Introduction

Flavonoids and polyphenols have great potential to treat a variety of cancers [1,2,3,4,5]. A subset of these compounds are flavonoids whose hydroxy groups are methylated and this increases metabolic stability and thus improves their biological properties [6, 7]. Calycopetrin and xanthomicrol (hereinafter referred to as “Cal” and “Xan,” respectively) are two examples of these compounds. Cal, (5, 4'- dihydroxy-3,6,7,8-tetramethoxyflavone) is a flavonoid first extracted and identified from leaves of Calycopteris floribunda Lamk. and Digitalis thapsi [8, 9]. Many biological properties have been reported for Cal, including immunoinhibitory, anti-helminthic, anti-spasmodic, and hyperlipidemic agents [10, 11]. The effect of this compound on the treatment of neurodegenerative diseases and rheumatoid diseases such as Alzheimer’s and cancer diseases has also been studied and good results have been obtained [12, 13]. Xan (5, 4 '- dihydroxy-6,7,8-trimethoxyflavone), like Cal, is a methoxylated flavonoid found in the leaves of various plants, including Dracocephalum kotschyi Boiss [14]. Unique biological properties such as anti-cancer and anti-angiogenic properties have been reported for this compound [15,16,17,18].

Free radicals are highly active and reactive due to the unpaired electrons of the species. Free radicals in the body are created by the activity of various parts and compounds. These include the activity of mitochondrion and phospholipase enzymes. In addition, the human body can be exposed to other types of free radicals from various environmental sources such as cigarette smoke or air pollution. Free radicals can damage cells through oxidative stress. On the other hand, free radicals have vital functions in the body, including fighting infectious agents to boost the immune system. For this reason, the body needs to balance the required free radicals with antioxidants [19,20,21].

Antioxidants are compounds that inhibit oxidation in the body’s cells through various mechanisms. An antioxidant usually acts through the chemical mechanism of hydrogen atom transfer (HAT) and single electron transfer followed by proton transfer (SET-PT) [22, 23]. In the first mechanism, a free radical receives hydrogen from the antioxidant and the antioxidant is transformed into a stable radical. In this mechanism, bond dissociation energy (BDE) for the O–H bond is an important parameter for evaluating antioxidant activity so that the weaker O–H bond shows strong antioxidant properties and vice versa [24, 25]. In the SET-PT mechanism, the antioxidant compound can give an electron to a free radical and turn itself into a radical cation. In this mechanism, ionization potential energy (IP) is discussed so a combination with lower IP should have more robust antioxidant properties [26, 27]. Two of the most important natural and non-enzymatic antioxidants are phenolic and flavonoid compounds [28,29,30]. Cal and Xan can be expected to have good antioxidant properties. The rapid and reliable development of quantum chemistry allows the calculations of BDEs and IPs of organic compounds to be obtained with great accuracy. Density functional theory (DFT) calculations methods can be used as a powerful tool to predict the relationship between chemical structure and the activity of an organic compound [31, 32]. Numerous quantum studies have been conducted to investigate the antioxidant properties and design new compounds as antioxidants [33,34,35,36,37,38,39,40]. Scientific sources indicate that no DFT studies have been performed to obtain Cal and Xan flavonoids physico-chemical properties. In the present work, the structure of these two valuable flavonoids was comprehensively considered to obtain antioxidant capacity, acidity, electronic, and structural and spectral data using the DFT method. Their structures consist of a polymethoxylated phenol ring A and a fused γ-pyrone ring C, with the phenol ring B attached to the 2-position of the γ-pyrone ring.

Computational details

The chemical structures of Cal and Xan, their anions, radicals, and radical cations were optimized using the DFT/B3LYP method in conjunction with basis set 6–31 + G(d, p) using Gaussian 09 software [41]. The unrestricted open-shell method was used to optimize radical and radical cation species. Vibrational frequencies were calculated at the same level to ensure that each stationary point is a real minimum. All calculations were performed in the gas phase and water. We have employed solvent effects into account by using the conductor-like polarizable continuum model (CPCM). The B3LYP/6–31 + G (d, p) optimized Cartesian coordinates of Cal and Xan, their anions, radicals, and radical cations have been collected in the Supplementary material.

