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

Authors: Aymard Didier Tamafo Fouegue; Julius Numbonui Ghogomu; Désiré Bikélé Mama; Nyiang Kennet Nkungli; Elie Younang
Journal: Bioinorganic Chemistry and Applications
 (2016)

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## Abstract

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 from1B, 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 of1A 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.


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## Body

## 1. 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 [7–11] 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 Fe2+ and Cu+) leading to the formation of stable complexes, thereby preventing these metals from participating in free radical generation [15–18], 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 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, 21–25].It has been demonstrated experimentally that deprotonated juglone has the capacity to chelate Fe2+ [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 Fe2+ 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 Fe2+ by three antioxidants in their neutral forms is studied at DFT/B3LYP level theory. The main antioxidant studied is juglone (L1), and the rest are its derivatives obtained by replacing the hydrogen atomortho to the hydroxyl group of juglone either by OH (L2) or by CN (L3) 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 (L1, L2, and L3).Figure 1
Optimized geometries of the studied molecules, obtained by applying the B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E) level of theory.


## 2. 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 [30–32]. Also, when compared toab 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
-
31
G
∗ 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 metal-ligand bonds, with the aim of determining their degree of covalency. QTAIM analysis was performed as implemented in multiwfn [39].


### 2.2. Theoretical Background

The chelatesF
e
L
i
2
+ (i
=
1, 2 and 3) (Figure 1) optimized in this work are presumed to be formed according to(1)
F
e
2
+
+
L
i
⟶
F
e
L
i
2
+The complexes F
e
L
i
X
4
2
+, (i
=
1, 2 and 3; and X = H2O or CH3OH) are presumed to be formed according to(2)
F
e
2
+
+
L
i
+
4
X
⟶
F
e
L
i
X
4
2
+The use of water and methanol molecules as other ligands is because of the difficulty to find isolated form of Fe2+ 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 Fe2+ ion, in order to determine the geometry with the lowest ground-state energy. The binding energies (Δ
E
i
n
t), free energies (
Δ
G
), and enthalpies (
Δ
H
) of formation of the most stable geometries at standard conditions were calculated as follows: (3)
Δ
E
i
n
t
=
E
c
o
m
p
-
E
L
-
4
E
X
-
E
F
e
2
+
,
(4)
Δ
H
=
H
c
o
m
p
-
H
L
-
4
H
X
-
H
F
e
2
+
,
(5)
Δ
G
=
G
c
o
m
p
-
G
L
-
4
G
X
-
G
F
e
2
+
.In these equations E, H, and G 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, E
X, H
X, and G
X terms are nonexistent in their expressions for Δ
E
i
n
t, Δ
H, and Δ
G.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:(6)
X
-
H
⟶
X
•
+
H
•
(7)
B
D
E
=
H
H
•
+
H
X
•
-
H
X
-
H(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:(8)
X
-
H
⟶
X
-
H
+
•
+
e
-
(9)
I
P
=
H
X
-
H
+
•
+
H
e
-
-
H
X
-
H
(10)
X
-
H
+
•
⟶
X
•
+
H
+
(11)
P
D
E
=
H
X
•
+
H
H
+
-
H
X
-
H
+
•(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: (12)
X
-
H
⟶
X
-
+
H
+
(13)
P
A
=
H
X
-
+
H
H
+
-
H
X
-
H
(14)
X
-
⟶
X
•
+
e
-
(15)
E
T
E
=
H
X
•
+
H
e
-
-
H
X
-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).


## 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 [30–32]. Also, when compared toab 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
-
31
G
∗ 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 metal-ligand bonds, with the aim of determining their degree of covalency. QTAIM analysis was performed as implemented in multiwfn [39].


## 2.2. Theoretical Background

The chelatesF
e
L
i
2
+ (i
=
1, 2 and 3) (Figure 1) optimized in this work are presumed to be formed according to(1)
F
e
2
+
+
L
i
⟶
F
e
L
i
2
+The complexes F
e
L
i
X
4
2
+, (i
=
1, 2 and 3; and X = H2O or CH3OH) are presumed to be formed according to(2)
F
e
2
+
+
L
i
+
4
X
⟶
F
e
L
i
X
4
2
+The use of water and methanol molecules as other ligands is because of the difficulty to find isolated form of Fe2+ 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 Fe2+ ion, in order to determine the geometry with the lowest ground-state energy. The binding energies (Δ
E
i
n
t), free energies (
Δ
G
), and enthalpies (
Δ
H
) of formation of the most stable geometries at standard conditions were calculated as follows: (3)
Δ
E
i
n
t
=
E
c
o
m
p
-
E
L
-
4
E
X
-
E
F
e
2
+
,
(4)
Δ
H
=
H
c
o
m
p
-
H
L
-
4
H
X
-
H
F
e
2
+
,
(5)
Δ
G
=
G
c
o
m
p
-
G
L
-
4
G
X
-
G
F
e
2
+
.In these equations E, H, and G 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, E
X, H
X, and G
X terms are nonexistent in their expressions for Δ
E
i
n
t, Δ
H, and Δ
G.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:(6)
X
-
H
⟶
X
•
+
H
•
(7)
B
D
E
=
H
H
•
+
H
X
•
-
H
X
-
H(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:(8)
X
-
H
⟶
X
-
H
+
•
+
e
-
(9)
I
P
=
H
X
-
H
+
•
+
H
e
-
-
H
X
-
H
(10)
X
-
H
+
•
⟶
X
•
+
H
+
(11)
P
D
E
=
H
X
•
+
H
H
+
-
H
X
-
H
+
•(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: (12)
X
-
H
⟶
X
-
+
H
+
(13)
P
A
=
H
X
-
+
H
H
+
-
H
X
-
H
(14)
X
-
⟶
X
•
+
e
-
(15)
E
T
E
=
H
X
•
+
H
e
-
-
H
X
-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).


## 3. Results and Discussion

### 3.1. 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 (Figure1) has been investigated. This was done in order to select the multiplicities of the molecules studied that correspond to their lowest energy (or most stable) geometries. In this regard, the singlet and quintet states corresponding to geometries in which the central Fe2+ ion has no unpaired electron and four unpaired electrons, respectively, were investigated for each chelate and complex. S
2 values, calculated for all quintet states, are in the range of 6.0001–6.0006, which is close to the value of 6.000, corresponding to the pure quintet wave function. The total energies of the said states are displayed in Table 1. In this table, the complexes of L1 (juglone), L2 (the derivative with the OH group), and L3 (the derivative with the CN group) are denoted by1,2, and3, respectively. The chelates are represented by the symbolYA (where Y
=
1, 2 or 3). Similarly, the complexes containing the ligands H2O and MeOH are, respectively, represented byYB andYC.Table 1
Energies (Hartree) of the compounds related to their multiplicities obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
Spin multiplicity
Singlet
Quintet
[Fe(L1)]
2+
1A
−1873.21293208
−1873.12426700
[Fe(L1)(OH2)4
]
2+
1B
−2179.23172776
−2178.98173479
[Fe(L1)(CH3OH)4
]
2+
1C
−2336.10729027
−2336.15725602
[Fe(L2)]
2+
2A
−1948.45209999
−1948.33220631
[Fe(L2)(OH2)4
]
2+
2B
−2254.13720775
−2254.18434320
[FeL2(CH3OH)4
]
2+
2C
−2411.68291413
−2411.72799125
[Fe(L3)]
2+
3A
−1965.22170297
−1965.31620465
[Fe(L3)(OH2)4
]
2+
3B
−2271.13120555
−2271.17906337
[Fe(L3)(CH3OH)4
]
2+
3C
−2428.30591545
−2428.35653764It can be seen from Table1 that the singlet state of1A and1B which are complexes of L1, 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 L2,2A has the lowest energy singlet state, while2B and2C containing H2O and MeOH ligands, respectively, are constrained to the quintet state. The three complexes of L3 (3A,3B, and3C) are restricted to the quintet state. From the foregoing observations, the rest of this work has been limited to the singlet states of1A,1B, and2A and the quintet states of1C,2B,2C,3A,3B, and3C.


