The CPCM (Conductor-like Polarizable Continuum Model) calculation simulates the physiological environment. All calculations were performed with the GAUSSIAN 09 software [25]. Frequency calculations verify local and global minima. TD-DFT method permits to analyze the electron transitions in the ultraviolet (UV) range. The research determines the energies of the frontier molecular orbitals including the highest occupied one (HOMO) and the lowest unoccupied one (LUMO). It uses NBO calculation [26] examining the NBO. Gaussian’s calculations provide access to the frontier orbitals of a molecule. Their HOMO and LUMO contribute interpreting the reactivity of a molecule [27] [28].

The energies of these two frontier orbitals lead to the determination of several reactivity parameters. According to Koopmans theorem [29], the ionization energy I and the electronic affinity A are directly related to the energy of the HOMO and the LUMO respectively.

I = − E HOMO (1)

A = − E LUMO (2)

The chemical electron potential μ and chemical hardness η are defined in terms of ionization energy and electron affinity [30]:

μ = A + I 2 (3)

η = I − A 2 (4)

Also, global index of electrophilicity ω, introduced by Parr [31], is defined by the following formula:

ω = μ 2 / η (5)

Local reactivity index is also accessible by calculation. While the global reactivity parameters evaluate that of a molecule, Fukui [32] introduces indices (Fukui parameters) to describe the reactivity of each atom.

These parameters denote either a nucleophilic attack ( f k + ), an electrophilic attack ( f k − ), or a radical attack ( f k 0 ). The following equations [33] help to determine them:

f k + = q k ( N + 1 ) − q k ( N ) (6)

f k − = q k ( N ) − q k ( N − 1 ) (7)

f k 0 = [ q k ( N + 1 ) − q k ( N − 1 ) ] / 2 (8)

With

q k ( N ) : the electron population of atom k in the neutral molecule.

q k ( N + 1 ) : the electron population of atom k in the cationic molecule.

q k ( N − 1 ) : the electron population of atom k in the anionic molecule.

The acidity represents an important parameter to integrate the intermolecular interactions. The calculations give access to the pKa.

Catechin and epicatechin represent polyphenols with both five hydroxyl groups. They’re therefore likely to exchange one or more protons with other molecules, either during hydrogen bonding interactions or “antiradical” mechanisms [34]. The pKa of each hydroxyl group evaluates the proton transfer reactions between catechin and epicatechin and additional molecules. It helps classifying their acidity. The thermodynamic cycle below allows calculating it by considering the effect of solvation due to the presence of H₂O [35].

The free energy of solvation Δ G s o l becomes:

Δ G s o l = Δ G g + Δ G s o l v ( A − ) + Δ G s o l v ( H 3 O + ) − Δ G s o l v ( AH ) − Δ G s o l v ( H 2 O ) (9)

The value of Δ G s o l v ( H 3 O + ) equals −110.2 kcal/mol. Pliego and Riveros [36] determined it experimentally.

pKa = Δ G s o l 1.364 − log [ H 2 O ] (10)

where [H₂O] = 55.5 M. However, since the free energy of the hydronium ion constitutes a source of error. According to Pliego [35], the corrected formula for pKa is written as follows. On the other hand, this calculation of Pka leads to the NBO analysis.

pKa ( corrected ) = pKa − 4.54 (11)

NBO analysis [26] evaluates the charge transfer properties in molecules. It provides a deep understanding of intramolecular and intermolecular orbital interactions between occupied NBO donors and empty NBO acceptors [37] [38]. The charge transfer involves delocalization of electrons from an electron donor site Lewis-type orbital: lone pairs (n), natural bond (σ and π) to an electron acceptor one (anti-Lewis orbital: σ* and π*). This electron delocalization is with a decrease in the donor electronic density and an increase in the acceptor one. For each donor NBO (i) and acceptor NBO (j), the electron delocalization i → j is evaluated by the stabilization energy E⁽²⁾ using second-order perturbation theory [39]. This latter is expressed as:

E ( 2 ) = Δ E i j = q i F ( i , j ) 2 ε i − ε j (12)

where q i denotes the electronic density in the donor orbital, F ( i , j ) designs a non-diagonal element of the Fock matrix, ε i and ε j correspond to the energies of the occupied i and empty j orbitals respectively. The higher E ( 2 ) , the more redistribution of electrons between donor and acceptor confers stability. This affirmation introduces the presentation of the results and their analysis.

These vibrations are divided into 34 stretching, 33 deformations and 32 torsions. The 34 stretching is repartitioned into five O–H, nine C–H, 13 C–C and seven C–O. This agrees with the structure of the two molecules (Figure 1). The analysis of the potential energy distribution (PED) by VEDA can efficiently assign the calculated normal modes of vibration. Table 1 presents the O–H elongation vibration frequencies of catechin and epicatechin. It indicates that the catechin and epicatechin O–H elongation frequencies vary from 3788 to 3845 cm⁻¹. These agree with the experimental values of the O–H bonds of aromatic rings [40].

