1 Introduction

Despite recent technological advances, cancer is still one of the most serious problems of humanity [1–3]. This outlook is aggravated due to difficulty of preoperative and postoperative diagnoses. In this line, one of the greatest challenges of diagnostic imaging is to develop a system able to locate species in different environments with high resolution for detecting focus of cancer in surgical margins for clinical use [1, 4]. However, due to sensitivity and easy operation analysis in live systems, the interest in fluorescence probes and their application to the detection of tumors by spectroscopic techniques has increased [5–7].

Recently, amino-naphthoquinone derivatives, such as 2-amino-1,4-naphthoquinone (ANQ keto), have been used with success as fluorescent probes. Laurieri et al. showed that ANQ keto interacts with arylamine N-acetyltranspherase 1 (NAT1) enzyme, [1, 8], which was used for in vivo and in vitro detection of breast cancer. The authors related a color change in the compounds tested when they interact with the target enzyme [1, 5, 9].

It is well known that the fluorescence process can be modulated by different mechanisms, such as intramolecular charge transfer (ICT), excited-state proton transfer (ESPT) and excited-state intramolecular proton transfer (ESIPT) [10, 11]. So far, the fluorescence mechanism in ANQ has not been totally defined in the literature. Some previous studies suggest an amine group deprotonation, but there has been no further investigation into whether the proton transfer comes from an intramolecular chemical reaction or whether it is a chemical reaction between solvent and the amino group of the substrate [12, 13]. The ESIPT process can be one mechanism for the fluorescence process, and despite its great importance, there is no theoretical study reported for the ANQ derivatives. It is also important to keep in mind that the ESIPT process has attracted special attention due to very large fluorescence emission, allowing compounds that exhibit it to be used as spectroscopic probes in biological organisms [10]. Therefore, the investigation and understanding of the ESIPT mechanism in ANQ are important ways of developing more efficient and selective fluorescent probes [12–14].

The ESIPT process occurs when the keto form in the excited state is converted to an enol form through the fluorescence emission [15, 16]. During the ESIPT process, a proton on the amino group of ANQ migrates to the neighboring carboxyl group to give the ANQ-enol form [5].

In fact, the understanding of the ESIPT mechanism has an important impact on the development of fluorescent probes. In spite of its great importance, only a few theoretical studies involving the ESIPT process with 2-amino-1,4-naphthoquinone have been reported in the literature [10, 12, 13, 17, 18]. It is important to mention that ANQ derivatives reveal promising applications as fluorescence probes, as well as in anti-tumor, anti-leishmania, anti-bacterial, anti-inflammatory, anti-HIV and anti-Chagas activity [10, 12, 13, 17–19].

Previous theoretical studies for the ESIPT process have been carried out by using the time-dependent density functional theory (TD-DFT) [20]. This methodology is used to evaluate electronic properties and dynamics of many-body systems in the presence of time-dependent potentials, which is an extension of the formal foundation of DFT [20]. In fact, recent findings support the good agreement between TD-DFT and some multi-reference methods, such as CASSCF, for excited-state calculations [21].

A great concern with DFT is that the exact functional for exchange and correlation is not known except for the free electron gas [21]. However, some approximations exist and accurately permit the calculations of several physical properties. Currently, DFT functionals are classified into some groups, for instance the global hybrid functional (B3LYP, B3PW91 and mPW1PW91) [21] and long-range corrected hybrid functional (CAM-B3LYP and ωb97X-D) and GGA family (PBE), for the TD-DFT study of the ESIPT process [21–23]. Each one has its advantages and drawbacks, and careful validation is necessary in order to identify a particular functional (or a combination thereof) that affords reliable results.

In this context, the use of chemometric methods can significantly assist in the choice of the best density functional to describe the spectroscopic properties of compounds in solution, such as naphthoquinone derivatives [24, 25]. In this context, Barboza et al. employed principal component analysis (PCA) and hierarchical component analysis (HCA) for identifying similarities among different families of functionals for analysis of spectroscopic properties employed in TD-DFT study [23, 26–29].

