The optimized structure, FMO and MEP plots for GF were provided in Fig. 1. As shown in MEP plot, the negative charges (red color) are mainly localized over the carbonyl oxygen (O head), F atom (F head) and etheric oxygen (O head), which can be interacted with electrophile sites of nanocluster. The calculated P = O, P–O and P–F bond lengths were calculated 1.46, 1.59 and 1.59 Å, respectively. The FMO plot for GF is located on all atoms in the HOMO and LUMO regions.
The adsorption of GF on the B24N24 and AlB23N24
The most stable configuration of B24N24 and AlB23N24 nanoclusters was shown in Fig. 1. The calculated B–N bond length between 6–8, 6–4 and 4–8 membered rings are 1.42, 1.49 and 1.47 Å, respectively, and is completely in agreement with the previous reports [37, 46]. The calculated Al–N bond length in AlB23N24 for 6–8, 6–4 and 4–8 membered rings are 1.77, 1.83 and 1.80 Å, respectively. The MEP plots of the B24N24 and AlB23N24 indicated the electrostatic potential in the Al atom of AlB23N24 is significantly more positive (blue color) compared to the B and N atoms which makes it the most electrophilic site for GF molecule.
The reactivity of GF with nanoclusters has been studied in the various adsorption sites (Fig. 2). The adsorption energies of GF with the B24N24 in state A, B and C were calculated to be − 9.60 and − 5.57 and − 5.51 kcal mol−1, respectively (Table 1). Nejati et al. indicated the interaction of GF with BN nanosheet with weak adsorption energies of − 0.32 kcal mol−1 at the B3LYP-D method and 6-31G* basis set . Equilibrium distances between GF and nanocluster in state A, B and C were obtained to be 1.62, 2.67 and 2.43 Å, respectively. These results were shown the interaction of state A (carbonyl oxygen) is stronger than that of state B (F atom) and C (etheric oxygen) since adsorption energies were indicated in state B is more negative than that of state B and C. The adsorption energy of GF/AlB23N24 was calculated − 50.63, − 23.14 and − 30.61 kcal mol−1 with equilibrium distances 1.83, 1.88 and 1.98 Å in state D, E and F, respectively. These results indicated that GF adsorption on the AlB23N24 is stronger than that on the pure one. NBO charge transfers in state D, E and F were calculated 0.183, 0.151 and 0.160 e, respectively. Positive values of charge transfers are indicated charge transfer from GF to the nanoclusters.
Furthermore, the thermodynamic parameters (Gibbs free energy (ΔG), enthalpy (ΔH) and entropy (ΔS)) were calculated and listed in Table 1. The ΔH values for GF/B24N24 in state A, B and C were calculated − 12.35, − 6.32 and − 7.54 kcal mol−1, respectively, and in GF/AlB23N24 complexes were obtained − 52.88, − 27.75 and − 33.62 kcal mol−1 in state D, E and F, respectively. The negative values of ΔH indicated that the reactions are exothermic. The ΔG values were calculated 0.70, 5.30, 5.60, − 42.54, − 12.25 and − 18.89 kcal mol−1 in state A, B, C, D, E and F, respectively. Therefore, B24N24 interaction is non-spontaneous while AlB23N24 interaction is spontaneous. The calculated ΔG values are less negative compared to the ΔH values, indicating an entropy reduction. The calculated negative values of ΔS confirm this matter. These results were indicated the interaction of the AlB23N24 is more suitable compared to the B24N24 nanocluster. The MEP plot of GF/AlB23N24 in Fig. 3, shows significant change after adsorption in the electrostatic potential. These results reinforce the fact that GF gets chemically adsorbed on the AlB23N24.