### 3.2. 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.Table 2
Binding energy (Δ
E
i
n
t), enthalpy (Δ
H) and free energy change (Δ
G) of formation of the complexes all in kJ/mol, obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
Molecule
Δ
H
Δ
G
Δ
E
i
n
t
1A
−1000,08
−963,77
−997,60
1B
−4332,08
−1500,67
−4319,69
1C
−6230,60
−774,45
−6218,19
2A
−8900,34
−986,77
−8897,86
2B
−11483,96
−791,41
−11471,56
2C
−15004,90
−1677,43
−14992,50
3A
−16395,51
−609,87
−16393,04
3B
−19323,20
−757,95
−19310,81
3C
−21880,49
−668,61
−21868,09By inspection of Table2 it can be seen that the free energies of formation of the three chelates (1A,2A, and3A) are negative, meaning that their formation is spontaneous. Among the chelates, the computed free energies increase in the order2A <1A <3A, showing that L2 has the highest Fe2+ ion binding capacity and L3 has the lowest. This result is attributable to the fact that the presence of the EDG (the -OH group of L2) 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 presence of H2O ligands decreases Δ
G of formation of1A, while the MeOH ligands rather result in its increment. In the case of2A, the opposite of the previous observation is evidenced in Table 2, implying that while the presence of water ligands increases Δ
G of formation of2A, the presence of the methanol ligands instead leads to its reduction. The presence of H2O and MeOH ligands in3A decreases its Δ
G by 148 and 58 kJ/mol, respectively.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.


### 3.3. Geometric Parameters

This section is dedicated to Fe-ligand and O1-H bond lengths obtained from the optimized geometries of the complexes presented in Figure 1. It is clear from this figure that the chelates1A,2A, and3A are perfectly planar, and the complexes2B,2C,3B, and3C are octahedral. The values of the bond lengths around the central metal are presented in Table 3.Table 3
Metal-ligand and O-H bond lengths (Ǻ) of the complexes obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
O
1-H
O
1-Fe
O
2-Fe
X
1-Fe
X
2-Fe
X
3-Fe
X
4-Fe
1A
0.979
1.870
1.785
—
—
—
—
1B
0.971
1.982
1.898
2.029
2.021
2.023
2.024
1C
0.977
2.185
1.991
2.140
2.080
2.187
2.111
2A
0.9930.972∗
1.863
1.796
—
—
—
—
2B
0.9910.976∗
2.145
1.994
2.088
2.145
2.140
2.139
2C
0.9770.969∗
2.221
2.010
2.196
2.117
2.186
2.137
3A
0.997
1.963
1.854
—
—
—
—
3B
0.986
2.167
1.987
2.090
2.145
2.138
2.137
3C
0.984
2.188
1.994
2.143
2.075
2.176
2.102The atomic numbering adopted in Table3 is as presented in Figure 1. The length of the O1-Fe bond in each chelate increases in the order,2A <1A <3A, which is the same order of their Δ
G of formation. Hence, the values of Δ
G and the O1-Fe bond lengths for the chelates are directly proportional. It can also be observed from Table 3 that the presence of H2O and MeOH ligands increases the values of the O1-Fe bond lengths in all the chelates. Some discrepancies between the O1-Fe bond lengths in1A,2A,3A relative to those in the corresponding methanol complexes of 0.315, 0.358, and 0.225 Ǻ, respectively, have been observed.The O2-Fe bond lengths have been found to be shorter than the O1-Fe counterparts in all chelates investigated. The lengths of the former have also been found to increase in presence of H2O 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 Xn-Fe bonds (n
=
1, 2, 3 and 4; X = H2O or MeOH) are larger than 2 Ǻ. Among the complexes of juglone, that possessing MeOH ligands (1C) has the longest Xn-Fe bond, and its formation is found to be the least spontaneous.From inspection of the O1-H bonds of the three chelates, the ranking1A <2A <3A can be made, showing that the bond is the longest in3A with a length of 0.997 Ǻ. This is surprising because the O1-H group of2A is involved in hydrogen bonding as depicted in Figure 1, which should elongate its O1-H bond rendering it the longest relative to those of the other chelates. Since the AOA is greatly influenced by the length of the phenolic O-H bond, these differences in O1-H bond lengths could have great consequences on the values of associated thermodynamic descriptors of AOA. Still from these findings, it can be predicted that among the chelates,1A which has the shortest O1-H bond length should have the highest associated BDE value. The presence of the H2O and MeOH ligands is found to slightly decrease the length of the said bond. The presence of the methanol ligands has a more significant effect on the O1-H bond length of2A. Indeed, the presence of the methanol ligand is found to reduce the length of the bond by 0.016 Ǻ. This is attributable to hydrogen bond strength reduction in2B. The presence of the water ligands in2A has virtually no effect on the length of the O1-H bond. The presence of both ligands individually reduces the length of the hydroxyl link of3A by 0.011 and 0.013 Ǻ, respectively.The lengths of the hydrogen bonds of1B,2B, and3B are, respectively, 1.909, 1.920, and 1.961 Ǻ, which are in good agreement with those of the O1-H groups of the said molecules, since they are inversely proportional to the O1-H bond length. The lengths of the additional O-H bonds in2A,2B, and2C (marked in Table 3 with ∗) are shorter than those of O1-H groups, due to the fact that they are not engaged in any hydrogen bond.


### 3.4. Thermodynamic Descriptors of Antioxidant Properties

#### 3.4.1. HAT Mechanism

The calculated gas phase BDE values of the molecules investigated are presented in Table4.Table 4
Values of BDE, BDFE, IP, IPFE, PDE, PDFE, PA, PAFE, ETE and ETFE of the compounds studied, all in kJ/mol obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
BDE
BDFE
IP
IPFE
PDE
PDFE
PA
PAFE
ETE
ETFE
L1
417
377
834
824
899
864
1422
1386
312
309
1A
608
575
1919
1917
6
−23
1014
910
1041
1038
1B
1001
977
2132
2142
186
154
793
629
1710
1720
1C
233
211
1299
1309
251
222
898
679
897
904
L2
380359∗
341323∗
805
795
892
874
13771361∗
13661330∗
319314∗
315312∗
2A
111798∗
74765∗
1967
1967
−539
−574
11501008∗
1039981∗
4141107∗
4071104∗
2B
271358∗
250327∗
1338
1351
251
218
868658∗
685636∗
9281016∗
9371009∗
2C
12401324∗
12171301∗
2255
2273
245
262
19041648∗
16781625∗
908993∗
910994∗
L3
421
381
874
863
864
828
1366
1353
371
368
3A
283
250
1833
1979
−233
−410
570
447
1176
1175
3B
248
232
1375
1394
191
157
829
641
953
963
3C
234
211
1308
1319
243
211
881
653
924
930
∗ refers to the parameters related to the O-H substituent present on L2.It is evident in Table2 that the BDEs of the O1-H bond for the chelates increase in the order2A <3A <1A. The fact that the BDE of O1-H is the lowest in2A suggests that the hydrogen bond in which this group is engaged weakens the O1-H bond in this molecule. In addition, the phenoxy radical formed due to HAT by2A is stabilized by an O-H⋯O1 hydrogen bond, further strengthening the AOA of2A. The low BDE of3A relative to that of1A can be explained by the fact that its O1-H bond is longer and therefore weaker than that of1A. From the foregoing observations, it can be concluded that the addition of the OH or CN groups to1A reduces the BDE value of its hydroxyl group.It is also clear from Table4 that the BDE of the O1-H bond of juglone (L1) is lower than that of1A by 191 kJ/mol, implying that Fe(II) chelation by juglone leads to an increase in the BDE of its O-H group. The presence of the water ligands in1B results in a BDE value increment of 397 kJ/mol relative to that of1A, which contains no H2O ligands. This can be attributed to the reduction in the O1-H bond length due to the presence of H2O ligands, as previously observed in Section 3.3. On the contrary, the introduction of the MeOH ligands into1A decreases its BDE value.It can be seen from Table4 that the O1-H BDE of2A is lower than that of L2 by 269 kJ/mol. Among the compounds studied,2A has been found to exhibit the lowest O1-H BDE, showing that the HAT mechanism is most favorable in this molecule. Besides the electron donating ability of the hydroxyl substituent of2A, the hydrogen bond in its phenoxy radical could have a great stabilizing effect that lowers its BDE value. The BDE value of2B lies between those of2A and L2. On the other hand the BDE value of2C is much higher than those of both2A and L2. Among the molecules investigated in this work, the highest BDE value (1240 kJ/mol) has been recorded for2C. This is probably due to the fact that the hydrogen bond in2C that involves the O1-H group is weaker than similar bonds in2A and2B. From these results it can be concluded that Fe(II) chelation by L2 decreases its BDE value, as opposed to the presence of MeOH ligands which greatly increases the BDE value.Fe (II) chelation by L3is found to decrease its BDE value by 128 kJ/mol. It has been found that the BDE values of3B and3C are lower than that of3A by 35 and 49 kJ/mol, respectively. Generally, our results have shown that the BDEs of the O1-H bonds of the species currently investigated increases in the order2A <1C <3C <3B <2B <3A < L2< L1 < L3<1A <1B <2C.The BDE value of the additional O-H substituent in L2, designated by an asterisk (∗) in Table 3, is found to be lower than that of the O1-H bond, whereas the reverse is observed for its complexes. Therefore, the H atom of the O1-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].


