Hydrogen-bonding Interactions between Apigenin and Ethanol/Water: A Theoretical Study

In this work, hydrogen-bonding interactions between apigenin and water/ethanol were investigated from a theoretical perspective using quantum chemical calculations. Two conformations of apigenin molecule were considered in this work. The following results were found. (1) For apigenin monomer, the molecular structure is non-planar, and all of the hydrogen and oxygen atoms can be hydrogen-bonding sites. (2) Eight and seven optimized geometries are obtained for apigenin (I)–H2O/CH3CH2OH and apigenin (II)–H2O/CH3CH2OH complexes, respectively. In apigenin, excluding the aromatic hydrogen atoms in the phenyl substituent, all other hydrogen atoms and the oxygen atoms form hydrogen-bonds with H2O and CH3CH2OH. (3) In apigenin–H2O/CH3CH2OH complexes, the electron density and the E(2) in the related localized anti-bonding orbital are increased upon hydrogen-bond formation. These are the cause of the elongation and red-shift of the X−H bond. The sum of the charge change transfers from the hydrogen-bond acceptor to donor. The stronger interaction makes the charge change more intense than in the less stable structures. (4) Most of the hydrogen-bonds in the complexes are electrostatic in nature. However, the C4−O5···H, C9−O4···H and C13−O2···H hydrogen-bonds have some degree of covalent character. Furthermore, the hydroxyl groups of the apigenin molecule are the preferred hydrogen-bonding sites.

solution. In liquids, intermolecular interactions, particularly hydrogen-bonding interactions, greatly influence the extraction progress and the physical properties of the solution 10 . The investigation of the hydrogen-bonding interactions in mixtures of flavonoids and water/ethanol is particularly important to understand the mechanism of the extraction process and the physical essence of the mixture. Quantum chemical calculations have been widely and effectively used to study the intermolecular interactions theoretically [11][12][13][14][15][16][17][18][19][20][21] . In this work, the hydrogen-bonding interactions between ethanol/water and flavonoids were investigated from a theoretical perspective. 5,7-Dihydroxy-2-(4-hydroxyphenyl)-phenylchromen-4-one (apigenin) was selected as the representative flavonoid. Density functional theory (DFT) and MP2 methods were used to reveal the hydrogen-bonding interactions from a theoretical viewpoint.

Results and Discussion
Apigenin monomer geometry analysis. Two conformations of the apigenin molecule, labeled apigenin (I) and apigenin (II), were considered in this work. The conformation and atom numbering for the apigenin monomer are shown in Fig. 1. The labels of oxygen, hydrogen and carbon atoms are in red, blue and gray colors, respectively. In apigenin (II), the binding distance between H7 and O4 is approximately 1.7 Å, which is less than the sum of the van der Waals atomic radii of hydrogen and oxygen 22 . This result indicates that there is an intramolecular hydrogen-bond between H7 and O4 in apigenin (II).
The optimized bond lengths, bond angles and dihedral angles for apigenin (I) and apigenin (II) calculated using the B3LYP/6− 31 + + G(d, p), M062X/6− 31 + + G(d, p) and MP2/6− 31 + + G(d, p) methods are listed in Tables S1 and S2. As shown in Tables S1 and S2, the C9− O4 bond shows typical double bond characteristics, whereas the other C− O bonds exhibit single bond characteristics. Most values of the C− C bond lengths are approximately 1.400 Å, close to the normal C− C single bond length in both methods. The C1− C7 bond connecting the phenyl ring to the chromone part is approximately 1.470 Å based on calculations using the three abovementioned methods for apigenin (I) and apigenin (II). Because this bond plays a bridging role between the chromone part and the phenyl ring of apigenin, the conjugation of the phenyl ring and chromone is suggested. C8− C9 and C9− C10 bond lengths are approximately 1.460 Å for the two conformations. The longer bond length mainly due to the electronegativity of the keto substituent in the heterocyclic ring.
The bond angles of the aromatic ring are approximately 120°. However, the C8− C9− C10 bond angle in the heterocyclic ring deviates from 120°, mainly due to the conjugation across the heterocyclic ring and the keto group.
