Structural and Antioxidant Properties of Compounds Obtained from Fe2+ Chelation by Juglone and Two of Its Derivatives: DFT, QTAIM, and NBO Studies

The chelating ability of juglone and two of its derivatives towards Fe2+ion and the antioxidant activity (AOA) of the resulting chelates and complexes (in the presence of H2O and CH3OH as ligands) in gas phase is reported via bond dissociation enthalpy, ionization potential, proton dissociation enthalpy, proton affinity, and electron transfer enthalpy. The DFT/B3LYP level of theory associated with the 6-31+G(d,p) and 6-31G(d) Pople-style basis sets on the atoms of the ligands and the central Fe(II), respectively, was used. Negative chelation free energies obtained revealed that juglone derivatives possessing the O-H substituent (L2) have the greatest ability to chelate Fe2+ ion. Apart from 1B, thermodynamic descriptors of the AOA showed that the direct hydrogen atom transfer is the preferred mechanism of the studied molecules. NBO analysis showed that the Fe-ligand bonds are all formed through metal to ligand charge transfer. QTAIM studies revealed that among all the Fe-ligand bonds, the O1-Fe bond of 1A is purely covalent. The aforementioned results show that the ligands can be used to fight against Fe(II) toxicity, thus preserving human health, and fight against the deterioration of industrial products. In addition, most of the complexes studied have shown a better AOA than their corresponding ligands.


Introduction
Juglone (5-hydroxy-1,4-naphthoquinone) is a phenolic allelochemical responsible for walnut allelopathy and the inhibitory effect of black walnut (Juglans nigra) in associated plant species [1,2]. It is a natural product that has shown a multitude of properties that are deemed beneficial in the fields of medicine, farming and aquaculture [3]. In the field of medicine, juglone has been shown to possess good antifungal properties, which are similar to those of some commercially available antifungal agents [4,5]. In addition, it has been shown that juglone could be a promising chemopreventive agent for human intestinal neoplasia [6]. Furthermore, its antitumour [7][8][9][10][11] and antibacterial properties [5,12] have been reported. Some experimental and theoretical studies have also emphasized the ability of juglone and its derivatives to inhibit the degradation of cells and foods by offering resistance to oxygen and its reactive species (known as antioxidant activity (AOA)) [10,13,14].
Antioxidants are capable of chelating transition metal ions (especially Fe 2+ and Cu + ) leading to the formation of stable complexes, thereby preventing these metals from participating in free radical generation [15][16][17][18], but the mechanism has not been studied exhaustively. The production of free radicals can lead to lipid peroxidation, protein modification, and DNA damage. Among the transition metals, iron is the most dangerous lipid oxidation prooxidant due to its high reactivity. In fact, the ferrous state of iron accelerates lipid oxidation by breaking down hydrogen and lipid peroxides to reactive free radicals via the Fenton reaction [19], thus 2 Bioinorganic Chemistry and Applications degrading the quality of foods and causing several diseases [20]. Antioxidants are well known radical scavengers that are largely used to fight against these negative effects of free radicals, via the above mentioned mechanism. Besides removal of the metals, metal-chelating compounds can also alter their redox potentials, rendering them inactive. The use of natural metal chelators instead of the synthetic counterparts which may present some toxicity problems should be encouraged [21]. Several experimental and theoretical studies have been devoted to the elucidation of the metal-chelation mechanism of AOA [19,[21][22][23][24][25].
It has been demonstrated experimentally that deprotonated juglone has the capacity to chelate Fe 2+ [13]. A Theoretical study to complement this experimental result is warranted. To the best of our knowledge, no such theoretical work exists in the literature. In this paper, we aim to investigate the Fe 2+ chelating ability of neutral juglone and two of its derivatives (shown in Figure 1), as well as evaluate the AOA of the resulting compounds by the means of density functional theory (DFT) [26]. This work is therefore expected to contribute toward the development of new antioxidants, which has been the ambition that has attracted a great deal of researchers' attention in recent years, owing to the significance of antioxidants in biological processes as well as the processes in the food, pharmaceutical, and material industries. Specifically, the chelation of Fe 2+ by three antioxidants in their neutral forms is studied at DFT/B3LYP level theory. The main antioxidant studied is juglone (L 1 ), and the rest are its derivatives obtained by replacing the hydrogen atom ortho to the hydroxyl group of juglone either by OH (L 2 ) or by CN (L 3 ) groups, which are electron donating (EDG) and withdrawing (EWG) groups, respectively. The structural and electronic parameters of the resulting chelates or complexes have been analyzed, followed by the evaluation of the AOA of all compounds studied ( Figure 1) by means of bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA) and electron transfer enthalpy (ETE) [17,18]. Our main objective here is to study the effect of iron(II) chelation on the AOA of the three ligands (L 1 , L 2 , and L 3 ).

