Covalent Triazine Framework C6N6 as an Electrochemical Sensor for Hydrogen-Containing Industrial Pollutants. A DFT Study

Industrial pollutants pose a serious threat to ecosystems. Hence, there is a need to search for new efficient sensor materials for the detection of pollutants. In the current study, we explored the electrochemical sensing potential of a C6N6 sheet for H-containing industrial pollutants (HCN, H2S, NH3 and PH3) through DFT simulations. The adsorption of industrial pollutants over C6N6 occurs through physisorption, with adsorption energies ranging from −9.36 kcal/mol to −16.46 kcal/mol. The non-covalent interactions of analyte@C6N6 complexes are quantified by symmetry adapted perturbation theory (SAPT0), quantum theory of atoms in molecules (QTAIM) and non-covalent interaction (NCI) analyses. SAPT0 analyses show that electrostatic and dispersion forces play a dominant role in the stabilization of analytes over C6N6 sheets. Similarly, NCI and QTAIM analyses also verified the results of SAPT0 and interaction energy analyses. The electronic properties of analyte@C6N6 complexes are investigated by electron density difference (EDD), natural bond orbital analyses (NBO) and frontier molecular orbital analyses (FMO). Charge is transferred from the C6N6 sheet to HCN, H2S, NH3 and PH3. The highest exchange of charge is noted for H2S (−0.026 e−). The results of FMO analyses show that the interaction of all analytes results in changes in the EH-L gap of the C6N6 sheet. However, the highest decrease in the EH-L gap (2.58 eV) is observed for the NH3@C6N6 complex among all studied analyte@C6N6 complexes. The orbital density pattern shows that the HOMO density is completely concentrated on NH3, while the LUMO density is centred on the C6N6 surface. Such a type of electronic transition results in a significant change in the EH-L gap. Thus, it is concluded that C6N6 is highly selective towards NH3 compared to the other studied analytes.