Results and discussion

Benchmarking study of computational method

The DFT method is a valuable and powerful computational method because it predicts the physical and chemical data of the studied system with high accuracy. Nowadays, DFT/B3LYP method is widely used for various quantum computations [42,43,44,45,46,47,48]. This method was used with the basis set 6–31 + G(d, p) to study the Cal and Xan structures in the present study. Spectral data (1HNMR and 13CNMR) of Cal have been reported experimentally [10]. These data can be used to benchmark the computational method B3LYP/6–31 + G(d, p). Given that NMR data were obtained in acetone-d6 as a solvent, the structure of Cal in this solvent was also optimized using the conductor-like polarizable continuum model (CPCM) as the solvation model [49]. Spectral data (regarding hydrogens and carbons of tetramethylsilane) were obtained by the gauge-independent atomic orbital (GIAO) method [50] in acetone. Experimental and computational NMR data of Cal have been collected in Table 1S (supplementary material).

As can be seen from the 1HNMR and 13CNMR data regression curves (Fig. 1), there is an excellent agreement between the experimental and calculated data; regression was obtained R2 = 0.9964 for 1HNMR and R2 = 0.9966 for 13CNMR data. Therefore, the computational method of B3LYP/6–31 + G(d, p) can be used to continue the calculations and obtain the physical and chemical properties of Cal and Xan flavonoids.

Fig. 1
figure 1

The linear regression between experimental and calculated 1H and 13CNMR data of calycopterin

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Structural characterization of Cal and Xan

The Cal and Xan structures optimized using the B3LYP/6–31 + G(d, p) method have been shown in Fig. 2. Some structural data of the studied compounds are tabulated in Table 1.

Fig. 2
figure 2

The B3LYP/6–31 + G(d, p) optimized geometry of calycopterin and xanthomicrol in water (distance in Å)

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Table 1 The calculated structural data and aromatic indices of calycopterin and xanthomicrol by B3LYP/6–31 + G(d, p) method
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As can be seen from the optimized structure of the molecules, all three polymethoxylated phenyl (A) phenolic (B), and γ-pyrone (C) rings are almost in the same plane, and the molecules are in an extended conjugation system that can be viewed from dihedral angles. The angle of 17C–9C–8C–7C in Cal is 179.07˚ and the 16C–9C–8C–7C in Xan is 179.91̊. The bond length of C = O in Xan and Cal is 1.262 and 1.264 Å, respectively, which is longer than the bond length of a group of a normal ketone. On the other hand, the calculated vibration frequency of the carbonyl group in Cal and Xan is 1670 and 1673 cm−1, respectively, which is much lower than the frequency of a normal ketone group (1715 cm−1). The carbonyl group can be conjugated with the endo alkene double bond and the endo-oxygen atom. This phenomenon decreases the bond order of the carbonyl bond and makes it more single. In the resonance form, the γ-pyrone core is an aromatic ring. The presence of intramolecular hydrogen bonding (IMHB) increases the tendency for this resonance (Scheme 1).

Scheme 1
scheme 1

Resonance form of calycopterin

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As can be seen from the optimized structures of Cal and Xan (Fig. 2), there is a very strong IMHB with the hydrogen atom of the hydroxy group as the donor center and the oxygen atom of the carbonyl group as the acceptor site. In the section on evaluating the antioxidant properties of the studied compounds, we will see how this IMHB will affect these properties. Calculation of γ-pyrone ring aromatics indices using the B3LYP/6–31 + G(d, p) method can confirm the existence of this resonance form. The Harmonic Oscillator Model of Aromaticity (HOMA) and the Nucleus-Independent Chemical Shifts (NICS) are two structural and magnetic aromatics indices widely used today to evaluate the aromaticity of unsaturated system rings [51, 52]. The HOMA index is used to evaluate all carbon systems such as hydrocarbons. The Harmonic oscillator model of electron delocalization (HOMED) is used to evaluate the aromaticity of rings containing heteroatoms such as the pyrone ring (Eq. (1)) [53, 54].

