Introduction

Chemical detection of nitroaromatic compounds (NACs) has acquired a special relevance in recent years. The growing interest in the sensing of NACs is mainly due to their adverse impacts on the environment and human health. On the one hand, some of these compounds have been classified as toxic or carcinogenic compounds [1, 2], while others with high explosive power are used in the manufacture of improvised explosive devices that represent a potential risk in terms of security [3, 4]. Besides, NACs are considered hazardous pollutants, mainly due to presence in the environment by their extensive use in many industrial processes, such as agrochemical, dyes, explosives, among others [5, 6]. This is one of the reasons that NACs are found in the environment in risky concentrations to health and ecosystems [7, 8]. In this regard, chemical sensors, besides of providing information in situ about the detection of chemical species, have certain advantages in terms of rapid response time, accuracy, reliability and low cost [9, 10]. This fact has led luminescent metal–organic frameworks (L-MOFs) as successful alternatives to develop chemosensors based on the luminescence changes upon recognition of the analytes [11, 12]. Among these chemosensors, luminescent systems have currently encouraged researchers to focus on designing materials that show a remarkable response in their optical properties, induced by the host–guest interactions with a specific analyte (guest) [13, 14]. L-MOFs have interesting structural features that are responsible of special luminescent properties, since light emission in L-MOFs generally arises from their building components: linkers (conjugated organic ligands) and/or nodes (metal ions or clusters). The linkers are coordinated to the ions from the nodes in a rigid coordination network, which causes the components to be almost immobilized in the structure, with an ordered orientation. This restricts at least to some degree, rotation, or vibration modes of the structure. The luminescent properties of the L-MOFs are described by different mechanisms such as ligand-to-ligand charge transfer (LLCT), ligand-to-metal charge transfer (LMCT), metal-to-ligand charge transfer (MLCT), metal-centered emission and ligand-centered emission, see Scheme 1 [15, 16].

Scheme 1
scheme 1

Schematic representation of possible photophysical processes from L-MOFs, where blue balls represent the nodes (metal ions or metal clusters) and the red sticks represent linkers (organic ligands)

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In these systems, the chemical sensing is based on the change in the emission intensity, either the enhancement or quenching of the luminescence upon the interaction of the analyte with the L-MOF. According to these feasible responses, the chemosensor is called “turn-off” when luminescence quenching occurs, while a sensor with a “turn-on” response involves a luminescence activation or enhancement upon the interaction of the sensor with the analytes [17, 18]. Both types of chemosensors are illustrated in Scheme 2.

Scheme 2
scheme 2

Schematic representation. a Luminescence turn-off type chemosensor; b Luminescence turn-on type chemosensor, where blue balls represent the nodes (metal ions or metal clusters), the red sticks represent linkers (organic ligands) and black ball represents a “guest” which is an analyte

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More recent research has employed theoretical approaches thorough computational simulations to elucidate the detection principle in L-MOF-based chemosensors, as it is reported in a review by Jian-Qiang Liu et al. [19]. Nevertheless, the enhancement or quenching of luminescence has not been fully studied taking into account the interaction of L-MOF with the analyte as a whole interacting system. For example, many previous reports have discussed that the energy value of the LUMO of the analytes such as NACs should be located between the conduction band (CB) and valence band (VB) of the sensor. This is to explain the photoinduced electron transfer (PET) process that governs the observable property in terms of the luminescent change from the sensor [20, 21]. Besides, it should also be noted, as mentioned earlier, that the sensing process implied a change in the emission properties of the chemosensor upon the incorporation of the analyte. Thus, it is crucial to have a precise description of electronic states involved in the optical properties of the host–guest system. In this sense, it is worthy to mention that host–guest systems have also attracted great attention for other recently reported applications of MOFs, such as the biomedical field (e.g., the development of drug carriers [22], biosensors [23], among others). So, considering that the computational simulations have been helpful tools to provide detailed description and interpretation of the capture and selective interaction of target molecules by MOFs, several approaches have been explored. For example, the Grand canonical Monte Carlo simulations have been used to study the adsorption of small molecules [24], the semi-empirical extended Hückel method was used to describe the electronic densities of states (DOS) [25], or the analysis of the host–guest interaction was performed via energy decomposition analysis (EDA) and non-covalent interaction (NCI) analysis [14, 26]. Finally, to the best of our knowledge, the available theoretical works have not yet clarified the responsible phenomena of the L-MOFs chemosensors selectivity toward NACs considering the energies of the excited states. In this sense, the photoluminescence emission (fluorescence or phosphorescence) occurs from the lowest excited state of a given multiplicity, according to Kasha’s rule [27]. Regarding this, it should be considered the relative energies and structures of the first excited states (S1 or T1), to explain in detail the sensing mechanism of the chemosensor luminescence [28, 29]. In consequence, we consider that there is a lack of rigorous theoretical studies of these processes, not only in the sense of elucidating the feasible pathways of activation/deactivation of luminescence but also for the design and synthesis of novel chemosensors with suitable properties for sensing analytes of interest.

Having all these facts in mind, here we propose a computational procedure using density functional theory (DFT) and time-dependent DFT (TD-DFT) approaches, which successfully allowed to understand the sensing mechanism of Cd-based MOF, i.e., [Cd2((H2L)2(H2O)5]0.5H2O where H4L corresponds to the ligand 5,5'-((thiophene-2,5-dicarbonyl)bis(azanediyl)) diisophthalic acid, reported by Fengqin Wang et al. [30] in 2017, selective to 4-nitroaniline (pNA). In detail, this sensor exhibits high selectivity to pNA, compared to the other nitro compounds, through a turn-off fluorescence response. Also, we have studied Cd-MOF/analyte systems using the Morokuma–Ziegler energy decomposition scheme (EDA) and the natural orbital of chemical valence (NOCV). These results along with the evidence of most sophisticate analyses such as, ab initio molecular dynamics (AIMD) calculations and non-covalent interactions (NCI) index, supplied deeply insights of the nature of host–guest interactions and their role on the sensing response of the studied MOF. Furthermore, we addressed the elucidation of changes that govern the sensing mechanism of the chemosensor based on relative energies of the ground and the first excited states, as well as from the interacting system Cd-MOF/analyte. Our theoretical approach provided a basis for elucidating the selective NACs detection mechanism by L-MOFs, by means of an accurate description of interactions of the chemosensor with the analytes and the excited states energies of the Cd-MOF and Cd-MOF/analyte systems.

