In order to obtain an insight into the anion-sensing mechanism, the interactions between hosts and guests were investigated exploiting the density functional method. Table 1 presents the most important geometrical parameters with and without BSSE corrections for complexes AIC⁻·HF and AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄). The corresponding geometrical parameters of complexes for 1–5 are given in Table SI, Supporting Information. According to the suggested geometry cutoffs for D–H···A hydrogen bond definition, i.e. H···A distances <3.0 Å and D–H···A angles >110° [36,37], the interaction between pyrrole N and H for complex AIC⁻·HF and between Cl, Br, AcO, and H₂PO₄ and pyrrole-NH in AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄) can be identified as hydrogen bonds. Comparing the optimized geometries with and without BSSE correction, one may find that the deviations of the hydrogen bond length between pyrrole-N and H (R_N·_H) and the distance between H and F (R_H–F) for complex AIC⁻·HF are 0.005 and 0.001 Å, respectively. The angles θ_N–H·_F in complex AIC⁻·HF without BSSE correction is equal to that of with BSSE correction. For complexes AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄), the deviations of R_N–H and R_H·_X are within 0.004 and 0.15 Å, respectively. The corresponding deviations of angles θ_N–H·_X are within 6°. Therefore, BSSE correction is necessary for the optimization of this kind of system to some extent. Compared with the H–N bond in AIC (1.025 Å), obviously, the H–N bond is broken (0.447 Å elongation) and R_H···N = 1.4712 Å and R_H–F = 1.030 Å forming AIC⁻·HF. Namely, the pyrrole-H can be efficiently deprotonated by F⁻. In the cases of Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻, however, R_H–N values only change slightly (<0.044 Å elongation, see Table 1). This suggests that deprotonation indeed takes place from the acidic pyrrole-NH of the host chemosensor to form AIC⁻ and HF in the presence of F⁻. However, for Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻, the host chemosensor prefers to form the hydrogen-bonded complexes between AIC and X⁻ (X = Cl, Br, AcO, and H₂PO₄), rather than formation of the AIC⁻ form. Similar phenomena are also found for 1–5 (see Table SI, Supporting Information).

The interaction energies with BSSE corrections for complexes n⁻·HF and n·X⁻ (n = AIC and 1–5, X = Cl, Br, AcO, and H₂PO₄) are listed in Table 2. It is clear that the BSSE-corrected interaction energy (ΔE_BSSE) of complex AIC⁻·HF is much more favorable for the distinct selectivity of F⁻ than other anions. The ΔE_BSSE of complex AIC⁻·HF is more than those of AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄) by about 20 kcal/mol. Therefore, the sensors can easily detect F⁻ in the presence of Cl⁻, Br⁻, AcO⁻, and H₂PO₄ ⁻. These calculation results are in good agreement with the reported experimental observations that intermolecular proton transfer (IPT) between chemosensor substrate AIC and F⁻ occurs when the concentration of F⁻ reaches a certain level with the addition of F⁻ to the sensor substrate solution [21]. Similar phenomena are also found for 1–5. Thus, one can conclude that the host chemosensors have a much stronger affinity to F⁻ than to Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻ through intermolecular proton transfer, which leads to the formation of chemosensor anions by F⁻. The hydrogen bond acceptor F⁻ is stronger than those of Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻. On the other hand, the more pronounced the proton transfer reaction, the higher the intensity of the hydrogen bond interaction and the higher the stability of the complex [37,38]. Furthermore, the ΔE_BSSE, R_H–N, and R_H–X (X = F, Cl, Br, AcO, and H₂PO₄) values of the complexes also support the distinct selectivity for F⁻ from Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻.