$$\mathrm{HOMA\; or\; HOMED }= 1-(\sum \mathrm{\alpha }\sum {[\mathrm R_{opt }- R_{x}]}^{2})/n$$
(1)

In this equation, the parameters n, α, Ropt and Rx are the number of bonds within the ring, the normalization constant, the optimized bond length for the reference molecule, and the calculated bond length for the study ring, respectively. HOMED is equal to unity for the benzene ring. It should be noted that α and Ropt are different for different types of bonds. In this study, for the C–C bond, Ropt and α were equal to 1.394 and 88.09 Å, respectively, and for C–O, Ropt, and α were 1.281 and 75.00 Å, respectively [53]. In addition to the HOMA index, the magnetic susceptibility of the ring is an indicator of its aromatic properties, which can be measured by the NICS descriptor [55]. The absolute magnetic shielding is measured using the hypothetical Bq atom at a distance of 1 Å above the ring. Negative and positive NICS values indicate aromaticity and anti-aromaticity, respectively. The HOMA parameters in water for the γ-pyrone ring in Cal and Xan are 0.72 and 0.71, respectively, indicating its aromatic nature. Also, the NICS value of this ring in Cal and Xan in water is 4.91 and 3.68 ppm, respectively, which confirms its relative aromaticity. The same trend is also seen in the gas phase (Table 1). Molecular electrostatic potential (MEP) maps for Cal and Xan also confirm the γ-pyrone aromaticity and the negative charge on the carbonyl oxygen atom. In these maps, red indicates negative electron density and blue indicates positive electron density [56] (Fig. 1S, supplementary material).

The resonance form and IMHB for Cal and Xan can be better investigated by natural bond orbital (NBO). NBO analysis gives numerically the valuable information about intermolecular and intramolecular interactions such as hydrogen bonding and delocalization according to the second-order perturbation energy (E(2)). The NBO analysis is a useful method for the study of the charge transfer in a chemical system [57]. Significant intramolecular interactions and E(2) in Cal and Xan structures were collected in Table 2. It should be mentioned that the E(2) value demonstrates the electron transfer from the donor NBOs to acceptors ones.

Table 2 Representative calculated donor–acceptor interactions in Cal and Xan at B3LYP/6–31 + G (d,p) level
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As seen from Table 2, the LP (2) O14 → BD*(1) O10 H29 as a remarkable interaction with energy 25.91 kcal/mol in Cal structure is attributed to the IMHB interaction. The energy of intramolecular hydrogen interaction in Xan molecule is 26.97 kcal/mol. Moreover, the BD (2) C8–C9 → BD*(2) C7–O14 and LP (2) O15 → BD*(2) C8–C9 in Cal show other significant interactions with 25.57 and 31.77 kcal/mol, respectively. The analogous trend can be seen in the Xan system (Table 2). Such interactions were a consequence of π-bond delocalization and aromaticity of γ-pyrone ring (Scheme 1) which demonstrates a significant ring current. Such findings confirm that the strongest interactions in Cal and Xan structure are related to the IMHB, aromaticity, and conjugation.

Electronic characterization of Cal and Xan

Electronic data calculated by B3LYP/6–31 G + (d, p) method for Cal and Xan have been collected in Table 3. The Cal and Xan dipole moments in water are 6.46 and 8.50 Debye, respectively, indicating the high polarity. The presence of polar groups such as the carbonyl group and the assumed resonance form (Scheme 1) is the reasons for this high dipolar moment value. A noteworthy point is the high polarity of these compounds in the polar solvent such as water relative to the gas phase (Table 3).