Computational details

The theoretical study of a MOF-based system via electronic structure calculations is a particular challenge due to the large size of this system. From the computational point of view, a very useful reported alternative is to truncate an extended structure to a finite fragment, which represents the structure of interest [26, 31]. In the herein study, the structural model proposed consists of the representative fragment [Cd2(H2L)2(H2O)6], H4L: 5,5'-((thiophene-2,5-dicarbonyl)bis(azanediyl))diisophthalic acid, designed starting from the reported structure of the extended system, which we will refer as Cd-MOF, see Fig. 1.

Figure 1
figure 1

Optimized geometry of the structural model [Cd2(H2L)2(H2O)6] at B3LYP/TZ2P theoretical level. Atoms: Gray: C, white: H, blue: N, red: O, cyan: Cd and yellow: S

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In this study, the analytes were chosen based on fluorescence quenching efficiency of the Cd-MOF as previously reported by Fengqin Wang et al. [30], i.e., pNA, highest quenching effect, nitrobenzene (NB), smaller quenching effect; and nitromethane (NM) which shows non-quenching of the luminesce of the Cd-MOF.

As first stage in this study, geometry optimizations of the Cd-MOF and Cd-MOF/analyte systems were carried out in the framework of the Density Functional Theory (DFT) approach, with the hybrid exchange and correlation Becke-three-parameter Lee–Yang–Parr (B3LYP) functional [32, 33], using ORCA 4.4 program package [34]. Further, the basis set, triple-ζ valence with two sets of polarization functions, def2-TZVPP [35], was used for the C, H, N, O and S atoms. Taking into account that the Cd atom does not present a marked relativistic effect, the Stuttgart–Dresden-type effective core potential (ECP) to treat scalar effects was incorporated [37]. All calculations were performed using the SDD pseudopotential for Cd that replaces 28 core electrons and while the outer electrons are treated with def2-TZVPP basis set. The solvation effects were considered via a conductor-like screening model (CPCM) using the parameters of 2-propanol as solvent (dielectric constant, ε = 18.23 and refraction index = 1.377) [36].

The charge distributions of the Cd-MOF/analyte systems were visualized through the method of molecular electrostatic potential (MEP) of the molecular surface. This approach allows us a three-dimensional visualization of the distribution of the electrostatic potential (electrons + nuclei) of the system, which is based on the electronic density function of the system given by Eq. 1 [37, 38]:

$${\text{V}}\left( r \right) = \sum\nolimits_{A} {\;\frac{{Z_{A} }}{{\left| {R_{A} - \vec{r} } \right|}}} - \int {\frac{{\rho \left( {\overrightarrow {r} } \right){\text{d}{r}^\prime}}}{{\left| {\overrightarrow {r} - \vec{r} } \right|}}}$$
(1)

where V(r) is defined in terms of the electronic density function of the molecule ρ(r′), and the charge of the nucleus A (ZA), located in RA.

To perform the analysis of the host–guest interactions, the Cd-MOF/analyte systems were optimized in their ground (S0) and the first singlet excited (S1) states. In the first step, the host–guest interactions were analyzed through energy decomposition analysis (EDA) proposed by Morokuma–Ziegler scheme [39, 40]. This analysis was carried out using the Amsterdam Density Functional (ADF) package [41]. The systems were divided into two fragments, i.e., Cd-MOF and analyte, where analyte is 4-nitroaniline (pNA), nitrobenzene (NB) or nitromethane (NM), according to fragmentation scheme of the EDA analysis. The interaction energy (ΔEint) between the two fragments decomposes into four terms, as indicated in Eq. 2.

$$\Delta E_{{{\text{int}}}} = \, \Delta E_{{{\text{Pauli}}}} + \Delta E_{{{\text{Elec}}}} + \, \Delta E_{{{\text{Orb}}}} + \;\Delta E_{{{\text{Disp}}}}.$$
(2)

Here, ΔEPauli describes the repulsive interaction of Pauli, between occupied orbitals of both molecular fragments. The second term ΔEElec refers to the classical electrostatic interaction between both fragments. The third term ΔEOrb accounts for possible interactions between molecular orbitals (MOs) related to the charge transfer, polarization, etc. This term can be analyzed by the natural orbital of chemical valence (NOCV) method proposed by Mitoraj [42]. The term ΔEDisp is related to dispersion forces acting between the fragments, which was incorporated with Grimme’s D3 dispersion correction for EDA calculations [43]. For all systems, the interaction energies between Cd-MOF and analyte were corrected via the counterpoise method to the basis set superposition error (BSSE) [44]. In addition, the interaction between the Cd-MOF and the NACs was also investigated through the non-covalent interaction (NCI) approach [45, 46]. The optimized structures of the S0 and S1 states of the system were the input data to calculate the non-covalent interaction (NCI) index. The NCI analysis was performed employing Multiwfn [47] and NCIPlot programs[45]; the scripts used to automate the analysis of NCI index as well as the visualization and creation of the corresponding images were carried out through the VMD program [48, 49].

The optical properties of the (absorption and emission) of the Cd-MOF and Cd-MOF/analyte systems were calculated using time-dependent density functional theory (TD-DFT), with the B3LYP functional and the same basis set employed in the geometry optimizations [50, 51].

Fluorescence rate constant kF is determined through the simplified version of the Strickler–Berg equation (3) [52, 53]:

$$k_{{\text{ F, SB}}} = 4.34*10^{7} \left[ {s^{ - 1} {\text{eV}}^{ - 2} } \right]\frac{{ E_{{\text{F, vert}}}^{3} }}{{E_{{\text{A, vert}}} }}f$$
(3)

where EF,vert, and EA,vert are the energies of vertical excitations Franck–Condon, computed through TD-DFT, for the emission and absorption, respectively, and f is the oscillator strength of the emitting state.

To analyze the existence of an excited state with the appropriate electronic configuration for the PET from the Cd-MOF to the NACs (i.e., pNA or NB) mechanism, the complete active space self-consistent field (CASSCF) method was used [54]. The dynamical correlation was also included through n-electron valence state perturbation theory (NEVPT2) approach [55], to correct energies of CASSCF calculations. Active space of ten electrons in ten orbitals was used to obtain the energy values of the S0, S1 and T1 states.

