Figure 1 shows the structure and chemical numbering system of F and 7HF. The UV-vis absorption spectra of F exhibit two absorbance maxima (band I and band II). Band I can be found in 286 to 295 nm range and band II next to 250 nm depending on the used solvent. The solvent exerts an influence on the electronic absorption, changing their shape, and spectral maxima positions. Figure 2 shows as example the electronic absorption spectra of F in three representative solvents, cyclohexane (Cy), acetonitrile (ACN) and methanol (MeOH). Some of the solvents employed, 1-butanol (1-BuOH), N,N-Dimethylformamide (DMF) and dimethylsulfoxide (DMSO), absorb radiation in the region of the spectra where F exhibits the higher energy band (band II). In addition, the solvatochromism is only observed in the lower energy band (band I) of the absorption spectrum. This band presents a bathochromic shift with increasing π* values of the solvents.

In Table 1 the maximum absorption wavelength (λ_max) of the band I of F in neat solvents along with relevant solvents parameters [22] are summarized. A red shift on band I of 4.3 nm and 8.0 nm is observed upon going from Cy (α = 0, β = 0 and π* = 0) to ACN (α = 0.19, β = 0.40 and π* = 0.75) and from Cy to MeOH (α = 0.98, β = 0.66 and π* = 0.60) respectively. It is important to notice that the λ_max in DMSO is closer to the values obtained in polar protic solvents than the corresponding values registered in electron pair donating (EPD) solvents. In solvents with specific interactions (high values of α and β) there is no clear trend between the solvent polarity and λ_max values.

Figure 3 shows the characteristic electronic absorption spectra of 7HF in ACN and MeOH. In Table 1 the λ_max values of the band I of 7HF in pure solvents are summarized. For non-polar solvents 7HF presents a very limited solubility and the UV-vis spectra were not recorded. In 1,4-dioxane (α = 0, β = 0.37 and π* = 0.55) band I is located at 300.0 nm and suffers a bathochromic shift with increasing π* values in EPD solvent. For this group of solvents, the maximum shift is observed in DMSO, where λ_max is at 308.1 nm. Band I is located between 308.4 nm and 310.1 nm in polar protic solvents and there is no clear trend between λ_max and the analyzed parameters of the solvents.

The electronic transitions were calculated using the TD-B3LYP/6-311+G(2d,p) and TD-PBE0/6-311+G(2d,2p) methods. The values of the calculated absorption wavelengths (λ_TD-DFT), oscillator strength (f) and the Molecular Orbitals (MOs) involved in the main transitions are reported in Table 2. The calculated (λ_TD-DFT) are found to be associated with solvent polarity function Δf. This parameter can be calculated as Δf = (ɛ − 1)/(2ɛ + 1) − (n² − 1)/(2n² + 1), where ɛ is the dielectric constant and n is the refractive index. For the calculation of this parameter the ɛ reported in Table 1 and the n values taken from tabulated data [23] were used. A good linear relation between λ_B3LYP and λ_PBE0 with Δf is found and shown in Figure 4. It can be observed from this figure that the λ_TD-DFT in DMSO presents a remarkable deviation from linearity. Zhao et al. have studied the solvatochromism of Coumarin 102 by means of TD-DFT methods and they observed the same deviation in DMSO [24]. These authors attribute this anomaly to strong long-range bulk electrostatic effects and a very large π* value of DMSO. In Figure 5 the simulated and experimental UV-vis spectra of F are shown in Cy and MeOH. It can be seen from this figure that the experimental spectra are well reproduced by the simulated ones. The maximum absorption wavelength of band I is predicted at λ_B3LYP = 289.3 nm and λ_PBE0 = 281.0 nm (λ_exp = 286.1 nm) in Cy and λ_B3LYP = 295.1 nm and λ_PBE0 = 286.3 nm (λ_exp = 294.1 nm) in MeOH. The shoulder is predicted at λ_B3LYP = 304.4 nm and λ_PBE0 = 296.1 nm (λ_exp = 305.02 nm) in Cy and λ_B3LYP = 306.8 nm and λ_PBE0 = 298.4 nm (λ_exp ≈ 307 nm) in MeOH. The results reported in Table 2 indicate that B3LYP overestimate the λ_exp while PBE0 underestimate them. The mean absolute error (MAE) of the λ_TD-DFT calculated with the B3LYP is of 2.1 nm whereas for PBE0 the MAE is 6.7 nm. On the basis of the agreement with λ_exp values, the B3LYP would be the functional of choice to calculate the absorption wavelengths of F. A statistical analysis using simple linear regression between the λ_TD-DFT and the λ_exp values does not improve the theoretical results.