#### 3.4.2. 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 Table4. It is clear in Table 4 that Fe2+ chelation leads to an increase in the IPs of L1, L2, and L3. This result is in good agreement with some literature findings [21]. The IP values of the chelates have been found to increase in the order3A <1A <2A. Surprisingly from this ranking,3A possessing EWG exhibits the greatest electron transfer capability, while2A containing EDG together with a hydrogen bond shows the least electron transferability.While the presence of water ligands increases the IP of1A, the MeOH ligands instead lead to its reduction. These ligands have been found to have a similar effect on the BDE of1A as explained in Section 3.4.1. In the case of2A, 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 of3A in which case the effect of the MeOH is found to be the greatest. The presence of these ligands similarly affects the BDE of3A 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 Table4. The only exceptions to this trend are the IPFEs of1A and2A which are lower than IP (by 2 kJ/mol) and equal to IP, respectively.The PDE values of the complexes displayed in Table4 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 of2A (−539 kJ/mol) and3A (−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, and3A) 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.


#### 3.4.3. 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 Table4. This table shows that, apart from2C, the chelates and complexes have lower PA values than their respective ligands. Like the IP values, the PAs of the chelates can be classified in the order3A <1A <2A. This can be explained by the fact that EWG (-CN) increases the acidity of the H atom of the hydroxyl group whereas EDG (-OH) reduces the hydroxyl H atom’s acidity. The presence of water and MeOH ligands reduces the PA of1A, the latter having the least effect. Like the case with IP, the presence of H2O ligands reduces the PA of2A, while the presence of MeOH ligands increases that PA. The presence of water and MeOH ligands is observed to increase the PA of3A, with the latter having the greatest effect.The hydrogen of the O-H substituent is more acidic that that of the O1-H group of all L2 complexes, since the P
A
∗ and P
A
F
E
∗ of the former are lower than PA and PAFE of the latter, as shown 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 for1A and3C, 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.


#### 3.4.4. 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 Figure2.Figure 2
Superposition of BDFE, IPFE, and PAFE of juglone, its derivatives, and their complexes.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 of1B, 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 of1B, the second preferred mechanism is HAT.


#### 3.4.5. 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.Figure 3
Mulliken spin densities of the radicals of the chelates and complexes studied.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 of2A, 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 complex1B, 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 Fe2+ 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.


### 3.5. 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 metal-ligand 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, E
(
2
) associated with the delocalization from i
→
j ((
i
) and (
j
) being the donor and acceptor orbitals, resp.), was estimated using(16)
E
2
=
-
q
i
F
i
j
ε
j
-
ε
i
.Here, q
i is the orbital occupancy, ε
i, ε
j are diagonal elements, and F
i
j is the off-diagonal NBO Fock matrix element. Values of E
(
2
) are proportional to the intensities of NBO interactions, and the greater the electron donating tendency from donor to acceptor NBOs, the larger the E
(
2
) values and the more intensive the interaction between the electron donors and the electron acceptors [42, 43].In Table5, the values of E
(
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 E
(
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.Table 5
NBO analysis of the metal-ligand bonds and NPA atomic charge of the central Fe in the chelates and complexes obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
NPA atomic charge Fe (e)
Donor (i)
Acceptor (j)
E
(
2
) (kJ/mol)
Donor (i)
Acceptor (j)
E
(
2
) (kJ/mol)
1A
1.45
LP(2) O1
LP∗(4) Fe
71.83
LP(1) O2
LP∗(6) Fe
27.02
LP(2) O1
LP∗(6) Fe
11.87
LP(2) O2
LP∗(5) Fe
12.16
1B
1.17
LP(2) O1
LP∗(4) Fe
69.90
LP(2) X1
LP∗(8) Fe
34.08
LP(2) O1
LP∗(7) Fe
26.77
LP(2) X2
LP∗(7) Fe
38.23
LP(2) O2
LP∗(5) Fe
25.54
LP(2) X3
LP∗(8) Fe
32.17
LP(2) O2
LP∗(9) Fe
32.31
LP(2) X4
LP∗(5) Fe
32.58
1C
1.46
LP(2) O1
LP∗(6) Fe
13.53
LP(2) X1
LP∗(9) Fe
10.55
LP(1) O2
LP∗(6) Fe
8.27
LP(2) X2
LP∗(8) Fe
10.22
LP(2) O2
LP∗(7) Fe
7.15
LP(2) X3
LP∗(7) Fe
10.40
LP(2) O26
LP∗(6) Fe
7.52
LP(2) X4
LP∗(9) Fe
11.09
2A
1.33
LP(2) O2
LP∗(4) Fe
68.47
LP(1) O2
LP∗(6) Fe
8.73
LP(2) O2
LP∗(6) Fe
11.65
LP(1) O1
LP∗(6) Fe
27.90
LP(1) O2
LP∗(6) Fe
9.44
LP(2) O1
LP∗(5) Fe
12.37
2B
1.43
LP(2) O1
LP∗(2) Fe
19.56
LP(2) X1
LP∗(7) Fe
8.42
LP(2) O1
LP∗(4) Fe
8.28
LP(2) X2
LP∗(4) Fe
15.23
LP(1) O2
LP∗(7) Fe
12.00
LP(2) X3
LP∗(5) Fe
13.71
LP(1) O2
LP∗(2) Fe
7.84
LP(2) X4
LP∗(5) Fe
13.72
2C
1.51
LP(2) O1
LP∗(2) Fe
18.76
LP(2) X1
LP∗(7) Fe
10.24
LP(2) O1
LP∗(4) Fe
11.33
LP(2) X2
LP∗(4) Fe
13.09
LP(1) O2
LP∗(7) Fe
9.25
LP(2) X3
LP∗(5) Fe
13.71
LP(1) O2
LP∗(2) Fe
10.44
LP(2) X4
LP∗(5) Fe
12.24
3A
1.66
LP(2) O1
LP∗(3) Fe
14.10
LP(1) O2
LP∗(4) Fe
7.86
LP(1) O2
LP∗(2) Fe
25.40
—
—
—
3B
1.17
LP(2) O2
LP∗(2) Fe
19.41
LP(2) X1
LP∗(6) Fe
10.44
LP(2) O2
LP∗(4) Fe
8.90
LP(2) X2
LP∗(4) Fe
15.45
LP(1) O1
LP∗(7) Fe
13.02
LP(2) X3
LP∗(5) Fe
13.70
LP(1) O1
LP∗(2) Fe
7.26
LP(2) X4
LP∗(5) Fe
13.82
3C
1.20
LP(2) O2
LP∗(2) Fe
14.45
LP(2) X1
LP∗(6) Fe
9.12
LP(2) O2
LP∗(5) Fe
7.55
LP(2) X2
LP∗(5) Fe
9.53
LP(1) O1
LP∗(2) Fe
7.74
LP(2) X3
LP∗(3) Fe
12.40
LP(1) O1
LP∗(6) Fe
5.91
LP(2) X4
LP∗(2) Fe
7.93It can be observed fromE
(
2
) values in Table 5 that, with the exception of1A, the interactions between the lone pairs on O2 and the antibonding L
P
∗ on the metal ion are stronger than those between the lone pairs on O1 and the antibonding L
P
∗ 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
) O1 → L
P
∗
(
4
) Fe in1A, with a stabilization energy of 71.83 kJ/mol.The atomic charges on Fe (Table5) in the molecules under investigation have shown that ligand-metal charge transfer is effective, since the metal’s formal charge of +2 now lies between 1.17 and 1.66. The highest atomic charge on Fe (1.66) is obtained in3A, while the lowest value (1.17) is found in1B and3B.


