The C₂N surface as a highly selective sensor for the detection of nitrogen iodide from a mixture of NX₃ (X = Cl, Br, I) explosives

Abstract

Explosives are quite toxic and destructive; therefore, it is necessary to not only detect them but also remove them. The adsorption behavior of NX₃ analytes (NCl₃, NBr₃ and NI₃) over the microporous C₂N surface was evaluated by DFT calculations. The nature of interactions between NX₃ and C₂N was characterized by adsorption energy, NCI, QTAIM, SAPT0, NBO, EDD and FMO analysis. The interaction energies of NX₃ with C₂N are in the range of −10.85 to −16.31 kcal mol⁻¹ and follow the order of NCl₃@C₂N > NBr₃@C₂N > NI₃@C₂N, respectively. The 3D isosurfaces and 2D-RGD graph of NCI analysis qualitatively confirmed the existence of halogen bonding interactions among the studied systems. Halogen bonding was quantified by SAPT0 component energy analysis. The SAPT0 results revealed that ΔE_disp (56.75%) is the dominant contributor towards interaction energy, whereas contributions from ΔE_elst and ΔE_ind are 29.41% and 14.34%, respectively. The QTAIM analysis also confirmed the presence of halogen bonding between atoms of NX₃ and C₂N surface. EDD analysis also validated NCI, QTAIM and NBO analysis. FMO analysis revealed that the adsorption of NI₃ on the C₂N surface caused the highest change in the E_HOMO–LUMO gap (from 5.71 to 4.15 eV), and resulted in high sensitivity and selectivity of the C₂N surface towards NI₃, as compared to other analytes. It is worth mentioning that in all complexes, a significant difference in the E_HOMO–LUMO gap was seen when electronic transitions occurred from the analyte to the C₂N surface.

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1. Introduction

Chemical warfare and toxic explosives pose serious threats to civilians and the military defense system. It is essential to quickly detect and dispose of these chemical warfare agents (CWAs) and toxic explosives for the safety and security of civilian and military defense systems. Nitrogen halides are extremely explosive materials in which the N-atom is connected with one of the halogen atoms (Cl, Br and I). NI₃ is a highly shock-sensitive red crystalline material and can even explode under slight mechanical stress.^1,2 It is usually stable in NI₃·NH₃ adduct form. NCl₃ is a bright yellow volatile liquid that has an unpleasant smell, with a reported melting point of −27 °C and can auto-ignite in the range of 71–73 °C.³ The red oily volatile liquid NBr₃ is also a temperature-sensitive agent.⁴ The literature review revealed that many studies have been carried out for the detection of NCl₃ on different surfaces with different chemical methods.^5–8 As far as we know, no such studies have been reported for NBr₃ and NI₃ due to their extreme explosive nature.

In recent times, researchers have been mainly working to develop a method for the disposal and detection of these explosives.^9,10 For the detection and decay of these explosives, various expensive techniques, such as gas and liquid chromatography¹¹ and spectroscopic techniques have been applied; however, these techniques fail to detect these explosives at low concentrations.¹² Moreover, these techniques also require sophisticated sample preparation and skilled persons. The prime requisites for a quality sensor are low cost, fast response, metal-free nature, high selectivity and reproducibility.^13,14 Moreover, it should have a high surface to volume ratio over which the analyte can easily and effectively interact.¹⁵

A large number of materials such as zeolites,¹⁶ metal–organic frameworks,^2,3,17,18 metal clusters,¹⁹ pristine and boron-doped graphene,²⁰ graphene,^21–23 semiconductor nanowires,²⁴ carbon nitride,²⁵ boron nitride,²⁶ aluminum nitride²⁷ and phosphorous carbide sheets,²⁸ have been studied in the past few decades as sensors for detecting trace quantities of these explosives. The major problems still faced by the sensor industries are cost, limited sensitivity, and the lack of reproducibility and sensitivity of the sensor to humidity and temperature.