For the two conformations of the apigenin molecule, the C9− C10− C15− C14 and C13− C14− C15− C10 dihedral angles are very close to 180° and 0°, respectively. These results indicate that the chromone part is almost planar in orientation. The dihedral angles between the chromone and the phenyl group (C2− C1− C7− C8 and C2− C1− C7− O1) are approximately 160/156/154° and − 19/− 23/− 25° as calculated using the B3 LYP, M062X and MP2 methods, respectively, which indicates that the phenyl substituent is out of the plane with the chromone part. Therefore, the molecular structure of apigenin is non-planar. For apigenin (II), the optimized results are very close to the data from the literature 23 , which further verify the calculated results of this work.
Charge analysis of apigenin monomer. The calculation of the effective atomic charge plays an important role as an indicator of the possible interaction sites of the apigenin monomer. Figure 2 presents the charge distributions of the optimized apigenin monomer examined using the NBO (natural bond orbital) analysis.
In the apigenin monomer, all of the oxygen atoms have negative charges, and the oxygen atoms (O2, O3 and O5) of the hydroxyl groups have the most negative charges, followed by the carbonyl oxygen atom (O4) and the ether oxygen atom (O1). All of the hydrogen atoms have positive charges, and the hydrogen atoms on the hydroxyl groups (H3, H7 and H9) have more positive charges than the other hydrogen atoms due to their bond with the more electronegative oxygen atom (O2, O3 and O5). These results indicate that all of the oxygen and hydrogen atoms in apigenin can be hydrogen-bond acceptors and donors and that the oxygen and hydrogen atoms in the hydroxyl groups may be the preferred interaction sites over the other oxygen and hydrogen atoms.
The carbon atom C9 has the highest positive charge compared with the other ring carbon atoms, as shown in the histogram, owing to the electronegative keto group.
Optimized geometries of apigenin-H 2 O/CH 3 CH 2 OH complexes. The hydrogen-bonding interactions in liquids play important roles; thus, in this work, the hydrogen-bonds in apigenin-H 2 O/CH 3 CH 2 OH complexes were examined in detail. The definition of hydrogen-bond according to IUPAC is that a hydrogen-bond is an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X-H, in which X is more electronegative than H, and an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation 24 . The hydrogen-bond is often expressed as X− H···Y. Based on the definition of a hydrogen-bond, in this work, the sum of van der Waals atomic radii of hydrogen and oxygen (2.5 Å) was used as a critical value for judging the existence of a hydrogen-bond 22 . The optimized geometries were performed using the B3 LYP/6− 31 + + G(d, p) method. The above section states that all of the hydrogen atoms and oxygen atoms can serve as an interaction site. Therefore, in the optimization process, H 2 O and CH 3 CH 2 OH were The optimized geometries of apigenin-H 2 O and apigenin-CH 3 CH 2 OH complexes are shown in Figs 3, 4, 5 and 6. Only the most stable optimized geometries are presented in this paper. As shown in the figures, for apigenin (I), both apigenin (I)-H 2 O and apigenin (I)-CH 3 CH 2 OH complexes have eight interaction structures. For apigenin (II), both apigenin (II)-H 2 O and apigenin (II)-CH 3 CH 2 OH complexes have seven interaction structures. For simplicity, the structures that have similar interaction sites are labeled with the same letters. The binding distances are in the 1.794-2.500 Å range and for the thirty structures are less than 2.5 Å. These results show that all of these structures are stable hydrogen-bonded complexes. For the structure with only one hydrogen bond, the X-H···Y bond angles are larger than 154°. For the structures possessing two hydrogen-bonds, the X-H···Y bond angles are between 119° and 166°. These values are within the X-H···Y bond angles range that is characteristic of hydrogen-bond complexes, thus indicating the formation of hydrogen-bond interactions in these complexes.