The first three O–H elongation frequencies stay at 3845 cm⁻¹, 3833 cm⁻¹, and 3830 cm⁻¹ correspond to ν O 28 − H 28 , ν O 32 − H 33 , and ν O 34 − H 35 , respectively, of the two molecules. Their intensities are approximately the same. The ranking of the –H bonds by their elongation frequencies is: ν O 28 − H 28 > ν O 32 − H 33 > ν O 34 − H 35 > ν O 26 − H 27 > ν O 30 − H 31 for epicatechin and ν O 28 − H 28 > ν O 32 − H 33 > ν O 34 − H 35 > ν O 30 − H 31 > ν O 26 − H 27 for catechin. ν O 30 − H 31 changes from 3803 cm⁻¹ in catechin to 3788 cm⁻¹ in epicatechin. Their intensities of this vibration also change. They increase from 28.44 km/mole in the catechin to 61.35 km/mole. O₃₀–H₃₁ is affected by the asymmetry of carbon C₁₂.

The TD-DFT method at the level of the theory B3LYP/6-31 + G (d, p), in the gas phase evaluates the electron transitions of catechin or epicatechin in the ultraviolet and visible regions. It gives molecule excitation energy. This latter quantity permits comparing the reactivity of two molecules. Its higher value corresponds to the more stable compound. Table 2 shows the results of the TD-DFT calculations. It displays the first three excited states of both molecules as presented in Figure 2.

For epicatechin, the first excited state wavelength is 262 nm. This is the most intense excitation. Its main component refers to the HOMO → LUMO transition with a weight of 61%. Its excitation energy is 4.7355 eV. The second one relates to the band with a wavelength equals 260.20 nm. It associates with the HOMO − 2 → LUMO + 1 transition. Its excitation energy is 4.7453 eV. The latter is greater than that of the first excited state. This result means that epicatechin is more reactive than catechin.

To access the chemical reactivity of catechin or epicatechin, it’s necessary to determine their molecular border orbital HOMO and LUMO [27]. More, the first orbitals can explain the physical and chemical properties of molecules [23]. Here, they help to provide insight into intramolecular charge transfers; an electron-rich HOMO orbital acts as a donor; an electron-poor LUMO functions as an acceptor. Figure 3 and Figure 4 illustrate the HOMO − 3 to LUMO + 3 boundary orbitals of catechin and epicatechin. These molecular orbitals have a π character.

For HOMO, the π character is distributed over all the catechin and epicatechin. This means that the delocalization of electrons occurs through the molecules of catechin and epicatechin. Unlike LUMO, the π character of these molecules is concentrated on the B-cycle with a residual contribution of its oxygen atoms. The global reactivity indices are presented in Table 3. The smaller the energy gap (∆E) between HOMO and LUMO is, the more reactive is the molecule [27]. The energy gap of epicatechin (5.347 eV) is the lowest. It indicates that this molecule is most receptive. The global electrophilicity indices ω confirms this observation. Its epicatechin’s value is slightly higher than those of catechin. The epicatechin is more able to acquire electronic charges. The chemical hardness of epicatechin η (2.674 eV) is lower than that of catechin (2.720 eV). The epicatechin is softer than catechin. The Fukui indices f k + , f k − , and f k 0 represents the local reactivity descriptors.

Fukui indices are used to assess the reactivity of atoms or functional groups (nucleophilic or electrophilic attack site) of a molecule [33]. This work is based on a natural population analysis (NPA) in gas and aqueous phase to estimate the electron population [41]. This leads to the Fukui indices, reported in Tables 4-6. The Molecular Electrostatic Potential (MEP) map displays the electron density of a molecule as a function of colour. It constitutes a descriptor of the local reactivity for a molecule. Colours indicate the electron density of areas of the molecule [42]. A red region illustrates an electron-rich site. A blue zone describes an electron-poor site. A green area is a neutral site. Figure 5 gives the plots of the catechin and epicatechin electrostatic potential.

These tables data show that the highest f k + values in both the aqueous and gas phases link to the hydrogen atoms H₂₇, H₂₉, H₃₁, H₃₃, and H₃₅ of catechin and epicatechin. These constitute the preferential sites of nucleophilic attack. On the other hand, some are favoured on the oxygen atoms and the carbon atoms of the aromatic rings. The properties are preserved when the molecule passing from the gas phase of the aqueous phase.

This map indicates that the hydroxyl groups O₂₈–H₂₉, O₃₂–H₃₃, and O₃₄–H₃₅, are more depleted in electrons than those of O₃₀–H₃₁, O₂₆–H₂₇ and of the different C_i–H_j bonds. These hydrogen atoms of the O_i–H_j hydroxyl groups and C_i–H_j bonds of catechin and epicatechin are sites conducive to nucleophilic attack on the following decreasing order of reactivity : O₂₈–H₂₉ > O₃₂–H₃₃ > O₃₄–H₃₅ > O₂₆–H₂₇ > O₃₀–H₃₁ > C_i–H_j. The regions of the oxygen atoms and the aromatic rings are, on the other hand, favourable sites for electrophilic attacks.