Computational Details and
Theoretical Background 2.1. Computational Details. All calculations were carried out using Gaussian 09W [27]. The input structures were prepared using the GaussView 5.0.8 program [28]. The DFT method which was designed especially for the study of coordination compounds [24] was associated with the B3LYP hybrid functional in this research endeavor [29]. In addition, DFT has been chosen because it has been used successfully to study radical scavenging activities of phenolic compounds [30][31][32]. Also, when compared to ab initio methods, DFT is very rapid and is often said to ally precision and the rapidity [33]. Faced with limited computational resources and large molecular sizes, we used a mixed basis set comprising the 6-31G * basis for the central metal ion and the 6-31+G * * basis for every other element in the molecules studied. In addition, mixed basis sets have been recently employed for many studies on complexes and have been shown to speed up calculations, without altering the quality of theoretical results [21,34,35]. All computations on the closed shell systems were performed using the Restricted Kohn-Sham formalism while the Unrestricted Kohn-Sham formalism was adopted in open shell systems, in order to reduce spin contamination [36]. Ground-state geometries for all complexes have been fully optimized without any symmetry constraints. Vibrational frequency calculations have further been undertaken on the optimized geometries in order to confirm that the resulting equilibrium geometries were minima (no negative frequency) on the potential energy surface. Central metal-ligand charge transfer was evaluated by means of Natural Bond Orbital (NBO) analysis [37] as implemented in Gaussian 09. The Quantum Theory of Atom in Molecules (QTAIM) proposed by Bader [38] was used to evaluate the nature of all metalligand bonds, with the aim of determining their degree of covalency. QTAIM analysis was performed as implemented in multiwfn [39].

Theoretical
Background. The chelates [FeL ] 2+ ( = 1, 2 and 3) ( Figure 1) optimized in this work are presumed to be formed according to The complexes [FeL (X) 4 ] 2+ , ( = 1, 2 and 3; and X = H 2 O or CH 3 OH) are presumed to be formed according to The use of water and methanol molecules as other ligands is because of the difficulty to find isolated form of Fe 2+ and the abundance of such polar molecules in organisms [23]. The effect of multiplicity on the stability of all the nine chelates and complexes resulting from both (1) and (2) as presented in Figure 1 was first investigated. This was done via geometry optimizations of all the input structures in the singlet and quintet states based on the possible number of unpaired electrons of the central Fe 2+ ion, in order to determine the geometry with the lowest ground-state energy. The binding energies (Δ int ), free energies (Δ ), and enthalpies (Δ ) of formation of the most stable geometries at standard conditions were calculated as follows: In these equations , , and stand for the thermal energies, enthalpies, and free energies of formation of the respective species. Due to the absence of X ligands in the chelates, X , X , and X terms are nonexistent in their expressions for Δ int , Δ , and Δ .
Using the most stable optimized geometry of each compound, the usual schemes of hydrogen transfer by antioxidants and the related parameters were calculated. These include the following. (i) The Direct Hydrogen Atom Transfer (HAT). The direct hydrogen atom transfer (HAT) is the mechanism in which the phenolic H atom is transferred in one step by the antioxidant. BDE, which is the parameter used to evaluate HAT, is the reaction enthalpy for the mechanism. This parameter has been evaluated on all the hydroxyl groups of juglone and its two derivatives studied. The lower the BDE, the easier the dissociation of the phenolic O-H bond, as elucidated in (6) and (7) where X-H represents the ligands, chelates, or complexes and X • is the radical compound resulting from the H atom abstraction: (ii) The Sequential Electron Transfer Proton Transfer (SETPT).
Here, an electron abstraction from X-H (characterized by the ionization potential (IP) of X-H) is followed by a proton transfer (characterized by the proton dissociation enthalpy (PDE) of the cationic radical X-H +• ) as shown in the following:

(iii) The Sequential Proton Loss Electron Transfer (SPLET).
Here, a proton loss is followed by an electron transfer. The reaction enthalpy of the first step in the SPLET mechanism corresponds to the proton affinity (PA) of X − . The reaction enthalpy of the next step, the transfer of an electron by X − , is denoted as electron transfer enthalpy (ETE) and is calculated using the following equations: The free energies of all aforementioned descriptors have also been calculated and denoted BDFE (bond dissociation free energy), IPFE (ionization potential free energy), PDFE (proton dissociation free energy), PAFE (proton affinity free energy), and ETFE (electron transfer free energy).

Effect of Multiplicity on Electronic Energies.
Owing to the intrinsic relationship between spin multiplicity and ligand field, the effect of multiplicity on the total energies of the chelates and complexes studied ( Figure 1) has been investigated. This was done in order to select the multiplicities of the molecules studied that correspond to their lowest It can be seen from Table 1 that the singlet state of 1A and 1B which are complexes of L 1 , are the most stable, whereas the quintet state is instead the most stable in the case of its MeOH containing complex (1C). It is obvious from the table that among the complexes of L 2 , 2A has the lowest energy singlet state, while 2B and 2C containing H 2 O and MeOH ligands, respectively, are constrained to the quintet state. The three complexes of L 3 (3A, 3B, and 3C) are restricted to the quintet state. From the foregoing observations, the rest of this work has been limited to the singlet states of 1A, 1B, and 2A and the quintet states of 1C, 2B, 2C, 3A, 3B, and 3C.

Iron(II) Chelation
Capacity of the Ligands. The capacity of juglone and its derivatives to chelate Fe(II) has been evaluated at 298.15 K and 1 atm via Gibbs free energy of formation calculations on the complexes, as shown in (5). The enthalpies of formation of the complexes as well as their binding energies were also calculated, and the results are presented in Table 2.
By inspection of Table 2 it can be seen that the free energies of formation of the three chelates (1A, 2A, and 3A) are negative, meaning that their formation is spontaneous. Among the chelates, the computed free energies increase in the order 2A < 1A < 3A, showing that L 2 has the highest Fe 2+ ion binding capacity and L 3 has the lowest. This result is attributable to the fact that the presence of the EDG (the -OH group of L 2 ) increases the electron density on the ligating oxygen atoms, thus increasing the metal-ligand interaction. The reverse is observed in presence of -CN (3A). The negative values of the binding energies have proven that the complexes investigated are stable [25], corroborating the fact that their formation is thermodynamically feasible. The values of the enthalpies of formation of all complexes are also negative, showing that their formation is exothermic at 298.15 K and under 1 atm.

Geometric Parameters.
This section is dedicated to Feligand and O 1 -H bond lengths obtained from the optimized geometries of the complexes presented in Figure 1. It is clear from this figure that the chelates 1A, 2A, and 3A are perfectly planar, and the complexes 2B, 2C, 3B, and 3C are octahedral. The values of the bond lengths around the central metal are presented in Table 3.
The atomic numbering adopted in Table 3 is as presented in Figure 1. The length of the O 1 -Fe bond in each chelate increases in the order, 2A < 1A < 3A, which is the same order of their Δ of formation. Hence, the values of Δ and the O 1 -Fe bond lengths for the chelates are directly proportional. It can also be observed from Table 3  The O 2 -Fe bond lengths have been found to be shorter than the O 1 -Fe counterparts in all chelates investigated. The lengths of the former have also been found to increase in presence of H 2 O and MeOH as ligands. Our results are in good agreement with those in the literature for similar studies on three naturally occurring phenolic antioxidants [23].
The lengths of all the X n -Fe bonds ( = 1, 2, 3 and 4; X = H 2 O or MeOH) are larger than 2 >. Among the complexes of juglone, that possessing MeOH ligands (1C) has  the longest X n -Fe bond, and its formation is found to be the least spontaneous.  Table 3 with * ) are shorter than those of O 1 -H groups, due to the fact that they are not engaged in any hydrogen bond.  Table 4.