The final step was to analyze the behavior of the intermolecular hydrogen bonds (HB) over time, for the Cd-MOF/NACs system. These interactions were simulated through the ab initio molecular dynamics (AIMD) method [56, 57]. For each system, 100 fs of simulation time with 0.5 fs of time step at 298.15 K was performed. All ab initio MD simulations were carried out using the ORCA 4.4 program package [34] and trajectory analyses were computed using VMD program [48, 49].

Results and discussion

Molecular geometry

The optimization of the ground state geometries of all systems, in general, showed a good correlation with the experimental values. In all four systems, Cd-MOF and Cd-MOF/analyte (analyte: pNA, NB and NM), the computed bonds lengths Cd–O around the cadmium atom are in the range from 2.219 Å to 2.501 Å, being the experimental values for Cd-MOF, between 2.263 Å and 2.474 Å [30]. These results suggest that the structural models proposed are effective for the performance of the theoretical approach at this level of theory. An interacting model as starting structures to simulate the Cd-MOF/analyte interaction was considered for each analyte. The interaction occurs between the aromatic ring of the linker and the analyte. The final conformations of the ground state Cd-MOF/analytes systems consisted of the analyte, i.e., pNA, NB, or NM, confined into the Cd-MOF. The results indicate intermolecular HB formation, between an aqua ligand coordinated to the Cd2+ ion and nitro (–NO2) of analytes (O···H), as well as with amino (–NH2) groups (H···N), in the case of pNA. These results agree with the experimental results reported by Fengqin Wang et al. [30] in 2017 for this chemosensor. They pointed out that the analytes are encapsulated into the Cd-MOF through HB interactions. The intermolecular H bonds lengths of the, (O···H) and (H···N), of the Cd-MOF/analyte system under study are summarized in Table 1 for the S0 and S1 states. For the Cd-MOF/pNA the intermolecular HB (O···H) is shortened in the S1 state, while in the case of Cd-MOF/NB, the intermolecular HB (O···H) becomes slightly longer in the excited state. Nevertheless, the intermolecular HB (O···H) for Cd-MOF/NM system remains almost unaltered in the S1 state, compared to the S0 state. All these HB interactions are illustrated in Fig. S1, Electronic Supplementary Material.

Table 1 Ground (S0) and the first singlet excited (S1) states HB lengths for Cd-MOF/analyte, distances (Å) at B3LYP/ def2-TZVPP
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In this sense, in many previous works, it has been reported that the intermolecular HB strengthening in the excited state contributes to the non-radiative deactivations of the emissive state [58, 59]. It should be noted that the HB (O···H) interaction length between Cd-MOF and pNA is shortened from 1.867 A in the S0 state to 1.720 A in the S1 state. Thus, it could be thought that as a consequence of this strengthening of HB interaction in the S1 state, the optical behavior of interacting system Cd-MOF/pNA change. To get a deeper insight, we studied in detail the nature of the interaction between the Cd-MOF and analytes.

Host–guest interaction analysis

An analysis of molecular charge distributions can provide evidence about of intermolecular interactions in the host–guest system. In this sense, Politzer and Murray pointed out “it is through this potential that a molecule is first ‘seen’ or ‘felt’ by another approaching chemical species” [60]. From this perspective, the charge distributions in regions of intermolecular HBs interactions of the Cd-MOF with analyte through electrostatic potential maps analysis were explored. Figure 2a displays the gradient of charge distribution for Cd-MOF/pNA system where the intermolecular interactions of HBs are evidenced. It can be seen the regions, where Vs(r) > 0 (green zone) is around the aqua ligands, and Vs(r) < 0, (red zone) are located near the (–NO2) and (–NH2) groups of the pNA. A similar result is illustrated in Fig. 2b for Cd-MOF/NB system; note that in the zone of approximation between the Cd-MOF and NB green iso-surfaces located on the hydrogen atoms of aqua ligand can be identified, while a red iso-surfaces are located over oxygen atoms of (–NO2) group, for the HB (O···H) interaction. The mapping of the electrostatic potential of the Cd-MOF/NM system indicates also similar features respect to the intermolecular HB (O···H), see Fig. S2 in the Electronic Supplementary Material.

Figure 2
figure 2

Electrostatic potential maps computed at B3LYP/TZ2P level and isodensity value 0.003 a.u. of a Cd-MOF/pNA and b Cd-MOF/NB

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To gain a deeper understanding of these interactions both in the ground state and in the excited state, the analysis via the EDA scheme and the NOCV approach was performed. In all three studied cases, in the fragmentation scheme the Cd-MOF and analyte, i.e., pNA, NB and NM, were employed as fragments. As it is shown in Table 2, in the ground state the host–guest interaction energies suggest that the interaction between Cd-MOF and pNA (analyte that turns-off the luminescence of the sensor) is stronger, ΔEint = − 30.45 kcal/mol, than the interaction of Cd-MOF with NB and NM, ΔEint = − 18.68 kcal/mol and ΔEint = − 12.96 kcal/mol, respectively.

Table 2 Morokuma–Ziegler scheme energy decomposition analysis (EDA), values in kcal/mol, for the Cd-MOF/analyte interacting systems
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Furthermore, the electrostatic component is the most important stabilizing term for all three systems, both in the S0 state and in the S1 state. The results also revealed that the dispersive forces (van der Waals) that act between the Cd-MOF and analyte are relevant, specifically the dispersion component represented 20% of the total stabilizing energy in case of pNA, 32% for NB, and 22% for NM.

On the other hand, the calculations show stronger interaction energy for Cd-MOF/pNA system in the excited state S1 (− 35.66 kcal/mol) compared to the S0 state (− 30.45 kcal/mol). This stabilization is expected due to the decrease in the HB (O···H) distance in the S1 state. In case of Cd-MOF/NB system, interaction energy indicates that a slight change from the ΔEint value for the S1 state (− 19.10 kcal/mol) in comparison with ΔEint (− 18.68 kcal/mol) in the S0 state, while, for the Cd-MOF/NM system, the ΔEint are close, being (− 12.96 kcal/mol) for the S0 and (− 12.90 kcal/mol) for S1.