Introduction
In the last few decades, industrial pollutants have become serious threats to living beings. Industrial pollutants are adversely deteriorating our ecosystem. It is reported that every year, 4.2 million people are affected by direct exposure to industrial pollutants at levels beyond the safety limits [1]. Among industrial pollutants, hydrogen-containing substances such as HCN, H 2 S, NH 3 and PH 3 are highly poisonous to humans [2][3][4][5]. Hydrogen cyanide (HCN) is a poisonous gas with an almond-like odour. HCN is used as a reagent for the synthesis of various synthetic fibres, pesticides, plastics and dyes [6]. In cases of contact with skin, ingestion and inhalation, HCN is highly lethal to humans. HCN may cause suffocation, unconsciousness, cramps and heart problems. Hydrogen sulphide (H 2 S) is a gas with a rotten egg smell which is usually produced by decomposition of organic materials [7]. It rapidly reacts with the haemoglobin in blood and reduces the surface is more comparable to other available COFs for the detection of H-containing industrial pollutants such as HCN, H 2 S, NH 3 and PH 3 . The high amount of nitrogen in the C 6 N 6 unit also leads to a high surface area and a cavity size of 5.46 Å, which can efficiently interact with various analytes through H bonding, π-π stacking or other types of chemical interactions. According to the best of our knowledge, C 6 N 6 has not yet been tested as a sensor for the above-mentioned analytes. In the designed study, we used density functional theory simulations to investigate C 6 N 6 as a sensor surface. Changes in geometrical properties are explored through NCI, QTAIM and SAPT0 analyses, while changes in the electronic properties of analytes in C 6 N 6 complexes are determined by NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simulations in the current study. The selected geometries of bare C 6 N 6 and analyte@C 6 N 6 complexes were investigated at the Nanomaterials 2023, 13, x FOR PEER REVIEW 3 of 22 Keeping in view the above-mentioned characteristics of covalent triazine frameworks (CTFs), we selected a recently designed covalent triazine framework (C6N6), which contains six nitrogens in its cavity. Recently, C6N6 has been used in many fields such as catalysis [54], sensing [55], drug delivery [56] and energy storage [57]. These findings show that the C6N6 surface is more comparable to other available COFs for the detection of Hcontaining industrial pollutants such as HCN, H2S, NH3 and PH3. The high amount of nitrogen in the C6N6 unit also leads to a high surface area and a cavity size of 5.46 Å, which can efficiently interact with various analytes through H bonding, π-π stacking or other types of chemical interactions. According to the best of our knowledge, C6N6 has not yet been tested as a sensor for the above-mentioned analytes. In the designed study, we used density functional theory simulations to investigate C6N6 as a sensor surface. Changes in geometrical properties are explored through NCI, QTAIM and SAPT0 analyses, while changes in the electronic properties of analytes in C6N6 complexes are determined by NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simulations in the current study. The selected geometries of bare C6N6 and analyte@C6N6 complexes were investigated at the Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD functional was adopted in the current study because it is a range-separated functional which can effectively capture non-localized intermolecular interactions [58]. In Ꞷb97XD, the symbol "Ꞷ" represents the long range correction [59]. Additionally, the Ꞷb97XD functional also contains Grimme's D2 dispersion factor to efficiently study the van der Waals (vdWs) interactions [59]. The changes in the electronic properties of C6N6 before and after adsorption of analytes were explored by NBO, EDD and FMO analyses at the B3LYP/6-31G(d) level of theory. B3LYP/6-31G(d) is considered as the best to study the electronic changes of interacted systems [60][61][62][63][64][65]. The most stable configurations of the analyte@C6N6 complexes were investigated by adsorption of analytes through different orientations of C6N6. A frequency analysis was performed to confirm that the geometries of the complexes were true minima on the potential energy surface. The energies of adsorbed analytes in C6N6 are determined by Equation (1): where E(analytes@C6N6) is the interaction energy of the complexes, EC6N6 is the energy for bare C6N6 and Eanalytes is the energy of the industrial pollutants used as analytes.
A SAPT0 analysis was applied to determine the role of the individual components of the interaction energy in the stabilization of the analyte@C6N6 complexes [66]. The total SAPT0 energy is the sum of four factors: induction (∆Eind), dispersion (∆Edisp), electrostatic (∆Eelstat) and exchange (∆Eexch). Hence, the SAPT0 energy is calculated through Equation (2): The nature of adsorption, such as the electrostatic, dispersive and repulsive forces between the analyte and C6N6, was examined by an NCI analysis. The nature and strength of non-covalent interactions is given by the reduced density (s), The value of electron density (ρ) for non-covalent interactions is generally very small. However, small changes in (ρ) result in prominent changes in RDG values, which appear in the form of spikes in a 2D-RGD plot. An NCI analysis characterizes non-covalent interactions through 3D-isosurfaces and 2D-RGD plots. These plots use ρ and the second eigen value (λ2) to differentiate between the nature of interactions [68][69][70].
b97XD/6-31G (d, p) level of theory. The Nanomaterials 2023, 13, x FOR PEER REVIEW Keeping in view the above-mentioned characteristi (CTFs), we selected a recently designed covalent triazi tains six nitrogens in its cavity. Recently, C6N6 has been ysis [54], sensing [55], drug delivery [56] and energy s that the C6N6 surface is more comparable to other avail containing industrial pollutants such as HCN, H2S, N nitrogen in the C6N6 unit also leads to a high surface area can efficiently interact with various analytes through H types of chemical interactions. According to the best of been tested as a sensor for the above-mentioned analyte density functional theory simulations to investigate C6N geometrical properties are explored through NCI, QT changes in the electronic properties of analytes in C6 NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the sim selected geometries of bare C6N6 and analyte@C6N6 co Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD func study because it is a range-separated functional which ized intermolecular interactions [58]. In Ꞷb97XD, the range correction [59]. Additionally, the Ꞷb97XD funct dispersion factor to efficiently study the van der Wa changes in the electronic properties of C6N6 before and explored by NBO, EDD and FMO analyses at the B3LYP/6-31G(d) is considered as the best to study the el tems [60][61][62][63][64][65]. The most stable configurations of the ana tigated by adsorption of analytes through different orien ysis was performed to confirm that the geometries of th the potential energy surface. The energies of adsorbed a Equation (1): and Eanalytes is the energy of the industrial pollutan A SAPT0 analysis was applied to determine the rol the interaction energy in the stabilization of the analyt SAPT0 energy is the sum of four factors: induction (∆Ein (∆Eelstat) and exchange (∆Eexch). Hence, the SAPT0 energ The nature of adsorption, such as the electrostatic between the analyte and C6N6, was examined by an NCI of non-covalent interactions is given by the reduced den The value of electron density (ρ) for non-covalent in However, small changes in (ρ) result in prominent chan in the form of spikes in a 2D-RGD plot. An NCI analysis actions through 3D-isosurfaces and 2D-RGD plots. Thes value (λ2) to differentiate between the nature of interact b97XD functional was adopted in the current study because it is a range-separated functional which can effectively capture non-localized intermolecular interactions [58]. In Nanomaterials 2023, 13, x FOR PEER REVIEW Keeping in view the above-mentioned characteristics of c (CTFs), we selected a recently designed covalent triazine fra tains six nitrogens in its cavity. Recently, C6N6 has been used ysis [54], sensing [55], drug delivery [56] and energy storag that the C6N6 surface is more comparable to other available C containing industrial pollutants such as HCN, H2S, NH3 an nitrogen in the C6N6 unit also leads to a high surface area and can efficiently interact with various analytes through H bon types of chemical interactions. According to the best of our k been tested as a sensor for the above-mentioned analytes. In t density functional theory simulations to investigate C6N6 as a geometrical properties are explored through NCI, QTAIM changes in the electronic properties of analytes in C6N6 co NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simulatio selected geometries of bare C6N6 and analyte@C6N6 complex Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD functional study because it is a range-separated functional which can e ized intermolecular interactions [58]. In Ꞷb97XD, the symb range correction [59]. Additionally, the Ꞷb97XD functional dispersion factor to efficiently study the van der Waals (v changes in the electronic properties of C6N6 before and after explored by NBO, EDD and FMO analyses at the B3LYP B3LYP/6-31G(d) is considered as the best to study the electron tems [60][61][62][63][64][65]. The most stable configurations of the analyte@ tigated by adsorption of analytes through different orientation ysis was performed to confirm that the geometries of the com the potential energy surface. The energies of adsorbed analyte Equation (1): where E(analytes@C6N6) is the interaction energy of the complexes C6N6 and Eanalytes is the energy of the industrial pollutants use A SAPT0 analysis was applied to determine the role of th the interaction energy in the stabilization of the analyte@C6N SAPT0 energy is the sum of four factors: induction (∆Eind), dis (∆Eelstat) and exchange (∆Eexch). Hence, the SAPT0 energy is c (2): ∆ESAPT0 = ∆Eelstat + ∆Eexch + ∆Eind + ∆ The nature of adsorption, such as the electrostatic, disp between the analyte and C6N6, was examined by an NCI analy of non-covalent interactions is given by the reduced density ( The value of electron density (ρ) for non-covalent interac However, small changes in (ρ) result in prominent changes in in the form of spikes in a 2D-RGD plot. An NCI analysis char actions through 3D-isosurfaces and 2D-RGD plots. These plot value (λ2) to differentiate between the nature of interactions [ b97XD, the symbol " Nanomaterials 2023, 13, x FOR PEER REVIEW Keeping in view the above-mentio (CTFs), we selected a recently designe tains six nitrogens in its cavity. Recent ysis [54], sensing [55], drug delivery that the C6N6 surface is more compara containing industrial pollutants such nitrogen in the C6N6 unit also leads to a can efficiently interact with various a types of chemical interactions. Accord been tested as a sensor for the above-m density functional theory simulations geometrical properties are explored t changes in the electronic properties NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to selected geometries of bare C6N6 and Ꞷb97XD/6-31G (d, p) level of theory. T study because it is a range-separated ized intermolecular interactions [58]. range correction [59]. Additionally, th dispersion factor to efficiently study changes in the electronic properties of explored by NBO, EDD and FMO B3LYP/6-31G(d) is considered as the be tems [60][61][62][63][64][65]. The most stable configu tigated by adsorption of analytes throu ysis was performed to confirm that the the potential energy surface. The energ Equation (1): and Eanalytes is the energy of the in A SAPT0 analysis was applied to the interaction energy in the stabiliza SAPT0 energy is the sum of four factor (∆Eelstat) and exchange (∆Eexch). Hence, The nature of adsorption, such a between the analyte and C6N6, was exa of non-covalent interactions is given b The value of electron density (ρ) f However, small changes in (ρ) result i in the form of spikes in a 2D-RGD plot actions through 3D-isosurfaces and 2D value (λ2) to differentiate between the " represents the long range correction [59]. Additionally, the Nanomaterials 2023, 13, x FOR PEER REVIEW Keeping in view the above-mentioned characteristics of coval (CTFs), we selected a recently designed covalent triazine framew tains six nitrogens in its cavity. Recently, C6N6 has been used in m ysis [54], sensing [55], drug delivery [56] and energy storage [5 that the C6N6 surface is more comparable to other available COF containing industrial pollutants such as HCN, H2S, NH3 and PH nitrogen in the C6N6 unit also leads to a high surface area and a cav can efficiently interact with various analytes through H bonding types of chemical interactions. According to the best of our know been tested as a sensor for the above-mentioned analytes. In the d density functional theory simulations to investigate C6N6 as a sen geometrical properties are explored through NCI, QTAIM and changes in the electronic properties of analytes in C6N6 comple NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simulations i selected geometries of bare C6N6 and analyte@C6N6 complexes w Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD functional wa study because it is a range-separated functional which can effect ized intermolecular interactions [58]. In Ꞷb97XD, the symbol " range correction [59]. Additionally, the Ꞷb97XD functional also dispersion factor to efficiently study the van der Waals (vdWs changes in the electronic properties of C6N6 before and after adso explored by NBO, EDD and FMO analyses at the B3LYP/6-3 B3LYP/6-31G(d) is considered as the best to study the electronic ch tems [60][61][62][63][64][65]. The most stable configurations of the analyte@C6N tigated by adsorption of analytes through different orientations of ysis was performed to confirm that the geometries of the complex the potential energy surface. The energies of adsorbed analytes in Equation (1): where E(analytes@C6N6) is the interaction energy of the complexes, EC6 C6N6 and Eanalytes is the energy of the industrial pollutants used as A SAPT0 analysis was applied to determine the role of the in the interaction energy in the stabilization of the analyte@C6N6 co SAPT0 energy is the sum of four factors: induction (∆Eind), dispers (∆Eelstat) and exchange (∆Eexch). Hence, the SAPT0 energy is calcu The nature of adsorption, such as the electrostatic, dispersi between the analyte and C6N6, was examined by an NCI analysis. of non-covalent interactions is given by the reduced density (s), E The value of electron density (ρ) for non-covalent interaction However, small changes in (ρ) result in prominent changes in RD in the form of spikes in a 2D-RGD plot. An NCI analysis characte actions through 3D-isosurfaces and 2D-RGD plots. These plots us value (λ2) to differentiate between the nature of interactions  functional also contains Grimme's D2 dispersion factor to efficiently study the van der Waals (vdWs) interactions [59]. The changes in the electronic properties of C 6 N 6 before and after adsorption of analytes were explored by NBO, EDD and FMO analyses at the B3LYP/6-31G(d) level of theory. B3LYP/6-31G(d) is considered as the best to study the electronic changes of interacted systems [60][61][62][63][64][65]. The most stable configurations of the analyte@C 6 N 6 complexes were investigated by adsorption of analytes through different orientations of C 6 N 6 . A frequency analysis was performed to confirm that the geometries of the complexes were true minima on the potential energy surface. The energies of adsorbed analytes in C 6 N 6 are determined by Equation (1): where E (analytes@C6N6) is the interaction energy of the complexes, E C6N6 is the energy for bare C 6 N 6 and E analytes is the energy of the industrial pollutants used as analytes. A SAPT0 analysis was applied to determine the role of the individual components of the interaction energy in the stabilization of the analyte@C 6 N 6 complexes [66]. The total SAPT0 energy is the sum of four factors: induction (∆E ind ), dispersion (∆E disp ), electrostatic (∆E elstat ) and exchange (∆E exch ). Hence, the SAPT0 energy is calculated through Equation (2): The nature of adsorption, such as the electrostatic, dispersive and repulsive forces between the analyte and C 6 N 6 , was examined by an NCI analysis. The nature and strength of non-covalent interactions is given by the reduced density (s), Equation (3) [67].
The value of electron density (ρ) for non-covalent interactions is generally very small. However, small changes in (ρ) result in prominent changes in RDG values, which appear in the form of spikes in a 2D-RGD plot. An NCI analysis characterizes non-covalent interactions through 3D-isosurfaces and 2D-RGD plots. These plots use ρ and the second eigen value (λ 2 ) to differentiate between the nature of interactions [68][69][70].
The interaction between the analytes and C 6 N 6 was further studied through a QTAIM analysis. Through a QTAIM analysis, we can examine the nature of the interactions, which cannot be explored through any other method. The major factor through which noncovalent interactions can be studied through QTAIM analysis is the bond critical point (BCP). BCPs are based on various parameters such as the Laplacian (∇ 2 ρ), electron density (ρ), total energy density (H), potential energy density (V) and the Lagrangian kinetic energy density (G) [71][72][73]. Multiwfn 3.7 and VMD software were used to perform the QTAIM, NCI and EDD analyses [74][75][76].