As the counterpoise correction was unreliable for the H-bond with fluorine in some cases [39], we calculated the interaction energies of AIC⁻·HF and AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄) at the MP2/6-31+G(d,p)//B3LYP/6-31+G(d,p) level. It turns out that the interaction energy of AIC⁻·HF (36.9 kcal/mol) is larger than that of ΔE_BSSE by 6.2 kcal/mol. The corresponding values of AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄) are larger than those of ΔE_BSSE about 8–10 kcal/mol. However, the interaction energy of AIC⁻·HF is larger than those of complexes AIC·X⁻(X = Cl, Br, AcO, and H₂PO₄) by about 10 kcal/mol at the MP2/6-31+G(d,p) level, respectively. It suggests that the interaction energy values of complexes at MP2/6-31+G(d,p) level support the distinct selectivity for F⁻ from Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻. Furthermore, we selected complexes AIC⁻·HF and AIC·X⁻ (X = Cl and Br) as representatives. The geometrical structures of these complexes were optimized using the MP2 method with 6-31+G(d,p) basis set. The interaction energies were calculated using the same methods as for the geometry optimizations and compared with the BSSE-corrected interaction energy (ΔE_BSSE) at the B3LYP/6-31+G(d,p) level. The main geometrical parameters and the interaction energies of complexes AIC⁻·HF and AIC·X⁻ (X = Cl and Br) at the MP2/6-31+G(d,p) level are given in Table SII, Supporting Information. Comparing the results shown in Table SI with Table 1, one can find that the values of R_H···N, R_H–F, and angles θ_N–H·_F of AIC⁻·HF at the MP2/6-31+G(d,p) level are similar to those of AIC⁻·HF with BSSE corrections at the B3LYP/6-31+G(d,p) level, the corresponding deviations are 0.004, 0.004 Å, and 4.0°, respectively. Similar phenomena are found for complexes AIC·X⁻ (X = Cl and Br). The value of interaction energy for complex AIC⁻·HF (37.2 kcal/mol) is larger than that of ΔE_BSSE by 6.5 kcal/mol. The corresponding interaction energies deviations for complexes AIC·X⁻ (X = Cl and Br) are larger than that of complex AIC⁻·HF. However, the interaction energy of AIC⁻·HF is larger than those of complexes AIC·X⁻ (X = Cl and Br) by 19 and 10 kcal/mol at the MP2/6-31+G(d,p) level, respectively. These results indicate that the R_H–N, R_H–X (X = F, Cl, and Br), and the interaction energy values of the complexes also support the distinct selectivity for F⁻ from Cl⁻ and Br⁻.

The AIM theory is often applied to study hydrogen bonds [40–42]. The characteristics of bond critical points (BCPs) are very useful to estimate the strength of hydrogen bonds. To gain a deeper insight into the fundamental nature of NH···X (X = F, Cl, Br, AcO, and H₂PO₄) hydrogen bonds, it is crucial to obtain reasonable estimates of their relative energies. In particular, the electron densities, ρ(r)_bcp, and their Laplacians, ∇²ρ(r)_bcp, evaluated at BCPs are frequently used as indicators of hydrogen bonds. More specifically, the kinetic G(r)_bcp and potential V(r)_bcp electron energy densities are often used to gain additional insight into the strength and nature of a given hydrogen bond. The local kinetic electron energy density can be evaluated from the values of ρ(r)_bcp and ∇²ρ(r)_bcp as [43]:

The kinetic energy density G(r)_bcp is in turn related to the potential energy density V(r)_bcp through the local statement of the virial theorem [44]:

The hydrogen bond energy E_HB (defined as −D_e, where D_e is the hydrogen bond dissociation energy) in molecules can be estimated within the framework of the AIM analysis using the relationship [45]:

The relationship (3) is used to estimate the energy of intermolecular hydrogen bonding. However, the values of the intramolecular hydrogen-bonding energy obtained by means of this equation are somewhat different from the real ones, particularly for intramolecular hydrogen transfer [46]. One of the most reliable approaches to estimating the energy of intramolecular hydrogen bonding is the conformational method. Unfortunately, such a scheme cannot be applied in our calculations because of the lack of conformer. The second one by Musin and Mariam [47] is disposed to correlate E_HB with the interatomic separation (in Å) from donor (D) to acceptor (A) according to the empirical relationship. However, this relationship does not suit the hydrogen bonds in the chemosensors under investigation. Because the pyrrole-NH of the chemosensors are deprotonated by F⁻ and form complexes n⁻·HF (n = AIC and 1–5), the hydrogen bonds in complexes n⁻·HF can be regarded as intermolecular hydrogen bonds between chemosensors anions and HF. Therefore, the E_HB are estimated by this relationship within the framework of the AIM analysis.