Despite its great importance, surprisingly little detailed computational work on fluorescent probes based on naphthoquinone derivatives has appeared. For instance, in 2010, Jacquemin et al. studied the absorption and fluorescence parameters of hydroxy-naphthoquinone as well as the ESIPT process [23, 28, 30]. In 2013, Boo et al. [29] studied the ESIPT process for 5,8-dihydroxy-1,4-naphthoquinone. They evaluated the absorption and fluorescence processes via TD-DFT calculations, employing the B3LYP functional and cc-pVTZ basis set [29].

It is also important to keep in mind that the conformational analysis plays a crucial role in the ESIPT process, because changes in the dihedral angle of the compounds have great impact on the fluorescence emission [31, 32]. During the formation of keto–enol forms, the changes in the compound structure revealed new dihedral angles, and analysis of these modifications can generate high computational cost [31, 33, 34]. For the minimization of this cost, the use of surface response, in which the potential energy surface is investigated, employed the minimum number of structures necessary for the analysis of the global surface [35–37].

The goal of the present work is to study the ESIPT process of 2-amino-1,4-naphthoquinone by using TD-DFT and chemometric analysis in order to evaluate the solvent and the thermodynamics parameters, as well as to identify the best DFT functional for electronic and structural calculations by using chemometric calculations [24]. Thus, the work is divided into four parts. In the first, we have discussed the most appropriate exchange and correlation functional to obtain absorption values of ANQ keto and enol forms. In the second part, we have selected the best DFT geometry by chemometric analysis. In the third, we perform a conformational search of the ANQ keto and enol forms and also apply the DFT and TD-DFT functionals previously selected for the reaction mechanism of the ESIPT process. Finally, in the fourth part, by using the previous results, the solvent effects on thermodynamics parameters for the ESIPT process were obtained.

2 Computational details

For the ground state, the compounds were optimized with the DGTZVP basis set by two theoretical methods, second-order Møller–Plesset perturbation theory (MP2) [38–41] and density functional theory (DFT) with B3LYP, B3PW91, mPW1PW91, PBE, ωB97X-D and CAM-B3LYP. The MP2 geometry was used as reference, because MP2 geometries are in a good agreement with experimental values of X-ray [39, 40, 42]. Furthermore, a force constant calculation was made to verify whether the optimized structures were indeed local minima (no imaginary frequencies) or transition states (one imaginary frequency) [43]. From the ground state geometry, ANQ structures, enol and keto forms, were optimized in the excited state and electronic parameters, such as absorption, fluorescence wavelength and oscillator force, were calculated at the TD-DFT level. In this stage, the functional B3LYP, B3PW91, mPW1PW91, PBEPBE, CAM-B3LYP and ωB97X-D were employed for electronic structure calculations [22, 42, 44]. The absorption energy and the wavelength were compared to the experimental values. The error values were applied to PCA analysis for determining the adequate functional for the electronic property calculations. In addition, the potential energy surface along the dihedral angles angle C–C–O–H and C–C–N–H (Fig. 1b) of ANQ in ground and excited states, as well as in solution and gas phase, was evaluated by chemometric techniques based on response surface calculations [34] (for more information about potential energy curves, see Fig. S1 in Supplementary Material).

Fig. 1
figure 1

a Structure for the keto form of the ANQ and the dihedral angle (in red dihedral angle ABCD) employed to build the potential energy surface, b structure for the enol form of the ANQ and the two dihedral angles (in green αβγδ and in red ABCD) used for the surface response

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For the reaction mechanism of the ESIPT process, the thermodynamics properties were computed at the DFT and TD-DFT levels employing B3LYP/DGTZVP and CAM-B3LYP/DGTZPVP for ground and excited states, respectively. All the transition states, intermediates and precursors involved were calculated and characterized. The solvent effects were evaluated by using the polarization continuum model (PCM) and integral equation formalism polarization continuum model (IEF-PCM) [45–47] for methanol, water and chloroform. All electronic structure calculations were carried out with Gaussian program and visualized in the GaussView program [48, 49], while chemometrics techniques, such as PCA, HCA and response surface calculations, were performed in Statistica software [27, 35, 50].