For both systems, Cd-MOF/NM and Cd-MOF/NB, the variations in the interaction energy between the S0 state and the S1 state are negligible and are in good agreement with the changes in the distances of the intermolecular HBs interaction, pointed in the above section.

To explore in detail channels of donor–acceptor interaction between Cd-MOF and the analytes, we performed an analysis based on the NOCV methodology proposed by Mariusz P. Mitoraj and Artur Michalak [42, 61]. For Cd-MOF/pNA system, the donor–acceptor interaction is due to intermolecular HB (H···N) and (O···H), formed between Cd-MOF and the pNA molecule. Furthermore, the calculations show that these interactions involved a donation of the lone pair of nitrogen (from –NH2 group) and oxygen (from –NO2 group) of the pNA molecule, to the hydrogen atom of a Cd-MOF aqua ligand. The deformation density analysis revealed that (H···N) interaction, Δρ1, is a more stabilizing contribution with ΔEOrb (1) = − 5.28 kcal/mol compared to, Δρ2, ΔEOrb (2) = − 3.93 kcal/mol for (O···H) interaction, for (a) and (b) in Fig. 3. It should be noted that the contribution in the ground state of the ΔEOrb (1) (H···N) and ΔEOrb (2) (O···H) interaction to the total orbital interaction (ΔEOrb) is 31% and 23%, respectively.

Figure 3
figure 3

Contours of deformation density channels (Δρ) with the corresponding energies, in kcal/mol, describing the intermolecular HB (H···N) and (O···H) interactions in Cd-MOF/pNA (a) and (b) EDA-NOCV analysis of the ground state; c and d EDA-NOCV analysis of the S1 excited state

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NOCV analysis also indicated that the deformation density channel, Δρ1 which is originated predominantly from the electron donation due to intermolecular HB (H···N), displays a redistribution of electron density localized along the pNA molecule, in the S1 state, see Fig. 3c. This result is consistent with the lengthened of the intermolecular distance (H···N) in the excited state. In contrast, in the S1 state, the ΔEorb (2) indicate a stabilization of (O···H) interaction between Cd-MOF and pNA, see Fig. 3 (d). This result is consistent with the decrease in the (O···H) interaction distance in that state, as discussed in the previous section.

Figure S3 in the Electronic Supplementary Material illustrates the NOCV deformation density channels between NB and Cd-MOF. This donor–acceptor interaction involves the (O···H) interaction from a lone electron pair of an oxygen atom, of (–NO2) group of the analyte and the hydrogen atom of a Cd-MOF aqua ligand. According to the orbital energy term this interaction is weaker in S1 (− 2.6 kcal/mol) state than in S0 (− 3.2 kcal/mol) state. These results agree with the intermolecular HB distance increase in the S1 excited state for this system.

Finally, in case of the Cd-MOF/NM system, the deformation density channel displays an HB (O···H) interaction between the analyte and framework, see Fig. S4 in the Electronic Supplementary Material. Through this analysis, we identified that intermolecular HB is due to the interaction between the hydrogen atoms of the aqua ligand with the lone pairs of the O atoms, of the –NO2 group. Furthermore, the deformation density channel, Δρ1 with ΔEOrb (1) = − 2.20 kcal/mol for S0 state showed similar features compared to Δρ1 channel with − 2.23 kcal/mol for (O···H) bonding interaction in the S1 state.

The analysis of non-covalent interaction through the NCI index has made it possible to extend theoretical studies to distinguish weak interactions such as hydrogen bonds, van der Waals interactions and repulsive steric interactions. Such approach allows distinguishing these interactions according to the second eigenvalue (λ2) of the electron-density Hessian (second derivative) matrix, e.g., attractive interactions sign(λ2)ρ > 0, where hydrogen bonds appear at (sign(λ2)ρ < 0), while the van der Waals interactions at values (sign(λ2)ρ ≈ 0) and repulsive interaction sign(λ2)ρ > 0) [45, 46]. To go deeper on the intermolecular HBs between the Cd-MOF and the NACs, this interaction was analyzed through the NCI index, for both the S0 state and the S1 state. As can be seen in Fig. 4a, in the plot of reduced density gradients (RDGs) versus sign(λ2)ρ for the geometry of the S0 state of the Cd-MOF/pNA system, a peak at around of − 0.030 a.u. appears, which corresponds to the HBs interactions. However, for the excited state, where the length of the intermolecular HB (O⋯H) between the Cd-MOF and pNA is shorter than in the S0, this peak appears at − 0.040 a.u., clearly shifted concerning the HB interaction in the S0 state, see Fig. 4b. Conversely, for the Cd-MOF/NB system can be distinguished a slight shift of the peak that appears in the HB region, from − 0.025 a.u. to near 0.020 a.u. for the simulated host–guest interaction in the S0 state and S1 state, respectively, see Fig. S5 in the Electronic Supplementary Material. Together, these results indicate a lengthening of the intermolecular interaction (O⋯H) from Cd-MOF/NB in the S1 state, as already mentioned above. Overall, these results are in good agreement with the analysis via EDA and the NOCV described in the previous section, where it is shown that the intermolecular HB (O⋯H) is stronger (ΔEorb (2) = − 4.52 kcal/mol) in the S1 state as compared to ΔEorb (2) = − 3.76 kcal/mol in the S0 state, due to enhancement of donor–acceptor interaction.

Figure 4
figure 4

NCI analysis of the Cd-MOF/pNA system: bi-dimensional plot of the reduced density gradient RGD versus sign(λ2)ρ; a 2D RDG plots obtained for the system in the S0 state. b 2D RDG plots obtained for the system in the S1 state

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Finally, it is worthy to highlight that our results provide strong evidence of the intermolecular HB strengthening between Cd-MOF and pNA in the S1 state. Regarding this, Fengin Wang et al. [30] suggest that the feasible HB between the Cd-MOF and pNA plays an important role in the fluorescence quenching effect. However, a definitive understanding of quenching of fluorescence will come from deep insights into the optical and electronic properties of Cd-MOF and Cd-MOF/analyte systems as follows in the next section.