In this study, we selected the electron-rich nitrogenated holey graphene (C₂N) surface as the electrochemical sensor for the detection and capture of nitrogen halide (NCl₃, NBr₃ and NI₃) explosives. In the recent past, several studies have been devoted to predicting the stabilities of yet to be synthesized 2D surfaces. For example, Gueorguiev and coworkers studied the stability of CFx surfaces through first-principles calculations. In another study, the effects of hydrogenation and fluorination in curved 2D carbon surfaces were explored.^29,30 The C₂N is a 2D material with controlled pore size and periodic geometry. It was recently synthesized by Mahmood et al., via wet chemistry.³¹ C₂N consists of fused rings of benzene and pyrazine, which make it a highly π-conjugated structure. C₂N has been used in many fields like batteries,^32–34 catalysis,^35,36 optical devices,³⁷ gas storage^38,39 and photo-catalysis,⁴⁰ C₂N surface with electron-rich nitrogenated cavity has tremendous potential of electrochemical sensor, as reported earlier by Xu et al.⁴¹ It has also been studied for physical adsorption of toxic and noble gases like H₂S, HF, NH₃, HCN, CH₄, N₂, CO₂, He, Ne and Ar.^42,43 To the best of our knowledge, the selected C₂N surface has not been previously studied as an electrochemical sensor for NX₃ explosives. The electron-rich nitrogenated cavity of C₂N is thermally stable with a high surface to volume ratio, which provides an ideal environment for the interaction of analytes. Density functional theory (DFT) calculations were executed to investigate the adsorption of NX₃ on the C₂N surface. The nature of the non-covalent interactions between NX₃ and the C₂N surface was further explored through Bader's quantum theory of atoms in molecules (QTAIM), non-covalent interactions (NCI), and symmetry adopted perturbation theory (SAPT0) analysis. The electronic properties of NX₃@C₂N complexes were studied through electronic density differences (EDD), natural bond orbital analysis (NBO) and frontier molecular orbital analysis (FMO).

2. Computational methodology

All DFT calculations for the adsorption of NX₃ analytes on C₂N surface were executed using the Gaussian 09 software due to its established accuracy and efficacy. For the geometry optimization of analtyes@C₂N complexes, the M05-2X/LANL2DZ level of theory was applied, which is the best for studies of non-covalent interactions.^44–53 The level of theory chosen was quite adequate for such a complex system. The literature revealed several examples where complex systems were treated with a comparable level of theory.^{47,50,54–56,58} The non-bonding interactions can play a vital role in deciding the properties of a system and need to be modeled accurately to determine the interactions of NX₃ analytes with the C₂N surface. Although NI₃ exists in the form of the NI₃·NH₃ adduct, we did not include this adduct in our study because we wanted to have a comparative study of NX₃ explosives. This adduct is important only for NI₃ but not for other NX₃ molecules. The visualization of the geometries and the evaluation of the structural parameters were carried out using the GaussView 5.0 ^57,59,60 and Chemcraft software.⁶¹ To confirm the optimized geometries as true minima on the potential energy surface, vibrational frequency analysis was performed at the same level of theory.

In search of stable geometries containing the analytes@C₂N complex, many different possible orientations of each analyte on the C₂N surface were simulated. The adsorption energies of analytes@C₂N surface are defined as follows:

ΔE = [E_NX3@C2N − (E_NX3 + E_C2N)] (1)

where E_NX3@C2N, E_NX3 and E_C2N are the energies of the complex, analytes and C₂N, respectively. The adsorption energies of stable geometries for these complexes were further corrected by the counterpoise method to avoid basis set superposition error (BSSE). The BSSE corrected energy is calculated as follows:

E_int.CP = E_int − E_BSSE (2)

where E_int.CP, E_int and E_BSSE are the counterpoised corrected energy, non-corrected interaction energy and basis set superposition error energies of NX₃@C₂N complexes.

Symmetry adapted perturbation theory (SATP0) analysis was performed with the PSI4 software.⁵¹ SAPT0 analysis gives a quantitative idea about the components of energies (induction, dispersion, exchange and electrostatic) involved in non-covalent interactions between NX₃ and the C₂N surface. The total energy of SAPT0 components is represented as follows:

ΔE_int = ΔE_elstat + ΔE_exch + ΔE_ind + ΔE_disp (3)

Induction energy (ΔE_ind) arises due to interactions between filled and partially filled orbitals, while the exchange (ΔE_exch) energy part of SAPT0 indicates repulsion between the two fragments of filled orbitals. Similarly, the dispersion energy (ΔE_disp) term represents attractive interactions between filled orbitals where the electrostatic energy (ΔE_elst) part arises due to interactions between polarized orbitals of two fragments.

Non-covalent interactions between NX₃ and C₂N were mapped using Multiwfn 3.7 software.^62,63 NCI analysis is described by two factors, i.e., the electron density (ρ) and reduced density gradient (RGD), for understanding the nature of the interactions. The relationship between these factors is represented as follows:

The sign and the value of the electron density (ρ) is a major descriptor for the characterization of the nature of non-covalent interactions. The plot of RDG versus (λ₂)ρ signifies the nature of the interactions. Here, λ₂ is the second Eigenvalue of the Hessian matrix, which gives better information for understanding the nature of interactions. The sign (λ₂)ρ < 0 represents the accumulations of the electron density (non-covalent interactions), while the sign (λ₂)ρ > 0 represents the depletion of the electron density (repulsive interactions). The signs and values of (λ₂)ρ are also represented in color-coded form, which are green ((λ₂)ρ < 0 to −0.01 a.u.), red ((λ₂)ρ > 0) and blue ((λ₂)ρ < −0.01 a.u.) to show weak van der Waals, repulsive and H-bonding interactions, respectively.^64,65