3 Results and discussion

3.1 Chemometric analysis for the selection of the best DFT method for geometry

It should be kept in mind that the reaction mechanism for the ESIPT process should be completely studied at the same theoretical level, in other words, at the DFT level. Although having an appropriate density functional for the optimization structure in ground state is important, MP2 geometries are in a better agreement with experimental values of X-ray for some naphthoquinone derivatives in ground state [38–41]. Thus, the MP2 geometries are considered as reference for the optimization step in ground state.

The ANQ geometry for the enol and keto forms was optimized at the DFT level employing six DFT functionals, one of the GGA families (PBE), three others of the global hybrid family (B3LYP, B3PW91 and mPW1PW91) and, finally, two functionals of the long-range corrected hybrid functional (CAM-B3LYP and ωB97X-D) following the classification according to Miranda et al. [22, 51–53]. The electronic effects were also evaluated for the reference geometry of ANQ structures in ground state by using the MP2 calculations. Afterward, the excited state was calculated at the TD-DFT level with CAM-B3LYP/DGTZVP functional to obtain the absorption wavelength. That was the best theoretical methodology obtained in the previous section. Then, the error between theoretical and experimental wavelength values was calculated. The solvent effects were taken into account by IEF-PCM and PCM.

To evaluate the best functional for the optimization structure, PCA and HCA calculations were evoked. Initially, HCA also showed three groups. The groups were formed for the global hybrid functional (B3LYP, B3PW91, mPW1PW91), GGA functional (PBE) and long-range hybrid functional (CAM-B3LYP, ωb97X-D). It is worth mentioning that ωb97X-D incorporates dispersive interactions, whose standard DFT functionals lack in the description of noncovalent interactions. For more information about PCA, see Supplementary Material in Table S4.

The PCA revealed four components with an explanation of 99.99 % of the total variance, component one being 99.21 % of accumulated explanation and component two, 0.72 % of explanation, as given in Table 1. The analysis of the two components showed a distribution of the functional into three groups and as in the previous section, Fig. 2a displays the hierarchical cluster analysis. This analysis revealed that in the long-range corrected hybrid functional, CAM-B3LYP functional showed less significance for the error when compared to ωB97X-D. It is also important to notice that B3LYP showed to be the best functional for the structure optimization. The order and distribution of the other functionals are shown in Fig. 2b.

Table 1 Eigenvalues and percentage of variance for each component for the PCA
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Fig. 2
figure 2

a Hierarchical clustering of the distances for the DFT functionals, b diagram of Factor 1 and Factor 2 for scores factors

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The PCA method employed in this study can evaluate the best functional for the electronic and geometric properties. The study of the more stable conformation for the keto–enol form of the ANQ was carried out by using B3LYP and CAM-B3LYP in ground and excited states, respectively. The current findings are supported by previous results [43, 51, 52, 54, 55].

3.2 Selection of the best TD-DFT method for absorption calculations

The selection of the best functional for the electronic properties was performed with the same six DFT functionals employed previously, PBE, B3LYP, B3PW91, mPW1PW91, CAM-B3LYP and ωB97X-D according to Yanai et al. and Kobayashi et al. [51–53]. The electronic effects were firstly evaluated for the reference geometry of ANQ structures in ground state by using B3LYP and MP2 calculations. The absorption and emission results were carried out at MP2 and B3LYP levels, and both geometric results were used for electronic properties calculations. Bearing in mind the high similarity of the obtained values, we have reported just the absorption results employing B3LYP geometries. Afterward, the absorption values were calculated for all functionals tested. The IEF-PCM and PCM were employed for reproducing the solvent effects in each case.