The NBO results in Section 3.2 show that all the hydrogen and oxygen atoms in apigenin can be interaction sites, however, as shown in Figs 3, 4, 5 and 6, not all of the hydrogen atoms have formed hydrogen-bonds with H 2 O and CH 3 CH 2 OH. Except for the H7 in apigenin (II), which has formed an intramolecular hydrogen-bond, all of the hydrogen atoms in the hydroxyl groups of apigenin interact with H 2 O and CH 3 CH 2 OH due to their large positive electron density compared with the other hydrogen atoms, as illustrated in Figs 3, 4, 5 and 6. Although, the electron densities of all the aromatic hydrogen atoms are very close, only the hydrogen atoms in the chromone part formed hydrogen-bonds with H 2 O and CH 3 CH 2 OH (structure D, F and G for apigenin (I), structure C, D, E for apigenin (II)) due to the synergistic effect of the other groups of the same structure. It is evident that in these structures (structure D, F and G for apigenin (I), structure C, D, E for apigenin (II)), the hydrogen atoms and oxygen atoms in H 2 O and CH 3 CH 2 OH interact with apigenin simultaneously, forming two hydrogen-bonds with a stable six-atom ring. An interesting phenomenon is that the hydrogen atom in the hydroxyl groups of H 2 O and CH 3 CH 2 OH formed dihydrogen-bonds with hydrogen atoms in the keto group and the hydroxyl group in apigenin, as illustrated in structure E of apigenin (I).
The above results indicate that H 2 O and CH 3 CH 2 OH formed different hydrogen-bonds with apigenin.
Interaction energies of apigenin-H 2 O/CH 3 CH 2 OH complexes. The interaction energy is a most convincing measure of the strength of non-covalent interactions. The relative stability of different conformers is in accordance with the calculated interaction energies. For a stable interaction complex, the value of the interaction    Fig. 7. As shown in the figure, the absolute value of ΔE decreases from structure A to H. H 2 O and CH 3 CH 2 OH form strong hydrogen-bonds with the hydrogen atoms in the hydroxyl groups (structures A, B, and C for apigenin (I), structures A and B for apigenin (II)) and the oxygen atoms of the carbonyl groups (structures D and E for apigenin (I), structure C for apigenin (II)) of apigenin. For apigenin (I)− H 2 O/CH 3 CH 2 OH, the energies of the conformers A to E are close to each other and significantly higher than those of F to H. For apigenin (II)− H 2 O/CH 3 CH 2 OH, the energies of conformers A to C are close to each other and significantly higher than those of D to G. Because the atomic charges of the hydrogen atoms in the hydroxyl group of the apigenin monomer are very close, the interaction energies of the corresponding apigenin-H 2 O/CH 3 CH 2 OH complex are very similar (structures A, B, and C for apigenin (I), structures A and B for apigenin (II)).

Vibrational frequency changes upon hydrogen-bond formation. One of the indications of the
presence of a hydrogen-bond is the shift of the vibration frequencies and the bond length 25,26 . In this work, the frequency analysis was performed using the B3LYP/6− 31 + + G(d, p), M062X/6− 31 + + G(d, p) and MP2/6− 31 + + G(d, p) methods with geometries that were optimized using B3LYP/6− 31 + + G(d, p  The sum of the atomic charges of each monomer in the complex systems could be defined as a charge transfer (CT) value. Here we observe a charge change in apigenin as the selected monomer for acquiring the CT amounts. Listed in Table 4 are the calculated charge changes of apigenin from complexes to a monomer. The negative value of the charge change means apigenin obtains more charge upon hydrogen-bond formation. The larger absolute value of the charge change indicates a larger CT. As shown in the table, apigenin gets a charge when it acts as a hydrogen-bond donor (structures A, B and C for apigenin (I), structures A, B for apigenin (II)). However, when it is hydrogen-bond acceptor, it loses its charge (structures E and H for apigenin (I), structures F, G for apigenin (II)). Electron transfers occur from the hydrogen-bond acceptor to the hydrogen-bond donor. The stronger hydrogen-bond causes the hydrogen-bond donor to lose more charge. Additionally, as shown in Table 4, when apigenin acts as an electron donor or acceptor only, the stronger interactions will make the charge transfer larger (absolute value: A > B > C > E > H for apigenin (I), A > B > F > G for apigenin (II)).
