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<p>Journal Pre-proofs</p><p>Theoretical investigations on the antioxidant potential of 2,4,5-trihydroxybu‐</p><p>tyrophenone in different solvents: a DFT approach</p><p>Jewel Hossen, Tarun Kumar Pal, Tariqul Hasan</p><p>PII: S2211-7156(22)00234-X</p><p>DOI: https://doi.org/10.1016/j.rechem.2022.100515</p><p>Reference: RECHEM 100515</p><p>To appear in: Results in Chemistry</p><p>Received Date: 5 April 2022</p><p>Accepted Date: 8 September 2022</p><p>Please cite this article as: J. Hossen, T. Kumar Pal, T. Hasan, Theoretical investigations on the antioxidant</p><p>potential of 2,4,5-trihydroxybutyrophenone in different solvents: a DFT approach, Results in Chemistry (2022),</p><p>doi: https://doi.org/10.1016/j.rechem.2022.100515</p><p>This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover</p><p>page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version</p><p>will undergo additional copyediting, typesetting and review before it is published in its final form, but we are</p><p>providing this version to give early visibility of the article. Please note that, during the production process, errors</p><p>may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.</p><p>© 2022 The Author(s). Published by Elsevier B.V.</p><p>https://doi.org/10.1016/j.rechem.2022.100515</p><p>https://doi.org/10.1016/j.rechem.2022.100515</p><p>1</p><p>Theoretical investigations on the antioxidant potential of 2,4,5-</p><p>trihydroxybutyrophenone in different solvents: a DFT approach</p><p>Jewel Hossena*, Tarun Kumar Pala, Tariqul Hasanb</p><p>aDepartment of Chemistry, Rajshahi University of Engineering & Technology, Rajshahi-6204, Bangladesh</p><p>bDepartment of Chemistry, University of Rajshahi, Rajshahi-6205, Bangladesh</p><p>Corresponding author:</p><p>Jewel Hossen, Department of Chemistry, Rajshahi University of Engineering & Technology, Rajshahi, Rajshahi-</p><p>6204, Bangladesh, E-mail: jewelhossenruet@gmail.com, Orchid ID: 0000-0003-4365-6272</p><p>mailto:jewelhossenruet@gmail.com</p><p>2</p><p>Abstract</p><p>2,4,5-trihydroxybutyrophenone (THBP) is a synthetic molecule possessing phenolic OH groups as well as non-</p><p>phenolic CHx (x = 2 and 3) groups which are believed to be responsible for its antioxidant behavior. The antioxidant</p><p>nature of THBP has been systematically investigated through quantum chemical calculation by density functional</p><p>theory (DFT) method with B3LYP hybrid functional and 6-311G++(d,p) basis set in gas, water and methanol media.</p><p>The principal pathways such as hydrogen atom transfer (HAT), sequential proton loss electron transfer (SPLET) and</p><p>single electron transfer-proton transfer (SETPT) were considered for antioxidant reactions. Changes of enthalpy (∆H)</p><p>and free energy (∆G) were computed for OH● radical scavenging by THBP. In addition, geometry, highest occupied</p><p>molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), energy gap (Eg), the other descriptors</p><p>(electron affinity (EA), ionization potential (IP), global hardness (η), softness (σ), electrophilicity (ω), chemical</p><p>potential (μ), electronegativity (χ) etc.), Fukui function, molecular electrostatic potential (MEP) surface and spin</p><p>density were also taken into account. The calculated data values were compared with those of gallic acid (GA), a well-</p><p>recognized antioxidant, calculated at the same level and also with literature of those compounds claiming efficient</p><p>antioxidant. The values of the calculated thermochemical parameters convey evidence in favor of THBP as an</p><p>antiradical molecule which is strongly supported by the descriptor values. The free radical scavenging reaction may</p><p>occur preferentially at 5-OH>4-OH>α-CH2 positions of the molecule.</p><p>Keywords: 2,4,5-trihydroxybutyrophenone, THBP, DFT, antioxidant, free radical.</p><p>Introduction</p><p>Formation of free radicals in the living cells is a normal biological phenomenon in human body. In addition, some</p><p>peripheral aspects like radioactivity, pollutants, physical hassle, medicaments, some physiological dealings etc.</p><p>accelerate the free radical formation [1][2]. Detrimental chain reaction can be initiated by the highly active free</p><p>radicals that interact with lipids, proteins and DNA which causes the cell tissue’s damage [3]. Antioxidant contained</p><p>food items can minimize the disorders triggered by the free radicals [4]. Compounds with phenolic OH and flavonoids</p><p>either synthetically or naturally occurred can defend living cells against unanticipated oxidation caused by the radicals.</p><p>This way, the antioxidant prevent the progressive illness initiated in presence of the active free radicals and propagated</p><p>later on [5][6].