Non-covalent interactions were further quantified by Bader's quantum theory of atoms in molecules (QTAIM).^66,67 The topological parameters of QTAIM analysis used in non-covalent interactions are electron density (ρ), the Laplacian (∇²ρ), −V/G, energy density (H(r)) and E_int (individual bond interactions energy). The non-covalent interactions between interacting systems in QTAIM analysis are usually predicted by the bond critical point.⁶⁸ Besides the above-mentioned interaction properties, we also studied the charge transfer of NX₃@C₂N complexes through electron density differences (EDD)^69–71 and natural bond orbitals (NBO). EDD analysis was conducted by taking the difference in the electron density of the complex from its constituents (C₂N and analyte). Frontier molecular orbital analysis (FMO) was executed to study the changes in the conductivity of the C₂N before and after complexation with analytes.

3. Results and discussion

3.1 Geometric optimization and interaction energies

The optimized C₂N single-layer structure selected as the electrochemical sensor is presented in Fig. 1, which consists of benzene and pyrazine rings in the fused form. The nitrogen atoms present in the pyrazine ring are arranged periodically in such a way that they form an electron-rich nitrogenated cavity with 8.30 Å diameter.³¹ The existence of the electron-rich nitrogenated cavity of the C₂N surface offers powerful binding and capturing frameworks for shock sensitive agents (NX₃).

Fig. 1 The optimized geometry of the nitrogenated holey graphene (C₂N) at the M05-2X/LANL2DZ level of theory.

The binding sites over the C₂N structure are represented as A (center of cavity), B (triangle between two nitrogen), C (at top of benzene) and D (at pyrazine rings) (see Fig. 1). To find the stable geometry of the analytes@C₂N complexes, all possible orientations of each analyte over the four possible binding sites are tested. The most stable optimized geometries of analytes@C₂N are given in Fig. 2, while the rest of the geometries are shown in Fig. S1 (ESI†).

Fig. 2 Graphical representation of the interactions and BSSE energies of NX₃@C₂N complexes.

The interaction energies and bond lengths of the studied analytes are given in Table 1 and Fig. 2 (graphical form). The observed interaction energies of the most stable studied NX₃@C₂N complexes are −10.85 kcal mol⁻¹ (NCl₃), −13.78 kcal mol⁻¹ (NBr₃) and −16.33 kcal mol⁻¹ (NI₃), while other interaction energies are given in Table S1.† Similarly, energies of complexes are also corrected by the basis set superposition error (see Table 1).

Table 1 Interaction and BSSE energies (kcal mol⁻¹) of NX₃@C₂N complexes

Bond length (Å)	A	Bond length (Å)	B	Bond length (Å)	C	Bond length (Å)	D	Bond length (Å)	Eint (kcal mol^−1)	BSSE (kcal mol^−1)
NCl3@C2N	Cl4⋯N1	3.18	Cl4⋯N2	3.00	Cl4⋯N3	3.18	Cl4⋯X	1.84	−10.85	−7.96
NBr3@C2N	Br4⋯N1	3.22	Br4 ⋯N2	3.01	Br4⋯N3	3.18	Br4⋯X	1.87	−13.78	−11.34
NI3@C2N	I4⋯N1	3.25	I4⋯N2	3.01	I4⋯N3	3.24	I4⋯X	1.94	−16.33	−14.41

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The analytes studied for sensor studies were nitrogen halides. In most of the complexes, the halogen atoms (Cl, Br, I) of analytes interacted with the N-atoms of the C₂N cavity. Such non-covalent interactions where covalently bonded halogens interact with high electronegative atoms are known as halogen bonding. Halogen bonding is an intermolecular force of attraction in which halogen atoms accept electrons from highly electronegative atoms.⁷² Halogen bonding interactions have been the topic of recent interest in the scientific community because of their potential for use in supramolecular chemistry,^73,74 crystal engineering,^75,76 molecular recognition,⁷⁷ rational drug design,⁷⁸ and catalysis.⁷⁹ In these interactions, a part of the halogen acts as the electrophile (σ-hole).⁸⁰ The σ-hole interactions increase as the size and polarizability of the halogen atoms (I > Br > Cl > F) increase.⁸¹ This trend of halogen polarizabilities shows that the I-atom should form stronger halogen bonds with Lewis bases (N-atoms). The same trend of halogen bonding was observed in our studied complexes (vide infra).

