Introduction

Echinatin (Ech, 4,4′-dihydroxy-2-methoxychalcone) is a chalcone derivative called retrochalcone, isolated from the roots of Glycyrrhiza echinata L., Glycyrrhiza uralensis Fisch., Glycyrrhiza inflata Bat., Glycyrrhiza glabra L., and Glycyrrhizae radix et rhizome. It has emerged as a strong antioxidant with cardioprotective and anti-inflammatory activities [1,2,3]. Recently, pharmacokinetic studies of Ech have been conducted using fast ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) in rat plasma [4]. Ech has been identified as a promising therapeutic agent in non-small cell lung cancer (NSCLC) therapy by inhibition of the epidermal growth factor receptor (EGFR) and MET [5]. It also triggers apoptosis of esophageal squamous cell carcinoma (ESCC), a poor prognostic cancer, by inducing ROS/ER stress generation [6]. Furthermore, it facilitates a protective effect against ischemia/reperfusion injury in isolated rat hearts [7]. Besides this, Ech is a potent NF-E2-related factor 2 (NrF2) activator responsible for the hepatoprotective activity of liquorice [8]. It was found to have strong potential to inhibit the angiotensin-converting enzyme (ACE) activity in vitro [9].

The structure of Ech includes two benzene rings, named A and B, connected by a propenal bridge. Many studies reported in the literature indicated that the rings A and B originate from the cinnamate and acetate pathways, respectively [10]. There is one methoxy group at the 2 position of ring B and two hydroxyl groups are attached to the 4′ and 4 positions of rings A and B, respectively. On the basis of the spatial arrangement of the C=O and C=C bonds with respect to the intervening single bond, Ech may exist in two isomeric forms, viz., s-cis if synperiplanar and s-trans if antiperiplanar, as shown in Fig. 1. Among these, the s-cis form has been found to be more stable than the s-trans form. In the case of s-trans, the steric hindrance between the hydrogens attached to C9 of the propenal bridge and C2’ of ring A forces the structure to be non-planar and hence less stable in comparison to s-cis, which seems to be fully planar [11].

Fig. 1
figure 1

s-cis (a) and s-trans (b) conformers of the E form of echinatin

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However, one more geometric isomer, in which both the hydrogens of the α,β-double bond are on the same side, as shown in Fig. S1 of the Supporting Information, is also possible for echinatin. The steric interaction between the carbonyl group and the hydrogen attached to the 6-position of ring B can be considered responsible for the non-planar structure and hence instability of this isomer.

The presence of various single bonds in Ech makes it a flexible molecule and a number of conformations can be generated by rotation about these bonds. The possible dihedral angles (D1–D6) are displayed in Fig. 2.

Fig. 2
figure 2

Molecular structure of Ech with the marked dihedral angles (D1–D6) and atom numbering scheme used throughout this study

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In this paper, the stability of all the conformations has been explored using DFT calculations. Then, an extensive study has been performed at the molecular level in the gas phase and aqueous solution. The deprotonation sites and the corresponding pKa values have been studied in aqueous solution. The different reactive sites have been predicted using electrostatic potential (ESP) maps and partial atomic charges. Further, an in-depth analysis of the effect of pH and the dielectric medium on the electronic properties and electronic spectra of Ech has been performed. This is followed by a calculation of the vibrational and NMR spectra of both the neutral and deprotonated states.

Computational details

A conformational search was first performed to find all the possible conformations of both E and Z forms of echinatin with the Merck molecular force fields (MMFFs) using the MacroModel module available in the Schrödinger suite [12,13,14,15,16]. Then, all the conformations were subjected to quantum mechanical treatment with density functional theory at the B3LYP/6-311++G** level [17,18,19] using the Gaussian 09W suite [20]. Geometry optimizations were followed by harmonic frequency calculations to verify the nature of the stationary points and to account for the zero-point energy corrections [21].

Natural bond orbital (NBO) analysis was carried out to identify the best resonance structures using the NBO program [22,23,24,25,26] incorporated in the Gaussian suite. The partial charges on different atoms have been expressed as Mulliken [27], natural [28] and ESP [29] charges. Bond orders are expressed as Wiberg bond orders [30].