### 3.6. 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 (
ρ
(
r
)
) and its Laplacian (
∇
2
ρ
(
r
)
) 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
ρ
(
r
)
) at a bond critical point reveals whether charge is concentrated as in covalent bond interactions (
∇
2
ρ
(
r
)
<
0
) or depleted as in closed shell (electrostatic) interactions (
∇
2
ρ
(
r
)
>
0
) [41]. Specifically, for nonpolar and weakly polar covalent bonds ∇
2
ρ
(
r
)
<
0 and -
G
(
r
)
/
v
(
r
)
<
1. For intermediate interactions we have ∇
2
ρ
(
r
)
>
0, but -
G
(
r
)
/
v
(
r
)
<
1; and for closed shell interactions ∇
2
ρ
(
r
)
>
0 and -
G
(
r
)
/
v
(
r
)
>
1. Here, G
(
r
) is the kinetic energy density at the critical point (always positive), while v
(
r
) is the potential energy density at the critical point (always negative) by definition [44]. The values of ρ
(
r
), ∇
2
ρ
(
r
), and -
G
(
r
)
/
v
(
r
) for all the metal-ligand bonds, as well as for the O-H bonds, are presented in Table 6.Table 6
Topological analysis of the metal-ligand and O-H bonds of the complexes.
Parameter
O
1-H
1
O
1-Fe
O
2-Fe
X
1-Fe
X
2-Fe
X
3-Fe
X
4-Fe
1A
ρ
(
r
)
0.342
0.228
0.132
—
—
—
—
∇
2
ρ
(
r
)
−0.211
−0.108
0.894
—
—
—
—
-
G
(
r
)
/
v
(
r
)
0.088
0.477
0.941
—
—
—
—
1B
ρ
(
r
)
0.353
0.637
0.354
0.056
0.057
0.058
0.058
∇
2
ρ
(
r
)
−2.123
0.541
0.061
0.436
0.454
0.440
0.446
-
G
(
r
)
/
v
(
r
)
0.097
1.071
0.506
1.061
1.069
1.056
1.060
1C
ρ
(
r
)
0.327
0.048
0.075
0.054
0.062
0.049
0.058
∇
2
ρ
(
r
)
−1.576
0.213
0.464
0.278
0.313
0.227
0.297
-
G
(
r
)
/
v
(
r
)
0.116
0.093
0.987
0.949
0.960
0.922
0.947
2A
ρ
(
r
)
0.326
0.110
0.337
—
—
—
—
0.348∗
∇
2
ρ
(
r
)
−2.022
0.699
0.025
—
—
—
—
−2.214∗
-
G
(
r
)
/
v
(
r
)
0.088
0.963
0.503
—
—
—
—
0.093∗
2B
ρ
(
r
)
0.310
0.052
0.076
0.060
0.053
0.053
0.053
0.388∗
∇
2
ρ
(
r
)
−1.148
0.258
0.441
0.328
0.282
0.283
0.263
−16.76∗
-
G
(
r
)
/
v
(
r
)
0.113
0.951
0.980
0.972
0.956
0.956
0.950
0.004∗
2C
ρ
(
r
)
0.347
0.044
0.073
0.047
0.057
0.048
0.054
0.355∗
∇
2
ρ
(
r
)
−2.089
0.182
0.419
0.211
0.267
0.224
0.268
−2.128∗
-
G
(
r
)
/
v
(
r
)
0.099
0.918
0.981
0.925
0.946
0.926
0.946
0.099∗
3A
ρ
(
r
)
0.300
0.084
0.110
—
—
—
—
∇
2
ρ
(
r
)
−1.431
0.481
0.730
—
—
—
—
-
G
(
r
)
/
v
(
r
)
0.115
0.981
0.963
—
—
—
—
3B
ρ
(
r
)
0.316
0.050
0.077
0.060
0.053
0.054
0.053
∇
2
ρ
(
r
)
−1.511
0.239
0.451
0.328
0.239
0.286
0.284
-
G
(
r
)
/
v
(
r
)
0.117
0.943
0.983
0.972
0.950
0.958
0.957
3C
ρ
(
r
)
0.320
0.047
0.323
0.078
0.194
0.050
0.059
∇
2
ρ
(
r
)
−1.532
0.211
−0.341
0.031
0.172
0.238
0.311
-
G
(
r
)
/
v
(
r
)
0.117
0.934
0.453
1.214
0.436
0.929
0.956
∗ refers to the parameters related to the O-H substituent present on L2.From Table6, it can be seen that each Fe-O bond has a positive ∇
2
ρ
(
r
) value except that of the O1-Fe bond of1A which is negative (−0.108). This implies that the said O1-Fe bond is covalent in nature, while the rest of the Fe-O bonds are noncovalent. The covalent character of the O1-Fe bond of1A provides a probable explanation to the fact that the perturbation energy (E
(
2
) = 71.83 kJ/mol) corresponding to the interaction between O1and Fe is the largest among the metal-ligand interactions.The values of-
G
(
r
)
/
v
(
r
) for the Oi-Fe (i
=
1 and 2) bonds are all less than unity (except for the O1-Fe bond of1B which is a weak or closed shell interaction), meaning that these bonds are intermediate type interactions. Based on the values of -
G
(
r
)
/
v
(
r
), it can be concluded that the Xi-Fe (i
=
1, 2, 3 and 4) bonds of1C,2B,2C,3B, and3C (except the weak X1-Fe interaction of3C) are also intermediate type interactions. On the contrary, Xi-Fe (i
=
1, 2, 3 and 4) bonds of1B result from weak interactions. The negative values of ∇
2
ρ
(
r
) and the low values of -
G
(
r
)
/
v
(
r
) as presented in Table 6 have clearly shown that the O-H bonds are all covalent.The topological analyses of the complexes of L2have confirmed the hydrogen bond O1-H⋯O earlier observed in their optimized geometries (Figure 1). Surprisingly, the topological analysis of the complexes of L3 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 O1-H bond length for the complexes of L3 (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.Figure 4
Molecular graph of3A: bond critical points (small red spheres), ring critical points (small yellow sphere), bond paths (green lines), and O-H⋯CN VDW interaction (orange line).


## 3.1. 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 (Figure1) has been investigated. This was done in order to select the multiplicities of the molecules studied that correspond to their lowest energy (or most stable) geometries. In this regard, the singlet and quintet states corresponding to geometries in which the central Fe2+ ion has no unpaired electron and four unpaired electrons, respectively, were investigated for each chelate and complex. S
2 values, calculated for all quintet states, are in the range of 6.0001–6.0006, which is close to the value of 6.000, corresponding to the pure quintet wave function. The total energies of the said states are displayed in Table 1. In this table, the complexes of L1 (juglone), L2 (the derivative with the OH group), and L3 (the derivative with the CN group) are denoted by1,2, and3, respectively. The chelates are represented by the symbolYA (where Y
=
1, 2 or 3). Similarly, the complexes containing the ligands H2O and MeOH are, respectively, represented byYB andYC.Table 1
Energies (Hartree) of the compounds related to their multiplicities obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
Spin multiplicity
Singlet
Quintet
[Fe(L1)]
2+
1A
−1873.21293208
−1873.12426700
[Fe(L1)(OH2)4
]
2+
1B
−2179.23172776
−2178.98173479
[Fe(L1)(CH3OH)4
]
2+
1C
−2336.10729027
−2336.15725602
[Fe(L2)]
2+
2A
−1948.45209999
−1948.33220631
[Fe(L2)(OH2)4
]
2+
2B
−2254.13720775
−2254.18434320
[FeL2(CH3OH)4
]
2+
2C
−2411.68291413
−2411.72799125
[Fe(L3)]
2+
3A
−1965.22170297
−1965.31620465
[Fe(L3)(OH2)4
]
2+
3B
−2271.13120555
−2271.17906337
[Fe(L3)(CH3OH)4
]
2+
3C
−2428.30591545
−2428.35653764It can be seen from Table1 that the singlet state of1A and1B which are complexes of L1, 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 L2,2A has the lowest energy singlet state, while2B and2C containing H2O and MeOH ligands, respectively, are constrained to the quintet state. The three complexes of L3 (3A,3B, and3C) are restricted to the quintet state. From the foregoing observations, the rest of this work has been limited to the singlet states of1A,1B, and2A and the quintet states of1C,2B,2C,3A,3B, and3C.


