperature.²⁸

The 6-311G(d) basis set was also used producing negligible changes on the estimated gaps. It should be noted that the gap of the BC₃ system is of similar magnitude as the one reported for graphene doped with boron, where the gap is modulated using concentrations of 3.6%, 7.3%, 11.3% and 13.8% of boron atoms. Semi-metal signatures were found for these compositions because the observed gaps are in the 0.19–0.54 eV interval.²⁹ These results significantly differ from other theoretical estimations also using molecular or finite systems and the B3LYP/6-31g(d) functional; in this way, overestimated values of 2.67 and 2.65 eV were reported for the HOMO–LUMO gap of BC₃.^30,31

In a first approach, the chemical potential may grossly provide a measure of the chemical reactivity. The estimated values of −8.63 eV (pristine) and −8.88 eV (with vacancies) suggest low reactivity for the BC₃ systems as compared to graphene³² or to the BN nanosheet of hexagonal symmetry (hBN).³³ The reduction of reactivity may originate from the ordering of the boron atoms experienced in the BC₃ monolayer.

The contour plots of the molecular electrostatic potential (MEP) for the pristine BC₃ monolayer indicates that the regions of major negative charge, which may also define the reactive sites, are mainly located on the hexagons of carbon atoms (Fig. 6a). Hexagons with the 2B4C composition have less negative charge. Remarkably, for the BC₃ layer with carbon vacancies, it could be observed that the region of negative charge is mainly concentrated on the defects of the Stone–Wales type (Fig. 6b).

Fig. 6 Molecular electrostatic potential (MEP)³⁹ for the (a) BC₃, (b) BC₃/V_C, (c) BC₃–H₂O, and (d) BC₃/V_C–H₂O systems (the dissociation of the H₂O molecule is also shown). The zones marked with red indicate sites with the most negative charge.

The work function is important for the design of electronic devices. The pristine BC₃ structure presents a relatively high value (6.19 eV) for such property, as compared to the boron nitride and boron nitride oxide nanosheets.¹⁷ Thus, this nanosheet is not appropriate for such a design because the high energy barrier will produce a low electric conductivity. However, the introduction of point defects or vacancies of carbon produces a substantial reduction of the work function. In fact, the obtained value (0.58 eV) for the WF of BC₃–V_C suggests that this system is an appropriate candidate for the construction of electronic devices. In addition, further reduction of the work function may be obtained through the increasing of carbon vacancies and by the charge transfer effects carried out from the boron atoms towards the carbon sites located around the region defined by the Stone–Wales vacancy (Fig. 7a and c).

Fig. 7 Charge distribution analysis for (a) pristine BC₃, (b) BC₃–H₂O, (c) BC₃/V_C, (d) BC₃/V_B, and (e) BC₃/V_C–H₂O systems.

3.2. Pristine BC₃–H₂O interactions

The main motivation of this study is to investigate whether the interaction of the BC₃ nanosheet with a water molecule may allow exploration of possible biological applications. This purpose has been inspected using the quantum descriptors of polarity, reactivity, and absorption energy for the ground state of BC₃–H₂O. Full relaxation of geometry 2 yields the lowest energy state, a triplet (M = 3) for the pristine BC₃–H₂O system, where the water molecule, being nearer to a boron site, is oriented in a parallel way to the BC₃ monolayer. The H₂O–B equilibrium distance is 1.79 Å. It was found that this interaction promotes a change in the hybridization of the BC₃ mesh (Fig. 8a and b). The structural stability was confirmed using a vibrational analysis performed under the harmonic approximation. The calculated IR spectrum is reported in Fig. 3b. Compared to the pristine BC₃ sheet, red shifts (namely, a reduction of the values for the frequencies) are observed for the resonance centered at about 855.1 cm⁻¹. This band is assigned to the bending vibrational mode of both BC₃ and H₂O moieties.

Fig. 8 a and b) Final orientation of H₂O in the BC₃–H₂O system; (c and d) optimized structure for the BC₃/V_C–H₂O; and (e and f) optimized structure for the BC₃/VB–H₂O system according to the LC-wPBE/6-31G(d) level of theory.

For the BC₃–H₂O structure of minimal energy, the estimated adsorption energy of the H₂O molecule on the BC₃ surface is −0.45 eV, and it mainly originates from weak interactions of van der Waals type. Indeed, this value is smaller than the reported adsorption energy of the H₂O unit on the hBN system.³⁴ However, it is larger than the thermal energy of the human body at 36.5 °C (∼27 meV), implying that the adsorbed moieties (sorbates) may not produce significant changes on the properties of the nanostructure, as it has been found in recent studies on the transport of pharmaceuticals by nano-systems.³⁵

In addition, it should be noted that in the BC₃–H₂O interaction, the HOMO–LUMO gap suffers a negligible reduction of 10⁻² (0.43 eV), preserving its semi-metallic properties. This is principally accounted by weak interactions between the BC₃ surface and the water molecule (see Table 4). Similarly, the chemical reactivity, as measured by the chemical potential (μ) or the Fermi level, approximately indicates the experienced sensibility of the BC₃ system due to its reaction with the water molecule. With reference to the pristine BC₃ monolayer, an increase of 0.12 eV was found for μ, yielding a final value of −8.51 eV. This change is due to charge transfer effects.