Table 3 The calculated electronic data of calycopterin and xanthomicrol by B3LYP/6–31 + G(d, p) method
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According to Frontier molecular orbital theory, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are usually involved in chemical reactions. In terms of energy, it is easier to separate electrons from HOMO, and this orbital can donate electrons, while LUMO accepts electrons more easily. The geometric shape of the frontier molecular orbitals for Cal and Xan was obtained through the B3LYP/6–31 + G(d, p) method. As shown in Fig. 3, HOMO in both compounds is essentially present in the entire chemical structure. LUMO is present in both compounds on polar groups such as carbonyl and alkene double bond. In general, LUMO is located on A and C rings. HOMO energy measures radical scavenging activity through its electron donation ability to free radical electrons [33]. Calculations show that the HOMO energy level in Cal is higher than in Xan. Therefore, it is suggested that the ability of radical scavenging of Cal is higher than Xan, which will be explained in detail in the section on the antioxidant properties of these compounds. Also, the difference between HOMA and LUMO energy levels (Eg) for Cal and Xan is 3.82 and 3.91 eV, respectively (Fig. 3).

Fig. 3
figure 3

The HOMO and LUMO gap for calycopterin and xanthomicrol in water

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General reactivity indices including chemical potential (μ), chemical hardness (η), global electrophilicity (ω), and global nucleophilicity (N) were calculated for both Cal and Xan flavonoids using the B3LYP/6–31 + G(d, p) (Table 3) method [58, 59]. Chemical hardness, which indicates the resistance of cloud polarization or deformation of chemical compounds, is used to predict reactivity. According to the chemical hardness of Cal and Xan, it seems that Cal has higher reactivity than Xan because it has a lower chemical hardness. Indices ω and N are useful and reliable parameters to determine the electrophilic and nucleophilic nature of organic compounds [60,61,62]. Organic compounds can be classified on the Domingo scale for ω and N indices [63]. This scale divides electrophiles and nucleophiles into strong, moderate, and weak categories. When ω is higher than 1.5 eV, it is a strong electrophile, in the range 0.8–1.5 eV the electrophile is mild and less than 0.8 eV represents the weak electrophile. Also, a strong nucleophile has a nucleophilicity index above 3 eV, while a moderate nucleophile has an N in the range of 2–3 eV and a weak nucleophile has an N lower than 2 eV. Based on this rating and the data in Table 3, it can be seen that Cal and Xan are both strong electrophiles and moderate nucleophiles. It should be noted that the global nucleophilicity value of a molecule is calculated from the difference of its EHOMO energy with the EHOMO energy of the tetracyanoethylene molecule (TCE). The TCE has the lowest HOMO energy among many organic molecules [64]. The antioxidant activity of an organic molecule depends not only on its chemical properties but also on its ability to penetrate the medium. To prevent peroxidation lipid, an antioxidant must have high lipophilicity. The classical descriptor for lipophilicity can be expressed as the value of Log Po/w, where P represents the partition coefficient between n-octanol and water. Log Po/w can be calculated from Eq. (2) where R is the gas constant, T is the system temperature (298.15 K) and ΔG is the difference between the solvation Gibbs energies in water and n-octanol for the study compound [65]. Cal has higher lipophilicity than Xan so that Cal can penetrate the lipid layer better than Xan (Table 3).

$$\mathrm{Log}\;{\mathrm P}_{\mathrm o}/{\mathrm P}_{\mathrm w}=-\mathrm{\Delta G}/2.303\mathrm{RT}$$
(2)

DFT study on antioxidant activity of Cal and Xan

In this section, two antioxidant mechanisms, including hydrogen atom transfer (HAT) and single electron transfer followed by proton transfer (SET-PT) were considered to evaluate the antioxidant properties of Cal and Xan. Bond dissociation enthalpies (BDEs) and ionization potentials (IPs) data were calculated using the B3LYP/6–31 + G(d, p) method in the gas phase and water as polar and biological solvent with the CPCM solvation model. In the final step, the reactivity of the studied compounds with the radical species OH°, OOH°, and O2°¯was also investigated. Reactions ((3) and (4)) related to both mechanisms have been given below [33].

  1. 1.

    Hyrdrogen atom transfer (HAT):

    $$\mathrm R^{\bullet}+\mathrm{ArOH}\rightarrow\mathrm{RH}+\mathrm{ArO}^{\bullet}$$
    (3)
  2. 2.