Optical properties of Cd-MOF

To gain a deeper understanding of the turn-off fluorescence mechanism, we explored the optical properties of Cd-MOF and 5,5'-((thiophene-2,5-dicarbonyl)bis(azanediyl))diisophthalic acid, ligand, we named as Linker, and Cd-MOF/analyte systems that were simulated via TD-DFT approach. In our previous studies, we verified the importance of considering the geometry of both the S0 and the excited states (such as S1 or T1) to arrive at a robust interpretation of the sensing mechanisms [29, 28, 62, 63]. Therefore, the optical spectra, i.e., absorption and emission of Cd-MOF were simulated, taking the optimized structures of the S0 and S1 states, respectively, as inputs in the TD-DFT calculations. Following the same procedure that was employed to compute the optical properties of the Cd-MOF/analyte system, discussion of the results is given in the next section.

The geometry of the S0 state of Cd-MOF and linker was optimized with the aim of simulated their UV–Vis absorption spectra. In both cases, TD-DFT calculations reproduce the most important transitions in good agreement with the experimental report, see Table 3 and Fig. S6. From these results, it was observed that the MOs involved in the absorption band are localized along the linker. These π-type transitions that characterize the main absorption band correspond to a strong mixture of linker-centered transitions (LC), from the highest occupied MO (HOMO) to the orbital above the lowest unoccupied MO (LUMO), labeled as (L + 1), and the second transition from the HOMO-1 to LUMO. The wavelength of this computed absorption band is 337 nm, which shows great concordance with the reported experimental data being 340 nm [30].

Table 3 Singlet–singlet electronic transitions for absorption and emission processes of the Cd-MOF and 5,5'-((thiophene-2,5-dicarbonyl)bis(azanediyl))diisophthalic acid (Linker) at B3LYP/def2-TZVPP theoretical level
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The experimental emission spectrum of Cd-MOF, excited at 340 nm, exhibits the maximum emission at 480 nm with more intensity than the linker [30]. Furthermore, this emission band was ascribed to the π − π* ligand transition, which also is a very similar emission band of the linker with a small redshift (~ 20 nm) [30]. To carry out a theoretical analysis of the chemosensors emission origin, the emission spectrum of both Cd-MOF and linker through TD-DFT calculations was simulated. The geometry of the S1 state of both systems was used as input data to compute the excitations that constitute the emission spectra. According to the oscillator strength (f) and fluorescence rate constant kF, SB, a high emission is evidenced in Cd-MOF in comparison with the free linker (Table S1, (a) and (b) in Fig. 5), when the linker coordinates the Cd2+ ions, in Cd-MOF, are almost immobilized with ordered orientation in the extended network structures which restricts at least to some degree, rotation, or vibration modes of the structure. This produces an increase in the linkers rigidity, which restrict non-radiative decay, from the excited state, concerning the free linker. Thus, the coordination of the linker to the node (Cd2+ ions) enhances the emission in the Cd-MOF. These results do not only corroborate the experimental emission of Cd-MOF but also demonstrates that the emission comes from the linker, with an intra-linker charge-transfer character (ILCT). This emission band is associated with a π → π* transitions, which have a composition of 97% (L → H), see Table 3 and Fig. 5a. According to the results, the structural model based on the truncated system reproduces the optical properties in good agreement with the experimental results reported for the studied material, which also leads us to state that the level of theory used in this study presented a good accuracy in the computation of the electronic properties.

Figure 5
figure 5

The most relevant electronic transition involved in the emission of the Cd-MOF (a) and linker (b), where λEm is theoretical wavelength of emission (red), f is the oscillator strength and kF, SB is fluorescence rate constant kF (Strickler–Berg)

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The sensing mechanism of 4-nitraniline (pNA)

The Cd-MOF chemosensor displays changes in the fluorescence intensity after addition of some NACs, especially in the presence of pNA, which reaches above 70% of quenching efficiency upon excitation at 340 nm. To compare different optical responses, NB was also selected as it shows a smaller quenching effect as well as NM which does not affect the luminescence of the system [30]. To gain a deeper understanding of the sensing mechanism of the pNA, TD-DFT calculations of the chemical sensor with the analyte included explicitly in the cavity of the Cd-MOF were carried out.

The calculation of the fluorescence rate constant (kF,SB) allowed us a deeper insight into the change in the optical properties of the Cd-MOF/analyte systems. This parameter was computed using the simplified version of the Strickler–Berg equation [52, 53], where it is imperative to correct the determination of the vertical excitation energies involved both in the absorption and emission profiles. Thus, it is necessary to obtain the configurations of the first excited states (S1 or T1) besides the ground state, for the interacting system MOF/analyte. As shown in Table 4, the fluorescence rate constant (kF, SB = 2.6*108 s−1) obtained for Cd-MOF/NM is very similar to that of the Cd-MOF (kF, SB = 2.6*108 s−1).

Table 4 Fluorescence rate constant kF,SB determined from the energies of vertical excitations Franck–Condon for absorption and emission, and oscillator strength (f), computed through TD-DFT, considering the solvent effect (2-Propanol, ε = 18.23 and refraction index = 1.377)
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It can be seen clearly that the calculated kF,SB are within the magnitude orders of the fluorescence decay, which agrees with the emissive response of Cd-MOF, and Cd-MOF upon addition of NM. In case of Cd-MOF/NB, the computed kF,SB value decreased by only one order of magnitude (1.8*107 s−1) relative to kF,SB value of analyte-free Cd-MOF, while, kF,SB values for Cd-MOF/pNA are three orders of magnitude lower (6.5*105 s−1) than this constant for the free Cd-MOF (2.6*108 s−1). Therefore, this system has longer lifetimes in the excited state, which makes the non-radiative decay pathways more likely to act, while the f magnitude (f = 0.003) also manifests a low emission in Cd-MOF/pNA concerning the f found for the free Cd-MOF (f = 0.862). The f and the calculated kFSB values are consistent with the experimental trend in the luminescence response of Cd-MOF upon interaction with the studied analytes. It is important to note that the kF,SB is smaller for Cd-MOF/pNA, which shows an intermolecular HB strengthened in the S1 state.