The effect of different solvents was evaluated using an implicit solvation model, SMD (steered molecular dynamics) [31]. This method is reported to produce better solvation Gibbs energies compared to the other solvation methods [32]. The NICS values were calculated at the GIAO-SCF/6-311++G(d,p) level of theory [33]. The gas and solution phase basicities and pKa values were calculated by the same methodology as that used in our previous work [34].

Results and discussion

Relative Gibbs energies of the conformers of Ech in the gas phase and aqueous solution

The conformational search revealed a total of over 30 conformers for the title molecule. Among these, 12 are in-plane conformers of the E form, ten are those of the Z form, and the others are out-of-plane conformers. Further, out of the 12 in-plane conformers of the E form, eight exist as s-cis and four as s-trans forms. Geometry optimizations of all the conformers of the E and Z forms were performed at the B3LYP/6-311++G(d,p) level. The optimized structures of the E and Z conformers are given, respectively, in Figs. S2 and S3 of the Supporting Information. The relative Gibbs energies and populations of all the conformers of Ech in the gas phase and in aqueous solution were also calculated (Table 1). The relative Gibbs energies of the Z conformers, given in Table S1, show that the lowest energy conformer is 5.7 kcal mol−1 higher in energy than the lowest energy E conformer. Hence, none of the Z conformers exists in the gas phase at room temperature.

Table 1 Relative Gibbs energies of the conformers of the E form of Ech in the gas phase and in aqueous solution
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It can be seen from Table 1 that the in-plane conformers of the E form constitute over 99.9% of the gas-phase population and the entire aqueous phase population, leaving the Z conformers with less than 1% of the total population. Therefore, we have proceeded with the in-plane conformers of the E form listed in Table 1. The isolation of these conformers seems to be difficult due to the very small difference in their relative Gibbs energies. Furthermore, the s-trans conformers (E9–E12) are relatively higher in energy and consequently have negligible population (Table 1). Among the s-cis conformers, the relatively higher in population E1–E4 conformers have little difference in their energy values in aqueous solution. On comparison with the gas phase parameters of the same conformers, it is found that the E1 conformer is relatively high in population and stability. Thus, E1 (Fig. 3) has been considered for our further studies on echinatin.

Fig. 3
figure 3

Optimized geometry of the E1 conformer of Ech

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Geometries and electronic properties

Selected geometrical parameters of the E1 conformer of Ech in the gas phase and in aqueous solution are tabulated in Table S2. The weakening of the C7–O11 and C8–C9 double bonds (Fig. 2), as shown by their Wiberg bond order values, indicates the extent of conjugation in the molecule. Some marginal changes are observed in the geometry of Ech in aqueous solution. The bond orders for both the O-H groups decrease due to intermolecular interactions with the solvent water molecules.

The computed partial charges (Mulliken, natural and ESP) on the various atoms of the E1 conformer of Ech in the gas phase and aqueous solution are listed in Table S3. The natural charge analysis shows that the carbon centers directly attached to an oxygen, i.e., C4’, C7, C2, and C4 (Fig. 2) have high positive charges, while all the others are negatively charged. Among these, C7 has the highest positive charge (0.505), and C9 is the least negatively charged (− 0.106) carbon. The oxygen atoms O10 and O12 are the most negatively charged sites (− 0.666) in the molecule and the hydrogens attached to these oxygen atoms, i.e., H10 and H12, respectively, are the most positively charged hydrogens.

For further understanding of the electronic interactions within the molecule, an NBO analysis was carried out on Ech in the gas phase (Table S4). The interactions between the antibonding orbitals of the C–C bonds of both the rings are observed to have the highest interaction energies. The electron density transfer from π(C2’–C1’) and π(C8-C9) to π*(C7–O11), and π(C1–C6) to π*(C8–C9) indicates the conjugation of the keto-ethylenic bridge with both the rings (Fig. 2). The lone pairs on the carbonyl oxygen (n1 and n2 on O11) also contribute some electron density to the σ*(C1’–C7) and σ*(C7–C8) molecular orbitals. Further, the charge transfer from the lone pairs of the oxygens of the hydroxyl groups (O10 and O12) to the antibonding π orbitals of the C–C bonds of the rings (C4’–C3’ and C5–C4) indicates conjugation within both the rings as well. The NBO analysis of Ech was also performed in the aqueous solution (Table S5), but no significant changes were observed in the interactions on solvation.