Geometry Optimization and Interaction Energy
The optimized structure of the selected model of C 6 N 6 is presented in Figure 1. The C-C and C-N bond lengths in C 6 N 6 are 1.53 Å and 1.33 Å, respectively, which are consistent with previously reported theoretical and experimental values [77]. Each unit of C 6 N 6 comprises of six C 3 N 3 rings which are connected with each other through C-N bonds [55]. The cavity of the selected model of C 6 N 6 has a high electron density due to the centring of the nitrogen atoms towards the cavity. The diameter of the C 6 N 6 cavity (between two nitrogen atoms) is 5.46 Å [78]. The nitrogenated, high electron density cavity of C 6 N 6 can act as a potential surface for the detection of hydrogen-containing industrial pollutants. The topologies of selected industrial pollutants (HCN, H 2 S, NH 3 and PH 3 ) were also simulated at the Nanomaterials 2023, 13, x FOR PEER REVIEW 3 of 22 Keeping in view the above-mentioned characteristics of covalent triazine frameworks (CTFs), we selected a recently designed covalent triazine framework (C6N6), which contains six nitrogens in its cavity. Recently, C6N6 has been used in many fields such as catalysis [54], sensing [55], drug delivery [56] and energy storage [57]. These findings show that the C6N6 surface is more comparable to other available COFs for the detection of Hcontaining industrial pollutants such as HCN, H2S, NH3 and PH3. The high amount of nitrogen in the C6N6 unit also leads to a high surface area and a cavity size of 5.46 Å, which can efficiently interact with various analytes through H bonding, π-π stacking or other types of chemical interactions. According to the best of our knowledge, C6N6 has not yet been tested as a sensor for the above-mentioned analytes. In the designed study, we used density functional theory simulations to investigate C6N6 as a sensor surface. Changes in geometrical properties are explored through NCI, QTAIM and SAPT0 analyses, while changes in the electronic properties of analytes in C6N6 complexes are determined by NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simulations in the current study. The selected geometries of bare C6N6 and analyte@C6N6 complexes were investigated at the Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD functional was adopted in the current study because it is a range-separated functional which can effectively capture non-localized intermolecular interactions [58]. In Ꞷb97XD, the symbol "Ꞷ" represents the long range correction [59]. Additionally, the Ꞷb97XD functional also contains Grimme's D2 dispersion factor to efficiently study the van der Waals (vdWs) interactions [59]. The changes in the electronic properties of C6N6 before and after adsorption of analytes were explored by NBO, EDD and FMO analyses at the B3LYP/6-31G(d) level of theory. B3LYP/6-31G(d) is considered as the best to study the electronic changes of interacted systems [60][61][62][63][64][65]. The most stable configurations of the analyte@C6N6 complexes were investigated by adsorption of analytes through different orientations of C6N6. A frequency analysis was performed to confirm that the geometries of the complexes were true minima on the potential energy surface. The energies of adsorbed analytes in C6N6 are determined by Equation (1): where E(analytes@C6N6) is the interaction energy of the complexes, EC6N6 is the energy for bare C6N6 and Eanalytes is the energy of the industrial pollutants used as analytes.
A SAPT0 analysis was applied to determine the role of the individual components of the interaction energy in the stabilization of the analyte@C6N6 complexes [66]. The total SAPT0 energy is the sum of four factors: induction (∆Eind), dispersion (∆Edisp), electrostatic (∆Eelstat) and exchange (∆Eexch). Hence, the SAPT0 energy is calculated through Equation (2): The nature of adsorption, such as the electrostatic, dispersive and repulsive forces between the analyte and C6N6, was examined by an NCI analysis. The nature and strength of non-covalent interactions is given by the reduced density (s), The value of electron density (ρ) for non-covalent interactions is generally very small. However, small changes in (ρ) result in prominent changes in RDG values, which appear in the form of spikes in a 2D-RGD plot. An NCI analysis characterizes non-covalent interactions through 3D-isosurfaces and 2D-RGD plots. These plots use ρ and the second eigen value (λ2) to differentiate between the nature of interactions [68][69][70]. The stable complex of H2S@C6N6 is obtained with an adsorption energy of − kcal/mol, which is the 2nd most stable complex among all studied analyte@C6N6 plexes. The optimized topology of the H2S@C6N6 complex shows that both H atoms o are positioned towards the C6N6 cavity. Interaction distances of 2.90 Å (N1---H7), 2 (N2---H7) and 2.68 Å N2---H7 are noted between N atoms (N1, N2 and N3) of C6N the H atom (H7) of H2S (see Figure 2). Moreover, similar interaction distances are obse between N4---H8, N5---H8 and N6---H8, respectively. However, these interaction tances between the N atoms of C6N6 and the H atoms of H2S reveal that the adsorpti H2S occurred at the centre of cavity, while the S atom is pointing upwards.
The stable complex of NH3@C6N6 resulted in an adsorption energy of −12.27 kcal Keeping in view the above-mentioned characteristics of covalent triazine frameworks (CTFs), we selected a recently designed covalent triazine framework (C6N6), which contains six nitrogens in its cavity. Recently, C6N6 has been used in many fields such as catalysis [54], sensing [55], drug delivery [56] and energy storage [57]. These findings show that the C6N6 surface is more comparable to other available COFs for the detection of Hcontaining industrial pollutants such as HCN, H2S, NH3 and PH3. The high amount of nitrogen in the C6N6 unit also leads to a high surface area and a cavity size of 5.46 Å, which can efficiently interact with various analytes through H bonding, π-π stacking or other types of chemical interactions. According to the best of our knowledge, C6N6 has not yet been tested as a sensor for the above-mentioned analytes. In the designed study, we used density functional theory simulations to investigate C6N6 as a sensor surface. Changes in geometrical properties are explored through NCI, QTAIM and SAPT0 analyses, while changes in the electronic properties of analytes in C6N6 complexes are determined by NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simulations in the current study. The selected geometries of bare C6N6 and analyte@C6N6 complexes were investigated at the Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD functional was adopted in the current study because it is a range-separated functional which can effectively capture non-localized intermolecular interactions [58]. In Ꞷb97XD, the symbol "Ꞷ" represents the long range correction [59]. Additionally, the Ꞷb97XD functional also contains Grimme's D2 dispersion factor to efficiently study the van der Waals (vdWs) interactions [59]. The changes in the electronic properties of C6N6 before and after adsorption of analytes were explored by NBO, EDD and FMO analyses at the B3LYP/6-31G(d) level of theory. B3LYP/6-31G(d) is considered as the best to study the electronic changes of interacted systems [60][61][62][63][64][65]. The most stable configurations of the analyte@C6N6 complexes were inves-tigated by adsorption of analytes through different orientations of C6N6.
A frequency analysis was performed to confirm that the geometries of the complexes were true minima on the potential energy surface. The energies of adsorbed analytes in C6N6 are determined by Equation (1): where E(analytes@C6N6) is the interaction energy of the complexes, EC6N6 is the energy for bare b97XD/6-31G (d,p) level of theory.
In order to obtain stable complexes of analyte@C 6 N 6 , several orientations of each analyte in C 6 N 6 were considered. Figure 1 shows a graphical representation of the adsorption energies of analyte@C 6 N 6 complexes. The most stable geometries of each analyte@C 6 N 6 complex are reported in Figure 2, while the remaining geometries are given in Figure S1 (Supplementary Materials). The following order of the adsorption energies of the stable complexes is obtained: HCN@C 6 N 6 > H 2 S@C 6 N 6 > NH 3 @C 6 N 6 > PH 3 @C 6 N 6 .  Keeping in view th (CTFs), we selected a r tains six nitrogens in its ysis [54], sensing [55], that the C6N6 surface is containing industrial p nitrogen in the C6N6 un can efficiently interact types of chemical inter been tested as a sensor density functional theo geometrical properties changes in the electron NBO, EDD and FMO a