</p><p>3</p><p>2,4,5-trihydroxybutyrophenone (THBP) is a synthetic compound possessing antioxidant capacity [7] and used as a</p><p>food additive [8]. THBP is specially applied to polyolefins and paraffin waxes as food additive. It is a very good</p><p>antioxidant for vegetable oils and animal fats; chemical preservative for animal feeds [9]. Its maximum permissible</p><p>limit in the manufacturing of food-packaging materials is 0.005% (FDA 121: 2001) and as antioxidant in vegetable</p><p>oil or fat in alone or with other permitted antioxidant is 0.02% maximum of the oil or fat content of food, including</p><p>essential (volatile) oil content (FDA 121.1116) [10]. Its antioxidant potential is well-known. THBP structure contains</p><p>three phenolic hydroxyl (OH) groups in the benzene ring which are considered the principle reason for its antioxidant</p><p>nature. In addition, it contains two CH2 (indicated as α and β) and one CH3 (indicated as γ) groups in the side chain</p><p>(Fig. 1). It is believed that, only the phenolic OH groups containing compounds behave as antioxidant and/or free</p><p>radical scavenger [11][12][13][14]. Now a days, a molecule is believed to have antioxidant activity for containing</p><p>CH2 and CH3 groups without having aromatic OH group. Baschieri et al. enlightened such activity of several natural</p><p>compounds without having any phenolic OH groups [15]. Several investigations support the contribution of CHx</p><p>(where, x = 1, 2 or 3) groups to the antioxidant characteristics [16][17]. Antioxidant power of THBP is documented</p><p>in several literature [8] [18]. Here, its antioxidant capability has been investigated through computational calculation</p><p>by DFT method considering both the phenolic OH and CHx groups of aliphatic chain comparing with recognized</p><p>standard antioxidant and literature.</p><p>In quantum chemical calculation, antioxidant potential of a molecule can be assessed by some thermochemical</p><p>parameters such as bond dissociation enthalpy (BDE), proton affinity (PA), electron transfer enthalpy (ETE),</p><p>ionization potential (IP), proton dissociation enthalpy (PDE) and some other molecular descriptors like HOMO-</p><p>LUMO energies, hardness, softness, chemical potential, electrophilicity, electronegativity, Fukui function, MEP, spin</p><p>density etc. Recently, quantum chemical approach, particularly DFT technique, has been creditably accounted to</p><p>calculate these parameters to explain antioxidant nature of a compound [3] [19].</p><p>4</p><p>C</p><p>C</p><p>H2</p><p>H2</p><p>C</p><p>H3C</p><p>OH</p><p>H</p><p>OH</p><p>OH</p><p>H</p><p>O</p><p>Fig. 1. THBP molecule with groups under antioxidant study</p><p>Fig. 2. The probable pathways for the antioxidant reaction of THBP with a free radical.</p><p>The antioxidant nature of a compound can be studied successfully applying the modern in-silico platform through</p><p>several concerned reaction mechanisms shown in Fig. 2. Hydrogen atom transfer (HAT) is well-known one</p><p>corresponding to the following reaction,</p><p>AOH + R● → AO● + RH</p><p>α</p><p>β</p><p>γ</p><p>5</p><p>Which is related to BDE of the associated bond (AOH) and connected to experimental study of antioxidant activity</p><p>[20] of the compound. Here AOH is analogous to antioxidant compound and R● is a free radical species.</p><p>BDE = H(AO●) + H(H●) – H(AOH)</p><p>Where, H(AO●), H(H●) and H(AOH) are the enthalpies of the radical AO● (formed after donating one hydrogen atom</p><p>from the AOH molecule), hydrogen atom and the AOH molecule respectively.</p><p>SETPT is another</p><p>important antioxidant pathway in which IP of and PDE are considered as follows [3].</p><p>AOH + R● → AOH●+ + R– → AO● + RH</p><p>IP = H(AOH●+) + H(e) – H(AOH)</p><p>PDE = H(AO●) + H(H+) – H(AOH●+)</p><p>Third pathway of antioxidant activity of a molecule is SPLET which refers to as [21]:</p><p>AOH → AO– + H+</p><p>PA = H(AO–) + H(H+) – H(AOH)</p><p>AO– + R● → AO● + R–</p><p>ETE = H(AO●) + H(e) – H(AO–)</p><p>Stability and chemical reactivity of a compound are believed to be important to predict its antiradical power and</p><p>largely depend on some chemical descriptors like chemical potential (µ) [22][23][24], electronegativity (χ) [25] [26],</p><p>chemical hardness (η), softness (σ) [27], Fukui function (f+, f- and Δf) [28], IP and EA. LUMO and HOMO energies</p><p>and the difference between them (ΔE = ELUMO - EHOMO) are also important in parallel to predict the chemical response</p><p>of a compound. Large value of ΔE represents lower reactivity and higher stability of the compound [29].</p><p>However, till date, computational investigation on the antioxidant potential of THBP has not been found in literature.</p><p>This article focuses on theoretical study to assess the antioxidant capability of the compound considering its phenolic</p><p>OH and three non-phenolic CHx (x=2 or 3) groups (Fig. 1).</p><p>Computational details</p><p>6</p><p>The computational calculations were completed in Gaussian 09 [30]. The geometries of THBP and GA (as reference),</p><p>their radicals and ions were optimized applying DFT with B3LYP functional [31][32][33], and 6-311G++(d,p) basis</p><p>set [34] in gas, water and methanol media. This quantum combination proved good bargain between computational</p><p>and experimental results [35][36]. B3LYP is the most applied functional tools in quantum chemical calculation, and</p><p>thus, enables comparison with forthcoming results [37][38][39][40]. Vibrational frequency of all the optimized species</p><p>were checked for any presence of imaginary frequency in order to have the minimum energy structure. The effects of</p><p>solvents on the antioxidant activity of THBP were investigated in water (ε = 78.3553) and methanol (ε = 32.613) to</p><p>mimic as high and medium polar solvents respectively employing the integral equation formalism polarizable</p><p>continuum model (IEFPCM) at the same condition. The BDE, IP, PDE, PA, ETE related to antioxidant reactions were</p><p>determined for the studied molecule [41][42] as per the following equations, where THBP is denoted as THBP-H.