NICS: an aromaticity criterion

The nucleus-independent chemical shift (NICS) [35] method was employed to quantify the aromaticity of Ech in comparison to phenol and 3-methoxy phenol, which constitute ring A and ring B, respectively (Fig. 1). The NICS values were calculated at the center of the ring, i.e., NICS(0), at planes 0.5, 1.0, 1.5, and 2.0 Å above and below the centers of the rings, denoted as NICS(0.5), NICS(1.0), NICS(1.5), NICS(2.0), and NICS(− 0.5), NICS(− 1.0), NICS(− 1.5), and NICS(− 2.0), respectively. Negative NICS values indicate aromatic character and positive values indicate anti-aromatic character. The NICS values computed below, at and above the planes of rings A and B of Ech, phenol, and 3-methoxy phenol are tabulated in Table S6. It is observed that the NICS values at first change little and then gradually decrease as we move away from the plane of the ring either upward or downward, as illustrated in Fig. 4. The NICS values above and below the center of the rings have little difference due to the spatial arrangement of the substituents attached to the rings. Here, it can be seen that the NICS values for ring A are slightly higher above the plane of the ring, while ring B has relatively higher NICS values below the plane of the ring.

Fig. 4
figure 4

Plot of NICS (in ppm) versus distance (in Å) from the planes of ring A, ring B, phenol, and 3-methoxy phenol

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Although the NICS values are most negative at a distance of 0.5 Å from the center of the ring, in order to reduce the effect of σ contributions [36], the NICS values calculated at 1 Å are usually considered for comparative studies. The NICS(1) values for phenol and 3-methoxy phenol are − 9.8 and − 9.3, respectively, which are slightly more negative than the calculated NICS(1) values of − 9.4 and − 8.2, respectively, for rings A and B of Ech. We may thus conclude that echinatin is an aromatic molecule, but rings A and B possess slightly less aromaticity than isolated phenol and 3-methoxy phenol. It can be assumed that the –R effect of the carbonyl group and the α,β-double bond of the propenal bridge, attached at the para positions of the phenol and 3-methoxy phenol ring systems in Ech, reduce their aromatic character. Furthermore, the aromaticity of ring A is slightly higher than that of ring B. This is due to the –I effect of the methoxy group, which decreases the aromaticity of ring B.

Gas-phase basicity (GPB) and acidity constant (pKa) determination

Echinatin has two phenolic groups, which may undergo deprotonation depending on the pH of the medium. Hence, the pKa value for each of the hydroxyl groups was calculated. The same methodology as that followed by Kakkar and Bhandari [34] was used for the calculation of the pKa values. The gas phase basicity was computed as the negative of the Gibbs energy change associated with the protonation of the anionic form in the gas phase [37].

Applying the thermodynamic cycle (Scheme 1), the basicity of Ech in aqueous solution was calculated from eq. (1):

$$ \Delta {G^{\uptheta}}_{\mathrm{deprot}}\ (aq)=\mathrm{GPB}+\Delta {G^{\uptheta}}_{\mathrm{solv}}\ \left({\mathrm{Ech}}^{-}\right)+\Delta {G^{\uptheta}}_{\mathrm{solv}}\ \left({\mathrm{H}}^{+}\right)-\Delta {G^{\uptheta}}_{\mathrm{solv}}\ \left(\mathrm{Ech}\right) $$
(1)

where the standard hydration Gibbs energy of the proton, ΔGθsolv (H+) was taken as − 265.9 kcal mol−1 at 298.15 K and 1 atm [38, 39]. ΔGθsolv (Ech) and ΔGθsolv (Ech−) represent the solvation energies of Ech and its anion, respectively. The basicities for Ech in aqueous solution for the ionization of 4-OH and 4’-OH were calculated to be 12.1 and 12.7, with the corresponding pKa values of 8.9 and 9.3, respectively (Table 2). The Gibbs energies of all the neutral, anionic and dianionic forms of Ech in the gas phase and aqueous solution are listed in Table S7 of the Supporting Information.

Scheme 1
scheme 1

Thermodynamic cycle to compute the pKa values for Ech

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Table 2 Calculated gas and aqueous solution basicities (kcal mol−1) and pKa values of Ech
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The lower pKa value for the 4-OH group can be explained on the basis of resonance stabilization of the corresponding anion. The extended conjugation in the echinatin-4-O-monoanion enhances the charge delocalization and hence the acidic character of the 4-OH group. In addition, the methoxy group attached at the meta-position of 4-OH withdraws electrons with the –I effect, which further stabilizes the echinatin-4-O-monoanion (Ia) and hence lowers the pKa value. On the other hand, the carbonyl group of the propenal bridge at the para position of 4’-OH is involved in conjugation with both the rings at the same time.