Computational Meth
Gaussian 09 softw selected geometries of Ꞷb97XD/6-31G (d, p) le study because it is a ra ized intermolecular in range correction [59]. A dispersion factor to effi changes in the electron explored by NBO, ED b97XD/6-31G (d,p) level of theory. Among the analyte@C 6 N 6 complexes, the most stable complex is formed between HCN and C 6 N 6 , with an adsorption energy value of −16.46 kcal/mol. In this complex, HCN is projected to be perpendicular to the C 6 N 6 cavity (see Figure 2). The H atom of HCN interacts with the N atoms of C 6 N 6 at bond distances of between 2.57 Å and 3.09 Å. Among these interactions, the strongest interaction is seen between the H7 atom of HCN and the N1 and N2 of C 6 N 6 , with interaction distances of 2.57 Å and 2.67 Å, respectively. These interaction distances show that HCN is more attracted to the two C 3 N 3 rings containing N1 and N2 atoms. When the input geometry was altered to have the nitrogen atom of HCN pointing towards the cavity of C 6 N 6 , the calculation converged to the same complex mentioned above (hydrogen pointing towards the cavity). This happened because of the repulsion between the N atom of HCN and the N atoms of C 6 N 6 .
The stable complex of H 2 S@C 6 N 6 is obtained with an adsorption energy of −13.64 kcal/mol, which is the 2nd most stable complex among all studied analyte@C 6 N 6 complexes. The optimized topology of the H 2 S@C 6 N 6 complex shows that both H atoms of H 2 S are positioned towards the C 6 N 6 cavity. Interaction distances of 2.90 Å (N1-H7), 2.29 Å (N2-H7) and 2.68 Å N2-H7 are noted between N atoms (N1, N2 and N3) of C 6 N 6 and the H atom (H7) of H 2 S (see Figure 2). Moreover, similar interaction distances are observed between N4-H8, N5-H8 and N6-H8, respectively. However, these interaction distances between the N atoms of C 6 N 6 and the H atoms of H 2 S reveal that the adsorption of H 2 S occurred at the centre of cavity, while the S atom is pointing upwards.
The stable complex of NH 3 @C 6 N 6 resulted in an adsorption energy of −12.27 kcal/mol, which is slightly lower than that of the H 2 S@C 6 N 6 complex. In the stable configuration of NH 3 @C 6 N 6 , two H atoms of NH 3 interact with the N atoms of C 6 N 6 , while the 3 rd H atom is projected away from the cavity. Among the observed interactions, strong interactions are observed between N1 and H5 and N4 and H6 of C 6 N 6 and H 2 S, with distances of 2.33 Å and 2.34 Å, respectively. The N2 and N3 of C 6 N 6 interact with H5 and H6 of NH 3 , with an interaction distance of 2.57 Å. The lower adsorption energy of the NH 3 @C 6 N 6 complex (−12.27 kcal/mol) compared to the H 2 S@C 6 N 6 complex (−13.64 kcal/mol) is attributed to longer interaction distances between the H atoms of NH 3 and the N atoms of C 6 N 6 compared to H 2 S. An adsorption energy of −9.36 kcal/mol is observed for the stable complex of PH 3 @C 6 N 6 , which is the lowest amongst all studied analyte@C 6 N 6 complexes. The stable structure of the PH 3 @C 6 N 6 complex consists of an inward pointing H atom of PH 3 , while the other two H atoms point upwards. The inward pointing H atom of PH 3 is almost at the centre of the C 6 N 6 cavity. The bond distances between the H atoms of PH 3 and the N atoms of C 6 N 6 range from 2.70 Å to 3.09 Å. The low adsorption energy (−9.36 kcal/mol) of the PH 3 @C 6 N 6 complex is due to the low polarity of the H atoms of PH 3 and the longer interaction distances. The results of adsorption energies (−9.36 kcal/mol to −16.46 kcal/mol) show all analytes (HCN, H 2 S, NH 3 and PH 3 ) physically absorb on the C 6 N 6 sheet.