</p><p>BDE = H(THBP●) + H(H●) – H(THBP-H)</p><p>IP = H(THBP-H●+) + H(e) – H(THBP-H)</p><p>PDE = H(THBP●) + H(H+) – H(THBP-H●+)</p><p>PA = H(THBP−) + H(H+) – H(THBP-H)</p><p>ETE = H (THBP●) + H (e) – H (THBP−)</p><p>Where H(THBP-H), H(THBP●), H(THBP-H●+) and H(THBP−) are the enthalpies of THBP molecule, radical, radical</p><p>cation, and anion respectively, and H(H●), H(H+) and H(e) are those of hydrogen atom, proton and electron</p><p>respectively. The values of H(H●), H(H+) and H(e) in gas phase were used -0.49765, 0.00236, and 0.00118 Hartree</p><p>respectively [3] [43] [44]. The experimental value of H(H+) in water was -1090 kJ/mole (-0.41500 Hartree) [45] [46].</p><p>The H(e) values was -105 kJ/mole (-0.039992 Hartree) in water and, in methanol H(H+) and H(e) were -1038 and -86</p><p>kJ/mole (-0.39535 and -0.032756 Hartree) respectively [46]. The H(H●) was taken from reference [47] and it was also</p><p>used for methanol phase here.</p><p>∆G and ∆H for OH● scavenging by THBP and GA were computed as follows.</p><p>Reactions: (THBP-H) + OH● = THBP● + H2O (for THBP)………….…………………….. (1)</p><p>(THBP-H) + OH● = (THBP-H)+● + OH– (for THBP)…….…………………..……… (2)</p><p>7</p><p>(GA-H) + OH● = GA● + H2O (for GA)………….………….…………….. (3)</p><p>(GA-H) + OH● = (GA-H)+● + OH– (for GA)…….………………….……..…… (4)</p><p>∆G and ∆H for reaction (1) are</p><p>∆G = {G(THBP●) + G(H2O)} – {G(THBP-H) + G(OH●)} and</p><p>∆H = {H(THBP●) + H(H2O)} – {H(THBP-H) + H(OH●)} respectively.</p><p>Similarly ∆G and ∆H for reaction (2) are</p><p>∆G = {G(THBP-H)+● + G(HO–)} – {G(THBP-H) + G(OH●)} and</p><p>∆H = {H(THBP-H)+● + H(HO–)} – {H(THBP-H) + H(OH●)} respectively.</p><p>Where, G(X) is Gibbs free energy and H(X) is enthalpy of species X obtained from the optimized structure. Similarly</p><p>the ∆G and ∆H were computed for GA considering the equation (3) and (4).</p><p>IP and EA are related to EHOMO and ELUMO as per the Janak’s Theorem [48].</p><p>𝐼𝑃 = ― 𝐸𝐻𝑂𝑀𝑂</p><p>𝐸𝐴 = ― 𝐸𝐿𝑈𝑀𝑂</p><p>Hardness (η) is the ability of a molecule to resist polarization of its electronic charge cloud and is related to IP and EA</p><p>as follows [49].</p><p>𝐻𝑎𝑟𝑑𝑛𝑒𝑠𝑠, 𝜂 =</p><p>𝐼𝑃 ― 𝐸𝐴</p><p>2</p><p>𝑜𝑟 𝐻𝑎𝑟𝑑𝑛𝑒𝑠𝑠, 𝜂 =</p><p>𝐸𝐿𝑈𝑀𝑂 ― 𝐸𝐻𝑂𝑀𝑂</p><p>2</p><p>Softness is inverse of η [50].</p><p>𝑆𝑜𝑓𝑡𝑛𝑒𝑠𝑠, 𝜎 =</p><p>1</p><p>𝜂</p><p>Chemical potential (µ) and electronegativity ( ) can be defined as per the following mathematical equations.𝜒</p><p>8</p><p>𝜇 = (∂𝐸</p><p>∂𝑁)</p><p>𝑣</p><p>χ = ― 𝜇 = ― (∂𝐸</p><p>∂𝑁)</p><p>𝑣</p><p>Where, is the infinitesimal change in energy when electronic charge (more specifically electron) is added to a (∂𝐸</p><p>∂𝑁)</p><p>𝑣</p><p>molecule (M). Electronegativity of a molecule can be calculated from the energies of its three species as E(M+), E(M0),</p><p>and E(M-) correspond to the cation (M+), neutral molecule (M0) and anion (M-) respectively. Then by definition</p><p>E(M+) – E(M0) = IP, the ionization potential (energy) of M and</p><p>E(M0) – E(M-) = EA, the electron affinity of M</p><p>Adding these two above equations we get,</p><p>E(M+) – E(M-) = IP + EA</p><p>So now we can write,</p><p>𝜇 = (∂𝐸</p><p>∂𝑁)</p><p>𝑣</p><p>=</p><p>𝐸(𝑀 ― ) ― 𝐸(𝑀 + )</p><p>2 ― 0 =</p><p>― (𝐼𝑃 + 𝐸𝐴)</p><p>2</p><p>So the electronegativity</p><p>𝜒 =</p><p>(𝐼𝑃 + 𝐸𝐴)</p><p>2</p><p>The values of µ and χ can be calculated from ELUMO and EHOMO following the equations</p><p>𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑖𝑡𝑦, 𝜇 =</p><p>(𝐸𝐻𝑂𝑀𝑂 + 𝐸𝐿𝑈𝑀𝑂)</p><p>2</p><p>𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑖𝑡𝑦, 𝜒 =</p><p>―(𝐸𝐻𝑂𝑀𝑂 + 𝐸𝐿𝑈𝑀𝑂)</p><p>2</p><p>Fukui function is an important function, which is extensively applied in the diagnosis of reactive sites of a compound</p><p>[51][52]. Fukui function is defined as follows [53],</p><p>9</p><p>𝑓 ― (𝑟) = (∂𝜌(𝑟)</p><p>∂𝑁 ) ―</p><p>𝑣</p><p>= lim</p><p>𝜀→0 ―</p><p>𝜌𝑁(𝑟) ― 𝜌𝑁 ― 𝜀(𝑟)</p><p>𝜀</p><p>and</p><p>𝑓 + (𝑟) = (∂𝜌(𝑟)</p><p>∂𝑁 ) +</p><p>𝑣</p><p>= lim</p><p>𝜀→0 +</p><p>𝜌𝑁 + 𝜀(𝑟) ― 𝜌𝑁(𝑟)</p><p>𝜀</p><p>Where, υ is nuclear coordinates for a discrete chemical system. N and ρ(r) are the number and density function of</p><p>electrons respectively. The condensed dual descriptor may be expressed as:</p><p>∆𝑓 =</p><p>1</p><p>2</p><p>{𝑓 + (𝑟) ― 𝑓 ― (𝑟)}</p><p>Thus, antioxidant potential of a substance can be investigated taking all these probable thermochemical and molecular</p><p>aspects into account.</p><p>Analysis of spin density distribution</p><p>Spin density (SD) is a significant quantum chemical characteristic in the guesstimate of radical hunting power of an</p><p>antioxidant. When an antioxidant molecule donates one electron to the active free radical (for example OH●, OOH●</p><p>etc.), the molecule itself becomes another radical whose stability largely be subject to the electron SD over the entire</p><p>structure. The higher the delocalization of SD over the radical, the easier will be its formation as well as higher will</p><p>be its stability which results in good free radical scavenging ability [54].