bond critical points (BCPs). All of the parameters were evaluated using the AIM (atoms in molecules) approach with the B3 LYP/6− 31 + + G(d, p), M062X/6− 31 + + G(d, p) and MP2/6− 31 + + G(d, p) methods. The results are shown in Tables 5 and 6. It can be observed that the values of ρ BCPs are in the range of 0.0063− 0.0314 au and 0.0059− 0.0354 au for apigenin− H 2 O and apigenin− CH 3 CH 2 OH complexes, respectively, which are within the range of 0.002− 0.04 au that was determined for hydrogen-bonds 28 . The values of ∇ 2 ρ BCPs are all positive, ranging from 0.0346 to 0.1047 au for apigenin− H 2 O complexes and 0.0304 to 0.1161 au for apigenin− CH 3 CH 2 OH complexes. These values are within the range of 0.020− 0.139 au that was determined for hydrogen-bond-including complexes 28 , thus indicating the formation of hydrogen-bond interactions in these complexes. It is well known that the higher value of ρ BCPs and the sum of ∇ 2 ρ BCPs implies stronger interactions. Therefore, as the results of Tables 5 and 6 shown, the ρ BCPs of A is the greatest and is in agreement with its highest interaction energy, followed by B, C, D, E, F, G and H.  As previously noted, H BCPs is a more appropriate index used to gain a deeper understanding of the non-covalent interactions 29 . When H BCPs < 0, the hydrogen-bond possesses an interaction of a dominantly covalent character. When H BCPs > 0, the hydrogen-bond is electrostatically dominant. As shown in Tables 5 and 6

Conclusions
In this work, the hydrogen-bonding interactions between ethanol/water and apigenin were investigated from a theoretical perspective using quantum chemical calculations. Two conformations of the apigenin molecule were considered in this work. The equilibrium structures were analyzed using the B3LYP/6− 31 + + G(d, p) method. Based on the optimized geometries from the B3LYP/6− 31 + + G(d, p) method, the molecular energies, charges, vibrational frequencies, NBO analysis and topological analysis were analyzed using the B3LYP/6− 31 + + G(d, p), the M062X/6− 31 + + G(d, p) and the MP2/6− 31 + + G(d, p) methods. The main conclusions are as follows: (1) For the apigenin monomer: the chromone part is in the plane, whereas the phenyl substituent is out of the plane with the chromone part. Therefore, the molecular structure of apigenin is non-planar. All of the hydrogen atoms can be used as hydrogen-bond donors, and the oxygen atoms can act as hydrogen-bond acceptors.  Methods Computational details. All of the calculations were performed using the Gaussian 09 program 30 . The geometries of the monomers and apigenin− H 2 O/CH 3 CH 2 OH complexes were optimized by B3LYP/6-31 + + G(d, p). The most stable optimized geometries at a local energy minimum were verified by the lack of any imaginary vibrational frequency. The molecular energies, charge, and vibrational frequencies of the monomers and apigenin-H 2 O/ CH 3 CH 2 OH complexes were calculated using the B3LYP/M062X/MP2 methods with the 6-31 + + G(d, p) basis set using the optimized geometries of the B3LYP/6− 31 + + G(d, p) method. The interaction energy in the complexes can be regarded as the energetic difference between the complex and the sum of the individual monomers: In Equation (1), 2625.5 is unit conversion from au to kJ/mol. Moreover, the calculation of the interaction energy is corrected by the basis set superposition error (BSSE) correction according to the counterpoise procedure of Boys and Bernardi 31 .
To better understand the nature of the intermolecular hydrogen-bonding interactions in the apigenin− H 2 O/ CH 3 CH 2 OH complexes, NBO 27 and AIM 32 analyses were also carried out at the B3LYP/6− 31 + + G(d, p), M062X/6− 31 + + G(d, p) and MP2/6− 31 + + G(d, p) levels. NBO analysis was performed to elucidate charge transfer upon hydrogen-bond formation. The NBO program as implemented in the Gaussian 09 package is used to do the NBO analysis. In the NBO analysis, the donor and acceptor interactions could be estimated through the second-order perturbation theory, described using the following equation: where q i is the donor orbital occupancy, ε j and ε i are diagonal elements, and F(i, j) is the off-diagonal NBO Fock matrix element.
In the AIM analysis, the search of BCPs and a detailed topological analysis was performed with the Multiwfn 3.3.8 suite 33 . The topological parameters, such as ρ, ρ ∇ 2 and H at the BCPs, were used to predict the nature of the hydrogen-bonding interaction.