Thermodynamic Descriptors of Antioxidant
It is evident in Table 2 The BDE value of the additional O-H substituent in L 2 , designated by an asterisk ( * ) in Table 3, is found to be lower than that of the O 1 -H bond, whereas the reverse is observed for its complexes. Therefore, the H atom of the O 1 -H bond in the complexes is more available for a radical attack.
The trend in the BDFE values of the molecules studied is similar to that of the BDE values. As a general observation, the BDFE values are found to be lower than the corresponding BDE values. The differences between the values of these descriptors are in the range 21-37 kJ/mol for the complexes studied. Furthermore, the BDFEs are all positive, signifying that the HAT mechanism is not spontaneous for all the complexes and ligands studied. These results are in good agreement with those found in the literature [23,40].

SETPT Mechanism.
The first and the determining step in this mechanism is electron transfer which is characterized by the associated IP of the antioxidants. The calculated adiabatic IP values of the complexes and ligands are presented in Table 4. It is clear in Table 4 that Fe 2+ chelation leads to an increase in the IPs of L 1 , L 2 , and L 3 . This result is in good agreement with some literature findings [21]. The IP values of the chelates have been found to increase in the order 3A < 1A < 2A. Surprisingly from this ranking, 3A possessing EWG exhibits the greatest electron transfer capability, while 2A containing EDG together with a hydrogen bond shows the least electron transferability.
While the presence of water ligands increases the IP of 1A, the MeOH ligands instead lead to its reduction. These ligands have been found to have a similar effect on the BDE of 1A as explained in Section 3.4.1. In the case of 2A, the opposite trend is observed wherein the presence of the water ligands instead leads to a reduction in its IP, whereas the MeOH ligands result in its increment. The introduction of either water or MeOH ligands reduces the IP value of 3A in which case the effect of the MeOH is found to be the greatest. The presence of these ligands similarly affects the BDE of 3A and its complexes.
Unlike BDFE, the values of IPFE for the complexes are generally found to be slightly higher than their IP, as shown in Table 4. The only exceptions to this trend are the IPFEs of 1A and 2A which are lower than IP (by 2 kJ/mol) and equal to IP, respectively.
The PDE values of the complexes displayed in Table 4 are all lower than those of the ligands. We have attributed this to the fact that the cation radicals of the complexes are less stable and are therefore more reactive than those of the ligands, as shown by the IP values presented in this table. The PDE values of the chelates are smaller than those of the free ligands as well as those of complexes. The PDE values of 2A (−539 kJ/mol) and 3A (−233 kJ/mol) are negative, which is an indication that the proton transfer process of their cation radicals is exothermic. Since the PDFE values of the chelates (1A, 2A, and 3A) are all negative, it can be concluded that the proton transfer process by their cation radicals is spontaneous, which is not the case for the rest of the compounds in Table 4.

SPTET Mechanism.
This mechanism begins with the transfer of a proton, designated as PA. This is followed by an electron transfer from the resulting anion, also designated as ETE. The values of PA and ETE for the ligands and their complexes as well as their free energies (PAFE and ETFE) calculated in this work are presented in   Table 4. It can be seen from Table 4 that the values of PAFE and PA for the chelates and complexes follow the same trend even though the PAFEs are lower than PAs. In fact, the differences between these PAs and PAFEs for the molecules studied range from 104 to 228 kJ/mol for 1A and 3C, respectively. However, both the PAs and PAFEs are higher than the PDEs and PDFEs, respectively, due to the high reactivity of the cationic radicals. As evidenced in Table 4, the values of ETE and ETFEs are, respectively, lower than those of IP and IPFEs.

Thermodynamically Preferred Mechanism.
In order to select the thermodynamically preferred mechanism among the antioxidant mechanisms studied, the free energies of the first step of each mechanism have been compared. To facilitate this process, free energies for all the molecules investigated were plotted on the same axes as shown in Figure 2.
It is clear from this figure that the preferred mechanism for all the ligands as well as their chelates and complexes is the HAT, since each of these compounds exhibits the lowest free energy for this process. In the case of 1B, the SPLET is the most preferred mechanism since the free energy for PA is lower than that for direct HAT. While the second preferred antioxidant mechanism for the ligands is SETPT, that for the chelates and complexes is SPLET. In the case of 1B, the second preferred mechanism is HAT.