The ρ(r)_bcp, ∇²ρ(r)_bcp, and E_HB of the complexes AIC·HF⁻ and AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄) are given in Table 3. The corresponding topological parameters of the complexes n⁻·HF and n·X⁻ (n = 1–5, X = Cl, Br, AcO, and H₂PO₄) are given in Table SIII, Supporting Information. As a general rule, hydrogen bonds are characterized by positive values of ∇²ρ(r)_bcp and low ρ(r)_bcp values. Covalent bonds (shared interactions) have negative ∇²ρ(r)_bcp values and high values of ρ(r)_bcp, whereas the values of ∇²ρ(r)_bcp become positive when the bonds are of a ionic nature [48]. The results displayed in Tables 3 and SIII reveal that the ρ(r)_bcp and ∇²ρ(r)_bcp values of H···N in n⁻·HF (n = AIC and 1–5) are about 0.09 and 0.06 au, respectively. This suggests that the interactions between N and H in n⁻·HF (n = AIC and 1–5) are hydrogen bonds in nature. The ρ(r)_bcp and ∇²ρ(r)_bcp values of H–F in n⁻·HF (n = AIC and 1–5) are about 0.25 and −1.1 au, respectively. Hence, H–F bonds of n⁻·HF (n = AIC and 1–5) are of a covalent bond nature. On the contrary, for complexes n·X⁻ (n = AIC and 1–5, X = Cl, Br, AcO, and H₂PO₄), BCPs at H–N provides ∇²ρ(r)_bcp < 0 (about −1.5 au) and high positive values for ρ(r)_bcp (about 0.3 au), which are characteristics of covalent type interactions. For H···X bonds in complexes n·X⁻ (n = 1–5, X = Cl, Br, AcO, and H₂PO₄), the values of ρ(r)_bcp and ∇²ρ(r)_bcp are about 0.04 and 0.06 au, respectively. This indicates that H···X bonds in complexes n·X⁻ (n = 1–5, X = Cl, Br, AcO, and H₂PO₄) are of hydrogen bond nature. Furthermore, the E_HB values of H···N and H···X in complexes confirm the expectation. The E_HB values of H···N bonds in n⁻·HF (n = AIC and 1–5) are about 27 kcal/mol, while the H···X bonds in n·X⁻ (n = AIC and 1–5, X = Cl, Br, AcO, and H₂PO₄) are 4–20 kcal/mol. The above results show qualitative agreement with the results based on their geometries.

It is well known that the electronic reorganization derived from the formation of a hydrogen bond is associated with a charge transfer between the two moieties of the complex [49]. The overall NBO charge transfer has been evaluated by summing up the NBO atomic charges on the two moieties of each hydrogen-bonded complex (the host chemosensor and halides). We select the parent compound AIC as representative of the system under investigation. The calculated NBO charge densities for AIC⁻·HF and AIC·X⁻ (X = Cl, Br, AcO, and H₂PO₄) are collected in Table SIV in supplementary information. It clearly shows that the sum of charges on the AIC⁻ moiety is −0.856, while the corresponding value of HF is only −0.144 in complex AIC⁻·HF. The sum of charges on the AIC moiety and Cl⁻ in AIC·Cl⁻ are −0.098 and −0.902, respectively. The corresponding values in AIC·Br⁻, AIC·AcO⁻, and AIC·H₂PO₄⁻ are −0.072 and −0.928, −0.120 and −0.88, and −0.060 and −0.933, respectively. Hence, the NBO charge analysis also indicates that the proton is almost completely abstracted by F⁻. In the cases of Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻, however, the host chemosensor prefers to form the hydrogen-bonded complexes between AIC and Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻, rather than the AIC⁻ form.