The stable conformation of NCl₃@C₂N resulted in the adsorption energy of −10.85 kcal mol⁻¹ (BSSE = −7.96 kcal mol⁻¹). The optimized geometry of the stable NCl₃@C₂N complex revealed that one of the Cl atom of NCl₃ was projected towards the center of the C₂N cavity (site A) with the interaction distance of 1.84 Å, while the other two Cl atoms moved upwards. The Cl atom of NCl₃ and N-atoms (site B) of the C₂N surface interacted through a longer bond distance as compared to site A (see Table 1). However, halogen bonding between the Cl atom of NCl₃ and N-atoms of the C₂N produced a stable optimized geometry of the complex.

The same strategy was adopted for the NBr₃@C₂N complex (as with the NCl₃@C₂N complex) to obtain a stable geometry. The stable NBr₃@C₂N complex had an interaction energy of −13.78 kcal mol⁻¹ (BSSE = −11.78 kcal mol⁻¹). The interaction energy of NBr₃@C₂N was greater than that of the NCl₃@C₂N complex. The orientation of NBr₃ over C₂N in the stable conformation was similar to that of the NCl₃@C₂N complex (Fig. 3). The Br-atom of NBr₃ interacts at site A of the C₂N cavity through an interaction distance of 1.87 Å. The interaction distances were in the range of 3.01 to 3.22 Å, through which the other Br-atoms of NBr₃ interact with the N-atoms of the C₂N surface.

Fig. 3 The top and side views of the optimized geometries of analytes@C₂N at the M05-2X/LANL2DZ level of theory.

The stable optimized geometry of the NI₃@C₂N complex (E_int = −16.31 kcal mol⁻¹; BSSE = −14.41 kcal mol⁻¹) had the same orientation as the other two NX₃@C₂N complexes. The I-atom of NI₃ interacted at site A of the C₂N cavity at the interaction distance of 1.94 Å. The optimized geometry of the NI₃@C₂N complex revealed that the I-atom of NI₃ interacted with the N-atoms of C₂N with interaction distances ranging from 3.01 Å to 3.25 Å.

The results of all complexes showed that the X-atoms (halogens) acted as electrophiles (σ-hole) in non-covalent interactions with the electron-rich nitrogenated cavity of C₂N. The interaction energy results of the NX₃@C₂N complexes supported the existence of the physisorption mechanism. The interaction energy trend observed for the NX₃@C₂N complexes was NCl₃@C₂N > NBr₃@C₂N > NI₃@C₂N. The interaction energy results indicate that C₂N can accommodate NX₃ analytes on its surface, but the highest interaction energy was seen for the NI₃@C₂N complexes (−16.31 kcal mol⁻¹). The I-atoms of NI₃ interacted through longer bond distances with the C₂N surface as compared to the NBr₃ and NCl₃. The possible reason for the high interaction energy for the NI₃@C₂N complex was the stronger halogen bonding between the I-atoms of NI₃ and N-atoms of C₂N.

3.2 Non-covalent interaction (NCI) analysis

NCI analysis was carried out to understand the nature of the intermolecular interactions. The NCI analysis consists of 3D isosurfaces and 2D reduced density gradient (RDG) graphs of the complexes. The 2D-RDG graph and 3D isosurfaces of the NCI analysis for the NX₃@C₂N complexes are presented in Fig. 4. The 3D isosurfaces of all the analytes showed the presence of green patches between the surface of C₂N and the analytes. Similarly, the red patch projection was also seen in the benzene and pyrazine ring of the C₂N cavity. For NCl₃@C₂N, the 3D isosurface showed the presence of weak dispersive interactions between the Cl atoms of NCl₃ and N&C-atoms of the C₂N surface; this can be seen in the 2D-RGD graph. The projection of green spikes appeared between 0 to −0.01 a.u. at the (λ₂)ρ axis, which confirmed the existence of the non-covalent dispersive interactions in the NCl₃@C₂N complex. The higher density of green patches was observed in the NBr₃@C₂N complex as compared to that of the NCl₃@C₂N complex.

Fig. 4 NCI isosurfaces and 2D-RDG graphs of the optimized geometries of stable complexes obtained via the M05-2X method (iso value = 0.05 a.u.).

The shattered spikes of the 2D-RGD graph of the NBr₃@C₂N complex also appeared at −0.01 a.u. of (λ₂)ρ at the X-axis, which illustrated the stronger forces of interactions between the Br-atoms of NBr₃ and the N & C-atoms of C₂N as compared to that of NCl₃@C₂N complex (see Fig. 4). Among the NX₃@C₂N analytes, NI₃ exhibited the strongest interaction with the C₂N surface, which was confirmed by the thick and wide green patches seen in the 3D isosurface, and the projection of spikes between 0.01 to −0.02 a.u. at the X-axis of (λ₂)ρ. The results of NCI analysis are consistent with those of the interaction energy of the NX₃@C₂N complexes.

