Introduction

Propolis (or bee glue) has been used as a popular natural remedy in folk medicine for centuries all over the world1. Propolis is a strongly adhesive, resinous substance that honey bees collect from buds, barks and plant exudates and use in their beehives as a protective barrier against invaders and contamination2,3. It is reported that propolis possesses a broad array of biological properties, such as anti-septic, anti-mycotic, anti-viral, spasmolytic, anti-inflammatory and immunostimulatory activities2. Due to these characteristics, which can yield health benefits, propolis has attracted much attention in recent years as an important substance for use in foods and medicines to improve health and to prevent diseases.

Although the precise composition of raw propolis varies based on several factors, such as geographical zones and botanical origins, propolis is generally composed of 50% resin and balsam, 30% wax, 10% aromatic oil, 5% pollen and 5% various other substances3. The chemical composition of propolis is complicated. More than 300 compounds, including aromatic acids, esters, waxy acids, flavonoids and terpenoids have been isolated from raw propolis2. Among those constituents, flavonoids are one of the most important bioactive compounds and are reported to be responsible for some of the medicinal properties of propolis such as anti-microbial, anti-cancer, anti-oxidant and anti-viral activities4,5.

As raw propolis is a hard resinous product, it cannot be consumed in its natural form. Before used, raw propolis must be purified by solvent extraction to remove the inert materials (such as resin, balsam and beeswax) and to preserve the flavonoid fractions. Ethanol6,7 and water8,9 have been considered as good solvents to extract flavonoids from propolis. The anti-oxidant activity of ethanolic propolis from various geographical origins was studied, and different activities were found for each sample6. Aqueous propolis extracts also showed an effective antioxidant activity in several in vitro assays8,9. The bioactive properties of the aqueous and ethanolic extracts are attributed mainly to the high content of flavonoids in the mixture. Although, the extraction of flavonoids from propolis by water and ethanol under different conditions have been investigated6,7,8,9, few works have focused on the mechanism of the extraction process, the microstructure and the physical properties of the extracting solution. In liquids, intermolecular interactions, particularly hydrogen-bonding interactions, greatly influence the extraction progress and the physical properties of the solution10. 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 theoretically11,12,13,14,15,16,17,18,19,20,21. 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 oxygen22. This result indicates that there is an intramolecular hydrogen-bond between H7 and O4 in apigenin (II).

Figure 1
figure 1

Conformations and atom numberings for all of the atoms of apigenin (I) and apigenin (II).

The labels of oxygen, hydrogen and carbon atoms are in red, blue and gray colors, respectively.

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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 literature23, 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.

Figure 2
figure 2

Histogram of the calculated NBO charges for apigenin.

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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–H2O/CH3CH2OH complexes

The hydrogen-bonding interactions in liquids play important roles; thus, in this work, the hydrogen-bonds in apigenin–H2O/CH3CH2OH 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 formation24. 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-bond22. 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, H2O and CH3CH2OH were placed around all of the hydrogen atoms and the oxygen atoms to examine all of the possible apigenin−H2O/CH3CH2OH geometries.

The optimized geometries of apigenin–H2O and apigenin–CH3CH2OH 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)–H2O and apigenin (I)–CH3CH2OH complexes have eight interaction structures. For apigenin (II), both apigenin (II)–H2O and apigenin (II)–CH3CH2OH 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.

Figure 3
figure 3

Optimized geometries for the apigenin (I)–H2O complex using the B3LYP/6−31 + + G(d, p) method.

Hydrogen-bonds are denoted by dashed lines, and the corresponding H···O distances (Å) and bond angles (°) are labeled in black and blue colors, respectively.

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Figure 4
figure 4

Optimized geometries for the apigenin (I)–CH3CH2OH complex using the B3LYP/6−31 + + G(d, p) method.

Hydrogen-bonds are denoted by dashed lines, and the corresponding H···O distances (Å) and bond angles (°) are labeled in black and blue colors, respectively.

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Figure 5
figure 5

Optimized geometries for the apigenin (II)–H2O complex using the B3LYP/6−31 + + G(d, p) method.

Hydrogen-bonds are denoted by dashed lines, and the corresponding H···O distances (Å) and bond angles (°) are labeled in black and blue colors, respectively.

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Figure 6
figure 6

Optimized geometries for the apigenin (II)–CH3CH2OH complex using the B3LYP/6−31 + + G(d, p) method.

Hydrogen-bonds are denoted by dashed lines, and the corresponding H···O distances (Å) and bond angles (°) are labeled in black and blue colors, respectively.

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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 H2O and CH3CH2OH. 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 H2O and CH3CH2OH 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 H2O and CH3CH2OH (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 H2O and CH3CH2OH 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 H2O and CH3CH2OH 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 H2O and CH3CH2OH formed different hydrogen-bonds with apigenin.