From the experimental data, ANQ exhibits two absorption regions in the UV–VIS spectra relative to benzenoid electron transfer bands [43, 52], which did not affect the amino group in the 256 and 335 nm regions. This absorption in chloroform and methanol is 279 and 333 nm, respectively. Also, ANQ exhibits two other bands in relation to quinoid electron transfer bands [43], which have great influence from the amino group. Those transitions occur in the regions of 287 and 414 nm, while in chloroform and methanol they occur at 284 and 471 nm, respectively [43, 52]. The absorption values in water were not found in the literature and for this reason were not employed in the discussion.

The triplets and singlet states of the molecule were calculated in the TD-DFT model. It should be kept in mind that triplet states were neglected during in the analysis, because they showed oscillator force equal to zero. However, the singlet states showed four signals with oscillator force different from zero.

The solvent effect was evaluated by IEF-PCM and PCM. By using the IEF-PCM in methanol with the B3LYP functional, the smallest error in relation to the experimental wavelength of 471 nm was obtained [17, 18]. The B3PW91 functional offers the second best result, followed by mPW1PW91, ωB97X-D and CAM-B3LYP. In the PCM method, the functional CAM-B3LYP showed smallest error for the 471 nm wavelength, followed by ωB97X-D, mPW1PW91, B3LYP and B3PW91.

In chloroform, the functional analysis showed the same trend obtained in methanol. Regarding the PCM and IEF-PCM, the CAM-B3LYP functional showed the smallest error. The PCM generated larger relative errors as compared to IEF-PCM.

Since the study of error in the wavelength showed wide variation, the PCA analysis was employed for understanding how the DFT method influences the error between theoretical and experimental findings. Thus, the PCA can assist in the interpretation of the best functional for the electronic properties calculations (Table 2).

Table 2 Theoretical wavelength values calculated for the four wavelengths of the ANQ and the relative error for the six TD-DFT functionals and the two solvents tested
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The multivariate analysis was performed on both methanol and chloroform with all error values found in the parameters. The HCA approach, based on the Euclidian distance, revealed three groups separated according to the functional family, see Fig. 3a (for more information about HCA, see Table S4 in Supplementary Material). The first group is formed by the PBE functional, while the second group is formed by CAM-B3LYP and ωB97X-D functional and the third highlighted the functionals mPW1PW91, B3LYP and B3PW91.

Fig. 3
figure 3

a Hierarchical clustering dendrogram for DFT functionals in terms of electronic parameters, b diagram of Factor 1 and Factor 2 for scores factors

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The PCA showed four components with explanation of 99.996 % of the variability, which provides a good rationalization and separation of the DFT functional, see Table 3. This analysis showed that the first component explains 99.676 % of all variance of the collected data and the second component explains just 0.256 % of the variability.

Table 3 Eigenvalues and percentage of explained variance of each component for the PCA
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Figure 3b shows the same three groups shown in Fig. 3a. Thus, the PCA was developed for each functional family; the first is for GGA, the second and third groups for long-range corrected hybrid functional and global hybrid functional, respectively.

Within groups, the LDA/GGA functional PBE showed more to the left and exhibit more significance for Factors 1 and 2. In the second group, ωB97X-D exhibited large distance from the center relative to the two factors; however, CAM-B3LYP showed distance only from Factor 2. The ωB97X-D exhibits more significance for the error in the wavelength represented in Factor 1. The hybrid functional family that forms the third group exhibits a central position in relation to the two components. The mPW1PW91 functional is less significant for the error in relation to experimental values; however, B3LYP is more significant. The B3PW91 functional showed intermediate significance by the experiment.

The CAM-B3LYP functional was selected for theoretical calculations in the excited states. The studies for the best functional generated the best geometry for the keto and enol forms for ANQ involving applied DFT/DGTZVP methodology with the functional cited in the methodology, and after that, the excited state was investigated with TD-DFT/CAM-B3LYP/DGTZVP for the error calculation in terms of absorption values.