It is useful to examine the frontier molecular orbitals (FMOs) of the compounds under investigation. The origin of the geometric difference introduced by excitation can be explained, at least in qualitative terms, by analyzing the change in the bonding character of the orbitals involved in the electronic transition for each pair of bonded atoms. An electronic excitation results in some electron density redistribution that affects the molecular geometry [49,50]. The qualitative molecular orbital representations of FMOs for AIC and AIC⁻ in S₀ are shown in Figure 1. The corresponding qualitative molecular orbital representations of FMOs for AIC and AIC⁻ in S₁ are shown in Figure SI, Supporting Information. The major assignments of the lowest electronic transitions for AIC and AIC⁻ are mainly as HOMO→LUMO, which corresponds to a π–π^* excited singlet state. From Figure 1, one can see that both the HOMO and LUMO of AIC and AIC⁻ are spread over the whole conjugated molecule. A careful inspection of the results displayed in Figure 1 reveals that the vertical S₀→S₁ transition of AIC and AIC⁻ shows the intramolecular charge transfer (ICT) in nature. Analysis of the FMOs for AIC and AIC⁻ indicates that the excitation of the electron from the HOMO to LUMO makes the electronic density flow mainly from the 4,5,6,7-tetrahydro-1H-indole moiety (part A) to 3-aminoisoxazole-4-carboxamide moiety (part B). The HOMO of AIC has contributions of 69.2% and 30.8% on parts A and B, while the corresponding values of LUMO are 35.5% and 64.5%, respectively. The HOMO of AIC⁻ has contributions of 68.9% and 31.1% on parts A and B, while the corresponding values of LUMO are 29.0% and 71.0%, respectively. Hence, the percentage of charge transfer from Parts A to B is 38.9% in AIC⁻, which is greater than that of 5.2% in AIC. It is obvious that deprotonation strengthens the electron-donating ability of part A, suggesting a stronger coupling between parts A and B. The molecular p-conjugation in AIC⁻ becomes higher than that of AIC. As a consequence, the electron can move more fluently from parts A to B. This suggests that the charge-transfer character of AIC⁻ is stronger than that of AIC. The ICT transition in the chemosensor system becomes much easier after deprotonation, resulting in a red shift between their UV-vis spectra. Similar phenomena are also found for S₁ (see Figure SI). However, the intensity of fluorescence may be weak because the AIC⁻ has a worse conjugation due to large twist angles between Parts A and B. The dihedral values of between Parts A and B for AIC and AIC⁻ are 179.0 and 78.7° respectively, suggesting that the molecular p-conjugation in AIC⁻ becomes lower than that of AIC. These results reveal that the deprotonation by F⁻ has obvious effects on the distribution of FMOs, resulting in a red shift between their fluorescence spectra and decreasing the intensity of fluorescence.

The original color and emissions change upon addition of F⁻ because of the formation of anions. The addition of F⁻ leads to an intermolecular proton transfer (IPT) between chemosensor AIC and F⁻ which forms the deprotonated anion AIC⁻ and HF. This shifts the equilibrium from AIC towards AIC⁻ (see Scheme I). Hence, the absorption and emission of AIC (340 and 340 nm) are decreased and a new absorption and emission of AIC⁻ has been observed when adding enough amounts of fluoride to the sensor’s solution. In contrast, the addition of Cl⁻, Br⁻, AcO⁻, and H₂PO₄⁻ leaves its absorption and emission spectra almost unchanged. Therefore, the absorption and emission bands can be assigned to AIC and AIC⁻ before and after the addition of F⁻, respectively. The driving force for the changing of the color and emission is the intermolecular proton transfer. The bathochromic or hypsochromic shifts between the two characteristic absorptions and emissions of AIC and AIC⁻ are chosen to calculate the colorimetric and ratiometric fluorescent fluoride anion chemosensor.

Table 4 presents the absorption λ_abs wavelengths, assignments, and the oscillator strength f for AIC and 1–5 and their anions in CH₃CN at the TD-B3LYP/6-31+G(d,p) level. The predicted λ_abs values are in excellent agreement with experimental results [21]. Namely, λ_abs = 340 and 375 nm before and after the addition of F⁻. The bathochromic shift between the two characteristic λ_abs values for AIC and AIC⁻ is 34 nm, which is comparable to the experimental 35 nm. The values of oscillator strength f for AIC and AIC⁻ are 0.67 and 0.55, respectively. This indicates that the intensity absorbance of AIC⁻ is weaker than that of AIC after the addition of F⁻. However, with increasing F⁻ concentration, the intensity of the absorbance for AIC at 340 nm decreases significantly and the intensity of a new absorption peak for AIC⁻ increases because the formation of AIC⁻ shifts the equilibrium from AIC towards AIC⁻. Furthermore, the higher molecular p-conjugation in AIC⁻ enhances the intensity of absorption for AIC⁻. Thus, this result is found thanks to the computational approach, so appropriate electronic transition energies can be predicted at these levels for this kind of chemosensor. The successful simulations indicate that the observed colorimetric and fluorescent signals truly originate from the formation of AIC⁻ anion.