    Single electron transfer (HAT):

    $$\mathrm R^{\bullet}+\mathrm{ArOH}\rightarrow\mathrm R^-+\mathrm{ArOH}^{\bullet +}\rightarrow\mathrm{ArO}^{\bullet}+\mathrm{RH}$$
    (4)

As can be deduced from these reactions, these two pathways involve the free radical reaction with the hydroxy group, which can be described by Eqs. (5) and (6):

$$\mathrm{BDE}={\mathrm H}_{\mathrm{ArO^\bullet}}+{\mathrm H}_{\mathrm H^{\bullet}}-{\mathrm H}_{\mathrm{ArOH}}$$
(5)
$$\mathrm{IP}={\mathrm H}_{\mathrm{ArO^{\bullet +}}}+{\mathrm H}_{\mathrm e}-{\mathrm H}_{\mathrm{ArOH}}$$
(6)

where HArO°, HArO°+, HArOH, HH°, and He are the enthalpies of radical, radical cation, neutral antioxidant, radical hydrogen, and electron, respectively. HH° and He in the gas phase and water were extracted from literature [66]. BDEs and IPs data for Cal and Xan were calculated and given in Table 4 and compared to phenol as the reference molecule. In the HAT mechanism, a hydrogen atom from the antioxidant donates to a typical free radical. Therefore, the lower BDE value of the O–H bond represents the higher antioxidant properties. There are two O–H groups in the structure of the studied two flavonoids. Therefore, the BDE of both hydroxy groups is calculated separately. For convenience, the symbols OHA (on ring A) and OHB (On ring B) are used to identify radical species.

Table 4 B3LYP/6–31 + G(d, p) bond dissociation energies (BDE), ionization potentials (IP), ΔBDE, ΔIP, and proton affinity (PA) values for calycopterin and xanthomicrola
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As can be deduced from the data, the O–HA bond, energy in Cal and Xan is higher than in phenol and this hydrogen as a radical is not donated to the free radical by these flavonoids. The cause of this phenomenon is due to IMHB, that this atom hydrogen is mainly involved with two oxygen atoms. The hydrogen atom on OHA is trapped between the two groups through an IMHB. But the BDE of the O–HB bond is about the same as phenol, and this hydrogen can be released in reaction with a free radical to neutralize the free radical. BDE of this bond in Cal is lower than Xan, so the antioxidant properties of Cal are higher than Xan. Both Cal-OHA and Cal-OHB radicals are more stable than Xan-OHA and Xan-OHB radicals by amounts of 0.69 and 0.82 kcal/mol, respectively. Cal has an additional methoxide group on the γ-pyrone ring compared to Xan. The methoxy group is considered an electron-donating group. These groups generally reduce the BDE, while the electron-withdrawing groups increase this value. Spin density plots analysis shows that delocalization has occurred for an unpaired electron in OHB species (Fig. 4). It should be emphasized that unlocalized spin density in the radical leads to the easy formation, so the BDE decreases. By spreading the spin density throughout the molecule, the spin on each atom decreases, resulting in reduced reactivity and increased stability.

Fig. 4
figure 4

Maps of spin density for various radicals of calycopterin and xanthomicrol in water

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The spin density distribution in Cal-OHB and Xan-OHB indicates the involvement of ring A and ring C along with α, β unsaturated carbonyl group in unpaired electron delocalization. The spin density plots of radicals show that the pyrone ring plays an important role in the spin distribution and antioxidant properties of the studied compounds. Because free radical scavenging activities always occur in the solvent and because the physiological medium is water, antioxidant calculations in water were also performed. The data in Table 4 show that the BDE of O–H bonds is not highly solvent-dependent. A closer look at the BDE data in the gas phase and water reveals a very valuable point. The dissociation energy of OHB bonds in the gas and aqueous phases is slightly different from 0.77 kcal/mol for Cal and 0.89 kcal/mol for Xan, which completely agrees with the above findings. But the difference is more remarkable for cleaving the OHA bond involved with the IMHB. So for Cal and Xan in the aqueous phase, it is 10.02 and 10.69 kcal/mol lower, respectively. This is due to the reduction of the IMHB process in water, and the carbonyl and hydroxy functional groups form intermolecular hydrogen bonding with water. Antioxidants can also prevent the destructive action of a free radical using the SET-PT mechanism. The antioxidant is converted to a radical cation (reaction (4)). The most crucial factor that affects the IP value of an antioxidant is the extended delocalization of electron spin density and positive charge through the resonance process. IP data and ΔIP values for Cal, Xan, and phenol at the computational level of B3LYP/6–31 + G (d, p) have been presented in Table 4. The IP of both flavonoids is less than phenol, with positive values ΔIP. IP for Cal in water is 6.98 kcal/mol lower than Xan. Both flavonoids based on IP data are effective antioxidants. According to Fig. 2S, radical cation Cal°+ and Xan°+ show the spin density distribution more on ring A and ring C. MEP maps also show a positive charge on ring A. Three methoxy substitutions stabilize the positive charge (Supplementary material).