3.3 Potential energy surface and reaction mechanism for the ESIPT process

It is worth mentioning that the ESIPT process takes place for the proton transfer from the amino group to the carbonyl group, which can produce the tautomer, i.e., enol form. However, in order to investigate the reaction mechanism of the ESIPT process, it is important to ensure that the reaction pathway comes from the global minimum reactant structures and reaction intermediates in solution. In this line with that, to determine the global minimal in the potential energy surface for the enol structure of ANQ, we have employed a chemometric method, named chemometric response surface [34]. This method is able to evaluate the variation in the two or more variables at the same time [34]. In the surface analysis, the dihedral angles 1 (C–C–O–H) and 2 (C–C–N–H) were used as variables, Fig. 1. The potential energy surface, shown in Fig. 4a, was employed in the ground state with DFT/B3LYP/DGTZVP in gas phase. The PES in solution showed some minimum energy (see Supplementary Material).

Fig. 4
figure 4

a Potential energy surface for the enol form of ANQ, b graph of contours for the potential energy surface in gas phase for the enol form of ANQ

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From our PES calculations, the most stable structure is formed by dihedral angles 1 and 2 of 180° and 0°, respectively. These angles were selected in the response surface calculation, see Fig. 4a. Thus, this conformation was employed for the absorption and fluorescence calculation in the enol form in the ESIPT process.

This methodology was employed to allow a robust analysis of the potential energy surface along the dihedral angles C–C–O–H and C–C–N–H (Fig. 1b) of ANQ. The selected conformations from the potential energy surface calculations were optimized with DFT/TD-DFT methodologies and used as the initial point for the reaction mechanism in ground and excited states.

The ESIPT process study, shown in Fig. 5, for ANQ was carried out from the DFT selected geometries of the enol form in ground and excited states in the response surface analysis. Bearing in mind that the first step of the ESIPT mechanism is the energy absorption for keto form of ANQ (Fig. 5), the TD-DFT method was employed to compute six absorption bands. However, only four of the six bands showed oscillator force different from zero, coincident with the four experimental absorption bands [43]. The energy value for the first excited state in gas phase was 3.23 eV corresponding to 383.79 nm (violet color) from the UV–VIS results. The maximum absorption value was 4.35 eV, which represents the first step of the process, corresponding to excited state transfer to the keto compounds at 284.43 nm (ultraviolet region).

Fig. 5
figure 5

Reaction mechanism for the ESIPT process, exhibiting keto to keto* absorption energy (E1) and enol to enol* emission energy (E3)

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The second step was to determine the energy value of the proton transfer from the keto* to enol* form (Fig. 5). In the excited state, this transfer occurs from the amino group to the carbonyl group. The process showed an energy barrier of 0.51 eV for the proton transfer. The third step involves the emission energy between enol* and enol forms. The energy difference from enol* to the enol was 2.79 eV, which corresponds to a fluorescence emission in the region of the spectra of 445.18 nm, emitting blue color. Afterward, the enol form in the ground state is converted to keto form, emitting 1.07 eV of energy. Figure 5 shows the ESIPT process mechanism.

Theoretical calculations suggest a small energy barrier between keto* and enol* in the excited states. Certainly, this energy barrier can be influenced by solvent effects as well as modification in the ANQ structure. Actually, the solvent effect can favor or hinder the transfer process and the application of the compounds as fluorescent probes.

3.4 Solvent effects and thermodynamics properties for the ESIPT process mechanism

The solvent effects were taken into account by using the IFE-PCM for the water and methanol, polar solvents, and chloroform, nonpolar solvent. The methodology employed was similar to that previously employed in the gas phase calculations; the energy values are given in Table 4.

Table 4 Energy values (eV) associated to transition between keto–enol in the solvents tested
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On going from the ground state transition to the excited state in keto form, the absorption energy (E1) is higher in the gas phase and is 4.53 eV for the methanol and 4.50 eV for water, although in chloroform, the energy was 5.74 eV. The proton transfer energy (E2) between keto and enol in the excited state is higher in solution than in the gas phase. The E2 observed was 0.77, 0.75 and 1.98 eV for methanol, water and chloroform, respectively. The noncompetition for the proton by the solvent chloroform could, in principle, explain the higher energy barrier, which indicated that the enol form is more stable in the nonpolar solvent.