</p><p>Results and Discussions</p><p>Geometry analysis of THBP</p><p>In order to study the antioxidant comportment of a substance, it is decidedly commended to scrutinize its structural</p><p>geometry. The structures of THBP and its other concerned species were optimized in the gas, water and methanol</p><p>using DFT at B3LYP/6-311G++(d,p) level. Some geometrical characteristics of the studied compound in those media</p><p>are illustrated in Table 1. Fig. 1 shows the optimized geometry and labeled structure of THBP. Very little or no</p><p>significant geometrical change was found in gas, water and methanol phases. The distance between the hydrogen atom</p><p>of 2-OH group and carbonyl oxygen get closer (the H10-O21 distance was 1.676 Å in gas, whereas those were 1.657</p><p>10</p><p>and 1.658 Å in water and methanol respectively) in the polar solvents which influences the formation of weak</p><p>hydrogen bond between them. Changes of electronic energy along optimization steps are shown in the S-Fig. 1 which</p><p>demonstrated that THBP possesses slightly higher energy in gas phase than in aqueous</p><p>and methanol, whereas there</p><p>was no significant energy difference in water and in methanol media. THBP possesses 10.40 and 10.05 kcal/mole</p><p>more energy in gas phase than those in the water and methanol respectively.</p><p>Table 1. Some selected structural parameters (bond distances, bond angles and dihedral angles) of THBP in gas, water</p><p>and methanol</p><p>Bond distance (Å) Bond angle (o) Dihedral angle (o)</p><p>Bond Gas Water Methanol Angle Gas Water Methanol Dihedral angle Gas Water Methanol</p><p>C2-O9 1.341 1.349 1.348 C2-O9-H10 106.515 105.944 105.962 C1-C2-O9-H10 0.003 0.004 0.003</p><p>O9-H10 0.989 0.991 0.991 C2-C1-C14 119.675 119.952 119.942 C2-C1-C14-O21 0.007 0.002 0.007</p><p>C4-O11 1.355 1.355 1.355 C3-C4-O11 123.015 122.998 122.980 C3-C4-O11-H26 0.003 0.040 0.007</p><p>O11-H26 0.964 0.965 0.966 C4-O11-H26 109.651 110.262 110.220 C14-C1-C2-O9 0.006 0.000 0.003</p><p>C5-O12 1.369 1.370 1.371 C5-O12-H13 109.464 109.655 109.658 C4-C5-O12-H13 179.995 179.989 179.994</p><p>O12-H13 0.963 0.964 0.964 C14-C15-C18 114.125 114.591 114.569 C6-C1-C14-O21 179.998 179.989 179.994</p><p>C1-C14 1.466 1.466 1.466 C14-C15-H16 108.272 108.093 108.096 C1-C14-C15-C18 179.973 179.989 179.972</p><p>C14=O21 1.238 1.243 1.243 H16-C15-H17 105.584 105.448 105.457 C14-C15-C18-C22 179.986 179.992 179.990</p><p>C15-H16 1.097 1.096 1.096 C15-C18-C22 112.187 111.980 111.991 O21-C14-C15-C18 0.028 0.012 0.030</p><p>C18-H20 1.093 1.093 1.094 H19-C18-H20 105.803 106.281 106.260 H16-C15-C18-H20 64.346 64.073 64.083</p><p>H10..O21 1.676 1.657 1.658 H23-C22-H24 107.550 107.741 107.731 H19-C18-C22-H24 61.734 61.683 61.684</p><p>After withdrawal of hydrogen atom from phenolic OH group, permanent carbon-oxygen double (C=O) bonds formed</p><p>between carbon atom of benzene ring and concerned oxygen atom (S-Fig. 2). The case is similar for the three phenolic</p><p>OH groups of THBP in gas, water and methanol. Delocalization of electrons was extended to oxygen atoms of the</p><p>remaining OH groups upon the removal of a hydrogen atom from one OH group. In cases of α-, β- and γ-CHx radical</p><p>species, some differences were observed in the three phases. The structures of α-radical and anion were deviated</p><p>slightly from the plane with respect to the benzene ring in the calculated media. Electron delocalization was found</p><p>around the carbonyl carbon and α-carbon for α-radical (S-Fig. 2) and C=C double bond was found there for α-anion</p><p>(S-Fig. 3). One important modifications was noticed in α-anion species and that is, the distance between the carbonyl</p><p>oxygen (C=O) and hydrogen atom of 2-OH group got reduced significantly which causes the two groups come closer</p><p>to form hydrogen bond. In case of γ-anion, the structure was cleaved to form ethylene and a new anion species in gas</p><p>phase only. Delocalization of electrons was reduced in benzene ring but extended to phenolic OH groups after removal</p><p>11</p><p>of an electron from THBP (cation) in all the three phases studied here. The electrons’ delocalization supports</p><p>antioxidant behavior of the investigated compound [42].</p><p>BDE — HAT pathway indicator</p><p>BDE is a dominant parameter for the prediction of antioxidant activity of a molecule, because it concerns with the</p><p>ability of hydrogen atom donation and formation of a stable radical after that. For this reason, this is called HAT</p><p>mechanism of antioxidant behavior. The lower BDE of a compound refers to the higher hydrogen atom transfer ability</p><p>to other active free radicals, that means the compound is a stronger free radical scavenger [55]. The BDEs for the</p><p>studied groups of THBP were determined in gas, aqueous and methanol phases at B3LYP/6-311G++(d,p) level in</p><p>DFT method and the data are shown in Table 2. From the BDEs for the promising groups of THBP, it was found that,</p><p>2-OH, 4-OH, 5-OH, α-CH, β-CH and γ-CH possess BDEs of 93.03, 82.04, 75.47, 87.02, 95.03 and 98.61 kcal/mole</p><p>respectively in gas phase, 87.05, 79.79, 74.88, 86.47, 95.03 and 98.63 kcal/mole respectively in water and 87.29 79.90,</p><p>74.87, 86.51, 95.03 and 98.65 kcal/mole in methanol medium. Minimum BDE was found for 5-OH and maximum</p><p>was found for γ-CH. In parallel, the BDE of 3-OH and 4-OH groups of gallic acid (GA) have been calculated for</p><p>comparison and those are 77.17 and 76.86 kcal/mole respectively in gas, 78.50 and 76.11 kcal/mole respectively in</p><p>water and 78.45 and 76.16 