We also observed a relationship between the decreasing trend of kF, SB, and the behavior of the intermolecular HB in the S1 state, with the fluorescent response after the Cd-MOF/analyte interaction. These results agree with other previous works, which reported that the strength of intermolecular HB (host–guest), upon excitation, might induce changes in the photophysical properties. Thus, this interaction can lead to a turn-off luminescence quenching effect of the whole system [64, 65]. In this regard, several studies suggested dramatic changes in the vibrational modes, due to that intermolecular HB strengthened in the excited state. Being strengthened by this interaction, the vibronic modes associated with HB favors energy dissipation via non-radiative processes. In this context, it is also pointed out that this intermolecular HB strengthening behavior in the excited state could favor the internal conversion (IC) mechanism [59, 66, 67].

On the other hand, it is known that the photoinduced electron on the conduction band (CB) of the MOF could be transferred to a MOs of NACs with adequate energy. This PET process plays an important role in the change of luminescent properties that induced optical response in the interacting system MOF/analyte.

Thus, we wondered whether the electron structure of the Cd-MOF/pNA system was adequate for the PET process to occur from the Cd-MOF to the pNA. Based on the above results, we proceeded to investigate the sensing mechanism through TD-DFT calculations along with multiconfigurational ab initio methods.

The simulated UV–Vis absorption spectrum of the Cd-MOF/pNA displays two main bands regarding the strength of the oscillator (f), which are very close in energy. The first bands observed at 343 nm correspond to π → π* transitions, that has a composition of 78% (HOMO-2 → LUMO). According to the computations, the MOs involved in this absorption band are localized on the pNA analyte. On the other hand, the second band at 348 nm is assigned as linker-centered (LC) π → π* transitions with a composition of 89% (HOMO → LUMO + 2), see Fig. 6.

Figure 6
figure 6

Molecular orbitals involved in the electronic transitions of the two computed absorption bands for Cd-MOF/pNA, in isopropanol, where λA is the theoretical wavelength of absorption and f is the oscillator strength

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Recent works have suggested that fluorescence is quenched when the analyte absorbs into the excitation wavelength range of the chemosensor, by the so-called internal filter effect (IFE) [68, 69]. IFE is a process that can occur through two pathways: one requires the overlap between the absorption spectrum of the analyte (absorber) and excitation wavelength of the chemosensor (fluorophore); the another one involves the overlap of the absorption spectrum of the absorber with the emission spectrum of the fluorophore. These two pathways of attenuation of luminescence also are known as primary IFE and secondary IFE, respectively [70, 71].

Based on the simulated absorption spectra, it can be considered that there is significant competition between the pNA and Cd-MOF for the excitation energy, taking into account that the chemosensor is excited experimentally at 340 nm [30]. Therefore, to perform a deep analysis of the role of pNA and the IFE that could take place on the recognition process, we performed the following procedure. The analyte was separated from the Cd-MOF moiety in the S0 state of the Cd-MOF/pNA. This geometry was frozen and used as input to simulate the absorption spectrum through TD-DFT calculations. From these results, it was observed an absorption band centered at 350 nm (f = 0.41), see Table S2, which corresponds to π − π* transition in good agreement with previous experimental works [72, 73].

Through this analysis, we confirmed the overlap between the absorption spectra of the Cd-MOF and pNA, as can be observed in Fig. S7 in the Electronic Supplementary Material. Thus, competition between Cd-MOF and pNA by the excitation light could hinder the photoexcitation of the sensor. This result indicates that the primary IFE may contribute to the decreasing emission intensities of the Cd-MOF/pNA system.

For the Cd-MOF/NB and Cd-MOF/NM systems, the absorption spectra computed are characterized by transitions of π-type, which correspond to intra-linker-centered transitions (LC). MOs of the most important electronic transitions in the absorption bands can be seen in Fig. S8 (a) for Cd-MOF/NB and Fig. S9 (a) for Cd-MOF/NM, in the Electronic Supplementary Material. Therefore, the Cd-MOF/NB and Cd-MOF/pNA did not show any evidence of competition between chemosensor and these analytes by the excitation light, i.e., the IFE is negligible for these two interacting systems. The maximum absorption wavelengths, energies, oscillator strengths, and the corresponding assignments are listed in Table S3.

PET is a photophysical phenomenon that occurs in many systems of interest as chemical sensors. Therefore, their elucidation is of great relevance to understand and propose possible mechanisms of activation/deactivation of luminescence [74].

The PET process is a transfer of electrons after photoinduced excitation between an electron–donor (D) and electron–acceptor (A) species. The chemical entities D and A can be a moiety of individual molecules or moieties of the same molecule [4]. The PET process is divided into two types, based on the tends of the fluorophore to either gain or lose electrons, acceptor-PET and donor-PET, respectively [12, 75].

The electron-rich π-conjugated linkers increase the ability of the L-MOFs to electron transfer from the excited state to a MOs of a quencher such as the NACs [11, 15]; NACs are strong quenchers due to their high electron‐deficient nature [16, 6].

The host–guest interaction produces a mixture of MOs of sensor and analyte. Thus, the donor-PET process could take place if MOs of NACs (acceptor) appear located between the MOs involved in the emissive state of the L-MOF (donor). Upon excitation, an electron from an excited state of L-MOF is transferred to the MOs of NACs causing the non-radiative deactivation of the excited state [10, 12]. A L-MOF/analyte interaction, such as π-π stacking or hydrogen bonding, can generate stronger orbital overlap which could lead to greater PET, as has been pointed out by Lustig WP and co-workers [15].

As we reported in our recent works, the PET mechanisms in the molecular sensors based on Schiff-base can be correctly explained considering the relative energies of S0 and S1 electronic states of the interacting system [28, 29, 62, 63]. Based on these results, for the best of our knowledge, the optimized geometry of the S1 electronic state of Cd-MOF/pNA was employed for the first time to compute the excitations that constitute the emission spectrum and therefore go further the sensing mechanism. In this regard, as the fluorescence involves the spin-allowed transition (transitions between states of the same spin, S1 → S0) [76], it should be kept in mind that the radiative deactivation of the excited state arises from the lowest excited electronic state of a given multiplicity, following the Kasha’s rule. So, an accurate description of the electronic structure has to be performed [27].