Influence of pH on the ionization of Ech

It can be seen from the pKa values that both the hydroxyl groups undergo ionization in basic medium, i.e., at pH ~ 9. Thus, it is the neutral form which predominates at the physiological pH. With increasing pH, at first, the deprotonation of 4-OH takes place around pH ~ 9, resulting in the formation of echinatin-4-O-monoanion, as illustrated in Fig. 5. On further increase in the pH, the 4’-OH also undergoes deprotonation and Ech is converted to its dianionic form. The Gibbs energies of all the species are given in Table S7.

Fig. 5
figure 5

Effect of pH on the ionization of Ech

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Selected geometrical parameters of the Ech anion in the gas phase and in aqueous solution are tabulated in Table S8. On deprotonation, the O-H bond order increases to some extent, while the carbonyl group weakens due to the increased delocalization of the negative charge in the molecule. The partial charges (Mulliken, natural and ESP) on each atom in the Ech anion in the gas phase and in aqueous solution are given in Table S9. From the natural charges, it can be observed that most of the negative charge is located on the oxygen atoms, and C7 is the most positively charged atom in the molecule. Furthermore, the magnitude of the negative charge on the oxygen atoms increases on solvation, which enhances the possibility of intermolecular hydrogen bonding in the Ech anion.

Effect of the dielectric on the electronic properties

Frontier molecular orbital (FMO) analyses were performed to characterize the reactivity and kinetic stability of Ech and its anionic form. Figure 6 depicts the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of Ech and its anion in the gas phase and in aqueous solution, along with their respective energies. The HOMO (MO#71) of Ech is mainly concentrated on the B-ring and the olefinic region of the keto-ethylenic bridge, representing a π orbital, while the LUMO (MO#72) is delocalized throughout the molecule except the methoxy group, and represents an orbital of the π* type. Its negative energy (− 2.15 eV) implies that the molecule is a good electron acceptor. The HOMO-LUMO gap is 3.80 eV, which decreases to 3.51 eV on solvation, due to a lowering of the LUMO energy to − 2.45 eV. This makes the molecule a better electron acceptor, enhances its chemical reactivity and reduces its kinetic stability on solvation.

Fig. 6
figure 6

Effect of solvation and deprotonation on the frontier molecular orbitals of Ech

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Likewise, for the anionic form, the HOMO is primarily localized over the ring B and the propenal bridge, whereas the LUMO is delocalized all over the molecule. The HOMO and LUMO of the Ech anion are, thus, π and π* orbitals, respectively. Both the frontier orbitals of the Ech anion in the gas phase lie at very high energy, but interaction with water molecules lowers their energies. The HOMO-LUMO gap is relatively smaller for the anion compared to the neutral form, and hence, the anion is softer and more polarizable.

Further, in order to study the effect of the solvent on the electronic properties of Ech and its anion, an FMO analysis was carried out in a range of solvents of different polarities. The computed energies of the HOMO and LUMO, along with their energy gaps in various solvents, are listed in Table S10. It is observed that the ΔEgap decreases marginally with increase in the dielectric of the medium for the neutral form.

Global reactivity descriptors

Various global reactivity descriptors, viz., chemical hardness (η), chemical potential (μ), electronegativity (χ), global softness (S), global electrophilicity (ω), and nucleophilicity (N) indices, were calculated to measure the reactivity of Ech in the gas phase and in aqueous solution (Table 3). First, the vertical ionization energies (IE) and electron affinities (EA) were obtained from the respective HOMO and LUMO energies on the basis of Koopmans’ theorem [40], and then all the reactivity descriptors were calculated as η = (IP − EA)/2, μ = − (IP + EA)/2, χ = − μ, ω = μ2/2η and S = 1/2η [41,42,43]. The global nucleophilicity model (N) is the negative of the IP value relative to tetracyanoethylene, which has the lowest HOMO energy (− 0.349 Ha and − 0.324 Ha in the gas phase and aqueous solution, respectively) among a large number of compounds [44]. The energy parameters of Ech are given in Table S11. Further, the energy parameters of phenol, 3-methoxy phenol and benzene were also calculated in the gas phase for a comparative study, as shown in Table S12. A comparison of all the reactivity descriptors of Ech with phenol, 3-methoxy phenol and benzene is presented in Table 3.