kcal/mole respectively in methanol. BDEs of the groups decreased a bit in the water and</p><p>methanol that is consistent with literature [3]. BDEs for various groups of THBP are comparable to those calculated</p><p>here for GA and also close to or less than the literature values for myricetin [56], myricetin 3,4-di-O-α-</p><p>Lrhamnopyranoside [57], and ascorbic acid, GA [3]. The significant point is that, radical 5-OH has less BDE than GA</p><p>and the literature ones. The enthalpy changes (∆E) for the conversion of radicals and anions through the removal of</p><p>hydrogen atom and proton respectively were also determined and illustrated in the Table 2. The ∆E values show good</p><p>similarity with the previous study for antioxidant activity of thymoquinone [58]. The akin BDE data of HAT reaction</p><p>of THBP authorize its antioxidant activity as a free radical scavenger.</p><p>Table 2. BDE values for concerned groups of THBP and GA in gas, water and methanol</p><p>BDE, kcal/mole ∆E for radical, kcal/mole ∆E for anion, kcal/mole</p><p>Species Gas Water Methanol Gas Water Methanol Gas Water Methanol</p><p>2-OH 93.03 87.05 87.29 406.59 400.63 400.87 348.25 297.79 298.37</p><p>4-OH 82.04 79.79 79.90 395.60 393.37 393.48 327.66 283.00 283.92</p><p>5-OH 75.47 74.88 74.87 389.03 388.46 388.44 338.60 290.94 291.93</p><p>THBP</p><p>α-CH2 87.02 86.47 86.51 400.58 400.05 400.08 350.30 307.45 308.35</p><p>12</p><p>β-CH2 95.03 95.03 95.03 408.59 408.60 408.61 397.64 350.79 352.49</p><p>γ-CH3 98.61 98.63 98.65 412.17 412.21 412.22 363.23 350.58 351.74</p><p>3-OH 77.17 78.50 78.45 390.73 392.08 392.03 326.12 283.51 284.32GA</p><p>4-OH 76.86 76.11 76.16 390.42 389.69 389.74 326.39 281.51 282.41</p><p>3-CH 77.40 75.80 389.55 387.95 340.87 293.92TQ [58]</p><p>12-</p><p>CH3</p><p>83.68 83.07 395.84 395.22 341.63 296.30</p><p>AA [3] 3-OH 81.80 77.6</p><p>3-OH 87.40 85.3GA [3]</p><p>4-OH 79.10 79.2</p><p>4ʹ-OH 97.86 94.07</p><p>5΄-OH 97.70 93.80</p><p>ECPQ</p><p>[38]</p><p>4-OH 103.98 102.56</p><p>TQ stands for thymoquinone, AA for ascorbic acid, GA for gallic acid and ECPQ for eleocarpanthraquinone. The</p><p>square brackets indicate the references number.</p><p>The SD distributions of THBP● radicals after removal of hydrogen atom from different groups were plotted in the</p><p>studied phases to explicate the variations in BDEs and illustrated in Fig. 3 and those of GA were given in S-Fig. 4. It</p><p>is rationally a reliable measure to elucidate the constancy of the free radicals formed by elimination of a hydrogen</p><p>atom. A free radical’s stability is essentially contingent on its delocalization of SD. Basically a free radical with high</p><p>SD distribution is more stable [59]. It is clear from the Fig. 3 that, 2-OH, 4-OH, 5-OH and α-CH2 radicals showed the</p><p>most delocalized SD which corresponds well with the values of BDEs.</p><p>13</p><p>Fig. 3. Distribution of SD of THBP radicals after donation of a hydrogen from the concerned functional groups.</p><p>The SD of 2-OH, 4-OH, 5-OH and α-CH2 radicals are more distributed whereas those for β-CH2 radicals and γ-CH3</p><p>radicals are more localized around the groups concerned. There is a good agreement with GA data. This reflects the</p><p>indication for the high free radical scavenging power of THBP molecule with the respective groups. This affinity is</p><p>more or less alike for the radicals in gas, water and methanol. It can be inferred that, the 2-OH, 4-OH, 5-OH and α-</p><p>CH2 groups mainly contribute to the antioxidant potential of THBP via HAT pathway.</p><p>IP and PDE — SETPT pathway indicators</p><p>14</p><p>SETPT pathway consists of two steps: first step is donation of an electron and second step is transfer of a proton (AH</p><p>+ R● → AH●+ + R– → A● + RH). In this case, IP of the compound in the former step and PDE of the cation radical in</p><p>the later step are considered. IP and PDE are collectively taken into account to study antioxidant activity</p><p>in SETPT</p><p>mechanism. A good antioxidant should have low IP and PDE for SETPT pathway [42]. IP and PDE data of THBP are</p><p>presented in Table 3. The PDE value was lowest (214.96, -6.00 and 5.62 kcal/mole in gas, water and methanol</p><p>respectively) for 5-OH and highest (238.11, 17.75 and 29.39 kcal/mole in gas, water and methanol respectively) for</p><p>γ-CH3. The PDE values are less in polar phases than in the gas phases investigated here and the sequence of order</p><p>remains consistent in each case for the groups. The PDE values for all the groups of THBP are greater than those of</p><p>GA calculated here and that for 5-OH of THBP is closer to GA ones which is in good consistent with BDE. IP values</p><p>of THBP were 175.54, 73.67 and 99.21 kcal/mole in gas, water and methanol respectively which are significantly</p><p>lower than those of GA (188.86, 119.05 and 124.42 kcal/mole in gas, water and methanol respectively) as well as</p><p>literature [58] [3] and the decrements are much more in polar solvents. So, donation of electron is easier for THBP.</p><p>Actually, the capacity of electron-donation is associated with extended distribution of electron throughout the</p><p>molecular structure. A compound with higher π-electron delocalization is more active [60]. Above argument certify</p><p>that, THBP may pose antioxidant behavior through SETPT pathway.