## 3.2. 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.Table 2
Binding energy (Δ
E
i
n
t), enthalpy (Δ
H) and free energy change (Δ
G) of formation of the complexes all in kJ/mol, obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
Molecule
Δ
H
Δ
G
Δ
E
i
n
t
1A
−1000,08
−963,77
−997,60
1B
−4332,08
−1500,67
−4319,69
1C
−6230,60
−774,45
−6218,19
2A
−8900,34
−986,77
−8897,86
2B
−11483,96
−791,41
−11471,56
2C
−15004,90
−1677,43
−14992,50
3A
−16395,51
−609,87
−16393,04
3B
−19323,20
−757,95
−19310,81
3C
−21880,49
−668,61
−21868,09By inspection of Table2 it can be seen that the free energies of formation of the three chelates (1A,2A, and3A) are negative, meaning that their formation is spontaneous. Among the chelates, the computed free energies increase in the order2A <1A <3A, showing that L2 has the highest Fe2+ ion binding capacity and L3 has the lowest. This result is attributable to the fact that the presence of the EDG (the -OH group of L2) 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 presence of H2O ligands decreases Δ
G of formation of1A, while the MeOH ligands rather result in its increment. In the case of2A, the opposite of the previous observation is evidenced in Table 2, implying that while the presence of water ligands increases Δ
G of formation of2A, the presence of the methanol ligands instead leads to its reduction. The presence of H2O and MeOH ligands in3A decreases its Δ
G by 148 and 58 kJ/mol, respectively.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.


## 3.3. Geometric Parameters

This section is dedicated to Fe-ligand and O1-H bond lengths obtained from the optimized geometries of the complexes presented in Figure 1. It is clear from this figure that the chelates1A,2A, and3A are perfectly planar, and the complexes2B,2C,3B, and3C are octahedral. The values of the bond lengths around the central metal are presented in Table 3.Table 3
Metal-ligand and O-H bond lengths (Ǻ) of the complexes obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
O
1-H
O
1-Fe
O
2-Fe
X
1-Fe
X
2-Fe
X
3-Fe
X
4-Fe
1A
0.979
1.870
1.785
—
—
—
—
1B
0.971
1.982
1.898
2.029
2.021
2.023
2.024
1C
0.977
2.185
1.991
2.140
2.080
2.187
2.111
2A
0.9930.972∗
1.863
1.796
—
—
—
—
2B
0.9910.976∗
2.145
1.994
2.088
2.145
2.140
2.139
2C
0.9770.969∗
2.221
2.010
2.196
2.117
2.186
2.137
3A
0.997
1.963
1.854
—
—
—
—
3B
0.986
2.167
1.987
2.090
2.145
2.138
2.137
3C
0.984
2.188
1.994
2.143
2.075
2.176
2.102The atomic numbering adopted in Table3 is as presented in Figure 1. The length of the O1-Fe bond in each chelate increases in the order,2A <1A <3A, which is the same order of their Δ
G of formation. Hence, the values of Δ
G and the O1-Fe bond lengths for the chelates are directly proportional. It can also be observed from Table 3 that the presence of H2O and MeOH ligands increases the values of the O1-Fe bond lengths in all the chelates. Some discrepancies between the O1-Fe bond lengths in1A,2A,3A relative to those in the corresponding methanol complexes of 0.315, 0.358, and 0.225 Ǻ, respectively, have been observed.The O2-Fe bond lengths have been found to be shorter than the O1-Fe counterparts in all chelates investigated. The lengths of the former have also been found to increase in presence of H2O 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 Xn-Fe bonds (n
=
1, 2, 3 and 4; X = H2O or MeOH) are larger than 2 Ǻ. Among the complexes of juglone, that possessing MeOH ligands (1C) has the longest Xn-Fe bond, and its formation is found to be the least spontaneous.From inspection of the O1-H bonds of the three chelates, the ranking1A <2A <3A can be made, showing that the bond is the longest in3A with a length of 0.997 Ǻ. This is surprising because the O1-H group of2A is involved in hydrogen bonding as depicted in Figure 1, which should elongate its O1-H bond rendering it the longest relative to those of the other chelates. Since the AOA is greatly influenced by the length of the phenolic O-H bond, these differences in O1-H bond lengths could have great consequences on the values of associated thermodynamic descriptors of AOA. Still from these findings, it can be predicted that among the chelates,1A which has the shortest O1-H bond length should have the highest associated BDE value. The presence of the H2O and MeOH ligands is found to slightly decrease the length of the said bond. The presence of the methanol ligands has a more significant effect on the O1-H bond length of2A. Indeed, the presence of the methanol ligand is found to reduce the length of the bond by 0.016 Ǻ. This is attributable to hydrogen bond strength reduction in2B. The presence of the water ligands in2A has virtually no effect on the length of the O1-H bond. The presence of both ligands individually reduces the length of the hydroxyl link of3A by 0.011 and 0.013 Ǻ, respectively.The lengths of the hydrogen bonds of1B,2B, and3B are, respectively, 1.909, 1.920, and 1.961 Ǻ, which are in good agreement with those of the O1-H groups of the said molecules, since they are inversely proportional to the O1-H bond length. The lengths of the additional O-H bonds in2A,2B, and2C (marked in Table 3 with ∗) are shorter than those of O1-H groups, due to the fact that they are not engaged in any hydrogen bond.