Table 7 shows the theoretical values of pKa for each hydroxyl group of the catechin and its isomer. This statistic varies from 6.77 to 21.77 for catechin and from 6.77 to 21.70 for epicatechin. The pka of the hydroxyl group’s O₃₂–H₃₃, O₃₄–H₃₅ and O₂₆–H₂₇ are respectively 9.92, 10.47, 11.47 for catechin. For epicatechin, they’re 10.56, 11.21, 1171. These values are close to the pka experimental value of the phenol’s hydroxyl; the latter is equal to 9.95 [43]. The pKa values of the hydroxyl group O₂₈–H₂₉ are 7.53 in catechin and 6.77 in epicatechin. These values remain inferior to 9.85. Therefore, the hydroxyl group O₂₈–H₂₉ of catechin or epicatechin is more acidic than the phenol’s hydroxyl group and those of catechin or epicatechin. The difference between the pKa of the hydroxyl group O₃₀–H₃₁ and that of the phenol is great. It shows that the hydroxyl group isn’t on an aromatic ring. Its acidic character is very weak compared to the other hydroxyl groups of catechin and epicatechin. The hydroxyl group acidity becomes: O₂₈–H₂₉ > O₃₂–H₃₃ > O₃₄–H₃₅ > O₂₆–H₂₇ > O₃₀–H₃₁. The hydroxyl groups O₂₈–H₂₉, O₃₂–H₃₃, O₃₄–H₃₅ are much more acidic. They’re more favourable to the anti-radical processes than the hydroxyl groups O₂₆–H₂₇ or O₃₀–H₃₁.

Table 8 and Table 9 collate the second-order perturbation energies E⁽²⁾, the electron density (ED), the energy difference E(j) – E(i) of the donor NBO (i) and of the acceptor NBO (j) related to catechin and epicatechin. They show their elements of the Fock matrix F(i, j). These results indicate that for catechin and epicatechin, the main interactions are of two types. They’re intramolecular interactions of the types π C α − C β ( 2 ) → π C γ − C δ ∗ ( 2 ) and n O ε ( 2 ) → π C γ − C δ ∗ ( 2 ) where π C α − C β ( 2 ) , n O ε ( 2 ) ,

π C γ − C δ ∗ ( 2 ) are: Lewis π orbital of the C α = C β double bond, the lone pair 2 of the Oε atoms, anti-Lewis π orbital of the C γ = C δ double bond. α, β, γ, δ, ε are atomic numbers. In the aromatic ring A, the stabilization energies of the π C 1 − C 2 ( 2 ) → π C 5 − C 6 ∗ ( 2 ) , π C 3 − C 4 ( 2 ) → π C 1 − C 2 ∗ ( 2 ) and π C 5 − C 6 ( 2 ) → π C 3 − C 4 * ( 2 ) interactions are 25, 81, 25.41, 24.64 kcal/mol respectively for catechin and 25.74, 25.95, 24.71 kcal/mol for epicatechin.

In aromatic ring B, for the same intramolecular interaction π C i − C j ( 2 ) → π C m − C n * ( 2 ) , the maximum stabilization energy is equal to 20.33 kcal/mol for catechin and 20.25 kcal/mol for epicatechin. Thus, the aromatic ring B is less stable than of the A one. Regarding the n O i ( 2 ) → π C m − C n * ( 2 ) interactions, the lowest stabilization energy is obtained with n O 28 ( 2 ) → π C 22 − C 24 ∗ ( 2 ) . For catechin, it’s worthy 24.07 kcal/mol and 24.13 kcal/mol for epicatechin. The electronic density (ED) of the Lewis orbital π C i − C j ( 2 ) and n O i ( 2 ) undergo a decreasing (ED < 2e) while those of the anti-Lewis orbital π C m − C n ∗ ( 2 ) increase (ED > 0).

These results show that intramolecular interactions are associated with the delocalization of π-elections from Lewis’s orbitals to anti Lewis’s orbitals. They also indicate that ring A is more stable than ring B in both molecules. The ring B is therefore more reactive than the ring A. Its reactivity influences that of the hydroxyl group O₂₈–H₂₉. L P ( O 28 ) → π * ( C 22 − C 24 ) transition is the most active of the L P ( O i ) → π * ( C m − C n ) transitions. Its delocalization energy (24.07 kcal/mol) is the lowest of the four catechin.

This finding is too valid for epicatechin. More, it contrasts the reactivity priority order of the hydroxyls. Its strong reactivity also enhances that of the hydroxyl O₂₈–H₂₉. Under these conditions, any electrophilic or nucleophilic attack takes place primarily and respectively on O₂₈ and O₂₉. In the event of unavailability, hydroxyl O₂₆–H₂₇ becomes priority; it attaches to ring B. The other two hydroxyls of ring A (O₃₂–H₃₃ = O₃₄–H₃₅) follow in order of reactivity. Hydroxyl O₃₀–H₃₁ loops the latter from the ring C. This aspect of the research leads to this article’s conclusion.