Table 3 Comparison of global reactivity descriptors (eV) of Ech with those of phenol, 3-methoxy phenol, and benzene
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It can be observed that the electrophilicity of Ech is increased on solvation. The electrophilicity of Ech is found to be higher than that of phenol, 3-methoxy phenol, and benzene individually. On the other hand, the nucleophilicity decreases on solvation, but is higher than that of the individual ring systems in the gas phase. Thus, Ech behaves as a good nucleophile. The low value of the chemical hardness and a relatively high value for the softness indicate Ech to be a reactive molecule. Thus, it can be concluded that Ech is much more reactive than phenol, 3-methoxy phenol, and benzene in all respects.

Molecular electrostatic potential (MEP)

Next, the molecular electrostatic potential was calculated to explore the sites of electrophilic and nucleophilic attack. The electrostatic potential maps of Ech and its anion are displayed in Fig. 7. The blue regions indicate positive potential, i.e., the sites for nucleophilic attack, while the red regions are prone to electrophilic attack [45]. It can be seen that the blue region is close to the hydroxyl proton, whereas the red region lies near the oxygen atoms and olefinic carbons. At higher pH, when the anionic form is present, the entire molecule except the phenolic ring becomes prone to electrophilic attack. The electrostatic potential values at each atom in Ech and its anion in the gas phase and in aqueous solution are listed in Table S13.

Fig. 7
figure 7

Electrostatic potential map (isovalue = 0.0004 au) of a Ech [− 6.877 × 10−2 (red) to 6.877 × 10−2 (blue)] and b Ech anion [− 0.164 (red) to 0.164 (blue)] in the gas phase mapped on the total electron density

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The ESP charges reveal that the aromatic ring B is more susceptible to electrophilic attack. The two most probable sites for electrophilic attack are C3 and C5 with ESP charges − 0.468 and − 0.524, respectively, in the gas phase. We may conclude that the presence of the propenal bridge activates ring B with respect to the electrophilic substitution reaction. Between these two sites, C5 is found to be more prone to electrophilic attack due to the smaller inductive effect of the methoxy group at this position. Steric hindrance at C3 also makes it less reactive to electrophilic attack compared to C5. On solvation, C3 becomes more liable to electrophilic attack.

The sites favorable for nucleophilic addition in Ech are C7 and C9 for direct and conjugate addition, respectively, as evident from the high positive ESP charges at these positions. The way that a nucleophile reacts depends upon its type. Hard nucleophiles tend to react at C7, whereas soft nucleophiles react at the β-carbon (soft center). Nucleophilic substitution reaction is not possible at C7 due to the non-availability of a leaving group at this position.

Electronic spectra

Effect of pH

The electronic spectra of Ech and its anion were computed in aqueous solution using the TD-DFT method [46, 47]. The effect of pH on the computed UV-Visible spectra of Ech is depicted in Fig. 8. A red hyperchromic shift to the visible region is observed for Ech in aqueous solution on increasing the pH.

Fig. 8
figure 8

Effect of pH on the computed UV-Visible spectra of Ech

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The calculated λmax values are 400 nm (f = 0.9368) and 445 nm (f = 1.1382) for Ech (blue curve) and the anion (red curve), respectively, in aqueous solution. These bands corresponds to the HOMO-LUMO (71 → 72) transition, which represents a π → π* transitions. With reference to Fig. 3, this transition causes a shift of electron density from ring B to ring A (Fig. 1). In the case of the Ech anion, a small peak is also observed at 312 nm (f = 0.1619). This peak has major contribution from HOMO-2 to LUMO (69 → 72), corresponding to an n → π* transition, as also evident from its low oscillator strength. Here, HOMO-2 is mainly concentrated on the oxygen atoms on ring A, as shown in Fig. S4. Thus, this transition causes a shift in electron density from ring A to ring B.

Effect of solvent

Next, the effect of the dielectric constant of the medium on the electronic spectra of Ech and its anion was studied by computing the electronic spectra in a range of solvents using the SMD model (Fig. 9). The most prominent peaks, along with their oscillator strengths and the MOs involved in the transition, are listed in Table S14 and the complete transition data are given in Table S15.