The TD-B3LYP results indicate that for the band I of F the MOs responsible for the electronic transition are HOMO-2 → LUMO with a ππ* character. This is only observed in Cy, n-Hp and CCl₄. In solvents with specific solute–solvent interactions the transition is HOMO-1 → LUMO presenting also a ππ* character. In Figure 6 the shape of the MOs involved in the electronic transitions in Cy and MeOH is depicted. This figure shows that the electronic density on the HOMO-1 is delocalized all over the molecular structure in MeOH whereas in Cy the electronic density is more localized on the carbonylic oxygen atom. The opposite phenomenon is observed for HOMO-2. In MeOH the electronic density is localized on the carbonylic oxygen and in Cy it is delocalized over the whole molecule. This result is consistent with the red shift observed in F upon going from non-polar to polar protic solvents. The HOMO-2 → LUMO transition posses a higher energy than the HOMO-1 → LUMO, and therefore the absorption band is shifted to higher wavelengths in solvents with specific interactions. Similar results are observed with MOs calculated with the TD-PBE0 method. The only difference with the TD-B3LYP results is that the MOs responsible for the electronic transition are HOMO-1 → LUMO for all the analyzed solvents. The ππ* character of this transition is also reproduced by the TD-PBE0 method. All the MOs of F in the analyzed solvent are shown in the supplementary material (Figures S1 and S3).

Figure 7 shows the simulated and experimental spectra of 7HF in ACN and MeOH. A fairly good agreement between the experimental and the calculated absorption wavelengths is also observed. For example, the maximum absorption wavelength of band I is predicted at λ_B3LYP = 318.1 nm and λ_PBE0 = 308.6 nm (λ_exp = 301.5 nm) in ACN and λ_B3LYP = 318.0 nm and λ_PBE0 = 308.0 nm (λ_exp = 308.4 nm) in MeOH. No statistical analysis can be made here since there are only four solvents to compare λ_TD-DFT values with λ_exp values. However, on the basis of the agreement between λ_exp with λ_TD-DFT, the PBE0 would be the functional of choice to calculate the absorption wavelengths of 7HF. A good linear relation between λ_B3LYP and λ_PBE0 with Δf is also found and the same anomaly observed for F in DMSO is detected for 7FH.

Lapouge and Cornard have simulated the electronic absorption spectra of some hydroxylated flavones; 3-hydroxyflavone (3HF) and 5-hydroxyflavone (5HF) by means of a TD-DFT method similar to the one used in this work [25]. These authors report a HOMO to LUMO transition in MeOH for band I of 3HF and 5HF, with an electronic redistribution over the molecule for 3HF and a charge transfer from the chromone moiety to the B ring for 5HF. Our results indicate that in the case of 7HF the transition is HOMO → LUMO with a ππ* character in all the analyzed solvents. Figure 8 illustrates the shape of the MOs involved in the electronic transitions of 7HF in ACN and MeOH. It can be seen that there is no charge transfer; the transition corresponds to an electronic redistribution over the whole molecule. No significant changes are observed between TD-B3LYP and TD-PBE0 results. All the MOs of 7HF in the analyzed solvent are also shown in the supplementary material (Figures S2 and S4).

The frequency analysis showed that 7HF have more vibrational modes than F due to the presence of the OH group. It is important to notice that the UV-vis absorption spectra were calculated from vertical transitions between electronic states of the ground states, without taking vibrations into account. Moreover, the calculated excitation energies indicate that the transition for F presents a higher energy (lower absorption wavelength) than the corresponding to 7HF. These results are in good agreement with the experimental measurements.

The PCM model used in the DFT calculations takes into account the dielectric constant and the refractive index of each solvent. These parameters describe the solvent fairly well, but they are not adequate to characterize specific solute–solvent interactions. For this reason, in order to obtain a better description on the solvatochromism of F and 7HF, the empirical solvation parameters of Kamlet and Taft were analyzed. Table 1 summarizes the corresponding parameters α, β and π* of the used solvents. The maximum absorption wavenumber (ν̄_max) can be related to these parameters separately. However, the use of a multiparametric equation provides a better quantitative description of the solvatochromic shifts and takes into account specific (α and β) and non-specific (π*) interactions. The following multiparametric relationship was obtained for F applying Equation (1) and using the ν̄_max values listed in Table 1:

The relative contributions of the parameters are: π*-47.3%, α-41.7% and β-10.9%. The selected variables explain 90.6% of the variability of ν̄_max in different solvents. It must be noticed that the standard error of the β term indicates that there is not a statistically significant variable in the regression equation and this parameter may be neglected. This is a reasonable result because F is incapable of HBD abilities. Equation (2) reveals that the solvation of F is mainly determined by dipolar interactions (π*) and the donation of hydrogen bonds (α) by the solvent molecules. For this reason the multiparametric equation can be expressed as a biparametric equation,

The relative contributions of both parameters are similar (π*-53.3%, α-46.7%). Moreover, the negative signs of the π* and α coefficients indicate that the specific and non-specific interactions in protic solvents may stabilize the excited state more than the ground state, resulting in bathochromic shift. Taking into account the contribution of non-specific interactions, the previously mentioned anomalous ν̄_max value in DMSO could be explained. The π* parameter of this solvent is considerably higher than the corresponding values of the polar protic solvents.

When Equation (1) is used to analyze the solvatochromism of 7HF, the following result is obtained:

The relative contributions of the parameters are: π*-18.3%, α-16.2% and β-65.5%. The selected variables explain 94.67% of the variability of ν̄_max in different solvents. It can be observed that specific interactions have the main contribution to the solvatochromism of 7HF. For this reason Equation (4) can be presented as,

The relative contributions of the parameters now are: α-10.5% and β-89.5%. Various types of intermolecular hydrogen bonding (IHBs) may affect the electronic transitions of this compound. However, the results obtained suggest that the HBA ability of the solvent is the most important factor to explain the solvatochromism. The negative sign of β is consistent with the bathochromic shift observed in solvents with higher β values, indicating that the hydrogen bonds formed by the OH group of 7HF with the solvent may stabilize the excited state more than the ground state. It is important to notice that the β parameter of the DMSO is comparable with the corresponding values of the polar protic solvents. This could be the reason for the observed spectral shifts. For example, ν̄_max = 34.01 × 10³ cm⁻¹ in DMSO and in EtOH.

To summarize, the solvatochromic shifts of F can be explained by the polarization effects of the solvents and by the formation of IHBs in the oxygen atom of the carbonyl of F in protic solvents. These interactions stabilize the excited state more than the ground state, and a bathochromic shift is observed in solvents with higher π* and α parameters. Conversely, the solvatochromic shifts of 7HF are mainly due to the formation of IHBs between the H in the hydroxyl group of 7HF and the solvents. This interaction stabilizes the excited state more than the ground state, and a bathochromic shift is observed in solvents with a higher β parameter.

The solvent effects on the electronic absorption spectra of F and 7HF in binary mixtures were also analyzed. If the binary mixture is considered as an ideal one, ν̄_max of the solute should follow a linear additive model according to the following equation [26].

In this equation X₁ and X₂ are the mole fraction of solvents 1 and 2, and ν̄₁, ν̄₂, ν̄₁₂ are the values of ν̄_max of the studied flavonoids in solvent 1, solvent 2 and in the binary mixture, respectively.

The ν̄_{12 ideal} values in the mixtures can be calculated by using Equation (6) over the entire range of solvent composition. The calculated (ν̄_{12 ideal}) and experimental (ν̄₁₂) values for binary mixtures (Cy-EtOH and ACN-EtOH) are plotted (Figures 9–11) against the bulk mole fraction of EtOH (X₂). As can be observed, the experimental values deviate from the linearity and the curvature of the plot indicates that the solute is preferentially solvated by one of the solvents. In order to analyze the interactions observed, the preferential solvation approach [27] can be used. This approach considers the solvent to be distributed between two phases, the bulk and the solvation shell of the solute. It is assumed that the solvation shell is made up of independent sites that are always occupied. In a non-ideal mixture, the ν̄₁₂ can be expressed by Equation (7)

where X₁^L and X₂^L represent the mole fraction of the solvents 1 and 2 in the solvation shell of the solute, respectively. X₂^L can be calculated from experimental measurements through the following expression:

In order to quantify the extent of preferential solvation, a parameter δ_S2 may be used. This parameter can be defined as the difference between X₂^L and X₂ [28]

A positive value of δ_S2 indicates a preference for solvent 2 over solvent 1, while a negative value of δ_S2 signifies the opposite.