Some of the electronic properties like HOMO, LUMO and Eg were reported in Table 1. The Eg is decreased from 7.04 eV in B24N24 to 5.55 eV in AlB23N24. Salari investigated Eg of B24N24 7.11 eV at the M06/6-31G* level of theory . The HOMO and LUMO values in the B24N24 and AlB23N24 nanoclusters were shifted to higher energy after adsorption (except GF/B24N24 in state B). These results indicated that the adsorption of GF on the B24N24 and AlB23N24 nanoclusters destabilizes the HOMO and LUMO levels. In GF/B24N24 complexes the Eg values were revealed that no significant change compared with pure B24N24 (− 4.62%, − 0.86% and − 0.09% in state A, B and C, respectively) but in GF/AlB23N24, Eg values were increased from 5.55 eV in pure AlB23N24 to 6.45, 6.60 and 6.44 eV in state D, E and F, respectively. The DOS plot of the pure AlB23N24 and GF/AlB23N24 in state D indicated this change (Fig. 3). The change of Eg will exponentially increase the sensitivity and electrical conductivity of the nanostructure [49,50,51]. Therefore, it is clear that the GF/AlB23N24 is more sensitive rather than B24N24. change of Eg indicated that the AlB23N24 can detect the GF.
The adsorption of GF on the B16N16 and AlB15N16
Furthermore, we examined adsorption of GF molecule on the B16N16 and AlB15N16 nanoclusters. The optimized structures, MEP and FMO plots of B16N16 and AlB15N16 are shown in Fig. 4. The B–N bond lengths of B16N16 in 6–6 and 6–4 membered rings were calculated 1.45 and 1.47 Å, respectively and Al–N bond lengths for AlB15N16 were calculated 1.80 and 1.81 Å in 6–6 and 6–4 membered rings, respectively.
After adsorption of GF on the B16N16, adsorption energies were calculated − 14.30, − 1.46 and − 16.52 kcal mol−1 in state G, H and I, respectively (Table 2). When GF is located from its etheric oxygen (state I) on the B16N16 nanocluster, it reoriented and attached from carbonyl oxygen to the B16N16 (Fig. 5). Equilibrium distances in state G, H and I were calculated 1.59, 2.53 and 1.57 Å, respectively. The adsorption energies of AlB15N16 complexes were obtained − 54.84, − 28.28 and − 35.22 kcal mol−1 in state J, K and L, respectively. These results were indicated the interaction of the AlB15N16 nanocluster is stronger than that of the B24N24, AlB23N24 and B16N16 nanoclusters. NBO charge transfer were calculated 0.190, 0.157 and 0.176 e and equilibrium distances were investigated 1.82, 1.86 and 1.93 Å in state J, K and L, respectively.
The ΔH (ΔG) values of GF/B16N16 and GF/AlB15N16 were calculated − 17.86 (− 3.94), − 2.19 (9.80), − 19.76 (− 6.12), − 57.53 (− 45.79), − 32.06 (− 20.22) and − 38.80 (− 24.63) kcal mol−1 in state G, H, I, J, K and L, respectively. The negative values of ΔH and ΔG indicated the reactions are exothermic and spontaneous. Upon adsorption of GF on AlB15N16 in state J, their MEP changes significantly. These results confirm the fact that GF gets chemically adsorbed on the AlB15N16.
The HOMO, LUMO and Eg values for B16N16 and AlB15N16 at the M06 method were shown in Table 2. The HOMO values for the B16N16 and AlB15N16 were − 8.06 and − 7.65 eV while the LUMO values were − 1.25 and − 3.06 eV, respectively. The Eg is decreased from 6.82 eV in B16N16 to 4.59 eV in AlB15N16. Soltani et al. calculated Eg of B16N16 6.37 eV at the B3LYP method  and Shakerzadeh et al. investigated Eg of B16N16 and AlB15N16 6.17 and 3.97 eV at the M06-2X method . The HOMO and LUMO values after adsorption process were increased to higher energy and destabilizes the HOMO and LUMO levels. Eg values after adsorption in GF/B16N16 reveal that no significant change compared with pure B16N16 and indication of B16N16 nanocluster cannot detect the GF. The Eg values are increased from 4.59 eV in AlB15N16 to 5.92, 6.09 and 6.42 eV in state J, K and L, respectively. Compared to the B24N24, AlB23N24 and B16N16, the Eg represent more sensitivity in AlB15N16 (29.00% in state J, 32.71% in state K and 39.95% in state L). The DOS plot of AlB15N16 and GF/B15N16 in state J in Fig. 6 confirm this increase. The change of Eg was indicated the AlB15N16 nanocluster can detect the GF nerve agent.