The MEP contour plots (Fig. 6c) reveal some transfer of charge between the sorbate and the BC₃ network. This is confirmed by the charge distribution analysis reported in Fig. 7b. In fact, the H₂O unit behaves as a donor of electrons, specifically towards the boron atom (which is the site nearer to H₂O). Note the pattern of charge distribution (according to the chosen scale of colors in Fig. 7): from green to red for the zones of negative charge. This type of charge transfer suggests some feasibility of these nanostructures for their use as sensors.³⁶

The pristine BC₃ layer presents a null dipole moment. It was found that the BC₃–H₂O system clearly experiences an increase in polarity, because it presents a value of 3.35 D. Thus, solvation induces marked dipole moments on the nanosheets, making them feasible for the transportation of pharmaceutical species, as has been observed for BN nanotubes.³⁷ Other effect of solvation is a considerable reduction of the work function: from 6.19 eV in BC₃ up to 0.10 eV in BC₃–H₂O. The reduction in the potential energy barrier (increasing or improving the electrical conductivity, as it was discussed in Section 3.1) opens a possible route for the design of electronic devices.

3.3. BC₃/Vc–H₂O interactions

In this section, the effects of the vacancies of carbon atoms (V_C) on the structural and electronic properties of BC₃ are studied (Fig. 8c and d). The effects of such vacancies on the adsorption of a water molecule also are addressed. According to the IR spectrum (Fig. 3c) for the quintuplet (M = 5) low-lying state, the full optimization procedure reveals structural stability for the functionalized BC₃/V_C–H₂O system. Large structural changes are produced on BC₃/V_C, being visible by the induced curvature through the X (of 7.0°) and Y axis (of 131.7°). Remarkably, the BC₃/V_C layer is able to produce reduction of the H₂O molecule, which is dissociated into hydroxyl (HO) and hydrogen (H). As seen in Fig. 9, the evolution of the total energy during the interaction of the BC₃/Vc layer with the H₂O molecule reveals the absence of barrier energies in the dissociation process. As quoted above, the H₂O unit behaves as a donor towards the boron atom. The transfer of electrons from H₂O to B increases the positive charge on the H^δ+ atoms of H₂O, which promotes the bonding of one of such H^δ+ atoms with the nearest (negatively charged) carbon, C^δ−, atom of the BC₃/Vc sheet. Thus, there is a cooperative effect of the C^δ− and B^δ+ sites in the H₂O rupture. At the end, the OH group is bonded to a boron atom, whereas the hydrogen atom is attached to the carbon site that is nearer to the Stone–Wales vacancy. The nature of the BC₃/V_C–H₂O dissociative interaction produces an adsorption energy of −2.11 eV, being classified in the chemisorption regime. The absence of energy barriers has been also observed in the dissociation of the N₂O molecule by a rhodium cluster.³⁸

Fig. 9 Optimization step number vs. total energy (a.u.) for BC₃/V_C–H₂O, indicating the absence of barrier energies.

It should be noted that the BC₃ network experiences some rearrangement, forming a nonagon (where the vacancy was located before the H₂O absorption) and a hexagon of 2B4C composition; it is also observed that other adjacent pentagons are formed by carbon atoms (see Fig. 4a). Another noteworthy feature produced by the curvature is the variation of the C–C bond lengths being contained within 1.36–1.44 Å, whereas the B–C bond length ranges from 1.52 to 1.63 Å. The O–H bond distance has a value of 0.97 Å, which is similar to the reported value for this functional group. The boron atom (of BC₃/V_C) is bonded to the OH functional group with a shorter distance (of 1.36 Å) than the one observed (1.79 Å) for the BC₃–H₂O case. The generation of vacancies in BC₃/V_C–H₂O promotes visible changes on the IR spectrum (see Fig. 3c), as compared to the spectrum of BC₃–H₂O without vacancies. For instance, the spectrum of BC₃/V_C–H₂O reveals the appearance of a resonance at 893.2 cm⁻¹, corresponding to a bending mode of the OH group. The resonance located at 1114.5 cm⁻¹ presents stretching signatures from the O–H group and from the dissociated hydrogen atom (which is bonded now to the carbon atoms nearest to the vacancy).