</p><p>Table 3. PDE and IP values of THBP and GA in gas, water and methanol</p><p>PDE, kcal/mole IP, kcal/moleSpecies</p><p>Gas Water Methanol Gas Water Methanol</p><p>2-OH 232.53 6.17 18.04 175.54 73.67 78.66</p><p>4-OH 221.54 -1.10 10.65</p><p>5-OH 214.96 -6.00 5.62</p><p>α-CH2 226.51 5.59 17.26</p><p>β-CH2 234.53 14.14 25.78</p><p>THBP</p><p>γ-CH3 238.11 17.75 29.39</p><p>3-OH 203.34 3.78 -0.92 188.86 119.05 124.42GA</p><p>4-OH 203.04 1.40 -3.20</p><p>AA [3] 3-OH 202.92 -14.57 191.82 122.00</p><p>3-OH 212.60 -6.30 189.20 164.20GA [3]</p><p>4-OH 204.30 -12.40</p><p>3-CH 193.04 198.73 169.28TQ [58]</p><p>12-CH3 199.32</p><p>PA and ETE — SPLET pathway indicators</p><p>15</p><p>Thirdly, SPLET pathway of antioxidant nature is assessed by PA and ETE. PA is the enthalpy of H+ transfer from</p><p>antioxidant species (AOH → AO– + H+) and ETE is the enthalpy of electron transfer from the anion (AO– + R● →</p><p>AO● + R–). The lower values of PA and ETE correspond to higher antioxidant capacity in SPLET method [42]. Table</p><p>4 shows PA and ETE data of THBP and GA in the studied media calculated at B3LYP/6-311G++(d,p). PA values for</p><p>OH bonds of THBP were close to the literature data of other compound with antioxidant potential [58] [3]. PA values</p><p>of THBP decreased in polar media showing similarity with the data of GA and literature [42]. PA values were in the</p><p>range of 329.14-399.12, 22.69-90.49 and 43.94-106.50 kcal/mole in gas, water and methanol respectively. The lower</p><p>PA values were found for phenolic OH groups than CHx groups in the studied phases which support the higher</p><p>antioxidant potential of phenolic hydroxyl groups that alkylic CHx groups [61]. ETE values for OH and CHx groups</p><p>of THBP were higher in polar media showing similar harmony with other articles [58] [60]. ETE values of THBP</p><p>were 10.96-67.93 kcal/mole in gas, 32.72-85.28 kcal/mole in water and 56.12-109.56 kcal/mole in methanol which</p><p>are consistent with another analogous work [58]. The values were comparable to the respective values of other alike</p><p>research [59] [60] [62]. Lower PAs were observed for OH groups, whereas lower ETEs were found for CHx groups</p><p>in the three phases studied. The data revealed the antioxidant competency of THBP through SPLET mechanism.</p><p>Table 4. PA and ETE data of THBP and GA in gas, water and methanol</p><p>PA, kcal/mole ETE, kcal/moleSpecies</p><p>Gas Water Methanol Gas Water Methanol</p><p>2-OH 349.73 37.48 50.38 58.34 77.76 102.50</p><p>4-OH 329.14 22.69 35.94 67.93 85.28 109.56</p><p>5-OH 340.08 30.63 43.94 50.43 72.43 96.52</p><p>α-CH2 351.78 47.14 60.37 50.27 67.51 91.73</p><p>β-CH2 399.12 90.49 104.50 10.96 32.72 56.12</p><p>THBP</p><p>γ-CH3 364.71 90.27 103.76 48.94 36.55 60.48</p><p>3-OH 327.60 23.20 36.33 64.61 83.48 107.71GA</p><p>4-OH 327.87 21.20 34.42 64.03 83.10 107.33</p><p>AA [3] 3-OH 328.98 20.98 65.76 86.45</p><p>3-OH 329.00 25.50 72.90 87.10GA [3]</p><p>4-OH 329.10 23.40 64.50 83.10</p><p>3-CH 342.35 49.42 94.77</p><p>12-CH3 343.12 54.94 99.65</p><p>5-CH3 357.88 56.74 106.06</p><p>TQ [58]</p><p>6-CH3 381.73 32.84 74.90</p><p>Frontier molecular orbitals (FMOs)</p><p>16</p><p>HOMO and LUMO are known as FMOs. FMOs are very crucial one to forecast the reactivity as well as antioxidant</p><p>activity of a molecule [63]. The HOMO energy (EHOMO) symbolizes the electron-giving capability, as it is</p><p>thermodynamically favorable, whereas LUMO energy (ELUMO) shows the ability of accepting electron [64] [65]. A</p><p>compound with lower EHOMO is less likely to donate electron and HOMO governs the location of free radical attack</p><p>[56]. The FMO of THBP in gas, water and methanol are illustrated in Fig. 4 and those of GA are shown in (S-Fig. 5).</p><p>The HOMO, LUMO distribution and the energy difference between them for GA are mostly similar as in another</p><p>literature [66] which support the THBP ones. Traditional π-like FMOs and distribution over the molecule</p><p>recommended antioxidant potential of the substance [42]. HOMO and LUMO were distributed approximately over</p><p>the entire THBP molecule except the ethyl in LUMO and propyl in HOMO for the investigated media. HOMO orbitals</p><p>were well distributed over 2-OH, 4-OH and 5-OH groups all along the benzene ring, signifying the plausible</p><p>involvement in antioxidant movement. The HOMO-1 orbital was mostly contributed to the delocalized π electrons in</p><p>the benzene ring and oxygen atoms. All the FMO demonstrates similar shapes in the studied phases except only the</p><p>LUMO+1 in gas phase. Theoretically, EHOMO is a remarkable gauge for free radical foraging ability [67]. LUMO is</p><p>spread over the benzene ring up to the two hydroxyl groups (2-OH and 4-OH) and extended to α-CH2 group of the</p><p>side chain. The energy difference between LUMO and HOMO is another important factor to determine the activity of</p><p>a compound. Small energy gap indicates softness (reactivity) whereas large gap signposts hardness (stability) of the</p><p>compound. A soft molecule can easily provide electron to the acceptor [68]. The global reactivity parameters deduced</p><p>from EHOMO and ELUMO are presented in Table 5. The electron donating easiness largely be subject to the</p><p>electronegativity and the values of THBP are less than those of GA. The other descriptors of THBP have data close</p><p>to those of other compounds demanded antioxidant activity [3] [69] [70].