3.3 SAPT0 analysis

Although NCI analysis indicates the presence of attractive and repulsive interactions between the components of a system, it would be better to understand the quantitative nature of the interactions in the studied complexes. In this regard, SAPT0 analysis was performed using the PSI4 software. The SAPT0 energy was divided into four terms, i.e., E_disp, E_exch, E_elst and E_ind. The results of the SAPT0 analysis are given in Table 2, whereas the graphical representation is given in Fig. 5. The SAPT0 values vary in each case, which indicates the different modes of interactions in the NX₃@C₂N complexes. The SAPT0 values observed for the NX₃@C₂N analytes were −14.59 kcal mol⁻¹ (NCl₃@C₂N), −18.84 kcal mol⁻¹ (NBr₃@C₂N) and −25.65 kcal mol⁻¹ (NI₃@C₂N), respectively. The results of the SAPT0 energy components are consistent with the interaction energy results. The components of the SAPT0 energy for NCl₃@C₂N were −8.39 kcal mol⁻¹ (E_elst), −4.21 kcal mol⁻¹ (E_ind) and −19.26 kcal mol⁻¹ (E_disp). These results indicate that the dispersion (60.47%) was the major stabilizing factor, whereas electrostatic (26.33%), and induction (13.20%) were less prominent in the total interaction energy.

Table 2 SAPT0 energy component analysis of the NX₃@C₂N complexes

	ΔEelst (%)	ΔEexch	ΔEind (%)	ΔEdisp (%)	ΔESAPT0
NCl3@C2N	−8.39 (26.33)	17.26	−4.21 (13.20)	−19.26 (60.47)	−14.59
NBr3@C2N	−12.42 (28.95)	24.06	−6.15 (14.34)	−24.33 (56.70)	−18.84
NI3@C2N	−18.53 (32.94)	30.59	−7.87 (13.98)	−29.85 (53.08)	−25.65

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Fig. 5 Graphical representation of the SAPT0 components of the NX₃@C₂N complexes.

In the case of the NBr₃@C₂N complex, the contributions of each component of energy towards total SAPT0 were −12.42 kcal mol⁻¹ (E_elst), −6.15 kcal mol⁻¹ (E_ind) and −24.33 kcal mol⁻¹ (E_disp). The trend of SAPT0 components (E_disp > E_elest > E_ind) of NBr₃@C₂N is comparable to that of NCl₃@C₂N, where E_disp (56.70%) is dominant. The E_disp component in NBr₃@C₂N was less significant as compared to E_disp (60.47%) of the NCl₃@C₂N complex. Similarly, the increase in the E_ind (14.34%) and E_elst (28.95%) terms was noticed in the NBr₃@C₂N complex. Among the studied NX₃@C₂N complexes, the highest SAPT0 energy (−25.65 kcal mol⁻¹) was observed for the NI₃@C₂N complex due to the stronger σ-hole interactions (halogen bonding) between the I-atoms of NI₃ and the N-atoms of the C₂N surface. The results (Table 2) revealed that the large contribution toward the total SAPT0 for the NI₃@C₂N complex was from E_disp (53.08%), quite similar to the NCl₃@C₂N and NBr₃@C₂N complexes. The contribution from E_elst (23.94%) and E_ind (13.98%) remained appreciable.

In the overall interactive components, the largest stabilizing factor remained E_disp (56.75%), whereas a moderate contribution was observed from E_elst (29.41%) and E_ind (14.34%), respectively. The trend of SAPT0 energy observed in the case of the NX₃@C₂N complexes is consistent with E_int, and NCI analysis.

3.4 Quantum theory of atoms in molecules (QTAIM) theory

Quantum theory of the atoms in molecules (QTAIM) analysis is well-known because of its ability to describe various intra- and intermolecular interactions (H-bonding, ionic bonding, van der Waals interactions). Many topological parameters such as electron density (ρ), the Laplacian (∇²ρ), and total electron energy density (H(r)) are used at the bond critical point to quantify and understand the nature of the interactions.

