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 C2N stoichiometry contains 12 C and 6 N atoms and its lattice constant is 8.33 Å. The fully relaxed C − N bond length is calculated to be 1.34 Å. The C − C bonds have two different values. The C − C(1) bond at the border of the hole is 1.48 Å and the C − C(2) bond shared between benzene and pyrazine rings is 1.41 Å. The results are in good agreement with those reported in the previous reports [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 [35–39].
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.
Table 1
Adsorption energy, Eads, and adsorption distance, d.
| heptanal | hexanal | pentanal | isoperene |
Eads (eV) | -0.30 | -0.19 | -0.17 | -0.35 |
d (Å) | 2.6 | 2.7 | 2.9 | 2.6 |
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).
Table 2
Energy band gap, Eg, and conductivity, σ, for n = 1–4 adsorbed molecules.
| n | heptanal | hexanal | pentanal | isoperene |
Eg (eV) | 1 | 1.30 | 1.25 | 1.25 | 1.39 |
2 | 1.16 | 1.13 | 1.16 | 1.25 |
3 | 1.13 | 1.07 | 1.0 | 1.25 |
4 | 1.12 | 0.92 | 0.91 | 1.24 |
σ | 1 | 1.1×10− 11 | 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 |
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).