As mentioned above, the value of IPs can be obtained from the enthalpy changes of reaction (8). Negative HOMO energy levels can also be used for antioxidant investigation. Accordingly, the HOMO orbital energy in water for Cal and Xan phenols is 6.90, 6.11, and 6.20 eV, respectively and, these numbers show that Cal is a more robust antioxidant than the rest. The enthalpy calculations of reaction (8) also confirm this result. The IP values for Cal are 11.40 and 6.98 eV lower than phenol and Xan in water, respectively. This arrangement is better seen in the gas phase (Table 4). It is worth noting that the SET-PT mechanism is highly dependent on the polarity of the environment. Findings have also been reported in the literature so that the SET-PT mechanism performs better in polar solvents such as water and has lower energy than the gas phase [67]. As can be deduced from IP data, the loss of an electron and the formation of a radical cation in water are more favorable for phenol, Cal, and Xan as 51.73, 56.19, and 72.89 kcal/mol, respectively, than for the gas phase. The reason for this is the solvation of radical cation in the polar solvent.

Another mechanism reported for the action of antioxidants in sources is the sequential proton loss electron transfer (SPLET) mechanism (reaction (7)):

  1. 3.

    Sequential proton loss electron transfer (SPLET):

    $$\mathrm{ArOH}\;{\rightleftharpoons\mathrm{ArO}}^-+\mathrm H^+;\quad \mathrm{ArO}^-\rightarrow\mathrm{ArO^\bullet}+\mathrm e$$
    (7)

As seen from reaction (7), the first step is the deprotonation of the antioxidant and the formation of the ArO− anion, which then converts to an ArO˚ radical by losing one electron. The first step is in an equilibrium state, and the more stable conjugate base results in the strong acid of ArOH. As a result, its antioxidant properties will improve. Therefore, the proton affinity (PA) values at 298.15 K in the gas phase were calculated as -ΔH of reaction (8) using Eq. (9).

$$\mathrm{ArO}^-+\mathrm H^+\rightarrow\mathrm{ArOH}$$
(8)
$$\mathrm{PA}=-\Delta \mathrm H={\mathrm H}_{\mathrm{ArO}^-}+{{\mathrm H}_{\mathrm H}}^+-{\mathrm H}_{\mathrm{ArOH}}$$
(9)

As seen in Table 4, the values of PAs are significantly lower than BDEs and IPs. Therefore, from a thermodynamic point of view, the first stage of the SPLET (Deprotonation) mechanism is more desirable in the studied structures. On the other hand, the PA values of Cal-OHB and Xan-OHB groups are lower and more acidic than the hydroxy group of ring A and also phenol, which is due to the stability of the resulting anion (ArO¯) through negative charge delocalization by ring B and pyrone ring (Scheme 2).

Scheme 2
scheme 2

Stabilization of anion of Cal-OHB by resonance

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The negative charge delocalization makes the IMHB bond stronger in the anion than in the neutral form. Comparison of the data in Table 5 with Table 1 confirms that the length of IMHB in the resulting anions is shorter and the bond angle is increasing and reaching a linear state. It is worth mentioning that the IMHB is stronger in the more linear case [68]. The bond length of the carbonyl group in Cal-OHB and Xan-OHB anions is longer than in the neutral state and the CB–CC bond length in the anion is shorter than in the neutral state (Tables 5 and 1), all of which indicate the negative charge distribution in the conjugate system of rings B and C. MEP maps also show the placement negative charge on rings B and C as well as the carbonyl group (Fig. 3S, supplementary material).