The strength of a bond is measured by the electron density ρ value at BCPs, whereas the nature of interactions is characterized by the Laplacian (∇²ρ), potential energy density V(r), kinetic energy density G(r), and total electron energy density H(r). For shared shell interactions (such as covalent bonds), the electron density is greater than 0.1 a.u., while the Laplacian (∇²ρ) remains always large and negative. For closed interactions, (van der Waals, ionic and H-bonding), ρ lies in the range of 0.002–0.034 a.u. and the Laplacian (∇²ρ) is in the range of 0.024–0.139 a.u. Through the Espinosa approach of individual bond interaction energy, non-covalent interactions, particularly H-boding (3 to 10 kcal mol⁻¹), can be better understood through eqn (5).^82–86

BCPs of closed and shared shells can also be explained by the following equations:

H(r) = G(r) + V(r) (7)

Here, E_int, V(r), G(r) and H(r) are the individual bond interaction energy, potential energy density, kinetic energy density and total electron energy density at BCPs. H(r) < 0 indicates a shared shell, while H(r) > 0 reveals closed-shell interactions. We can also use the values of H(r) and ∇²ρ(r) to project the nature and type of interactions. The values of ∇²ρ(r) and H(r) greater than zero indicate non-covalent interactions, whereas ∇²ρ(r) and H(r) less than zero indicate covalent interactions, ∇²ρ(r) greater than zero and H(r) less than zero at BCPs indicate the existence of partial covalent character. The BCPs values of the closed-shell interactions of analytes@C₂N complexes are given in Table S2 (ESI†) and topological complexes are shown in Fig. 6.

Fig. 6 QTAIM topological analysis of NX₃@C₂N complexes for non-covalent interactions.

The observed numbers of BCPs in NX₃@C₂N complexes were 9 (NCl₃@C₂N), 8 (NBr₃@C₂N) and 8 (NI₃@C₂N) through QTAIM analysis. The evaluated ρ(r) and ∇²ρ(r) values of intermolecular BCPs were positive for all NX₃@C₂N complexes, which indicated the presence of non-covalent interactions (see Table S2†). In addition to this, the −V(r)/G(r) ratio was <1 and it ranged from 0.74 to 0.84, which confirmed the existence of weak non-covalent interactions. The value of ρ(r) and ∇²ρ(r) at BCPs also quantified the nature of the interactions. The ρ(r) of the various intermolecular interactions in the NX₃@C₂N complexes ranged from 0.005 to 0.013, while ∇²ρ(r) was from 0.009 to 0.057.

The observed ρ(r) and ∇²ρ(r) were the highest for the NI₃@C₂N complex due to the stronger halogen bonding between the I-atoms of NI₃ and the N-atoms of C₂N. The smallest values of ρ(r) and ∇²ρ(r) at BCPs were observed for the NCl₃@C₂N complex due to weak halogen bonding between the Cl-atoms of NCl₃ and the N-atoms of C₂N. The ρ(r) and ∇²ρ(r) values for the NBr₃@C₂N complex remained intermediate between NCl₃@C₂N and NI₃@C₂N. In addition to X–N (X = Cl, Br, I) interactions between the analyte and C₂N, other weak interactions among the X-atoms of the analytes and the C-atoms of the C₂N surface were also seen (see Fig. 6). The X-atoms of analytes pointing towards the surface acted as electrophiles and developed non-covalent interactions with the highly electronegative N-atoms. The rest of the X-atoms away from the surface acted as nucleophiles and produced weak van der Waals interactions with the C-atoms of the C₂N surface (vide infra). Therefore, the trend established in the studied analytes@C₂N complexes according to the topological parameters was NI₃@C₂N > NBr₃@C₂N and NCl₃@C₂N complexes.

The results of the individual bond interactions of the NX₃@C₂N complexes were between −0.59 and −3.19 kcal mol⁻¹. The highest individual bond interactions were seen for the NI₃@C₂N complex. The other parameters (H(r), −V(r)/G(r)) were also in accordance with the ρ(r) and ∇²ρ(r) of the studied BCPs. This was due to the low individual bond interaction energy and longer interaction distance (1.8 Å) between interacting systems. The trend of individual bond interactions was also comparable to the rest of the topological parameters and consistent with the interaction energy results, NCI and SAPT0 analysis.

4. Electronic properties

4.1 Electron density differences analysis

We calculated the three-dimensional electron density differences and evaluated the charge transfer between analytes (NX₃) and the C₂N surface. The isosurfaces obtained by electron density differences are given in Fig. 7. The isosurface of NX₃@C₂N consists of green and purple shades to represent the depletion and accumulation of charge densities, respectively. It is worth mentioning that the accumulation of charge density takes place where the atoms of analytes interact with the C₂N surface of C₂N (see Fig. 7), this shows the existence of van der Waals interactions between the atoms of NX₃ and the C₂N surface.

Fig. 7 Electron density difference plots of analytes@C₂N (iso value = 0.004 a.u.). Purple represents the accumulation of electron density, while green surfaces show the depletion of electron density.