Symmetry Adapted Perturbation Theory (SAPT0) Analysis
A SAPT0 analysis is the most effective method for quantifying non-covalent interactions. The SAPT0 interaction energy is the sum of four factors, including induction, exchange, electrostatic and dispersion. Therefore, in SAPT0, the role of each factor is investigated in the stabilization of analytes in C 6 N 6 . The SAPT0 results of all the studied complexes are presented in Table 1 and Figure 3. In the SAPT0 graph, five bars are shown for each complex. The last green bar represents the total SAPT0, which is the sum of the first four bars. Out of these four bars, three bars with negative signs indicate attractive interactions, while the bars with +ve signs indicate repulsive interactions. The negative sign of the green bar (total SAPT0) reveals the dominance of attractive forces over repulsive forces during the interaction of analytes with the C 6 N 6 sheet.  Figure 3. Graphical projection of the SAPT0 energy and its components for analyte@C6N6 complexes.

Non-Covalent Interaction (NCI) Analysis
The nature of interactions between analytes and C6N6 was further explored throug non-covalent interaction analyses. Through an NCI analysis, the van der Waals, electr static and repulsive interactions can be differentiated based on a colour scheme. An NC analysis comprises 3D isosurfaces and 2D reduced density gradient (RDG) plots. The 3 isosurface topological analysis is based on three types of colours: red (repulsive), gree (van der Waals) and blue (electrostatic interactions). These colours appear in the form patches between the analytes and C6N6 through which the nature of interactions can b differentiated. A 2D RDG plot is obtained by taking the reduced density on the Y-axis an product of 2 nd value of the Laplacian (sign(λ2)) and density gradient on the X-axis. A 2 RGD plot gives information about the strength of each type of interaction. In 2D RD plots, non-covalent interactions appear as blue, green and red spikes in the low densi gradient region. The vdWs interactions are indicated by the green spikes which form th The SAPT0 energies of all the complexes obtained through PSI4 are −16.88 kcal/mol (HCN@C 6 N 6 ), −12.26 kcal/mol (H 2 S@C 6 N 6 ), −10.06 kcal/mol (NH 3 @C 6 N 6 ) and −9.22 kcal/mol (PH 3 @C 6 N 6 ). Among the studied H-containing industrial pollutants over C 6 N 6 , the highest SAPT0 value (−16.88 kcal/mol) is obtained for the HCN@C 6 N 6 complex, which is consistent with the results of the interaction energy analysis. The SAPT0 attractive component values for the HCN@C 6 N 6 complex are E elst (−14.60 kcal/mol: 52%), E ind (−3.78 kcal/mol: 13%) and E disp (−9.66 kcal/mol: 34%). These values indicate that E elst is the major stabilizing factor compared to E ind and E disp . The highest value of E elst results from the strong interactions of the H atom of HCN with the N atoms of C 6 N 6 through a shorter interaction distance (vide supra).
The second highest SAPT0 value is seen for the H 2 S@C 6 N 6 complex, at −12.26 kcal/mol. The energy values of the attractive components, i.e., E elst , E ind and E disp , observed for the H 2 S@C 6 N 6 complex are −12.58 kcal/mol (43%), −4.27 kcal/mol (15%) and −12.34 kcal/mol (42%), respectively. These values of the attractive components show that E elst (43%) and E disp (42%) play a major role in the stabilization of the H 2 S@C 6 N 6 complex, while a lower contribution is observed for E ind (15%). The SAPT0 values for the NH 3 @C 6 N 6 and PH 3 @C 6 N 6 complexes are −10.06 kcal/mol and −9.22 kcal/mol, respectively. The SAPT0 component analysis for the NH 3 @C 6 N 6 complex reveals that E elst (47%) and E disp (40%) are dominant in the stabilization of NH 3 over C 6 N 6 . Among the studied pollutant complexes, the lowest SAPT0 value is observed for the PH 3 @C 6 N 6 complex (−9.22 kcal/mol). The lowest SAPT0 value for the PH 3 @C 6 N 6 complex results from the lower polarity of the interacting H atoms of PH 3 with the N atoms of C 6 N 6 . Among the SAPT0 energy, a key role is noted for E disp (55%) in the stabilization of the PH 3 @C 6 N 6 complex, while E elst (33%) and E ind (12%) contribute less towards the total SAPT0 energy.
The SAPT0 analysis reveals that E elst is the dominant contributing factor in the case of HCN@C 6 N 6 , whereas a good balance between E elst and E disp is observed for H 2 S and NH 3 . In the case of PH 3 , the dispersion interaction played a dominant role in the stabilization of PH 3 over C 6 N 6 . The SAPT0 values of all the studied complexes are consistent with the interaction energy analysis.