Interaction energies of apigenin–H2O/CH3CH2OH 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 energy (ΔE) is often negative. The larger the absolute value of ΔE the stronger the strength of the corresponding hydrogen-bond. In this work, the ΔE values of different geometries are drawn as histograms in Fig. 7. As shown in the figure, the absolute value of ΔE decreases from structure A to H. H2O and CH3CH2OH 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)−H2O/CH3CH2OH, 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)−H2O/CH3CH2OH, 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–H2O/CH3CH2OH complex are very similar (structures A, B, and C for apigenin (I), structures A and B for apigenin (II)).

Figure 7
figure 7

Histogram for the interaction energies of apigenin–H2O/CH3CH2OH complexes.

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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 length25,26. 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 representative vibrational frequencies and bond length changes of X−H are shown in Tables 1 and 2. As shown in the tables, the thirty structures of apigenin−H2O and apigenin−CH3CH2OH complexes have one similar characteristic upon hydrogen-bond formation: the X–H bonds are elongated upon complexation, and the elongations of the X–H bonds are concomitant with a decrease in the X–H stretching frequencies (red-shift). For the O−H groups in apigenin, the red-shift and bond elongation are ordered A > B > C for the apigenin (I)−H2O/CH3CH2OH complexes and A > B for the apigenin (II) −H2O/CH3CH2OH complexes. For the O−H groups in H2O and CH3CH2OH, the red-shift and bond elongation are D > E > F > G for apigenin (I) −H2O/CH3CH2OH complexs and C > D > E > F > G for apigenin (II) −H2O/CH3CH2OH complexs. It is clear that the more red-shift and bond elongation values are related to the more stable apigenin−H2O/CH3CH2OH complex and the hydrogen-bonds in the apigenin–H2O/CH3CH2OH complexes are proper red-shift hydrogen-bonds (the vibrational frequency of X−H bond moves to lower wavenumber upon X−H···Y hydrogen-bond formation).

Table 1 The wavenumber, bond length and electron density (in σ*X−H) changes of the X−H bonds in apigenin−H2O complexes from different complexes to monomers at the B3LYP/6−31 + + G(d, p), M062X/6−31 + + G(d, p) and MP2/6−31 + + G(d, p) levels.
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Table 2 The wavenumber, bond length and electron density (in σ*X−H) changes of the X−H bonds in apigenin−CH3CH2OH complexes from different complexes to monomers at the B3LYP/6−31 + + G(d, p), M062X/6−31 + + G(d, p) and MP2/6−31 + + G(d, p) levels.
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NBO analysis of apigenin−H2O/CH3CH2OH complexes

Electron density rearrangement accompanies the formation of a hydrogen bond. NBO analysis provides an efficient method for studying intermolecular interactions and a convenient basis for investigating charge transfer in molecular systems. Herein, based on the optimized geometries using the B3 LYP/6−31 + + G(d, p) method, charge distributions of the apigenin−H2O/CH3CH2OH hydrogen-bonded complexes were examined in terms of the NBO analysis using the B3 LYP/6−31 + + G(d, p), M062X/6−31 + + G(d, p) and MP2/6−31 + + G(d, p) methods.

In most of the hydrogen-bond complexes, charge donating centers and charge accepting centers are often the lone pairs [in this work, the lone pairs belong to an oxygen atom, represented as LP(O)] of the hydrogen-bond acceptor and the anti-bonding orbitals of the hydrogen-bond donor (σ*X−H), respectively27. In the apigenin−H2O/CH3CH2OH complexes, the electron density change of the σ*X−H and the corresponding interacting stabilization energies computed using the second-order perturbation theory [E(2)] are listed in Tables 1, 2 and 3. As shown in the tables, the electron density and the E(2) in the related localized anti-bonding orbital are increased upon hydrogen-bond formation. These results suggest strong orbital interactions between the LP(O) and the σ*X−H. The increase in the electron density of σ*X−H is a result of the charge transfer from LP(O). This in turn results in the elongation of the X–H bond and a red-shift of the v(X−H) bond upon the apigenin−H2O/CH3CH2OH hydrogen-bonded complex formation as shown in Tables 1 and 2. Also shown in the tables, the electron densities change and the E(2) for the X−H···O bonds of structures A, B and C in apigenin (I)−H2O/CH3CH2OH and structure A and B in apigenin (II)−H2O/CH3CH2OH were much larger than the other conformers.

Table 3 Second-order perturbation theory analysis of the Fock matrix in the NBO basis for apigenin−H2O/CH3CH2OH.
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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)).

Table 4 Charge (q in e) changes of apigenin from different complexes to monomers obtained using the NBO theory at the B3LYP/6−31 + + G(d, p), M062X/6−31 + + G(d, p) and MP2/6−31 + + G(d, p) levels.
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AIM analysis of apigenin−H2O/CH3CH2OH complexes

The topological analysis of the electron density further validates the existence of hydrogen-bonds in all of the structures. The following parameters were analyzed: the electron density (ρ), the Laplacian of the electron density (ρ), and the energy density (H) at the 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.