Fig. 9
figure 9

Simulated UV-visible spectra of Ech (left) and its anion (right) in different solvents

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Ech (pH < 9)

The computed UV-visible spectra of Ech, left of Fig. 9, shows the variation of λmax with the polarity of the solvent. The high intensity peak in all the solvents corresponds to the HOMO-LUMO (71 → 72) transition, which is of the π → π* type. The absorption band moves to longer wavelengths on increasing the polarity of the solvent, as the dipole interactions with the solvent molecules lower the energy of the π* orbital more than that of the π orbital. There is a marginal decrease in the intensity of the peak as we move from polar protic (water, methanol) to polar aprotic (DMSO, acetone, dichloromethane, chloroform) and then to non-polar (benzene) solvents.

Ech anion (pH > 9)

The electronic spectra of the Ech anion, at the right of Fig. 9, show a high intensity peak on the higher wavelength side and a relatively low intensity peak at lower wavelength. The high intensity peak corresponds to the HOMO-LUMO (71 → 72) transition in all the solvents. The small intensity peak on the lower wavelength side corresponds to the 69 (HOMO-2) → 72 (LUMO) transition in the case of polar protic solvents, whereas in the case of polar aprotic and non-polar solvents, it corresponds to the 71 (HOMO) → 74 (LUMO+2) transition.

Vibrational spectra

The vibrational spectra of Ech and its anion are shown in Fig. 10. Selected high intensity vibrational wavenumbers are summarized in Table S16. All the vibrational wavenumbers are scaled by a factor of 0.9679 to account for anharmonicity and other factors [48].

Fig. 10
figure 10

Computed infrared spectra of Ech (left) and its anion (right)

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The most intense peaks in both the spectra correspond to the stretching vibrations of the olefinic carbon atoms. On deprotonation, the olefinic as well as carbonyl group stretching frequencies decrease due to the redistribution of charge in the resulting anion. The stretching vibration for the O–H group is observed above 3700 cm−1, which is higher than the free O-H stretch in vacuum, indicating strengthening of the O–H bond in Ech as well as in its anion. Likewise, the carbonyl group stretches at lower frequency owing to conjugation with the olefinic and phenyl ring systems. The region of C-H stretching vibrations includes the symmetric and asymmetric stretchings of the methoxy group, along with the C–H stretching bands of the aromatic rings. The bending modes majorly include the out-of-plane bending vibrations of the O–H and C–H groups attached to the aromatic rings.

NMR spectra

The NMR spectra were calculated using the Gauge-independent atomic orbital (GIAO) method [49], which provides magnetic shielding constants (σ). The chemical shifts were obtained on the δ-scale relative to TMS using the equation,

$$ {\updelta}_{\mathrm{i}}={\upsigma}^{\mathrm{TMS}}-{\upsigma}_{\mathrm{i}} $$
(2)

where the values of σTMS for 1H in DMSO and methanol, 31.9033 and 31.9007, respectively, were obtained at the same level of theory. The calculated and experimental δ values for 1H-NMR in methanol [50] and DMSO [8] are listed in Table 4.

Table 4 Calculated and experimental 1H chemical shifts (ppm) of Ech in methanol and DMSO
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The regression analysis of the calculated 1H-NMR chemical shifts with the experimental values in DMSO yielded the following equations:

$$ {\updelta}_{\mathrm{calc}}=0.401\ {\updelta}_{\mathrm{expt}}+3.813\kern1.25em \left({R}^2=0.210,\mathrm{including}\ \mathrm{OH}\ \mathrm{protons}\right) $$
(3)
$$ {\updelta}_{\mathrm{calc}}=1.086\ {\updelta}_{\mathrm{expt}}-0.138\kern1.5em \left({R}^2=0.989,\mathrm{excluding}\ \mathrm{OH}\ \mathrm{protons}\right) $$
(4)

The correlation between the calculated and experimental values for 1H-NMR is satisfactory on excluding the OH protons, while it is very poor when considering the OH protons also, as shown by the very low value of the regression coefficient in the latter case. This deviation can be attributed to the interaction of Ech with the solvent molecules, which is not taken into account in the implicit solvent treatment. The intermolecular hydrogen bonding causes deshielding of the OH protons of Ech and leads to higher values of the chemical shifts.