The electron density differences (Fig. 7) clearly indicate that the flow of electron was from the C₂N surface to analytes, as revealed by the appearance of green surfaces on the X-atoms (Cl, Br and I) of analytes and the purple surfaces on the N-atoms of C₂N. The charge transfer from C₂N to the X-atoms of analytes is due to halogen bonding. The EDD results in Fig. 7 also indicate that the X-atom of NX₃ oriented toward the C₂N surface shows the electrophilic character (σ-hole) due to the formation of green surfaces. The X-atoms of analytes projected away from the C₂N surface show nucleophilic character due to the formation of purple surfaces. The maximum accumulation of densities was seen between the Br-atoms of NBr₃ and the N-atoms of C₂N, which is consistent with the results of NBO analysis.

4.2 Natural bond orbital analysis

Charge analysis provides valuable information about the amount of charge transfer between the studied systems. During the interaction of NX₃ with the C₂N surface, the analytes take the negative charge and deliver positive charge to the C₂N surface (Table 3). The charges transferred from the C₂N surface to the analytes were −0.001e⁻ (NCl₃), −0.006e⁻ (NBr₃) and −0.004e⁻ (NI₃). Surprisingly, the charge analysis results show that NBr₃ extracted a relatively higher amount of charge (−0.006e⁻) from the C₂N surface as compared to NCl₃ (−0.001e⁻) and NI₃ (−0.004e⁻). This finding of charge analysis in the case of the NBr₃@C₂N complex is somewhat contradictory to the interaction energy results. In the case of the NI₃@C₂N complex, the higher interaction energy resulted from the strong halogen bonding of highly polarizable I-atoms of NI₃ with the N and C atoms of the C₂N surface (vide supra). The charge extracted by NI₃ from C₂N was slightly lower than NBr₃ due to the greater interaction distance in the former (from the C₂N surface). The lowest charge transfer was observed in the case of NCl₃ (−0.001e⁻) due to its weak halogen bonding. The halogen bonding increased in the order of F < Cl < Br < I due to σ-hole character. The NBO charge analysis values of NCl₃ were consistent with their low interaction energy results.

Table 3 The results of the frontier molecular orbital and NBO analyses of the analytes@C₂N surface

Analytes	HOMO (eV)	LUMO (eV)	EH–L gap (eV)	NBO (e^−) on analytes
C2N	−8.06	−2.35	5.71	—
NCl3@C2N	−8.12	−2.54	5.58	−0.001
NBr3@C2N	−7.98	−2.69	5.29	−0.006
NI3@C2N	−6.86	−2.71	4.15	−0.004

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4.3 Frontier molecular orbital (FMO) analysis

To better understand electronic changes caused by the interaction of analytes on the C₂N surface, FMOs were analyzed before and after the complexation of analytes (NX₃) over the C₂N surface. Energies of the highest occupied molecular orbitals (E_HOMO), lowest unoccupied molecular orbital (E_LUMO) and E_H–L gap for NX₃@C₂N complexes are given in Table 3, and their orbital densities are given in Fig. 8. The E_HOMO and E_LUMO of the bare C₂N surface were −8.06 eV and −2.35 eV, which resulted in a 5.71 eV E_H–L gap. The orbital density in the HOMO was distributed on the entire C₂N surface, while the density of LUMO was located mostly on the nitrogen atoms of the C₂N surface.

Fig. 8 Top and side views of the HOMO and LUMO densities of the analytes@C₂N surface.

The interaction of analytes (NX₃) over the C₂N surface not only causes changes in the E_HOMO and E_LUMO but also in their orbital densities. The E_H–L gaps observed upon the interaction of the analytes@C₂N surfaces were 5.58 eV (NCl₃@C₂N), 5.29 eV (NBr₃@C₂N) and 4.15 eV (NI₃@C₂N). For NCl₃@C₂N, E_HOMO and E_LUMO were −8.12 eV and −2.54 eV, respectively, which showed that the energies of both HOMO and LUMO were affected by complexation. The energies of the HOMO and LUMO slightly decreased with the adsorption of NCl₃ on the C₂N surface. However, the effect was more pronounced on the LUMO, which resulted in the decrease in the E_H–L gap to 5.58 eV.