Table 5 The electron density (ρ), the Laplacian of the electron density (ρ), and the energy density (H) at the bond critical points (BCPs) of the hydrogen-bonds of apigenin−H2O complexes, obtained using the AIM theory at the B3LYP/6−31 + + G(d, p), M062X/6−31 + + G(d, p) and MP2/6−31 + + G(d, p) levels.
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Table 6 The electron density (ρ), the Laplacian of electron density (ρ), and the energy density (H) at the bond critical points (BCPs) of the hydrogen-bonds of apigenin−CH3CH2OH complexes, obtained using the AIM theory at the B3LYP/6−31 + + G(d, p), M062X/6−31 + + G(d, p) and MP2/6−31 + + G(d, p) levels.
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It can be observed that the values of ρBCPs are in the range of 0.0063−0.0314 au and 0.0059−0.0354 au for apigenin−H2O and apigenin−CH3CH2OH complexes, respectively, which are within the range of 0.002−0.04 au that was determined for hydrogen-bonds28. The values of ρBCPs are all positive, ranging from 0.0346 to 0.1047 au for apigenin−H2O complexes and 0.0304 to 0.1161 au for apigenin−CH3CH2OH complexes. These values are within the range of 0.020−0.139 au that was determined for hydrogen-bond-including complexes28, thus indicating the formation of hydrogen-bond interactions in these complexes. It is well known that the higher value of ρBCPs and the sum of ρBCPs implies stronger interactions. Therefore, as the results of Tables 5 and 6 shown, the ρBCPs 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, HBCPs is a more appropriate index used to gain a deeper understanding of the non-covalent interactions29. When HBCPs < 0, the hydrogen-bond possesses an interaction of a dominantly covalent character. When HBCPs > 0, the hydrogen-bond is electrostatically dominant. As shown in Tables 5 and 6, in apigenin (I)−H2O/CH3CH2OH complexes, it is evident that for the hydrogen-bonds in conformers A, B, C, E and G, C8−H6···O in D, and C12−H8···O, they are essentially electrostatic in nature. In apigenin (II)−H2O/CH3CH2OH complexes, for the hydrogen-bonds in conformers A, B, D and E and C8−H6···O in C, they are essentially electrostatic in nature. However, negative values of HBCPs are obtained for C9−O4···H, C13−O2···H and C4−O5···H in apigenin−H2O/CH3CH2OH complexes, suggesting that the corresponding hydrogen-bonds in these conformers have some degree of covalent character.

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. 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.

  2. 2

    Eight and seven optimized geometries were obtained for apigenin (I)−H2O/CH3CH2OH and apigenin (II)−H2O/CH3CH2OH complexes, respectively. All the oxygen atoms can be used as hydrogen-bond acceptors, and all the hydrogen atoms in the chromone part can be hydrogen-bond donors. However, the aromatic hydrogen atoms in the phenyl substituent did not form hydrogen-bonds with H2O and CH3CH2OH. H2O and CH3CH2OH formed strong hydrogen-bonds with the hydrogen atoms of the hydroxyl groups and the oxygen atoms of the carbonyl group of apigenin.

  3. 3

    The formation of apigenin−H2O/CH3CH2OH complexes is accompanied by charge rearrangement. 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. In the apigenin−H2O/CH3CH2OH complexes, the sum of charge change transfers from the hydrogen-bond acceptor to the hydrogen-bond donor. The stronger interaction makes the charge change larger than observed in the less stable complexes.

  4. 4

    According to the topology analysis performed using the AIM theory, the C9−O4···H, C13−O2···H and C4−O5···H hydrogen-bonds have some degree of covalent character. However, the other hydrogen-bonds are electrostatic in nature. Furthermore, the hydroxyl groups are the preferred hydrogen-bonding sites.

Methods

Computational details

All of the calculations were performed using the Gaussian 09 program30. The geometries of the monomers and apigenin−H2O/CH3CH2OH 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–H2O/CH3CH2OH 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 Bernardi31.

To better understand the nature of the intermolecular hydrogen-bonding interactions in the apigenin−H2O/CH3CH2OH complexes, NBO27 and AIM32 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 qi is the donor orbital occupancy, εj and εi 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 suite33. The topological parameters, such as ρ, and H at the BCPs, were used to predict the nature of the hydrogen-bonding interaction.

Additional Information

How to cite this article: Zheng, Y.-Z. et al. Hydrogen-bonding Interactions between Apigenin and Ethanol/Water: A Theoretical Study. Sci. Rep. 6, 34647; doi: 10.1038/srep34647 (2016).