The ANQ-enol form emitted fluorescence in a longer wavelength than in gas phase, being 462, 458 and 463 nm in water, methanol and chloroform, respectively. All emission fluorescence was blue.

The Gibbs free energy was calculated for the keto–enol form in ground state. Turning now to the excited state, the Gibbs free energy was calculated employing a similar theoretical strategy reported previously by Jacquemin et al. [28, 56, 57]. In line with that, a thermodynamics cycle is shown in Fig. 6 for the equilibrium constant (K) calculation in the ground and excited states.

$$\Delta G^{0} = - RT\ln K$$
(1)
$$pK = \frac{{\Delta G^{0} }}{RT\ln 10}$$
(2)
Fig. 6
figure 6

Thermodynamics cycle of keto (K) and enol (E) form excitation during proton transfer. From the thermodynamic cycle in this figure, the equilibrium constant was calculated through Eqs. 1 and 2 in the ground and excited state [36]

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The excited-state equilibrium constant was calculated adding the variation between the keto form absorption energy (E1) and the enol form emission energy (E3), since the proton transfer in excited state is very rapid and the equilibrium not is completed [28, 56, 57]. The Franck–Condon principle was employed, and the compounds geometry is equal in the ground state. Thus, the theoretical K calculation in the excited states was performed with the incorporation of the term ∆E, which is the difference between the keto form transition energy and the enol form transition energy. In this perspective, the excited-state equilibrium constant calculated is according to Eq. 3 [57].

$$pK^{*} = pK + \frac{\Delta E}{RT\ln 10}$$
(3)

The equilibrium constant values are given in Table 5. The proton transfer in ground state showed to be unfavorable. The K value is on the order of ~10−8; this means that the keto form has more concentration than enol form in the thermodynamic equilibrium. Our theoretical findings, then, put in evidence that the proton transfer is not able to occur in these conditions. On the other hand, in excited states, the K* value is higher, on the order of 105, and the enol form is favorable in relation to the keto form; therefore, the proton transfer process can occur.

Table 5 Constant values in the ground state (K) and excited state (K*), and their respective pK and pK* values for the proton transfer in ANQ
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The constant value also revealed that the nonpolar solvent was more favorable for the proton transfer in the excited state, 8.91 × 1014, 9.14 × 105 and 7.26 × 105 in chloroform, methanol and water, respectively. In polar solvents, the proton transfer is favorable; however, a competition mechanism between solvent and substrate can occur.

4 Conclusions

From the theoretical data, the TD-DFT calculations were satisfactory for ANQ, the CAM-B3LYP functional exhibited better absorption and fluorescence properties results. However, for the optimization step, the B3LYP/DGTZVP functional was the best theoretical method. Furthermore, chemometric models based on the PCA analysis was satisfactory for selection of the best functional for the optimization step as well as spectroscopic properties. The solvent effect was better modeled by the IEF-PCM method. In fact, the IEF-PCM was employed in the calculations for the ESIPT process and thermodynamics properties. The ESIPT process showed blue emission in solution; chloroform was the most favorable solvent for the ESIPT process, revealing an equilibrium constant of 8.91 × 1014. The polar solvents were favorable to the process, having constant values of 9.14 × 105 in methanol and 7.26 × 105 in water. Our current findings showed that the ESIPT process was thermodynamically as well as kinetically favorable in all solvents tested and it is the most probable mechanism for the fluorescent process involving 2-amino-naphthoquinone. From our findings, ANQ reveals versatility in different solvents and potential fluorescent probe application. To our knowledge, this is the first application of this methodology to amino-naphthoquinone derivatives in the condensed phase. We strongly feel that this study could be helpful for the design and selection of fluorescent probes.