A significant decrease in the E_H–L gap (5.29 eV) was observed in the NBr₃@C₂N complex. Table 3 shows that the adsorption of NBr₃ on C₂N caused the energy of the HOMO to increase from (−8.06 eV to −7.98 eV) but the energy of the LUMO decreased from −2.35 to −2.69 eV), which resulted in a relatively small E_H–L gap (5.29 eV). Among the studied NX₃@C₂N complexes, the highest decrease in the E_H–L gap (4.15 eV) was observed for the NI₃@C₂N complex. The substantial increase in the energy of the HOMO (−6.86 eV) and the decrease in the energy of the LUMO (−2.71 eV) resulted in the lowering of the E_H–L gap. The results of the FMO analysis revealed that the complexation of NI₃ over the C₂N surface increased the conductivity of C₂N due to the highest decreases in the E_H–L gap of C₂N (4.15 eV) as compared to other analytes. These results also showed the strong sensitivity and selectivity of the C₂N surface towards NI₃ as compared to the rest of the analytes. FMO analysis revealed that the adsorption of analytes produced a more pronounced effect on the HOMO energies as compared to the LUMO, which led to the greatest decrease in the E_H–L gap.

The orbital plots showed significant changes in the HOMO and LUMO densities with the adsorption of analytes over the C₂N surface. The HOMO–LUMO density analysis of the NCl₃@C₂N complex showed that the HOMO density was completely concentrated over the C₂N surface, while the LUMO density was distributed on NCl₃ as well as on half of the C₂N. In the case of the NBr₃@C₂N complex, the distribution pattern of the HOMO densities was different from the NCl₃@C₂N complex, however, the LUMO distribution pattern was similar to the NCl₃@C₂N complex. The HOMO density was mainly contributed by NBr₃ with a small contribution from the N-atoms of the C₂N surface. In the NI₃@C₂N complex, the pattern of orbital density distribution is comparable to the NBr₃@C₂N complex, where the HOMO density is located on the analytes, whereas LUMO was distributed between the analytes and the C₂N surface (see Fig. 8). The E_H–L gap is presented in graphical form in Fig. 9.

Fig. 9 Graphical representation of the E_H–L gap of the bare C₂N surface and the NX₃@C₂N complexes.

FMO analysis revealed that the decrease in the E_H–L gap was observed when the electronic transition occurred from the analyte to the C₂N surface, which was evident in the case of the NI₃@C₂N complex. These findings clearly indicate that the shift in the electronic density is very important for the electrochemical identification of analytes over the C₂N surface. These results indicate that the C₂N sensor response is more toward NI₃ as compared to the rest of the studied analytes. The FMO results are in strong agreement with the NCI and SAPT0, QTAIM and interaction energy results.

5. Conclusion

The adsorption of the NX₃ analytes (NCl₃, NBr₃ and NI₃) over the C₂N surface was investigated by using DFT calculations at the M05-2X/LANL2DZ level of theory. For a thorough understanding of the NX₃@C₂N complexes, adsorption energy, NCI, QTAIM, SAPT0, NBO, EDD and FMO analyses were performed. The interaction energies of the NX₃@C₂N complexes were in the range of −10.85 to −16.31 kcal mol⁻¹. These results demonstrate that the physisorption phenomena were represented for the adsorption of analytes on the C₂N surface. The interaction energy trends observed for NX₃@C₂N complexes are NCl₃@C₂N > NBr₃@C₂N > NI₃@C₂N, respectively. The stable geometries of the analytes@C₂N complexes were mainly obtained by the interaction of the X-atoms (Cl, Br, I) of the analytes with the C₂N surface.

The 3D isosurfaces and 2D-RGD graph of the NCI analysis also confirmed the existence of halogen bonding interactions among the studied systems. The halogen bonding was also quantified by SAPT0 component energy analysis. The SAPT0 results revealed that dispersion was the most prominent contributor to SAPT0 energy, whereas lower contributions were observed from ΔE_elst (29.41%) and ΔE_ind (14.34%). The topological parameters ((ρ(r) and ∇²ρ(r)) of QTAIM analysis also confirmed the presence of halogen bonding between the X-atoms of NX₃ and C₂N. NBO analysis showed that in all cases, the transfer of charge happened from C₂N to the analytes. A significant amount of charge was received by NBr₃ (−0.006e⁻) and NI₃ (0.004e⁻). EDD analysis also validated the NCI, QTAIM and NBO analyses. FMO analysis revealed that the adsorption of NI₃ on the C₂N surface caused significant changes in the E_HOMO–LUMO gap (from 5.71 to 4.15 eV) as compared to bare C₂N units, which showed the strong sensitivity and selectivity of the C₂N surface towards NI₃ as compared to the rest of the analytes. The complexes of NCl₃@C₂N (5.58 eV) and NBr₃@C₂N (5.25 eV) failed to bring significant changes in the E_HOMO–LUMO energy gaps and were less selective by the C₂N surface. It is worth mentioning that in all complexes, a significant difference in the E_HOMO–LUMO gap was seen when charge transfer happened from the analyte to the C₂N surface.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ra04930a

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