## 3.4. Thermodynamic Descriptors of Antioxidant Properties

### 3.4.1. HAT Mechanism

The calculated gas phase BDE values of the molecules investigated are presented in Table4.Table 4
Values of BDE, BDFE, IP, IPFE, PDE, PDFE, PA, PAFE, ETE and ETFE of the compounds studied, all in kJ/mol obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
BDE
BDFE
IP
IPFE
PDE
PDFE
PA
PAFE
ETE
ETFE
L1
417
377
834
824
899
864
1422
1386
312
309
1A
608
575
1919
1917
6
−23
1014
910
1041
1038
1B
1001
977
2132
2142
186
154
793
629
1710
1720
1C
233
211
1299
1309
251
222
898
679
897
904
L2
380359∗
341323∗
805
795
892
874
13771361∗
13661330∗
319314∗
315312∗
2A
111798∗
74765∗
1967
1967
−539
−574
11501008∗
1039981∗
4141107∗
4071104∗
2B
271358∗
250327∗
1338
1351
251
218
868658∗
685636∗
9281016∗
9371009∗
2C
12401324∗
12171301∗
2255
2273
245
262
19041648∗
16781625∗
908993∗
910994∗
L3
421
381
874
863
864
828
1366
1353
371
368
3A
283
250
1833
1979
−233
−410
570
447
1176
1175
3B
248
232
1375
1394
191
157
829
641
953
963
3C
234
211
1308
1319
243
211
881
653
924
930
∗ refers to the parameters related to the O-H substituent present on L2.It is evident in Table2 that the BDEs of the O1-H bond for the chelates increase in the order2A <3A <1A. The fact that the BDE of O1-H is the lowest in2A suggests that the hydrogen bond in which this group is engaged weakens the O1-H bond in this molecule. In addition, the phenoxy radical formed due to HAT by2A is stabilized by an O-H⋯O1 hydrogen bond, further strengthening the AOA of2A. The low BDE of3A relative to that of1A can be explained by the fact that its O1-H bond is longer and therefore weaker than that of1A. From the foregoing observations, it can be concluded that the addition of the OH or CN groups to1A reduces the BDE value of its hydroxyl group.It is also clear from Table4 that the BDE of the O1-H bond of juglone (L1) is lower than that of1A by 191 kJ/mol, implying that Fe(II) chelation by juglone leads to an increase in the BDE of its O-H group. The presence of the water ligands in1B results in a BDE value increment of 397 kJ/mol relative to that of1A, which contains no H2O ligands. This can be attributed to the reduction in the O1-H bond length due to the presence of H2O ligands, as previously observed in Section 3.3. On the contrary, the introduction of the MeOH ligands into1A decreases its BDE value.It can be seen from Table4 that the O1-H BDE of2A is lower than that of L2 by 269 kJ/mol. Among the compounds studied,2A has been found to exhibit the lowest O1-H BDE, showing that the HAT mechanism is most favorable in this molecule. Besides the electron donating ability of the hydroxyl substituent of2A, the hydrogen bond in its phenoxy radical could have a great stabilizing effect that lowers its BDE value. The BDE value of2B lies between those of2A and L2. On the other hand the BDE value of2C is much higher than those of both2A and L2. Among the molecules investigated in this work, the highest BDE value (1240 kJ/mol) has been recorded for2C. This is probably due to the fact that the hydrogen bond in2C that involves the O1-H group is weaker than similar bonds in2A and2B. From these results it can be concluded that Fe(II) chelation by L2 decreases its BDE value, as opposed to the presence of MeOH ligands which greatly increases the BDE value.Fe (II) chelation by L3is found to decrease its BDE value by 128 kJ/mol. It has been found that the BDE values of3B and3C are lower than that of3A by 35 and 49 kJ/mol, respectively. Generally, our results have shown that the BDEs of the O1-H bonds of the species currently investigated increases in the order2A <1C <3C <3B <2B <3A < L2< L1 < L3<1A <1B <2C.The BDE value of the additional O-H substituent in L2, designated by an asterisk (∗) in Table 3, is found to be lower than that of the O1-H bond, whereas the reverse is observed for its complexes. Therefore, the H atom of the O1-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].


### 3.4.2. 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 Table4. It is clear in Table 4 that Fe2+ chelation leads to an increase in the IPs of L1, L2, and L3. This result is in good agreement with some literature findings [21]. The IP values of the chelates have been found to increase in the order3A <1A <2A. Surprisingly from this ranking,3A possessing EWG exhibits the greatest electron transfer capability, while2A containing EDG together with a hydrogen bond shows the least electron transferability.While the presence of water ligands increases the IP of1A, the MeOH ligands instead lead to its reduction. These ligands have been found to have a similar effect on the BDE of1A as explained in Section 3.4.1. In the case of2A, 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 of3A in which case the effect of the MeOH is found to be the greatest. The presence of these ligands similarly affects the BDE of3A 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 Table4. The only exceptions to this trend are the IPFEs of1A and2A which are lower than IP (by 2 kJ/mol) and equal to IP, respectively.The PDE values of the complexes displayed in Table4 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 of2A (−539 kJ/mol) and3A (−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, and3A) 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.


### 3.4.3. 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 Table4. This table shows that, apart from2C, the chelates and complexes have lower PA values than their respective ligands. Like the IP values, the PAs of the chelates can be classified in the order3A <1A <2A. This can be explained by the fact that EWG (-CN) increases the acidity of the H atom of the hydroxyl group whereas EDG (-OH) reduces the hydroxyl H atom’s acidity. The presence of water and MeOH ligands reduces the PA of1A, the latter having the least effect. Like the case with IP, the presence of H2O ligands reduces the PA of2A, while the presence of MeOH ligands increases that PA. The presence of water and MeOH ligands is observed to increase the PA of3A, with the latter having the greatest effect.The hydrogen of the O-H substituent is more acidic that that of the O1-H group of all L2 complexes, since the P
A
∗ and P
A
F
E
∗ of the former are lower than PA and PAFE of the latter, as shown 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 for1A and3C, 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.


### 3.4.4. 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 Figure2.Figure 2
Superposition of BDFE, IPFE, and PAFE of juglone, its derivatives, and their complexes.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 of1B, 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 of1B, the second preferred mechanism is HAT.


### 3.4.5. 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.Figure 3
Mulliken spin densities of the radicals of the chelates and complexes studied.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 of2A, 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 complex1B, 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 Fe2+ 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.


## 3.4.1. HAT Mechanism

The calculated gas phase BDE values of the molecules investigated are presented in Table4.Table 4
Values of BDE, BDFE, IP, IPFE, PDE, PDFE, PA, PAFE, ETE and ETFE of the compounds studied, all in kJ/mol obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
BDE
BDFE
IP
IPFE
PDE
PDFE
PA
PAFE
ETE
ETFE
L1
417
377
834
824
899
864
1422
1386
312
309
1A
608
575
1919
1917
6
−23
1014
910
1041
1038
1B
1001
977
2132
2142
186
154
793
629
1710
1720
1C
233
211
1299
1309
251
222
898
679
897
904
L2
380359∗
341323∗
805
795
892
874
13771361∗
13661330∗
319314∗
315312∗
2A
111798∗
74765∗
1967
1967
−539
−574
11501008∗
1039981∗
4141107∗
4071104∗
2B
271358∗
250327∗
1338
1351
251
218
868658∗
685636∗
9281016∗
9371009∗
2C
12401324∗
12171301∗
2255
2273
245
262
19041648∗
16781625∗
908993∗
910994∗
L3
421
381
874
863
864
828
1366
1353
371
368
3A
283
250
1833
1979
−233
−410
570
447
1176
1175
3B
248
232
1375
1394
191
157
829
641
953
963
3C
234
211
1308
1319
243
211
881
653
924
930
∗ refers to the parameters related to the O-H substituent present on L2.It is evident in Table2 that the BDEs of the O1-H bond for the chelates increase in the order2A <3A <1A. The fact that the BDE of O1-H is the lowest in2A suggests that the hydrogen bond in which this group is engaged weakens the O1-H bond in this molecule. In addition, the phenoxy radical formed due to HAT by2A is stabilized by an O-H⋯O1 hydrogen bond, further strengthening the AOA of2A. The low BDE of3A relative to that of1A can be explained by the fact that its O1-H bond is longer and therefore weaker than that of1A. From the foregoing observations, it can be concluded that the addition of the OH or CN groups to1A reduces the BDE value of its hydroxyl group.It is also clear from Table4 that the BDE of the O1-H bond of juglone (L1) is lower than that of1A by 191 kJ/mol, implying that Fe(II) chelation by juglone leads to an increase in the BDE of its O-H group. The presence of the water ligands in1B results in a BDE value increment of 397 kJ/mol relative to that of1A, which contains no H2O ligands. This can be attributed to the reduction in the O1-H bond length due to the presence of H2O ligands, as previously observed in Section 3.3. On the contrary, the introduction of the MeOH ligands into1A decreases its BDE value.It can be seen from Table4 that the O1-H BDE of2A is lower than that of L2 by 269 kJ/mol. Among the compounds studied,2A has been found to exhibit the lowest O1-H BDE, showing that the HAT mechanism is most favorable in this molecule. Besides the electron donating ability of the hydroxyl substituent of2A, the hydrogen bond in its phenoxy radical could have a great stabilizing effect that lowers its BDE value. The BDE value of2B lies between those of2A and L2. On the other hand the BDE value of2C is much higher than those of both2A and L2. Among the molecules investigated in this work, the highest BDE value (1240 kJ/mol) has been recorded for2C. This is probably due to the fact that the hydrogen bond in2C that involves the O1-H group is weaker than similar bonds in2A and2B. From these results it can be concluded that Fe(II) chelation by L2 decreases its BDE value, as opposed to the presence of MeOH ligands which greatly increases the BDE value.Fe (II) chelation by L3is found to decrease its BDE value by 128 kJ/mol. It has been found that the BDE values of3B and3C are lower than that of3A by 35 and 49 kJ/mol, respectively. Generally, our results have shown that the BDEs of the O1-H bonds of the species currently investigated increases in the order2A <1C <3C <3B <2B <3A < L2< L1 < L3<1A <1B <2C.The BDE value of the additional O-H substituent in L2, designated by an asterisk (∗) in Table 3, is found to be lower than that of the O1-H bond, whereas the reverse is observed for its complexes. Therefore, the H atom of the O1-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].