The MEP contour plots (Fig. 6d) and the population analysis (Fig. 7e) show small but important transfer of charge between dissociated H₂O and the BC₃/V_C layer, as has also been found by others.^24,25 Indeed, after dissociation, BC₃/V_C shows some different electronic distributions (Fig. 7e), principally around the region wherein the H₂O absorption occurs from the BC₃/Vc nanosheet (Fig. 7c). The relatively small changes in the electronic pattern produce a small decrease of the work function, from 0.58 eV in BC₃/V_C to 0.54 eV in BC₃/V_C–H₂O. These values are much smaller than that of pristine BC₃, 6.19 eV, marking the importance of the carbon vacancies on the WF. Such point defects are capable of modifying the charge of the BC₃ layer, thus yielding improvements in the conductivity and in the sensing process.

The quantum descriptors for BC₃/V_C–H₂O show that this system preserves a low value for the chemical reactivity (−8.89 eV) and a high regime of polarity (1.28 D). This is referred to the absence of vacancies: the BC₃–H₂O case (8.51 eV and 3.35 D). These results suggest that the functionalized BC₃/V_C–H₂O system doped with V_C defects may be feasible for the transportation of pharmaceuticals, as well as for the design of optoelectronic devices.

3.4. BC₃/V_B and BC₃/V_B–H₂O interactions

The introduction of a boron vacancy (V_B) on the BC₃ network produces, after relaxation, a quartet (M = 4) low-lying state for BC₃/V_B. Thus, its magnetic moment, 3.0 μ_B, is smaller than that of BC₃/V_C, 4.0 μ_B. However, the adsorption of a water molecule yields a doublet (M = 2) ground state for BC₃/V_B–H₂O, whereas the quartet is very near in energy, as presented in Table 2. Note that BC₃/V_B does not dissociate the H₂O molecule. The IR spectrum for BC₃/V_B–H₂O (Fig. 3d) indicates that the vibrational mode lying at 862.1 cm⁻¹ corresponds to H₂O–C stretching; that is, a carbon site on which the H₂O moiety is attached.

Contrarily to the BC₃/V_C layer, it can be seen that the V_B vacancy is preserved in the BC₃/V_B network, as shown in Fig. 4b, which suffers curvatures of 30.4° through the Y axis and of 19.3° through the X axis. Besides, the V_B vacancies induce visible changes in the C–C and B–C bond lengths, varying from 1.30 to 1.45 Å and from 1.51 to 1.58 Å, respectively. A comparison of these distances is shown in Table 4. It is important to point out that the HOMO–LUMO gaps for BC₃/V_B (0.49 eV) and BC₃/V_C (1.15 eV) signifies quite different behaviors: metallic and semiconductor, respectively. Therefore, doping with boron vacancies may improve the conductivity of the BC₃ nanosheets, as inferred from the expression in Section 3.1. These findings are in agreement with reported metallic results, but differ in the magnetic properties.²¹ The quantum descriptor of chemical reactivity of the BC₃/V_B nanosheet has a similar value (−8.63 eV) as the pristine BC₃ (−8.63 eV) and doped BC₃/V_C (8.88 eV) layers. However, with respect to BC₃/V_C, the polarity of BC₃/V_B is increased by a factor of 3.5, making the solubility of a BC₃ dot with boron vacancies more feasible, as shown in Table 4. Moreover, the small work function of BC₃/V_B (the transference of electrons from the boron to the carbon sites (Fig. 7d) may contribute to this WF behavior) suggests that this system is a good candidate for the design of electronic devices.

The attachment of the water molecule on the BC₃/V_B sheet produces a small binding energy of −0.21 eV, indicating a physisorption process because this value falls in the regime of a weak van der Waals interaction. Consistently, a relatively large distance (2.45 Å) was found between one of the hydrogen atoms of H₂O and the nearest carbon atom of the BC₃/V_B layer. Likewise, the distance between the oxygen atom and the nearest carbon site is 2.51 Å. Note that the H₂O moiety is adsorbed onto the nonagon region produced by the boron vacancy (Fig. 8e and f). These energetic and structural features are quite different from those of the BC₃/V_C–H₂O system, where, as discussed above, the H₂O molecules experience dissociation.

Despite the weak interaction, the adsorbed H₂O molecule promotes significant transfer of charge in BC₃/V_B–H₂O, as it is shown by the MEP plots (Fig. 10a and b) and the charge distribution (Fig. 10c).

Fig. 10 a and b) Molecular electrostatic potential (MEP)³⁹ for the BC₃/V_B–H₂O. The zones marked with red indicate the sites with the most negative charge. (c and d) Charge distribution of BC₃/V_B and BC₃/V_B–H₂O.

For instance, the oxygen atom of the H₂O molecule (Fig. 10d) has a larger negative charge (−0.769e) than the corresponding values in the BC₃–H₂O (−0.575e) and BC₃/V_C–H₂O (−0.522e) systems.