</p><p>17</p><p>Fig. 4. HOMO, LUMO, HOMO-1 and LUMO+1 of THBP in different media</p><p>The Fukui function is related to the local softness of a system. Hirshfeld charges are suitable one evaluating dual</p><p>descriptor and condensed Fukui function [71]. Hirshfeld charge of oxygen and carbon atoms of the concerned groups</p><p>have been determined in the N (neutral), N+1 (anion), and N-1 (cation) states of THBP using Multiwfn 3.8 software</p><p>[72]. The atomic charges are given in columns 2, 3, and 4 and , and are in columns 5, 6 and 7 respectively 𝑓 ― 𝑓 + ∆𝑓</p><p>in Table 6. In , negative values were found at 5-O and 2-O in THBP suggesting the most favorable sites for ∆𝑓</p><p>electrophilic attack which is very consistent with the other antioxidant parameters studied here. Electrophilic and</p><p>nucleophilic reaction sites are visualized for , and dual descriptors in Fig. 5. For dual descriptor, the negative 𝑓 + 𝑓 ―</p><p>18</p><p>regions (cyan color) were located mostly on the oxygen atoms of the hydroxyl groups and suggest higher tendency</p><p>towards both electrophilic and radical attack at the positions and contribute in antioxidant potential, whereas positive</p><p>isosurfaces (violet) indicate poor active site [73][74].</p><p>Fig. 5. (left), (middle) and dual descriptor (right) of THBP in gas𝑓 + 𝑓 ―</p><p>Table 5. HOMO and LUMO energy, energy gap and other descriptors of THBP and GA in gas, water and methanol</p><p>For THBP For GA</p><p>Property Symbol and/or</p><p>formula Gas Water Methanol Gas Water Methanol</p><p>LUMO energy (eV) ELUMO -1.907 -1.960 -1.958 -1.610 -1.721 -1.716</p><p>HOMO energy (eV) EHOMO -6.045</p><p>-6.216 -6.115 -6.534 -6.543 -6.542</p><p>Energy gap (eV) Eg = ELUMO – EHOMO 4.137 4.255 4.157 4.924 4.823 4.826</p><p>Ionization potential</p><p>(eV) IP = – EHOMO 1.907 1.960 1.958 1.610 1.721 11.368</p><p>Electron affinity (eV) EA = – ELUMO 6.045 6.216 6.115 6.534 6.543 6.542</p><p>Global hardness (eV) η = (ELUMO –</p><p>EHOMO)/2 2.069 2.128 2.079 2.462 2.411 2.413</p><p>Softness σ = 1/η 0.483 0.470 0.481 0.406 0.415 -4.129</p><p>Chemical potential</p><p>(eV)</p><p>μ = (ELUMO +</p><p>EHOMO)/2 -3.976 -4.088 -4.036 -4.072 -4.132 -6.542</p><p>Electrophilicity ψ = μ2/2η 3.821 3.927 3.919 3.367 3.540 -2.413</p><p>Electronegativity χ = – μ 3.976 4.088 4.036 4.072 4.132 4.129</p><p>Dipole moment</p><p>(Debye) D 2.457 3.666 3.621 4.630 6.361 6.302</p><p>Polarizability (a.u) α 140.462 188.097 186.455 102.865 140.027 138.719</p><p>Table 6. Hirshfeld charges, and dual descriptor for the oxygen and carbon atoms in THBP𝑓 ― , 𝑓 +</p><p>Site N N – 1 N+1 𝑓 ― 𝑓 + ∆𝑓</p><p>2-OH -0.190337 -0.095033 -0.253077 0.095305 0.062740 -0.032565</p><p>19</p><p>4-OH -0.165279 -0.107085 -0.226482 0.058193 0.061203 0.003010</p><p>5-OH -0.185909 -0.077296 -0.226384 0.108613 0.040475 -0.068137</p><p>α-CH2 -0.049371 -0.040796 -0.062681 0.008575 0.013310 0.004735</p><p>β-CH2 -0.043753 -0.036208 -0.051383 0.007545 0.007629 0.000084</p><p>γ-CH3 -0.082869 -0.074731 -0.093526 0.008138 0.010657 0.002519</p><p>Molecular electrostatic potential (MEP) surface</p><p>In order to investigate and anticipate antioxidant potential of a compound, MEP is an important measurement. The</p><p>MEP plots of THBP and GA (as a reference standard) were presented in Fig. 6. The electron-rich (negative) area and</p><p>electron-lean (positive) area on the surface are indicated with red and blue color mapping. The free radicals most</p><p>probably attack the positive sites [42]. The negative regions were located over the oxygen atoms whereas the positive</p><p>regions appeared over the polar hydrogen in the studied phases. Non-polar hydrogen and carbon atoms mostly in white</p><p>color indicate the junctions between the polar and non-polar regions over the MEP surfaces. These mappings are</p><p>useful to predict the positions of free radical attack toward THBP. However the chemistry of antioxidant is a complex</p><p>and multifarious fashion and can be subject to number of aspects [75].</p><p>20</p><p>Fig. 6. MEP surfaces of THBP and GA in gas, water and methanol at DFT/B3LYP/6-311G++(d,p)</p><p>∆G and ∆H — Thermodynamics of hydrogen abstraction (HA)</p><p>∆G and ∆H for OH● radical scavenging (THBP-H + OH● = THBP● + H2O) by THBP were computed as per the simple</p><p>rules of thermochemistry at DFT/B3LYP/6-311G++(d,p). And those of GA were also calculated at the same level.</p><p>The ∆G and ∆H of THBP and GA are presented in Table 7. The ∆G and ∆H values are interestingly negative for HA</p><p>from THBP which is very rational for spontaneous OH● radical scavenging in HAT mechanism. ∆G and ∆H values</p><p>were found lower for the OH groups in comparison with the CHx ones, (but the case is reversed for 2-OH and α-CH2</p><p>groups in the studied three phases). Minimum ∆G and ∆H values were found for 4-OH and 5-OH groups in the three</p><p>phases which show good consistency with BDE, PDE and PA. In addition, the order of ∆G and ∆H values for the</p><p>studied OH and CHx groups of THBP and OH of GA were almost similar in gas, water and methanol. The range of</p><p>∆G and ∆H for the HA reaction were -16.12 to -39.27 and -17.63 to -39.92 kcal/mole respectively in gas, -17.84 to -</p><p>41.62 and -19.23 to -42.35 kcal/mole respectively in water, and -17.79 to -41.56 and -19.18 