## 3.4.2. 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 Table4. It is clear in Table 4 that Fe2+ chelation leads to an increase in the IPs of L1, L2, and L3. This result is in good agreement with some literature findings [21]. The IP values of the chelates have been found to increase in the order3A <1A <2A. Surprisingly from this ranking,3A possessing EWG exhibits the greatest electron transfer capability, while2A containing EDG together with a hydrogen bond shows the least electron transferability.While the presence of water ligands increases the IP of1A, the MeOH ligands instead lead to its reduction. These ligands have been found to have a similar effect on the BDE of1A as explained in Section 3.4.1. In the case of2A, 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 of3A in which case the effect of the MeOH is found to be the greatest. The presence of these ligands similarly affects the BDE of3A 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 Table4. The only exceptions to this trend are the IPFEs of1A and2A which are lower than IP (by 2 kJ/mol) and equal to IP, respectively.The PDE values of the complexes displayed in Table4 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 of2A (−539 kJ/mol) and3A (−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, and3A) 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.


## 3.4.3. 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 Table4. This table shows that, apart from2C, the chelates and complexes have lower PA values than their respective ligands. Like the IP values, the PAs of the chelates can be classified in the order3A <1A <2A. This can be explained by the fact that EWG (-CN) increases the acidity of the H atom of the hydroxyl group whereas EDG (-OH) reduces the hydroxyl H atom’s acidity. The presence of water and MeOH ligands reduces the PA of1A, the latter having the least effect. Like the case with IP, the presence of H2O ligands reduces the PA of2A, while the presence of MeOH ligands increases that PA. The presence of water and MeOH ligands is observed to increase the PA of3A, with the latter having the greatest effect.The hydrogen of the O-H substituent is more acidic that that of the O1-H group of all L2 complexes, since the P
A
∗ and P
A
F
E
∗ of the former are lower than PA and PAFE of the latter, as shown 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 for1A and3C, 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.


## 3.4.4. 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 Figure2.Figure 2
Superposition of BDFE, IPFE, and PAFE of juglone, its derivatives, and their complexes.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 of1B, 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 of1B, the second preferred mechanism is HAT.


## 3.4.5. 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.Figure 3
Mulliken spin densities of the radicals of the chelates and complexes studied.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 of2A, 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 complex1B, 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 Fe2+ 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.


## 3.5. 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 metal-ligand 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, E
(
2
) associated with the delocalization from i
→
j ((
i
) and (
j
) being the donor and acceptor orbitals, resp.), was estimated using(16)
E
2
=
-
q
i
F
i
j
ε
j
-
ε
i
.Here, q
i is the orbital occupancy, ε
i, ε
j are diagonal elements, and F
i
j is the off-diagonal NBO Fock matrix element. Values of E
(
2
) are proportional to the intensities of NBO interactions, and the greater the electron donating tendency from donor to acceptor NBOs, the larger the E
(
2
) values and the more intensive the interaction between the electron donors and the electron acceptors [42, 43].In Table5, the values of E
(
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 E
(
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.Table 5
NBO analysis of the metal-ligand bonds and NPA atomic charge of the central Fe in the chelates and complexes obtained from B3LYP/6-31G(d)(Fe)U6-31+G(d,p)(E).
NPA atomic charge Fe (e)
Donor (i)
Acceptor (j)
E
(
2
) (kJ/mol)
Donor (i)
Acceptor (j)
E
(
2
) (kJ/mol)
1A
1.45
LP(2) O1
LP∗(4) Fe
71.83
LP(1) O2
LP∗(6) Fe
27.02
LP(2) O1
LP∗(6) Fe
11.87
LP(2) O2
LP∗(5) Fe
12.16
1B
1.17
LP(2) O1
LP∗(4) Fe
69.90
LP(2) X1
LP∗(8) Fe
34.08
LP(2) O1
LP∗(7) Fe
26.77
LP(2) X2
LP∗(7) Fe
38.23
LP(2) O2
LP∗(5) Fe
25.54
LP(2) X3
LP∗(8) Fe
32.17
LP(2) O2
LP∗(9) Fe
32.31
LP(2) X4
LP∗(5) Fe
32.58
1C
1.46
LP(2) O1
LP∗(6) Fe
13.53
LP(2) X1
LP∗(9) Fe
10.55
LP(1) O2
LP∗(6) Fe
8.27
LP(2) X2
LP∗(8) Fe
10.22
LP(2) O2
LP∗(7) Fe
7.15
LP(2) X3
LP∗(7) Fe
10.40
LP(2) O26
LP∗(6) Fe
7.52
LP(2) X4
LP∗(9) Fe
11.09
2A
1.33
LP(2) O2
LP∗(4) Fe
68.47
LP(1) O2
LP∗(6) Fe
8.73
LP(2) O2
LP∗(6) Fe
11.65
LP(1) O1
LP∗(6) Fe
27.90
LP(1) O2
LP∗(6) Fe
9.44
LP(2) O1
LP∗(5) Fe
12.37
2B
1.43
LP(2) O1
LP∗(2) Fe
19.56
LP(2) X1
LP∗(7) Fe
8.42
LP(2) O1
LP∗(4) Fe
8.28
LP(2) X2
LP∗(4) Fe
15.23
LP(1) O2
LP∗(7) Fe
12.00
LP(2) X3
LP∗(5) Fe
13.71
LP(1) O2
LP∗(2) Fe
7.84
LP(2) X4
LP∗(5) Fe
13.72
2C
1.51
LP(2) O1
LP∗(2) Fe
18.76
LP(2) X1
LP∗(7) Fe
10.24
LP(2) O1
LP∗(4) Fe
11.33
LP(2) X2
LP∗(4) Fe
13.09
LP(1) O2
LP∗(7) Fe
9.25
LP(2) X3
LP∗(5) Fe
13.71
LP(1) O2
LP∗(2) Fe
10.44
LP(2) X4
LP∗(5) Fe
12.24
3A
1.66
LP(2) O1
LP∗(3) Fe
14.10
LP(1) O2
LP∗(4) Fe
7.86
LP(1) O2
LP∗(2) Fe
25.40
—
—
—
3B
1.17
LP(2) O2
LP∗(2) Fe
19.41
LP(2) X1
LP∗(6) Fe
10.44
LP(2) O2
LP∗(4) Fe
8.90
LP(2) X2
LP∗(4) Fe
15.45
LP(1) O1
LP∗(7) Fe
13.02
LP(2) X3
LP∗(5) Fe
13.70
LP(1) O1
LP∗(2) Fe
7.26
LP(2) X4
LP∗(5) Fe
13.82
3C
1.20
LP(2) O2
LP∗(2) Fe
14.45
LP(2) X1
LP∗(6) Fe
9.12
LP(2) O2
LP∗(5) Fe
7.55
LP(2) X2
LP∗(5) Fe
9.53
LP(1) O1
LP∗(2) Fe
7.74
LP(2) X3
LP∗(3) Fe
12.40
LP(1) O1
LP∗(6) Fe
5.91
LP(2) X4
LP∗(2) Fe
7.93It can be observed fromE
(
2
) values in Table 5 that, with the exception of1A, the interactions between the lone pairs on O2 and the antibonding L
P
∗ on the metal ion are stronger than those between the lone pairs on O1 and the antibonding L
P
∗ 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
) O1 → L
P
∗
(
4
) Fe in1A, with a stabilization energy of 71.83 kJ/mol.The atomic charges on Fe (Table5) in the molecules under investigation have shown that ligand-metal charge transfer is effective, since the metal’s formal charge of +2 now lies between 1.17 and 1.66. The highest atomic charge on Fe (1.66) is obtained in3A, while the lowest value (1.17) is found in1B and3B.


