Application of nitrogenated holey graphene for detection of volatile organic biomarkers in exhaled breath of humans with chronic kidney disease: a density functional theory study

The possibility of using nitrogenated holey graphene (NHG) sheet to detect volatile organic biomarkers in exhaled breath of humans with kidney disease is investigated. Heptanal, hexanal, pentanal, and isoperene are known as the prominent biomarkers of chronic kidney disease. Adsorption of these molecules on NHG sheet is studied using density functional theory. All the molecules are weakly physisorbed on NHG sheet, which predicts easy desorption and the possibility of using NHG sheet as a reusable sensor. The NHG sheet acts as a semiconductor with a direct band gap. Adsorption of the considered molecules causes n-type semiconducting properties in the sheet. Increasing the concentration of the adsorbed molecules decreased the energy band gaps and consequently increased the electric conductivity of NHG sheet. Hence, the electronic properties of NHG sheet are sensitive to the presence and concentration of heptanal, hexanal, pentanal, and isoperene molecules. Our results open a new opportunity to design a new sensor to diagnose chronic kidney disease using exhaled breath analysis.


Introduction
Chronic kidney disease (CKD) is known as a global public health problem [1]. The number of patients suffering from CKD is significantly growing worldwide. Early treatment can prevent or delay complications of decreased kidney function, slow the progression of kidney disease, and reduce the risk of cardiovascular disease [1,2]. Unfortunately, most of patients are diagnosed at a late stage because the initial stage of CKD usually is clinically silent and asymptomatic. Thus, exploration of rapid, safe, and inexpensive methods for early unambiguous diagnosis of renal insufficiency is vital. Nowadays, the possibility of using the exhaled breath analysis as a non-invasive method for early diagnosis of progressive disease and response to therapeutic interventions in different illnesses has been investigated [3][4][5][6][7][8][9][10][11][12]. In this context, the impact of CKD on the composition of the exhaled breath in humans and experimental animals several studies has been explored [2,12]. It is found that CKD significantly changes the composition of exhaled breath [12]. Monitoring the concentration of over fifty gases in the exhaled breath of patients with CKD reveals that heptanal, hexanal, pentanal, and isoperene are the prominent biomarkers of CKD [2,12,13].
The past several decades have witnessed increasing attention by researchers to nanomaterials owing to some superior properties such as high stability, small size, high specific surface area, suitable surface modification property, and adjustable lifetime [14][15][16]. Nanomaterials have been the interest of many theoretical studies and became an exciting area for experimentalists . Among various nanomaterials, carbon-based ones especially carbon nanotubes, graphene, and graphyne have demonstrated their appropriateness for wide spectrum of applications ranging from electronics to optics, sensors, and biodevices [17][18][19][20][21]. One of the most promising applications is gas adsorption and sensing. The sensing performance of carbon nanotubes, graphene, and graphyne toward NO 2 , NH 3 , H 2 O, CO, H 2 S, SO 2 , etc. have been studied extensively [21][22][23][24][25][26]. The results showed that the sensors based on carbon nanotubes, graphene and its derivatives are capable for detecting individual molecules with a relatively high sensitivity. Furthermore, these materials are suggested as highly sensitive biosensors to detect the expression of typical biological molecules at early stage of cancer [27][28][29]. In terms of the application of nanomaterials as sensors, sheets and nanotubes based on phosphorene, silicene, germanene, antimonene, and arsenene are also receiving great attentions from both the academic and industrial communities [30][31][32][33][34]. The findings reported that different gas molecules could be sensed through adsorption on these materials. Motivated by these results, researchers continue to seek for novel sensitive sensors based on nanomaterials.
Two-dimensional crystals with C 2 N stoichiometry named nitrogenated holey graphene (NHG) have recently been synthesized [35][36][37][38]. This two-dimensional material, unlike pristine graphene which lacks a band gap and needs to be engineered to open the gap for practical application, has a direct band gap [35][36][37][38][39]. It could have applications similar to or even more fascinating than graphene. In this study, we have investigated the structural and electronic properties of NHG when adsorbing gas molecules using density functional theory (DFT).