For Cd-MOF/pNA, the computed emission spectrum exhibits the emission band at a wavelength of 486 nm, which agrees with the experimental luminescent wavelength, λexp = 480 nm. Besides, according to the oscillator strength, this system displays a “dark” excited state, with a low emission intensity f magnitude (f = 0.003) concerning the f found for the free Cd-MOF (f = 0.862). This result is consistent with the experimental behavior turn-off luminescent sensing mechanism, of Cd-MOF upon the addition of pNA. The involved MOs responsible for this process are localized on both, the linker and the guest, i.e., the pNA, see Table 5. Specifically, the LUMO (orbital π-type localized on the pNA) appears located just lower than the MOs located on the linker. According to our calculations, when pNA is confined into the Cd-MOF, it generates a mixture of MOs of both species, in the emissive state of Cd-MOF/pNA system. It is important to note here that the MOs have adequate energy to excited electrons transfers from the Cd-MOF to pNA. However, the PET process cannot be clearly explained only with this criterion of energy of the MO. Recently, we reported a theoretical procedure that allowed to confirm the existence of a state with the suitable electronic configuration and energy for the PET mechanism to occur on a molecular chemical sensor [77]. Therefore, in order to investigate whether the excited state of the interacting system Cd-MOF/pNA has the electronic configuration that favors photoinduced charge transfer, CAS(10/10)SCF/NEVPT2 calculations were performed.

Table 5 Singlet–singlet electronic transitions, absorption and emission data, for Cd-MOF/analytes at B3LYP/def2-TZVPP theoretical level
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This result shows that host–guest interactions produce a mixing of the Cd-MOF electronic states with those of the pNA, which are part of the active space of the interacting system Cd-MOF/pNA. At the same time, calculations showed an electronic transition that populates the S2 state (f = 0.366), with 90% of the contribution of a configuration that only involves an electronic transition between MOs located on the linker. Furthermore, the most intense electronic transition leads to a direct population of the S1 (f = 0.789) state. This electronic state has an 87% contribution of the configuration which only involved MOs located on pNA, see Fig. 7a. According to our calculations, after the geometry relaxation is finally reached, the S1 state has an 83% of the contribution of a configuration that involves a transition between MOs which are on the pNA. Besides, when the geometry relaxation of the Cd-MOF/pNA system is considered, this state appears at 24,216 cm−1, showing a stabilization of ~ 7772 cm−1. These results are consistent with previous reports suggesting that the HB strengthening promotes the radiation-less depopulation of the emissive estate, due to diminution of the S1 → S0 energy gap [59, 78].

Figure 7
figure 7

Electronic states and most important configurations obtained from a CAS(10,10)SCF/NEVPT2 calculation considering the S0 and S1 state geometries. Sn and Tn represent singlet and triplet states, respectively, where IC is internal conversion and ISC is intersystem crossing. The †S0 in the diagram refers to the configurations S0 electronic state in the geometry of S1 (first excited state) since fluorescence spectrum is computed as vertical transitions, as well as the simulation of phosphorescence spectrum

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Thus, based on these results, the most probable fluorescence quenching pathway of the Cd-MOF/pNA system involves the following steps: first occurs the population of S2 electronic state as a result of the direct electronic photoexcitation from S0 electronic state to S2 electronic state. After this occurs an internal conversion (IC) from the S2 electronic state to a vibrational resonance level of the S1 electronic state, which then deactivates to its lowest vibrational level. After the geometry relaxation finally reaches the S1 electronic state, from which the radiative deactivation to S0 electronic state is produced with a low oscillator strength. Importantly, the electronic configurations of this state, evidence an emissive state located on the pNA moiety of the interacting Cd-MOF/pNA system. This suggests that in the S1 electronic state the system has an electronic structure where the pNA-localized orbitals (acceptor) have adequate energy to accept an excited electron from the Cd-MOF (donor). Therefore, we can conclude that the mixture of states of Cd-MOF and pNA induces the S1 state to fulfill the conditions favoring a non-radiative deactivation process. This result is consistent with the commonly accepted luminescence quenching mechanism for a MOF chemosensor selective to NACs, ascribe to photoinduced electron transfer (PET) process, from the host (MOF) to the guest (NACs) [15, 19].

In case of Cd-MOF/NB system, the computed emission spectrum displays an emission band centered at 430 nm, with a deviation of around 50 nm, which is within the error range commonly reported for TD-DFT [28, 29]. From these results, it was found that the MOs involved in the emission bands are localized both on the linker and on the NB. These transitions of π-type were assigned as L → H, π*(NB) → π(linker), and L + 1 → H, π*(Linker) → π (Linker), see Table 5 and Fig. S8 (b). On the other hand, the CASSCF/NEVPT2 calculations also evidence the multiconfigurational character of the electronic states of the interacting system, due to the mixing of the Cd-MOF electronic states with those of the NB. According to the CAS(10,10)SCF/NEVPT2 calculations, the most intense electronic transition (f = 0.389) leads to the S3 electronic state, that after the geometry relaxation leads to the S1 electronic state, see Fig. S10. This electronic state has a 94% of the contribution of a configuration which involves a transition between MO located on NB. Based on the previously described outcomes, these results also evidence that the electronic structure of interacting system Cd-MOF/NB in the in the excited state favors the PET process between Cd-MOF and NB due to donor–acceptor interactions. Nevertheless, the oscillator strengths for this emission band only decrease one order of magnitude (f = 0.064 for Cd-MOF/NB) with respect to the free chemosensor (f = 0.826). These findings establish a strong contrast between the Cd-MOF/pNA and Cd-MOF/NB systems regarding emission intensity, based on the oscillator strength. This conclusion is consistent with two important results. First, the computed absorption spectrum for Cd-MOF/NB does not evidence that NB can compete with Cd-MOF in absorbing the excitation energy, i.e., IFE process. Second, only for Cd-MOF/pNA, intermolecular HB is strengthened in the excited state, which may activate the non-radiative deactivation channels.