Spin Density Analysis.
The spin density is the most important parameter that correlates with the AOA of antioxidants [41]. It characterizes the stability of free radicals, since the energy of a free radical can be efficiently decreased if the unpaired electrons are highly delocalized through the conjugated system after hydrogen abstraction [5]. In Figure 3 the Mulliken spin density values on selected atoms of the chelates and complexes studied are presented.
Analyses of the structures in this figure have revealed a huge concentration on Fe(II) and the oxygen atom from which the H atom transferred is abstracted. Among the radicals formed from the chelates, that of 2A, the chelate with the lowest BDE (111 kJ/mol), is found to have the lowest spin density value on the central metal (1.99). On the other hand, the complex 1B, among all the compounds studied, has shown the lowest spin density value on the central metal (0.93). As a general observation for the rest of the complexes, the spin densities on the central Fe 2+ ions are in the range 3.90-4.30. The spin density delocalization in all molecules studies has been greatly contributed by the carbon atoms in the two rings of juglone and its derivatives. As such, these carbon atoms significantly contribute to the stabilization of the radicals.

NBO Analysis.
Natural Bond Orbital (NBO) refers to a suite of mathematical algorithms for analyzing electronic wave functions in terms of localized Lewis-like chemical bonds [37,38]. In the current study, the strength of metalligand interactions has been estimated by means of the second-order perturbation theory, as applied in NBO analysis. For each chelate and complex, the stabilization energy or second-order perturbation energy, (2) associated with the  delocalization from → (( ) and ( ) being the donor and acceptor orbitals, resp.), was estimated using Here, is the orbital occupancy, , are diagonal elements, and is the off-diagonal NBO Fock matrix element. Values of (2) are proportional to the intensities of NBO interactions, and the greater the electron donating tendency from donor to acceptor NBOs, the larger the (2) values and the more intensive the interaction between the electron donors and the electron acceptors [42,43]. In Table 5, the values of (2) (greater than 5 kJ/mol) for the ligand-metal charge transfer are reported, as well as the NPA charges of the central metal ions. It is worth noting that the values of (2) are lower than 3 kJ/mol for metal-ligand charge transfer, signifying that these interactions are very weak and therefore ignored in this paper. It can be observed from (2) values in Table 5 that, with the exception of 1A, the interactions between the lone pairs on O 2 and the antibonding LP * on the metal ion are stronger than those between the lone pairs on O 1 and the antibonding LP * on Fe. In addition, the presence of water and methanol ligands which also interact strongly with Fe strengthens these ligand-metal interactions, thus accounting for the increment in the absolute values of the interaction energies as previously observed in Section 3.2 ( Table 2). Among the compounds investigated, the strongest NBO interaction (that with the highest energy) is LP(2) O 1 → LP * (4) Fe in 1A, with a stabilization energy of 71.83 kJ/mol.
The atomic charges on Fe (