Computational details
All DFT calculations are performed with the OpenMX3.8 code [40]. The Perdew, Burke, and Ernzerhof (PBE) approach from the generalized gradient approximation (PBE-GGA) is applied to describe the exchange-correlation functional [41]. The tractable norm-conserving pseudopotential proposed by Morrison, Bylander, and Kleinman [42], which is a norm-conserving version of the ultrasoft pseudopotential by Vanderbily [43] is used. The empirical correction method described by Grimme (DFT-D2) is used to describe the van der Waals (vdW) interactions [44]. The energy cutoff is adjusted to 100 Ry. The pseudoatomic orbitals (PAO) basis functions are specified by s2p2d1 for C, N, O, and H atoms with the cutoff radii of the basis functions set to the value of seven. Atomic coordinates are fully optimized until the forces on each of the constituent atoms are converged to 0.05 eV/Å. The periodic boundary conditions are applied in all dimensions. A vacuum space of 25 Å is left in the perpendicular direction to the NHG sheet to prevent the columbic interaction between the neighboring slabs. Mulliken population analysis is performed to obtain the charges on individual atoms [45].
In order to evaluate the stability of adsorption of the configurations, the adsorption energy is defined as, here, E molecule ,E sheet , and E sheet+molecule are the total energies of the molecule, NHG sheet, and NHG sheet with adsorbed molecule, respectively. With such definition, negative adsorption energy indicated that the adsorption is exothermic. The nudged elastic band (NEB) method [46] is employed to search for the optimal adsorption distance.
To study the electronic properties of, the electronic band structures and density of states (DOS) are calculated. Along each high symmetry line in the Brillouin zone, 21 K-points are considered. The electric conductivity of the systems, , is estimated by Here, E g is the band gap of the system. K B and T denote the Boltzmann's Constant and temperature, respectively. The electric conductivity is obtained at room temperature.