Table 5 The calculated structural data of anions of Cal-OHB and Xan-OHB by B3LYP/6–31 + G(d, p) method
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The oxygen radicals are active and reactive radical species produced by various biological processes in the human body and must be neutralized and eliminated with antioxidants. In order to have a deeper understanding of the ability of Cal and Xan to scavenge oxygen radicals (OH˚, HOO˚, and O2˚¯), the reaction of Cal and Xan with these active species using the computational method B3LYP/6–31 + G(d, p) was studied. These reactive oxygen radicals can separate a hydrogen atom from the flavonoid and form a new radical species that are more stable and less reactive (reactions (10)–(12)).

$$\mathrm{ArOH}+\mathrm{HO^\bullet}\rightarrow\mathrm{ArO^\bullet}+{\mathrm H}_2\mathrm O$$
(10)
$$\mathrm{ArOH}+\mathrm{HOO^\bullet}\rightarrow\mathrm{ArO^\bullet}+{\mathrm H}_2{\mathrm O}_2$$
(11)
$$\mathrm{ArOH}+{{\mathrm O}_2}^{\bullet -}\rightarrow\mathrm{ArO}^\bullet+\mathrm{HOO}^-$$
(12)

The Gibbs free energies (ΔGs) of these reactions in water and the gas phase have been given in Table 6. The reaction of the studied compounds with OH˚ is an exothermic reaction and ΔGOH˚ is between 39.00 and 29.97 kcal/mol. In general, hydroxy groups on Cal have a higher trapping ability than Xan hydroxy groups (Table 6). The reaction of the OHB group with the OH˚ radical releases more heat than the OHA group, which is in complete agreement with the data obtained from the antioxidant properties of the mechanisms discussed above.

Table 6 The Gibbs free energies (ΔG) for the interaction of calycopterin and xanthomicrol with HO˚, HOO˚, and O2˚¯ calculated by B3LYP/6–31 + G(d, p) methoda
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As can be seen from the data in Table 6, ΔG for HOO˚ radical reactions is almost endothermic, except for the hydroxy OHB group in the Cal compound. The reaction of all active sites in the compounds Cal and Xan with O2˚¯ is endothermic and the free energy in water is between 16.40 and 35.46 kcal/mol. These results indicate that the OH˚ radical is the most active species for abstraction of the hydrogen radical atom from Cal and Xan. On the other hand, the reactivity of the OHB group with reactive oxygen radicals is the highest.

Conclusions

In this study, for the first time, two valuable flavonoids with high biological properties (Cal and Xan) are comprehensively studied by computational method B3LYP/6–31 + G(d, p) to obtain structural and electronic information in the gas phase as well as water. The computational method was evaluated using 1HNMR and 13CNMR experimental data, and there was excellent agreement between computational and experimental chemical shifts. The optimized structure of these compounds shows the presence of strong intramolecular hydrogen bonds, which incidentally strongly affect their physical and chemical properties, including antioxidant properties. Acceptable aromaticity is seen in the pyrone ring, which was evaluated by HOMA and NICS indices. Calculation and data analysis on electron properties (HOMO and LUMO) and reactivity (electrophilicity and nucleophilicity indices) show that Cal has higher reactivity than Xan. In the last part of this study, the antioxidant properties of these compounds with different mechanisms in the gas and water phases were comprehensively investigated. The results show that these flavonoids have good antioxidant properties. The main reason for this property is the stability of radicals produced by the conjugate system in their structure. The presence of the methoxy as an electron donor group on the pyrene ring of Cal makes its antioxidant properties higher than Xan. Examination of the reactivity of the studied compounds with oxygen radicals showed that a possible reaction to abstract the hydrogen radical from these compounds will occur by OH˚. Given the dependence of antioxidant properties on lipophilicity, the lipophilicity index of these compounds was also calculated and the results confirmed that Cal is more lipophilic than Xan.