Non-Covalent Interaction (NCI) Analysis
The nature of interactions between analytes and C 6 N 6 was further explored through non-covalent interaction analyses. Through an NCI analysis, the van der Waals, electrostatic and repulsive interactions can be differentiated based on a colour scheme. An NCI analysis comprises 3D isosurfaces and 2D reduced density gradient (RDG) plots. The 3D isosurface topological analysis is based on three types of colours: red (repulsive), green (van der Waals) and blue (electrostatic interactions). These colours appear in the form of patches between the analytes and C 6 N 6 through which the nature of interactions can be differentiated. A 2D RDG plot is obtained by taking the reduced density on the Y-axis and product of 2 nd value of the Laplacian (sign(λ 2 )) and density gradient on the X-axis. A 2D RGD plot gives information about the strength of each type of interaction. In 2D RDG plots, non-covalent interactions appear as blue, green and red spikes in the low density gradient region. The vdWs interactions are indicated by the green spikes which form the when product of sign(λ 2 )ρ is in the range of −0.00 a.u. to −0.02 a.u. A large and negative value of the product of sign(λ 2 )ρ (above −0.02 a.u.) signifies the existence of electrostatic interactions (blue spikes). Red spikes in the 2D-RGD plot show repulsive interactions when the product of sign(λ 2 )ρ is positive and large.
The topologies obtained through NCI analyses are presented in Figure 4. In the studied complexes, the green spikes in the 2D RDG plots and the green isosurface in the 3D plots are explored. The green spikes and isosurface indicate vdWs interactions between the analytes and C 6 N 6 . The strength of the vdWs interaction in each complex is different, indicated by the variation in the thickness of 3D isosurface patches and a projection of green spikes in the 2D-RDG plots on the X-axis. In the case of the HCN@C 6 N 6 complex, a ring on the green isosurface develops between the H atom of HCN and the six N atoms of C 6 N 6 . This shows that all six N atoms of C 6 N 6 strongly interact with the H atom of HCN. Similarly, in the 2D-RDG plot, a mixture of bluish-green spikes arises at a low-density gradient between −0.01 and −0.02 a.u., which indicates that the complex is stabilized through electrostatic interactions. In the case of the H 2 S@C 6 N 6 complex, a stronger interaction is observed, where the H atoms of H 2 S closely interact with the N atoms of C 6 N 6 (see Figure 4). The rest of the interactions are present at longer distances due to the angular orientation of the H 2 S molecule over C 6 N 6 . The 3D isosurfaces and 2D-RGD plots of the NH 3 @C 6 N 6 complex reveal the weak interaction compared to the HCN@C 6 N 6 and H 2 S@C 6 N 6 complexes. The scattered green spikes and shattered green isosurface in the 3D NCI plots are due to the weak interaction between NH 3 and the C 6 N 6 cavity. The weak interaction of NH 3 is also described in the interaction energy section. In the case of the PH 3 @C 6 N 6 complex, the green spikes and isosurface are not as thick and dense as projected in the rest of the studied complexes. Out of the three hydrogens atoms of PH 3 , only one H is oriented towards the C 6 N 6 cavity. The H atom orientated towards the C 6 N 6 cavity is not as polar as the H atom of HCN and NH 3 , due to which weak vdWs interactions are established between PH 3 and the C 6 N 6 cavity. The NCI analysis indicated that dispersion and electrostatic interactions are dominant, which is consistent with the SAPT0 and interaction energy results.

Quantum Theory of Atoms in Molecule (QTAIM) Analysis
QTAIM analysis is a useful tool to investigate all non-covalent interactions which are impossible to capture through any other analysis. Through QTAIM analysis, inter-and intra-molecular interactions such as ionic interactions, hydrogen bonding, van der Waals

Quantum Theory of Atoms in Molecule (QTAIM) Analysis
QTAIM analysis is a useful tool to investigate all non-covalent interactions which are impossible to capture through any other analysis. Through QTAIM analysis, interand intra-molecular interactions such as ionic interactions, hydrogen bonding, van der Waals interactions and covalent bonds can be studied. These inter-and intra-molecular interactions are studied by various parameters such as cage critical points (CCP), nuclear critical points (NCP), ring critical points (NCP) and bond critical points (BCPs). In QTAIM analyses, non-covalent interactions are best explained by BCPs. BCPs between two interacting systems are represented by a brown line (see Figure 5). The nature and strength of each BCP is explained through several parameters such as (∇ 2 ρ), (ρ), (H), (G) and (V). The values of the BCP parameters of all complexes are given in Table 2.

Natural Bond Orbital (NBO) and Electron Density Differences (EDD) Analyses
The electronic properties of complexes were explored by EDD and NBO analyses. Through these analyses of the nature of interactions, the stability, charge transfer and  The nature of interaction is shared if ∇ 2 ρ(r) < 0, whereas for close shell interactions, the value of ∇ 2 ρ(r) > 0. For electrostatic interactions (H bonding), the values of (∇ 2 ρ) and (ρ) at BCPs are between 0.024 and 0.139 a.u. and 0.002 to 0.034 a.u., respectively [79,80]. In addition, a bond distance (N-H, O-H and F-H) of less than 1.2 Å indicates a strong interaction, while a bond distance greater than 1.8 Å shows a weak interaction [81]. The strength of an individual bond can also be characterized by the Espinosa approach, as presented in Equation (4) [82]. For H bonding, the energy value of an individual bond is >3 kcal/mol (in negative) [83].
In addition, the BCP can further be investigated by Equation (5): where G, H and V are the kinetic, potential and total energy density at the BCPs, respectively. For close shell interactions, the value of H is usually positive, while it is negative for shared shell interactions. The type of bonding is generally indicated by ∇ 2 ρ and H. The values of ∇ 2 ρ and H are less than zero for shared shell interactions and greater than zero for close shell interactions. If the values of ∇ 2 ρ are greater than zero and H is less than zero, it indicates H bonding. Another parameter used to explain the BCP is the ratio -V/G. If the ratio of -V/G is >2, it indicates covalent bonding, and a ratio of −V/G of < 1 represents non-covalent interactions [84,85].
QTAIM analyses of all the complexes shows that number of BCPs is six in each case due to interactions of six N atoms in the C 6 N 6 cavity with the H atoms of interacting analytes. However, the strengths and types of bonding in all complexes are different due to the different values of their BCP parameters (see Table 2). In the case of the HCN@C 6 N 6 complex, the ∇ 2 ρ and ρ values are in the range of 0.02429 a.u. to 0.0284 a.u. and 0.00706 a.u. to 0.00814 a.u., respectively. The most stable interaction is observed between H7 of HCN and N6 of C 6 N 6 . The values of ∇ 2 ρ and ρ at BCPs between H7 and N6 are 0.0284 a.u. and 0.00814 a.u., respectively. In addition, the rest of the BCP parameter values of the HCN@C 6 N 6 complex are in the range of electrostatic attractions, which is consistent with the SAPT0 analysis, where the dominant contribution was electrostatic. The other BCP parameters such as G, H, V, -V/G and E int are in the range of electrostatic interactions.
A topological analysis of the H 2 S@C 6 N 6 complex also shows six BCPs. Among these BCPs, two BCPs (H7-N2 and H8-N5) are in the strong electrostatic region, while the rest of the BCPs indicate dispersion interactions (see Table 2). Again, the results of the QTAIM analysis for the H 2 S@C 6 N 6 complex are well matched with the SAPT0, where a good balance between electrostatic and dispersion interactions was observed. The highest values of ∇ 2 ρ (0.03965), ρ (.01586 a.u), H (0.00 a.u.) and E int (−3.11 kcal/mol) are observed for H7-N2 and H8-N5, respectively. The BCP parameter such as ∇ 2 ρ, ρ and E int of H7-N2 and H8-N5 are in the range of H bonding, but no such types of blue isosurface and spikes are seen in the 3D isosurfaces and 2D-RGD plots of NCI analysis. The interaction distances between H7 and N2 and H8 and N5 are 2.29 Å each, which is greater than the 1.8 Å required for interacting system to demonstrate H bonding [81].
The BCP parameter values of the NH 3 @C 6 N 6 complex are in the range of medium to strong interactions between NH 3 and C 6 N 6 . The strongest interactions are observed between H7 and N2 and H9 and N6 of NH 3 and C 6 N 6 , respectively. The values of these two BCP parameters ∇ 2 ρ, ρ and E int are almost comparable (see Table 2). The values of the rest of the five BCPs indicate vdWs interactions. The number of BCPs for the PH 3 @C 6 N 6 complex are equal in number with other complexes. However, all BCP parameter values between the H atoms of PH 3 and the N atoms of C 6 N 6 are in the range of dispersion interactions, which is consistent with the SAPT0 interaction energy analysis, where PH 3 @C 6 N 6 was the least stable complex. In all studied analyte@C 6 N 6 complexes, the values of BCP parameters are in good agreement with NCI and SAPT0 analyses.