The maximum absorption wavenumber of F and 7HF were measured in two binary mixtures, Cy-EtOH and ACN-EtOH, using different solvent ratios. In the case of F, there is a decrease in the ν̄₁₂ values as the mole fraction of EtOH increases in the mixtures. Figure 9 shows the variation of ν̄₁₂ as a function of X₂. As can be seen from this figure, the decrease of ν̄₁₂ is more prominent in Cy rich regions. The preferential solvation is clearly observed and the index δ_S2 for EtOH is maximum at X₂= = 0.26. This means that at low concentrations of EtOH in the bulk phase, there are more EtOH than Cy molecules surrounding the solvation shell of F. In order to rationalize this effect, it must be noticed that our results for pure solvents indicate that the solvatochromism of F is mainly affected by the HBD ability of the solvent (see Section 2.1.). Then, the IHB formation between F and EtOH may be responsible for the preferential solvation of this solute in Cy-EtOH mixtures. In addition, the π* parameter of EtOH (0.54) is higher than the one corresponding to Cy (0.00), and the non-specific dipolar interactions may also contribute to the preferential solvation of F by EtOH.

Different observations can be made when Cy (solvent with non-specific interactions) is replaced by ACN (EPD solvent) in the binary mixture. In Figure 10 the variation of ν̄₁₂ with X₂ in ACN-EtOH mixtures is depicted. As EtOH is added in the mixture a decrease in the ν̄₁₂ values is also observed, but the deviations from linearity are smaller than in Cy-EtOH. Preferential solvation is detected and is almost constant in all the X₂ range. The index δ_S2 for EtOH is maximum at X₂ = 0.47. In Table 3 the values of δ_S2 for F in both analyzed mixtures are listed. The numerical values of δ_S2 are smaller when ACN is used as co-solvent than when Cy is the co-solvent. Thus, it can be concluded that the preferential solvation by EtOH is more clearly observed in Cy-EtOH than in ACN-EtOH mixtures. These results may be explained in terms of the α and π* parameters of the solvents. Cy is a non-polar solvent with no HBD ability (α = 0) and a very low polarization capacity (π* = 0). ACN has no HBD ability either (α = 0.19) but it presents a notable polarizability (π* = 0.75) due to the electron pair of the nitrogen atom. Then, ACN may present non-specific interactions with this solute.

The analysis for 7HF was made only in ACN-EtOH mixtures due to the very low solubility of the compound in pure Cy. Figure 11 shows the variation of ν̄₁₂ with X₂. Preferential solvation by EtOH is clearly observed from this figure and the index δ_S2 for EtOH is maximum at X₂ = 0.27 (Table 4). This means that at lower concentrations of EtOH in the bulk phase, the solvation shell of 7HF presents a higher concentration of this solvent. EtOH may form IHBs through the OH group or the carbonyl group of this solute, and these interactions may be responsible for the phenomenon observed. For X₂ > 0.80, the preferential solvation notably decreases, indicating that the solvation of 7HF in the mixture is close to the ideal behavior. In the EtOH rich regions there is always a possibility of self association through hydrogen bonding and this competes with solute–solvent interactions [29]. Then, a molecule of EtOH will be relatively preferred by other EtOH molecules rather than 7HF molecules.

Flavone and 7-hydroxyflavone were purchased from Sigma-Aldrich Chemical Co. and they were purified by recrystallization from methanol-water. The purity control was performed determining its chromatographic properties (TLC and HPLC). The solvent employed, Cy (≥99.9%), n-Hp (≥99.3%), CCl₄ (≥99.9%), 1,4-dioxane (≥99.9%), ACN (≥99.8%), DMF (≥99.9%), DMSO (≥99.8%), CHCl₃(≥99.8%), 1-Oc (≥99.0%), 1-Bu (≥99.9%), 2-Pr (≥99.9%), 1-Pr (≥99.8%), EtOH (≥99.9%) and MeOH (≥99.9%) from Merck KGaA (Germany) were all HPLC or spectroscopic grade and were used without further purification.

The solutions of F and 7HF were prepared with a concentration of 4.1 × 10⁻⁵ M in pure solvents. Binary mixtures of Cy-EtOH and ACN-EtOH were prepared from the corresponding solutions by mixing them in the following ratios: 1:9, 2:8, 3:7, 4:6, 5:5, 6:4, 7:3, 8:2 and 9:1. All the solutions were prepared by weight with an accuracy of ±0.0001 g and were stabilized at 25.0 ± 0.1 °C for 10 min. Then their spectra were recorded in a Cary 50-Varian spectrophotometer with thermostatizable cells of 1 cm optical path in the 200–400 nm interval. All spectra were corrected for solvent background by calibrating the instrument to the blank solvent and the experiments were carried out in duplicate.