Results and discussion
Initially, the structural and electronic properties of NHG are studied. To model a monolayer of NHG sheet, a 2 × 2 supercell is considered as shown in Fig. 2(a). The primitive unit cell of NHG with C 2 N stoichiometry contains 12 C and 6 N (1)  [47]. The electron density difference of NHG sheet is illustrated in Fig. 2(b). Here, the yellow color regions indicate electron accumulation, while the cyan regions indicate electron depletion. It is clear that the charge density is mainly distributed between C and N. This suggests that the covalent bond is formed between C and N. The holey site is surrounded by negatively charged N atoms. The results are in good agreement with previous studied [48,49]. Mulliken atomic populations indicate that each C atom donates 0.22 e, and each N atom gains 0.44 e.
The electronic band structure and DOS of NHG sheet are illustrated in Fig. 3. There is a band gap of 1.82 eV between top of the valence band and bottom of the conduction band at Γ point of the Brilliouin zone. Hence, NHG is a semiconductor with a direct band gap. It is in accordance with prior studies which predicted a band gap of 1.60, 1.66, 1.70, 1.82 and 2.47 eV based on DFT calculations, and optically measured a band gap of 1.96 eV [35][36][37][38][39].
To find the most stable adsorption configuration, the gas molecules are placed at all possible adsorption sites on  the sheet. The possible adsorption sites on NHG are top of C and N atoms, the center of C − N and C − C bond, the center of benzene and pyrazine rings, and hollow site. For each adsorption site, different molecular orientations are examined. The center of hollow site is found to be the most favorable site for heptanal, hexanal, and pentanal adsorption. The adsorption behavior of isoperene on NHG sheet is different from other molecules. Isoperene is preferably adsorbed on top of the pyrazine ring. As an example, NHG sheet with adsorbed heptanal and isoperene molecules are shown in Fig. 4(a and b). It is found that there is no structural deformation in NHG sheets after adsorption of the molecules, further indicating that the stability of NHG sheet. An energy scan of the adsorbed molecules at the most stable adsorption sites is performed to obtain the optimal adsorption distance of the molecules on NHG sheet. Adsorption distance is defined as the shortest atom-to-sheet distance between the molecule and NHG sheet.
The NEB is also used to analyze the change of total energy as a function of the adsorption distance. As an example, the change of total energy as a function of the adsorption distance for adsorption of heptanal, hexanal, pentanal, and isoperene on NHG sheet is shown in Fig. 5. The adsorption energies and distances of the most favorable structures are summarized in Table 1. A negative value of adsorption  energy indicated that the adsorption is exothermic. The greater absolute value of adsorption energy means the more stable system. The binding strength follows the trend: pentanal < hexanal < heptanal < isoperene. The considered molecules prefer to physically adsorb on NHG sheet with small adsorption energies.
In order to gain further insight about the interlayer interactions, the charge densities are calculated. As an example, the total electron density and electron density difference of NHG sheet with adsorbed heptanal are shown in Fig. 6. Here, no electron orbital overlap and electron accumulation between adsorbed molecule and NHG sheet are observed. This feature indicates there are no chemical bonds the molecules and NHG sheet, indicating that the systems are trend to physical adsorption. Mulliken charge analysis shows that the adsorbed molecules act as charge acceptors. Each adsorbed heptanal, hexanal, pentanal, and isoperene gain 0.012, 0.011, 0.10, and 0.059 e from NHG sheet, respectively. The little charge transfers as well as small adsorption energies confirm the physical adsorption of the considered molecules on NHG sheet.
The electronic band structure and DOS are studied for the most stable structures of each molecule adsorbed on NHG sheet (Fig. 7). As shown, flat occupied states and sharp DOS peaks are appeared in the band gap at energy of about -0.65, -0.64, -0.62, and -0.68 eV for heptanal, hexanal, pentanal, and isoperene, respectively. It means that NHG sheets in the presence of the considered molecules are n-type semiconductors. The energy band gap is defined as the difference between the highest occupied and lowest unoccupied states. The band gaps are 1.30, 1.25, 1.25, and 1.39 eV after adsorption of heptanal, hexanal, pentanal, and isoperene molecules, respectively ( Table 2).
The electric conductivity of NHG sheet at 300 K is calculated to be 4.8 × 10 -16 . The electric conductivity of NHG sheet after adsorption of the molecules is listed in Table 2. It is found that the electric conductivity of NHG sheet in the presence of the adsorbed molecules is more than that of pure NHG sheet.
To study the sensitivity of the electronic properties of NHG to the concentration of the considered molecules, the number of adsorbed molecules is changed from one to four. As an example, atomic structure NHG sheet in the presence of four hexanal molecules is shown in Fig. 4(c) and the electronic band structure and DOS of NHG in the presence of four pentanal molecules are shown in Fig. 8. As shown, the numbers of occupied states and sharp DOS peaks below the Fermi level are increased by increasing the number of adsorbed molecules. The energy band gap and electric conductivity as a function of the number of adsorbed molecule is listed in Table 2. Increasing the concentration of the adsorbed molecules decreased the energy band gap and consequently increased the electric conductivity (Table 2).

Conclusions
Heptanal, hexanal, pentanal, and isoperene molecules are the prominent biomarkers of CKD. Motivated by the recent realization of two-dimensional nanomaterials as gas sensors, we have investigated the adsorption of these molecules on NHG sheet. Adsorption energies, adsorption distance, electronic band structures, density of states, energy band gap, and electric conductivity are calculated using density functional theory calculations. The large adsorption distances and small indicate these molecules are energetically favorable to physically adsorb on NHG sheet. The NHG sheet with intrinsic semiconducting properties exhibit n-type semiconducting properties after adsorption of the considered molecules. It is found that the energy band gap of NHG sheet is sensitive to the concentration of the adsorbed molecules. Increasing the number of the adsorbed molecules decreased the energy band gap and consequently increased the conductivity. Our results suggested that NHG sheet could be used as a proper   3.0 × 10 -11 3.0 × 10 -11 2.0 × 10 -12 2 1.7 × 10 -10 3.1 × 10 -10 1.7 × 10 -10 3.0 × 10 -11 3 3.1 × 10 -10 9.9 × 10 -10 3.8 × 10 -9 3.0 × 10 -11 4 3.7 × 10 -10 1.8 × 10 -8 2.2 × 10 -8 3.7 × 10 -11 Fig. 8 Electronic band structures and DOS of NHG sheet with four adsorbed pentanal molecules gas sensor for detection of heptanal, hexanal, pentanal, and isoperene as the prominent biomarkers to diagnose CKD.