In Table 4, one can see that the λ_abs of 1 shows a slightly hypsochromic shift, while 2, 3, and 5 have slight bathochromic shifts compared with that of the parent compound AIC, with the maximum deviation being less than 38 nm. However, 4 has a strong bathochromic shift compared with that of the parent compound AIC, the deviation being 348 nm. In general, a larger oscillator strength corresponds to a larger experimental absorption coefficient or stronger fluorescence intensity. The f values of 2 and 5 are larger, while the corresponding f values of 1, 3, and 4 are smaller than that of AIC, particularly for 4. This suggests that 2 and 5 correspond to more intensive spectra. For n⁻ (n = 1–5) of the substituted derivatives, it is found that the λ_abs of 1⁻ and 2⁻ show slightly hypsochromic shifts, while 3⁻ and 5⁻ have slight bathochromic shifts compared with that of AIC⁻, the deviations are within 29 nm. However, 4⁻ has a strong bathochromic shift compared with that of the parent compound AIC (the deviation being 82 nm). The f values of 1⁻–5⁻ are larger than that of AIC⁻ except that the value of f for 4 is less than that for AIC⁻. This clearly shows that the functional group in 4 has more influence on the shifts of λ_abs for the substituted derivative and its anion, while the functional groups in 1, 2, 3, and 5 do not significantly affect the λ_abs of the substituted derivatives and their anions. Furthermore, derivatives 1–5 and their anions show a more intensive spectrum than those of AIC and its anion except for 4.

On the basis of the results displayed in Table 4 and taking into account the ΔE_BSSE, one can conclude that the substituted derivatives 1–4 are expected to be fluoride chemosensors. The bathochromic or hypsochromic shifts between the two characteristic λ_abs values of n and n⁻ (n = 1–4, i.e., λ_abs values before and after the addition of F⁻) are 12, 9, 20, and 232 nm, respectively. Therefore, 1–5 show changes in their UV-vis absorption spectra upon the addition of F⁻, resulting in high selectivity for fluoride detection over other anions, such as Cl⁻, Br⁻, AcO⁻, and H₂PO₄ in CH₃CN. However, 5 does not seem to be a chromogenic chemosensor because the shift between the two characteristic λ_abs values of 5 and 5⁻ is only 4 nm and the original color of the solution of 5 has no obvious change to the naked eye upon addition of F⁻.

Table 5 presents the fluorescence λ_fl wavelengths, assignments, and the oscillator strength f for AIC and 1–5 and their anions in CH₃CN at the TD-BLYP/6-31+G(d,p) level. The predicted λ_fl values are in agreement with experimental results [21]. Namely, λ_fl = 400 and 432 nm before and after the addition of F⁻, respectively. The bathochromic shift between the two characteristic λ_fl values for AIC and AIC⁻ is 56 nm, which is comparable to the experimental 32 nm. From Table 5, one can deduct that the λ_fl values of 2 and 3 have slight bathochromic shifts, while the corresponding values of 1, 4, and 5 show strong hypsochromic shifts compared with that of AIC. The f values of 2 and 5 are larger while the f values of 1 and 3 are smaller than that of AIC. The f value of 4 is the smallest among the substituted derivatives. For n⁻ (n = 1–5) of the substituted derivatives, the λ_fl values of 1⁻and 5⁻ have hypsochromic shifts, while the corresponding values of 2⁻–4⁻ show more bathochromic shifts compared with that of AIC⁻. Furthermore, the f values of AIC⁻ and 2⁻–4⁻ are small (<0.1), indicating that the intensity of fluorescence for AIC⁻ and 2⁻–4⁻ is weak. The results displayed in Table 5 and the ΔE_BSSE values indicate that all the substituted derivatives n (n = 1–5) are expected to be promising candidates for fluorescent fluoride chemosensors. The bathochromic or hypsochromic shifts between the two characteristic λ_fl values of n and n⁻ (i.e., λ_fl values before and after the addition of F⁻) are 62, 308, 111, 65, and 24 nm, respectively. Therefore, the original emissions of 1–5 may be quenched and new weak emissions appear upon the addition of F⁻.