## 3.6. 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 (
ρ
(
r
)
) and its Laplacian (
∇
2
ρ
(
r
)
) 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
ρ
(
r
)
) at a bond critical point reveals whether charge is concentrated as in covalent bond interactions (
∇
2
ρ
(
r
)
<
0
) or depleted as in closed shell (electrostatic) interactions (
∇
2
ρ
(
r
)
>
0
) [41]. Specifically, for nonpolar and weakly polar covalent bonds ∇
2
ρ
(
r
)
<
0 and -
G
(
r
)
/
v
(
r
)
<
1. For intermediate interactions we have ∇
2
ρ
(
r
)
>
0, but -
G
(
r
)
/
v
(
r
)
<
1; and for closed shell interactions ∇
2
ρ
(
r
)
>
0 and -
G
(
r
)
/
v
(
r
)
>
1. Here, G
(
r
) is the kinetic energy density at the critical point (always positive), while v
(
r
) is the potential energy density at the critical point (always negative) by definition [44]. The values of ρ
(
r
), ∇
2
ρ
(
r
), and -
G
(
r
)
/
v
(
r
) for all the metal-ligand bonds, as well as for the O-H bonds, are presented in Table 6.Table 6
Topological analysis of the metal-ligand and O-H bonds of the complexes.
Parameter
O
1-H
1
O
1-Fe
O
2-Fe
X
1-Fe
X
2-Fe
X
3-Fe
X
4-Fe
1A
ρ
(
r
)
0.342
0.228
0.132
—
—
—
—
∇
2
ρ
(
r
)
−0.211
−0.108
0.894
—
—
—
—
-
G
(
r
)
/
v
(
r
)
0.088
0.477
0.941
—
—
—
—
1B
ρ
(
r
)
0.353
0.637
0.354
0.056
0.057
0.058
0.058
∇
2
ρ
(
r
)
−2.123
0.541
0.061
0.436
0.454
0.440
0.446
-
G
(
r
)
/
v
(
r
)
0.097
1.071
0.506
1.061
1.069
1.056
1.060
1C
ρ
(
r
)
0.327
0.048
0.075
0.054
0.062
0.049
0.058
∇
2
ρ
(
r
)
−1.576
0.213
0.464
0.278
0.313
0.227
0.297
-
G
(
r
)
/
v
(
r
)
0.116
0.093
0.987
0.949
0.960
0.922
0.947
2A
ρ
(
r
)
0.326
0.110
0.337
—
—
—
—
0.348∗
∇
2
ρ
(
r
)
−2.022
0.699
0.025
—
—
—
—
−2.214∗
-
G
(
r
)
/
v
(
r
)
0.088
0.963
0.503
—
—
—
—
0.093∗
2B
ρ
(
r
)
0.310
0.052
0.076
0.060
0.053
0.053
0.053
0.388∗
∇
2
ρ
(
r
)
−1.148
0.258
0.441
0.328
0.282
0.283
0.263
−16.76∗
-
G
(
r
)
/
v
(
r
)
0.113
0.951
0.980
0.972
0.956
0.956
0.950
0.004∗
2C
ρ
(
r
)
0.347
0.044
0.073
0.047
0.057
0.048
0.054
0.355∗
∇
2
ρ
(
r
)
−2.089
0.182
0.419
0.211
0.267
0.224
0.268
−2.128∗
-
G
(
r
)
/
v
(
r
)
0.099
0.918
0.981
0.925
0.946
0.926
0.946
0.099∗
3A
ρ
(
r
)
0.300
0.084
0.110
—
—
—
—
∇
2
ρ
(
r
)
−1.431
0.481
0.730
—
—
—
—
-
G
(
r
)
/
v
(
r
)
0.115
0.981
0.963
—
—
—
—
3B
ρ
(
r
)
0.316
0.050
0.077
0.060
0.053
0.054
0.053
∇
2
ρ
(
r
)
−1.511
0.239
0.451
0.328
0.239
0.286
0.284
-
G
(
r
)
/
v
(
r
)
0.117
0.943
0.983
0.972
0.950
0.958
0.957
3C
ρ
(
r
)
0.320
0.047
0.323
0.078
0.194
0.050
0.059
∇
2
ρ
(
r
)
−1.532
0.211
−0.341
0.031
0.172
0.238
0.311
-
G
(
r
)
/
v
(
r
)
0.117
0.934
0.453
1.214
0.436
0.929
0.956
∗ refers to the parameters related to the O-H substituent present on L2.From Table6, it can be seen that each Fe-O bond has a positive ∇
2
ρ
(
r
) value except that of the O1-Fe bond of1A which is negative (−0.108). This implies that the said O1-Fe bond is covalent in nature, while the rest of the Fe-O bonds are noncovalent. The covalent character of the O1-Fe bond of1A provides a probable explanation to the fact that the perturbation energy (E
(
2
) = 71.83 kJ/mol) corresponding to the interaction between O1and Fe is the largest among the metal-ligand interactions.The values of-
G
(
r
)
/
v
(
r
) for the Oi-Fe (i
=
1 and 2) bonds are all less than unity (except for the O1-Fe bond of1B which is a weak or closed shell interaction), meaning that these bonds are intermediate type interactions. Based on the values of -
G
(
r
)
/
v
(
r
), it can be concluded that the Xi-Fe (i
=
1, 2, 3 and 4) bonds of1C,2B,2C,3B, and3C (except the weak X1-Fe interaction of3C) are also intermediate type interactions. On the contrary, Xi-Fe (i
=
1, 2, 3 and 4) bonds of1B result from weak interactions. The negative values of ∇
2
ρ
(
r
) and the low values of -
G
(
r
)
/
v
(
r
) as presented in Table 6 have clearly shown that the O-H bonds are all covalent.The topological analyses of the complexes of L2have confirmed the hydrogen bond O1-H⋯O earlier observed in their optimized geometries (Figure 1). Surprisingly, the topological analysis of the complexes of L3 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 O1-H bond length for the complexes of L3 (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.Figure 4
Molecular graph of3A: bond critical points (small red spheres), ring critical points (small yellow sphere), bond paths (green lines), and O-H⋯CN VDW interaction (orange line).


## 4. 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 Fe2+. The AOA of the resulting chelates and mixed ligand complexes with either H2O or CH3OH as another ligand were also evaluated. Precisely, the Gibbs free energies, the binding energies, and NBO analysis were used to evaluate the ability of L1, L2, and L3 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 Fe2+ chelation on the AOA of the ligands, chelates, and complexes.The negative values ofΔ
G and Δ
E
i
n
t 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 H2O or CH3OH 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 O2-Fe bonds of all the molecules with the exception of1A have been found to be higher than those of the O1-Fe bond indicating that the former bonds are relatively stronger than the latter. QTAIM showed that, apart from the O1-Fe bond in1A which is purely covalent, nearly all the O1-Fe and O2-Fe bonds of the rest of the molecules are intermediate type interactions. Also, the Xi-Fe (i
=
1, 2, 3 and 4) bonds in1C,2B,2C,3B, and3C (except the weak X1-Fe interaction in3C) are intermediate type interactions, whereas the Xi-Fe (i
=
1, 2, 3 and 4) bonds of1B result from weak interactions.Our results also revealed that while the chelation of Fe(II) reduces the BDE of L2 and L3, that of L1instead increases. Furthermore, the reduction in the O1-H bond length in1B and the presence of H2O ligands lead to an increase in the BDE of the chelate, while the addition of four CH3OH ligands to1A instead decreases its BDE. The presence of H2O and CH3OH ligands increases the BDE of2A but decreases that of3A. QTAIM has revealed a VDW interaction between the H atom of the hydroxyl group of L3 and the C atom of its CN group which elongates and weakens the O-H bond of the complexes of L3, conferring them relatively low BDEs. On the other hand, BDE of2B 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 Fe2+, an observation which agrees with those in the literature. With the exception of2C, 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.



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*Source: 8636409-2016-09-28.xml*