Overall, these results strongly argue that the PET process between the Cd-MOF and NACs is responsible for the fluorescence quenching of chemosensor. In addition, related to this remarkable fluorescent response to pNA, it is found that the strengthening of intermolecular HB in the S1 state and IFE process, via competitive absorption of excitation energy between Cd-MOF and pNA, is responsible for the turn-off mechanism. To go deeper into the sensing mechanism, the simulation of the Cd-MOF/NM emission spectrum was performed, where NM is the analyte that had no evident effects on the emission intensity of Cd-MOF. The calculations show that the emission band of this system appears at 426 nm and is characterized by transitions of π-type, which correspond to linker-centered (LC) transitions, see Table 5. These electronic transitions only involve active orbitals that are localized along with the H4L linker, see Fig. S9 (b).

Furthermore, the calculations predict that emission is due to a π* → π transition, which has a composition of 95% (L → H) for Cd-MOF/NM, while it is true that the host–guest interactions generate a mixture of MOs of Cd-MOF and NM. According to the results, the electronic structure for this system shows that the MOs localized on the NM do not have adequate energy to block the radiative deactivation of Cd-MOF. It should also be noted that the MOs localized in the NM do not appear as active MOs involved in the electronic transition (absorption and emission). It is important to point out that these optical properties computed for the Cd-MOF/NM did not show significant differences between Cd-MOF without the analyte.

Ab initio Molecular Dynamics (AIMD) simulations

Finally, we exploit the ab initio molecular dynamics (AIMD) to evaluate the dynamical behavior of the intermolecular HB over time. The purpose of this analysis was to understand the dynamics of the intermolecular HB between Cd-MOF and the target NACs in this study, (i.e., pNA and NB). Here, geometric criterion to describe an intermolecular interaction (O⋯H) and (H⋯N) of the Cd-MOF with pNA and NB, respectively, was adopted. The Cd-MOF and NACs are considered to be hydrogen-bonded if the distance R(O---H) or R(H---N) is smaller than 2.45 Å [79, 80]. The AIMD simulations show that when pNA is confined into the Cd-MOF, for all of the simulation time, four HBs facilitate intermolecular interactions between the host and the guest. Figure 8 presents the trajectories for HBs length vs. time for the Cd-MOF/pNA system. Note that three of these HBs satisfy the criterion for intermolecular HB, being the length (O---H) or (H---N) less than 2.45 Å. In the case of the Cd-MOF/NB system, the simulation indicated that there is a strong HB between the oxygen atom of the NB and the hydrogen atom of the coordinated water molecule, see Fig. S11 in the Electronic Supplementary Material. We also examined the dynamic behavior of HBs in the interacting system Cd-MOF/NACs using as input data the geometry of the S1 state for AIMD simulations. Similar trends appear in the results obtained by considering the geometries of S1 states for both systems, i.e., Cd-MOF/pNA and Cd-MOF/NB, see Fig. S12 and S13 in the Electronic Supplementary Material. Once more, the results suggested that the analytes are encapsulated into Cd-MOF through strong intermolecular HB.

Figure 8
figure 8

Time dependence of the distance intermolecular HB interactions between Cd-MOF and pNA considering the S0 state geometries according to AIMD simulation

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Conclusions

In summary, a theoretical protocol is depicted in this work which has enabled accurately to explain the selective recognition of 4-nitroaniline (pNA) by the Cd-MOF chemosensor. The elucidation of the sensing mechanism of the target analytes by the chemosensor Cd-MOF was addressed taking into account two points (the host–guest interaction and photophysical properties): First, the study of the interacting system Cd-MOF/analyte at a rigorous theoretical level was performed, to analyze the nature of intermolecular interactions. Second, the structural and photophysical properties were evaluated, to establish the relationship between the structure of the MOF chemosensor and analyte-induced luminescence change.

In our calculations, a structural model based on the reduction of the extended system, reaching a representative fragment, [Cd2(H2L)2(H2O)6], of the Cd-MOF was proposed. The computed structural and photophysical properties obtained as result evinced that these truncated models are in excellent agreement with the reported experimental values. Besides, this truncation of the extended structures of Cd-MOF to a finite structural model does not exceed one hundred fifteen atoms and allowed optimizing time and computational resources.

The focus of this work was to understand the selective sensing mechanism of the Cd-MOF to pNA, using the density functional theory (DFT) and time‐dependent DFT (TD-DFT) calculations along with multiconfigurational ab initio methods. The photoinduced electron transfer (PET) processes were elucidated based on a detailed investigation of the electronic configuration of both the ground state and the electronically excited state of the coupled system Cd-MOF/NACs. Here, as far as our knowledge goes, this is the first work that the PET process is addressed considering the electronic configuration of interacting system MOF/analyte. TD-DFT calculations in combination with CASSCF/NEVPT2 methodology allowed us to conclude that the coupling of the linker states with those of the NACs has the adequate energy and configurations to establish an intermolecular PET from Cd-MOF to NACs. Thus, PET between Cd-MOF and pNA in the S1 state can lock the radiative deactivation, resulting in the fluorescence quenching. Besides, we conclude that the high quenching efficiency of the Cd-MOF toward pNA is due to the strengthening of the intermolecular interaction of the HB in the S1 state, and the competition between of Cd-MOF and pNA for the excitation light.

In this sense, the analysis of host–guest interaction indicates that in the S1 state, these systems have adequate electron structure to produce PET from the Cd-MOF (donor) to the NACs (acceptor). The analysis of the interacting system Cd-MOF/analyte via the Morokuma–Ziegler energy decomposition scheme and natural orbital of chemical valence (NOCV) approach was useful to confirm this statement.

These results, together with the non-covalent interactions (NCI) index, allowed us to characterize these interactions, as intermolecular HB, which is considerably strengthened in the S1 excited state. Ab initio molecular dynamics (AIMD) simulations indicated that pNA is confined into the Cd-MOF through intermolecular HB and reveals that the HB distance is preserved during the simulation time.

Besides, this methodology allowed us to comprehend why the interaction of the NM with Cd-MOF does not lead to fluorescence quenching of this chemosensor, which is in perfect agreement with the reported experimental results. The electronic structure for this system shows that the MOs localized on the NM do not have suitable energy to block the radiative deactivation of Cd-MOF and, they do not appear as active orbitals involved in the electronic transition, both the absorption and the emission processes.

Finally, the proposed theoretical protocol allowed to explain the experimental behavior of this luminescent chemosensor. Therefore, this methodology can be used as the procedure for the accurate elucidation of the sensing mechanism proposed for other MOFs chemosensors selective to organic analytes.