Natural Bond Orbital (NBO) and Electron Density Differences (EDD) Analyses
The electronic properties of complexes were explored by EDD and NBO analyses. Through these analyses of the nature of interactions, the stability, charge transfer and sensing ability of the designed surface for selected analytes can be explored. An EDD plot is obtained by subtracting the charges of individual fragments from the charge of the analyte@C 6 N 6 complex. The topologies obtained through EDD analyses show two types of isosurface: yellow and green. The yellow surfaces reveal a depletion in charge, while a green colour illustrates an accumulation of charge. Among the studied complexes, both types of isosurface are observed in the adsorption site of analytes and the C 6 N 6 surface, which indicates an exchange of electronic charge between them. The topologies of the complexes determined through EDD analyses are presented in Figure 6. In addition, the NBO charge values of each analyte over C 6 N 6 are also displayed in Figure 6.
The charge transfer values from C 6 N 6 to the analytes are −0.019 e − (HCN), −0.026 e − (H 2 S), −0.015 e − (NH 3 ) and −0.008 e − (PH 3 ). These values of charges show that the analytes extracted charge from C 6 N 6 . In all studied analytes, the H atoms of analytes interacted with the electron rich cavity of C 6 N 6 , due to which charge is transferred from C 6 N 6 to the analytes. The highest charge value is extracted by H 2 S (−0.026 e − ) due to a close interaction of the H atoms of H 2 S with the N atoms of C 6 N 6 . Similarly, the accumulation and depletion of electron density in the interacting sites of C 6 N 6 and H 2 S clearly indicate that the nitrogen of C 6 N 6 transferred more charge towards H 2 S. In the case of HCN, a charge of −0.019 e − is determined, which is contrary to its interaction energies. The EDD analysis of HCN adsorption over C 6 N 6 shows that charge is transferred from the N atoms of C 6 N 6 to the H atom of HCN. However, the lowest values of charge are observed in NH 3 (−0.015 e − ) and PH 3 (−0.008 e − ) due to the weak interactions of these analytes with the C 6 N 6 sheet.

Frontier Molecular Orbital (FMO) Analysis
The electrical signal produced by an electrochemical sensor mainly depends on changes in its electronic properties after interaction with an analyte. To explore these changes in electronic properties of sensors, a frontier molecular orbital analysis was performed. The energy values determined from an FMO analysis of bare C 6 N 6 and analyte@C 6 N 6 complexes are shown in Table 3. The densities of HOMO and LUMO orbitals are presented in Figure 7. The energies of the HOMO and LUMO for C 6 N 6 are −7.16 eV and −3.30 eV, respectively, with a HOMO-LUMO energy gap (E H-L gap) of 3.86 eV. The interaction of selected industrial pollutants with C 6 N 6 causes prominent changes in the energy levels of the HOMO, LUMO and E H-L gap. The computed values of the E H-L gaps of HCN@C 6 N 6 , H 2 S@C 6 N 6 , NH 3 @C 6 N 6 and PH 3 @C 6 N 6 complexes are 4.02 eV, 2.76 eV, 2.58 eV and 3.35 eV, respectively. The results presented in Table 3 show that adsorption of H 2 S, NH 3 and PH 3 on C 6 N 6 causes a pronounced increase in the HOMO energy, while the LUMO energy of these complexes remains almost unchanged. However, adsorption of HCN shows the inverse behaviour, where a significant decrease in the HOMO energy (−7.43 eV) is noticed compared to C 6 N 6 (−7.16 eV). A more pronounced decrease in the HOMO energy causes an increase in the E H-L gap (4.02 eV) of the HCN@C 6 N 6 complex compared to bare C 6 N 6 (3.86 eV). This increase in the E H-L gap of the HCN@C 6 N 6 complex indicates a decrease in the conductivity of C 6 N 6 . As a result, C 6 N 6 cannot act as a good sensor for HCN.
Adsorption of H 2 S onto C 6 N 6 resulted in a prominent increase in the energy of the HOMO (−6.07 eV), while the LUMO energy (−3.31 eV) is almost comparable to bare C 6 N 6 (−3.30 eV). This increase in the HOMO energy resulted in a pronounced reduction in the E H-L gap (2.76 eV) of the H 2 S@C 6 N 6 complex. Among the different industrial pollutants adsorbed on C 6 N 6 , the most significant increase in electrical conductivity is observed for the NH 3 @C 6 N 6 complex due to an appreciable decrease in the E H-L gap. The energies of the HOMO and LUMO for the NH 3 @C 6 N 6 complex are 5.85 eV and −3.27 eV, respectively. The interaction of PH 3 changes the HOMO (−6.62 eV) and LUMO (−3.27 eV) energies in such a way that a negligible decrease in the E H-L gap (3.35 eV) is observed for the PH 3 @C 6 N 6 complex. Among the studied analyte@C 6 N 6 complexes, the highest decrease in the E H-L gap is observed for NH 3 @C 6 N 6 . This indicates that C 6 N 6 can act as potential surface for this analyte. Thus, it is concluded that C 6 N 6 is highly selective towards NH 3 compared to the other studied analytes.
After adsorption of industrial pollutants (HCN, H 2 S, NH 3 and PH 3 ) onto C 6 N 6 , the dispersal of orbitals densities was also explored in order to comprehend the sensing abilities of C 6 N 6 . We observed three types of orbital distribution patterns. In the case of the HCN@C 6 N 6 complex, the orbital densities are localized on the triazine ring. In the HOMO, the orbital densities are observed on the carbon and nitrogen of the triazine ring, while in the LUMO, the orbital densities are shifted to the carbon of the triazine ring. This shows that analytes do not participate in the electronic shift from the HOMO to the LUMO (see Figure 7). The intra shift of electronic orbital densities causes an increase in the EH-L gap com pared to bare C6N6. In H2S@C6N6 and PH3@C6N6 complexes, the major portion of the HOMO density is located on the analyte, with some sharing with the N atoms of C6N6 while the LUMO density is completely shifted onto C6N6. Such a type of electronic transi tion causes a significant change in the EH-L gap. A third type of electronic transition is ob The intra shift of electronic orbital densities causes an increase in the E H-L gap compared to bare C 6 N 6 . In H 2 S@C 6 N 6 and PH 3 @C 6 N 6 complexes, the major portion of the HOMO density is located on the analyte, with some sharing with the N atoms of C 6 N 6 , while the LUMO density is completely shifted onto C 6 N 6 . Such a type of electronic transition causes a significant change in the E H-L gap. A third type of electronic transition is observed in the NH 3 @C 6 N 6 complex, where the HOMO is completely located on NH 3 , while the LUMO is shifted to C 6 N 6 (see Figure 7). Such a type of electronic transition brings about a significant change in the E H-L gap. The same sort of behaviour was observed by us previously in a study of the same analytes over C 2 N. The transition of orbital density from analytes to the C 2 N surface causes considerable changes in the E H-L gaps [34,71,72].
We compared the adsorption energies of our studied system with those available in the literature for different COFs. The adsorption energies of H-containing analytes are comparable or somewhat higher than already reported values on other surfaces. An adsorption energy of −12.27 kcal/mol is observed for the NH 3 @C 6 N 6 complex, whereas in the literature, adsorption energies of −5.27 kcal/mol, −10.68 kcal/mol and −6.65 kcal/mol are observed for NH 3 @CTF-FUM, NH 3 @C 2 N and NH 3 @CTF-0 complexes, respectively. In addition, interaction energies of −15.24 kcal/mol, −3.79 kcal/mol and −2.34 kcal/mol are observed for HCN@CTF-FUM, H 2 S@CTF-FUM and PH 3 @CTF-FUM, respectively. The adsorption energies of the rest of the complexes are given in Table 4 and reveal that C 6 N 6 can act as a better surface for electrochemical sensing of H-containing analytes.