On the other hand, the chemical reactivity descriptor for the interacting BC₃/V_B–H₂O system (−8.89 eV) is similar to that of BC₃/V_B (−8.63 eV). The polarity presents a moderate increase, from 5.43 D (BC₃/V_B) to 7.24 D (BC₃/V_B–H₂O), whereas the HOMO–LUMO gap is reduced from 0.49 to 0.17 eV, as shown in Table 4. After solvation, the work function of BC₃/V_B–H₂O is even lower (0.09 eV) than that of BC₃/V_B (0.25 eV). These features are mainly due to the weak interaction of the H₂O molecule with the BC₃/V_B nanosheet.

4. Conclusions

We performed a first principles DFT theoretical study on the structural and electronic properties of magnetic BC₃ mono-layers, pristine as well as those with carbon, BC₃/V_C, and boron, BC₃/V_B, mono-vacancies. A planar structure was found for the pristine BC₃ layer, wherein the triplet and quintet states are degenerate. The inclusion of carbon vacancies preserves the magnetic properties of BC₃/V_C and promotes the formation of Stone–Wales defects, which produces a large deviation from planarity in this doped system. Such defects do not appear for the boron vacancies layer, BC₃/V_B, also showing a non-planar structure. The interaction of the BC₃, BC₃/V_C and BC₃/V_B nanosheets with a water molecule was also addressed. In BC₃–H₂O and BC₃/V_B–H₂O, the attachment of H₂O on the layers is essentially governed by weak van der Waals forces, producing relatively small adsorption energies of −0.45 and −0.21 eV, respectively. Notwithstanding the weak interaction, significant transfer of charged carriers is carried out in BC₃–H₂O, in reference to BC₃, which is reflected in the quantum descriptors. Indeed, the work function (0.10 eV) of the solvated BC₃–H₂O layer is considerably smaller than that of the pristine BC₃ reference system (6.19 eV). Presenting a weaker interaction (−0.21 eV), the work function of BC₃/V_B–H₂O (0.09 eV) also falls in a low regime, similar to the one exhibited by BC₃/V_B (0.25 eV). Thus, the WF behavior in BC₃/V_B and BC₃/V_B–H₂O is mainly accounted by the boron vacancies. Our results are based on the use of the LC-wPBE functional, accurately accounting for van der Waals forces and for the charge transfers in such long-range processes. Furthermore, it was found that the carbon vacancies produce a stronger interaction with the sorbate. Indeed, in BC₃/V_C–H₂O, the water molecule is dissociated into hydroxyl (HO) and atomic hydrogen (H). Such reduction process, carried out without barrier energies, involves a cooperative effect of the boron and carbon sites lying near the Stone–Wales vacancy of BC₃/V_C. It is initiated by a charge donation from H₂O towards the boron site, which promotes the bonding of one H atom from H₂O with the nearest carbon site. At the end, the OH and H moieties are bonded to such B and C atoms. Despite the B–OH and C–H bonding, we believe that BC₃/V_C is a promising system to obtain hydrogen, a required fuel nowadays. Roughly, in BC₃/V_C–H₂O, the H₂O moiety is chemisorbed with a larger binding energy of about −2.11 eV. Moreover, the obtained results in this study suggests that BC₃–H₂O, without and with (V_C and V_B) defects, is appropriate for the transport of pharmaceutical compounds, which is due to its solvation feasibility, as is indicated by its high polarity. This behavior is similar to the one found for boron nitride nanotubes. Remarkably, in the BC₃/V_B monolayer, with a polarity of 5.43 D, the adsorption of a water molecule occurs around the vacancy region, bonding weakly with both H and O atoms. It is expected that bigger (pharmaceutical) molecules would be more firmly bonded on such a region making their transport feasible. In the design of electronic devices, low values for the work function are required to improve the electrical conductivity. It was found that the functionalization of the BC₃ nanosheets (without and with V_C and V_B vacancies) with water molecules considerably reduces the work function: 98.4% for the functionalized case and 91.3% for the system presenting defects. Finally, the appearance of magnetic moments, 2 μ_B, 4 μ_B, and 3 μ_B for BC₃, BC₃/V_C, and BC₃/V_B, respectively, suggest that this type of two-dimensional nanostructure may be important in the construction of magnetic devices. Thus, the design of electronic and sensing devices based on boron-doped graphene systems, similar to those addressed in this study, are feasible. Overall, a recent report of graphene doped with boron provides support that the obtained results in the present study are in such a direction.⁴²

Acknowledgements

This study was partially supported by projects: VIEP-BUAP (Grant: CHAE-ING16-G) and Cuerpo Académico Ingeniería en Materiales (BUAP-CA-177). We thank the support given by the National Laboratory Supercomputing Southeast housed in the Benemérita Universidad Autónoma de Puebla. We also strongly acknowledge the financial support from DGAPA-UNAM under the PAPIIT-IN-212315 project.

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