to -42.29 kcal/mole</p><p>21</p><p>respectively in methanol. These data are very comparable to those calculated for GA at the same condition and close</p><p>to or less than the literature values (mentioned in the Table 7) for others compound claiming potent antioxidant. The</p><p>∆G of HA from 4-OH and 5-OH groups of THBP to OH● radical were -32.69 and -39.27 kcal/mole respectively in</p><p>gas, -36.58 and -41.62 kcal/mole respectively in water and -36.53 and -41.56 kcal/mole respectively in methanol and</p><p>these are less than or very comparable to the literature values (Table 7). Similarly, the ∆H values of HA from THBP</p><p>are very reasonable with the literature values. The evenhanded negative values of ∆G and ∆H convey suitable evidence</p><p>toward the antioxidant capacity of THBP as free radical scavenger via HAT. However, the ∆G and ∆H for electron</p><p>transfer reaction ((THBP-H) + OH● = (THBP-H)+● + OH–) were positive in gas, water and methanol but less than those</p><p>of GA and literature data for other antioxidants [42] [70] [76]. It is interesting to report that, the ∆G and ∆H values</p><p>for electron transfer reaction are highly decreased in the polar solvent compared to the gas media for all the groups.</p><p>So it can be said that, THBP demonstrates less potency in antioxidant action via electron transfer mechanism.</p><p>Table 7. ∆G and ∆H values for HO● radical scavenging by THBP and GA in gas, water and methanol</p><p>∆G, kcal/mole ∆H, kcal/mole ∆G, kcal/mole ∆H, kcal/moleSpecies (for HA to OH●) (for electron transfer to OH●)</p><p>Gas Water Methano</p><p>l Gas Water Methano</p><p>l Gas Water Methano</p><p>l Gas Water Methano</p><p>l</p><p>THBP</p><p>2-OH -21.70 -29.19 -29.14 -21.68 -28.99 -28.94</p><p>4-OH -32.69 -36.58 -36.53 -33.53 -37.45 -37.40</p><p>5-OH -39.27 -41.62 -41.56 -39.92 -42.35 -42.29</p><p>α-CH2 -27.72 -29.98 -29.93 -29.21 -31.57 -31.52</p><p>β-CH2 -19.70 -21.46 -21.40 -21.95 -23.98 -23.93</p><p>γ-CH3 -16.12 -17.84 -17.79 -17.63 -19.23 -19.18</p><p>134.84 14.03 16.19 135.07 14.05 16.03</p><p>GA</p><p>3-OH -37.56 -37.98 -37.98 -38.00 -37.81 -37.82</p><p>4-OH -37.87 -40.37 -40.26 -38.22 -40.17 -40.06 148.16 24.01 26.30 148.41 24.41 26.73</p><p>TQ [70]</p><p>3-CH -40.61 -43.54 -38.74 -40.34</p><p>12-CH3 -32.92 -35.39 -32.46 -33.07</p><p>5-CH3 -17.29 -19.14 -15.89 -15.99</p><p>6-CH3 -17.50 -19.18 -15.95 -15.88</p><p>-24.2</p><p>[76]</p><p>-31.7</p><p>[76]</p><p>-22.00</p><p>[76]</p><p>-29.40</p><p>[76]</p><p>156.73 157.29 47.76 48.42</p><p>Refer-</p><p>ences -9.37</p><p>[42]</p><p>-11.26</p><p>[42]</p><p>Conclusion</p><p>22</p><p>Antioxidant behavior of THBP was theoretically investigated in gas and polar solvents (water and methanol) applying</p><p>DFT technique considering some thermochemical aspects and molecular descriptors. The computationally calculated</p><p>data strongly support the antioxidant potential of THBP. The computed BDE, IP, PDE, PA and ETE values showed</p><p>that, the antioxidant tendency of hydroxyl groups is more than those of CHx groups of THBP studied here and polar</p><p>solvents are less energetic media then gas phase. The 5-OH among the hydroxyl groups and α-CH2 among the CHx</p><p>groups are thermochemically more active in THBP toward radical scavenging. HAT mechanism is energetically more</p><p>desirable than SETPT and SPLET pathways regarding the antioxidant nature of the studied compound. The results</p><p>strongly exhibited free radical scavenging power of THBP through its phenolic OH as well as CHx groups, which can</p><p>pave the way for studying antioxidant nature of other prospective compounds.</p><p>Funding</p><p>This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit</p><p>sectors.</p><p>Conflicts of interest/Competing interests</p><p>The authors declare that they have no known competing financial interests or personal relationships that could have</p><p>appeared to influence the work reported in this paper.</p><p>Availability of data and material</p><p>All the data are provided in the manuscript and supplementary file.</p><p>Ethics approval</p><p>The manuscript does not contain experiments on animals and humans; hence ethical permission not required.</p><p>Consent to participate</p><p>All the authors actively participated in this work.</p><p>Consent for publication</p><p>If this manuscript is accepted for publication in this journal, we would not withdraw it.</p><p>References</p><p>23</p><p>[1] E. 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Quantum Chem. 113 (2013) 966–974. https://doi.org/10.1002/qua.24060.</p><p>29</p><p>Declaration of interests</p><p>☒ The authors declare that they have no known competing financial interests or personal relationships</p><p>that could have appeared to influence the work reported in this paper.</p><p>☐The authors declare the following financial interests/personal relationships which may be considered</p><p>as potential competing interests:</p><p>Highlights</p><p> Antioxidant potential of THBP using DFT</p><p> Pathways studied: HAT: BDE, SETPT: IP, PDE and SPLET: PA, ETE</p><p> ∆G and ∆H, HOMO, LUMO, MEP, hardness, softness, chemical potential</p><p>CRediT statement</p><p>Jewel Hossen: Conceptualization; Data curation; Formal analysis; Methodology; Visualization;</p><p>Writing - original draft; Editing; Tarun Kumar Pal: Editing and reviewing; Tariqul Hasan:</p><p>reviewing.</p>