Likewise, in methanol, the calculated 1H-NMR chemical shifts agree well with the experimental values, on excluding the OH protons, as indicated by the high regression coefficient obtained using the equation:

$$ {\updelta}_{\mathrm{calc}}=1.108\ {\updelta}_{\mathrm{expt}}-0.191\kern1.25em \left({R}^2=0.991,\mathrm{excluding}\ \mathrm{OH}\ \mathrm{protons}\right) $$
(5)

The 13C-NMR spectrum of Ech was also determined at the same level of theory. The chemical shifts were obtained on the δ-scale relative to TMS with σTMS = 185.409 using DMSO as the solvent. The calculated, as well as experimental, δ-values for 13C-NMR [51] are given in Table 5.

Table 5 Natural partial charges (qCi), and calculated and experimental 13C chemical shifts (ppm) of Ech in DMSO
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A satisfactory correlation between the calculated and experimental δ-values for 13C-NMR was obtained, yielding the equation:

$$ {\updelta}_{\mathrm{calc}}=0.975\ {\updelta}_{\mathrm{expt}}+9.289\kern1.25em \left({R}^2=0.970\right) $$
(6)

The chemical shift value also depends on the charge density on the carbon atoms, as shown in Table 5. Regression analysis of the experimental 13C-NMR chemical shifts with the natural charge density on the respective carbon atoms in DMSO solution yielded the following equations:

$$ {\updelta}_{\mathrm{expt}}=88.35\ {q}_{\mathrm{Ci}}+134.6\kern1.5em \left({R}^2=0.680,\mathrm{including}\ \mathrm{the}\ \mathrm{methoxy}\ \mathrm{carbon}\right) $$
(7)
$$ {\updelta}_{\mathrm{expt}}=80.31\ {q}_{\mathrm{Ci}}+138.1\kern1.5em \left({R}^2=0.928,\mathrm{excluding}\ \mathrm{the}\ \mathrm{methoxy}\ \mathrm{carbon}\right) $$
(8)

The correlation between the experimental δ-values and natural charge densities on the carbon atoms is satisfactory on excluding the methoxy carbon, as seen by the high value of the regression coefficient (Eq. 8), whereas the correlation is not so good on including the methoxy carbon. This can be explained on the basis of the different hybridization of the methoxy carbon (sp3) in comparison to all other carbon atoms (sp2) present in the title molecule. The carbonyl carbon is found to be the most deshielded one, followed by the carbons directly bonded to the hydroxyl groups. The chemical shift values, along with the natural charge density on each carbon atom in methanol, are also given in Table S17. Further, the effect of deprotonation on the 1H and 13C chemical shift values in methanol and DMSO has also been studied (Tables S18 and S19).

Conclusions

Density functional calculations performed at the B3LYP/6-311++G** level indicated that the E1 conformer of Ech is preferred as the ground state conformation and was considered for further studies in both the gas phase as well as in aqueous solution. Bond length, bond order and NBO analyses suggest an extended conjugation through the keto-ethylenic group connecting the two ring systems. The aromaticity of the title molecule was confirmed using the NICS parameter and ring B was found to be less aromatic than ring A. The computed pKa values of both the hydroxyl groups suggest the existence of the neutral and mono-anionic form of Ech, respectively, at pH less than and above ~ 9. A variation in the HOMO-LUMO energy gap is observed with change in the dielectric constant of the medium. On solvation, the chemical reactivity of the neutral form increases, while that of the anionic form decreases, as indicated by the various global reactivity descriptors. Moreover, the ESP charges revealed that the C3 and C5 centers are more susceptible to electrophilic substitution, whereas C7 and C9 are preferred for the nucleophilic addition reaction.

The ionization of 4-OH in aqueous solution is accompanied by a red hyperchromic shift from 400 to 445 nm in the electronic spectral peak. With increase in the polarity of the dielectric medium, the absorption bands shift toward longer wavelength for Ech. An increase in the intensity of the IR peaks is observed on deprotonation due to the redistribution of charge. The correlation between the calculated and experimental values of the 1H-NMR chemical shifts in methanol and DMSO is found to be satisfactory on excluding the OH protons. Likewise, for 13C-NMR, a high regression coefficient is obtained on excluding the methoxy group in the correlation.