Conclusions
The electrochemical sensing application of C 6 N 6 is evaluated by DFT simulations at the wb97xd/6-31g(d,p) level of theory. The adsorption of industrial pollutants over C 6 N 6 occurred through physisorption, with adsorption energies ranging from −9.36 kcal/mol to −16.46 kcal/mol. Among the considered analytes, the maximum energy is observed for HCN@C 6 N 6 (−16.46 kcal/mol). The non-covalent interactions of analyte@C 6 N 6 complexes are explored through symmetry-adapted perturbation theory (SAPT0), quantum theory of atoms in molecules (QTAIM) analyses and non-covalent interaction (NCI) analyses. The attractive components in SAPT0 analyses show that electrostatic and dispersive interactions play a dominant role in the stabilization of analytes in the C 6 N 6 cavity. Similarly, NCI and QTAIM analyses also verified the findings of SAPT0 and interaction energy analyses. In addition, the electron density (ρ BCP ) and Laplacian of electron density (∇ 2 ρ bcp ) remained high for the HCN@C 6 N 6 complex, which is consistent with the NCI and SAPT0 results. The electronic properties of analyte@C 6 N 6 complexes are investigated by electron density difference (EDD), natural bond orbital analyses (NBO) and frontier molecular orbital analyses (FMO). Charge is transferred from the C 6 N 6 sheet to HCN, H 2 S, NH 3 and PH 3 . The highest exchange of charge is noted for H 2 S (−0.026 e − ). The results of FMO analyses show that the interaction of all analytes results in changes in the E H-L gap of the C 6 N 6 sheet. However, the highest decrease in the E H-L gap (2.58 eV) is observed for the NH 3 @C 6 N 6 complex compared to other studied analyte@C 6 N 6 complexes. The orbital density pattern shows that the HOMO density is completely concentrated on NH 3 , while the LUMO density is transferred towards C 6 N 6 . This indicates that C 6 N 6 can act as potential surface for these analytes. Hence, which analyte is more selective towards C 6 N 6 depends on its electrical conductivity and not its adsorption. Thus, it is concluded that C 6 N 6 is highly selective towards NH 3 compared to the other studied analytes.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nano13061121/s1, Figure S1 caption: Optimized geometries of least stable complexes of each analyte over C6N6 at tains six nitrogens in its cavity. Recently, C6N6 has been u ysis [54], sensing [55], drug delivery [56] and energy st that the C6N6 surface is more comparable to other availa containing industrial pollutants such as HCN, H2S, NH nitrogen in the C6N6 unit also leads to a high surface area can efficiently interact with various analytes through H types of chemical interactions. According to the best of o been tested as a sensor for the above-mentioned analytes density functional theory simulations to investigate C6N geometrical properties are explored through NCI, QTA changes in the electronic properties of analytes in C6N NBO, EDD and FMO analyses.

Computational Methodology
Gaussian 09 software was used to carry out the simu selected geometries of bare C6N6 and analyte@C6N6 com Ꞷb97XD/6-31G (d, p) level of theory. The Ꞷb97XD functi study because it is a range-separated functional which c ized intermolecular interactions [58]. In Ꞷb97XD, the s range correction [59]. Additionally, the Ꞷb97XD functio dispersion factor to efficiently study the van der Waal changes in the electronic properties of C6N6 before and a explored by NBO, EDD and FMO analyses at the B B3LYP/6-31G(d) is considered as the best to study the elec tems [60][61][62][63][64][65]. The most stable configurations of the analy tigated by adsorption of analytes through different orient ysis was performed to confirm that the geometries of the the potential energy surface. The energies of adsorbed an Equation (1): where E(analytes@C6N6) is the interaction energy of the compl C6N6 and Eanalytes is the energy of the industrial pollutants A SAPT0 analysis was applied to determine the role the interaction energy in the stabilization of the analyte SAPT0 energy is the sum of four factors: induction (∆Eind) (∆Eelstat) and exchange (∆Eexch). Hence, the SAPT0 energy (2):

∆ESAPT0 = ∆Eelstat + ∆Eexch + ∆Ein
The nature of adsorption, such as the electrostatic, between the analyte and C6N6, was examined by an NCI a of non-covalent interactions is given by the reduced dens The value of electron density (ρ) for non-covalent int However, small changes in (ρ) result in prominent chang in the form of spikes in a 2D-RGD plot. An NCI analysis actions through 3D-isosurfaces and 2D-RGD plots. These value (λ2) to differentiate between the nature of interactio