Analysis of Metal-Ligand Bonds by the QTAIM.
QTAIM is nowadays a strong tool used by quantum chemists to analyze the nature and strength of weak interactions [38]. In this work, the analysis of electron density ( ( )) and its Laplacian (∇ 2 ( )) for the metal-ligand bonds has been performed by the means of the Bader QTAIM, as implemented in multiwfn. According to this theory, the sign of the Laplacian of the electron density (∇ 2 ( )) at a bond critical point reveals whether charge is concentrated as in covalent bond interactions (∇ 2 ( ) < 0) or depleted as in closed shell (electrostatic) interactions (∇ 2 ( ) > 0) [41]. Specifically, for nonpolar and weakly polar covalent bonds ∇ 2 ( ) < 0 and − ( )/V( ) < 1. For intermediate interactions we have ∇ 2 ( ) > 0, but − ( )/V( ) < 1; and for closed shell interactions ∇ 2 ( ) > 0 and − ( )/V( ) > 1. Here, ( ) is the kinetic energy density at the critical point (always positive), while V( ) is the potential energy density at the critical point (always negative) by definition [44]. The values of ( ), ∇ 2 ( ), and − ( )/V( ) for all the metal-ligand bonds, as well as for the O-H bonds, are presented in Table 6. From Table 6, it can be seen that each Fe-O bond has a positive ∇ 2 ( ) value except that of the O 1 -Fe bond of 1A which is negative (−0.108). This implies that the said  Table 6 have clearly shown that the O-H bonds are all covalent.
The topological analyses of the complexes of L 2 have confirmed the hydrogen bond O 1 -H⋅ ⋅ ⋅ O earlier observed in their optimized geometries ( Figure 1). Surprisingly, the topological analysis of the complexes of L 3 revealed the existence of a Van der Waals (VDW) interaction between the hydrogen atom of the O-H group and the carbon atom of the -CN group as illustrated in Figure 4. This VDW interaction justifies the large O 1 -H bond length for the complexes of L 3 (see Table 3). Hence, the VDW interaction has caused the elongation and weakening of the O-H, resulting in the relatively low BDE values observed for these complexes.

Conclusion
A DFT/B3LYP study has been performed herein in order to determine the chelating ability of neutral juglone and two of its derivatives towards Fe 2+ . The AOA of the resulting chelates and mixed ligand complexes with either H 2 O or CH 3 OH as another ligand were also evaluated. Precisely, the Gibbs free energies, the binding energies, and NBO analysis were used to evaluate the ability of L 1 , L 2 , and L 3 to chelate Fe(II) ions. QTAIM was also used to investigate the degree of covalency of the metal-ligand bonds. The usual thermodynamic parameters BDE, IP, PDE, PA, and ETE and their free energies used in predicting the radical scavenging activities of antioxidants were used to study the effect of Fe 2+ chelation on the AOA of the ligands, chelates, and complexes.
The negative values of Δ and Δ int have indicated that the three ligands are capable of chelating the ferrous state of iron. These parameters have been relatively modified by the presence of H 2 O or CH 3 OH ligands in the complexes. NBO analysis has showed that metal-ligand bonds in the chelates and complexes result from metal-to-ligand charge transfer. Moreover, the second-order perturbation energy corresponding to the O 2 -Fe bonds of all the molecules with the exception of 1A have been found to be higher than those of the O 1 -Fe bond indicating that the former bonds are relatively stronger than the latter. QTAIM showed that, apart from the O 1 -Fe bond in 1A which is purely covalent, nearly all the O 1 -Fe and O 2 -Fe bonds of the rest of the molecules are intermediate type interactions. Also, the X i -Fe ( = 1, 2, 3 and 4) bonds in 1C, 2B, 2C, 3B, and 3C (except the weak X 1 -Fe interaction in 3C) are intermediate type interactions, whereas the X i -Fe ( = 1, 2, 3 and 4) bonds of 1B result from weak interactions.
Our results also revealed that while the chelation of Fe(II) reduces the BDE of L 2 and L 3 , that of L 1 instead increases. Furthermore, the reduction in the O 1 -H bond length in 1B and the presence of H 2 O ligands lead to an increase in the BDE of the chelate, while the addition of four CH 3 OH ligands to 1A instead decreases its BDE. The presence of H 2 O and CH 3 OH ligands increases the BDE of 2A but decreases that of 3A. QTAIM has revealed a VDW interaction between the H atom of the hydroxyl group of L 3 and the C atom of its CN group which elongates and weakens the O-H bond of the complexes of L 3 , conferring them relatively low BDEs. On the other hand, BDE of 2B has been found to be the lowest owing to the presence of a hydrogen bond which stabilizes its radical. The IPs of the three ligands have been found to increase following their chelation of Fe 2+ , an observation which agrees with those in the literature. With the exception of 2C, the PA values of all the complexes and chelates studied have been found to be lower than those of their corresponding ligands. Analyses of the free energies of the first step of each hydrogen transfer mechanism revealed that the direct HAT is the preferred mechanism of the radical scavenging activity of nearly all the molecules studied in the present work. Solvent effects are going to be addressed in a subsequent article.