Density Functional Theory Analysis of Luteolin Molecular Structure and Spectrum

Abstract

Luteolin is a natural flavonoid compound. Numerous studies have demonstrated that luteolin exhibits pharmacological activities such as antioxidant and antitumor effects; however, the molecular mechanisms linking its electronic structure to pharmacological activities have not been systematically elucidated. Structure determines properties, which are crucial factors for investigating the chemical characteristics and reaction mechanisms. This study aims to analyze its electronic structure parameters and reveal the correlation between active sites and biological functions by using density functional theory. The geometric configuration of luteolin was optimized by the B3LYP-D3­(BJ)/6–311G­(d,p) method. Frontier molecular orbitals (FMOs), electron affinity (EA), ionization energy (ionization potential (IP)), density of states (DOS), bond dissociation energy (BDE), proton affinity (PA), molecular surface electrostatic potential (MESP), and vibrational spectra were calculated. The chemical shifts of ¹H NMR and ¹³C NMR were predicted using the gauge-including atomic orbital theory. Results show that geometric optimization and spectral analysis confirm the presence of hydrogen bonds and conjugated systems in luteolin, indicating that its antioxidant and antitumor potential are closely associated with the electron delocalization capacity of the conjugated backbone and the stability modulation of intramolecular hydrogen bonds. DOS analysis reveals that the p-orbital-dominated conjugated system is the core of its chemical stability and antioxidant activity; functional groups such as carbonyl and hydroxyl groups participate in electronic state construction through p-orbital hybridization/conjugation, ultimately determining the molecular structure–function relationship. With a narrow HOMO–LUMO energy gap (4.37 eV), low BDE (304.27 kJ/mol), and low IP (724.44 kJ/mol), luteolin synergistically and efficiently scavenges free radicals via a hydrogen atom transfer-dominated mechanism, combined with sequential proton loss electron transfer (SPLET) and single electron transfer followed by proton transfer (SET-PT), suggesting potent antioxidant and antitumor capabilities. Based on the low BDE (304.27 kJ/mol) and the distribution of electrophilic/nucleophilic regions in MESP analysis, the phenolic hydroxyl group on ring B (O20–H30) and the carbonyl group on ring C (C3O11) are identified as potential key active sites for antioxidant and antitumor activities. This study investigates the structural characteristics, spectral properties, and key active sites of luteolin, providing a theoretical basis for its antioxidant and antitumor pharmacological effects and offering theoretical guidance for its targeted drug design.

1. Introduction

Luteolin is a natural flavonoid compound, classified as a weakly acidic tetrahydroxyflavone, which is present in various plants. It exhibits a range of pharmacological activities, including antioxidant, antitumor, anti-inflammatory, and antiallergic effects. Studies have shown that luteolin possesses specific advantages over other flavonoids in the treatment of gastric cancer lymph node metastasis. Euphorbia helioscopia has been found to contain abundant flavonoids, such as luteolin, quercetin, kaempferol, and naringenin; however, in the treatment of gastric cancer lymph node metastasis with E. helioscopia, luteolin may exert the most critical role by targeting the MMP9 gene. Therefore, luteolin holds a significant research value compared to other flavonoid compounds. Structure determines properties that are crucial factors governing its pharmacological effects and efficacy. It has been reported that the lower the bond dissociation energy (BDE), the higher the antioxidant activity of flavonoids via the hydrogen atom transfer (HAT) mechanism. Additionally, the electron-donating capacity of flavonoids is closely associated with their antioxidant activity. A lower ionization potential (IP) enables molecules to lose electrons more easily, thereby exhibiting stronger antioxidant activity. The higher the energy of the highest occupied molecular orbital (HOMO) and the smaller the HOMO–lowest unoccupied molecular orbital (LUMO) energy gap (HOMO–LUMO gap), the more readily molecules lose electrons and the stronger their antioxidant activity. The concentration of reactive oxygen species (ROS) in cancer cells is higher than that in normal cells; reducing ROS concentration or rapidly increasing ROS levels in cancer cells can induce tumor cell death. Most active centers of tumor targets contain electron-deficient sites (e.g., Fe³⁺, π empty orbitals of base pairs). Flavonoids can donate electrons to bind with metal atoms in the active centers, thereby exerting antitumor effects. Furthermore, electrophilic groups in drug molecules can form covalent bonds with nucleophilic groups of deoxyribonucleic acid (DNA), inhibiting DNA function and achieving antitumor activity.

Driven by innovations in computing architecture, quantum chemical methodologies have undergone a paradigm shift from auxiliary tools to core methods in analytical chemistry, and their ability to analyze drug molecules has transcended the limitations of traditional experiments. , Traditional experimental techniques (e.g., mass spectrometry, X-ray diffraction) excel at determining macroscale properties of molecules (e.g., molecular weight, crystal structure) but struggle to directly obtain electronic-level information (e.g., charge distribution, orbital interactions). Moreover, drug development based on these techniques features a long cycle, low success rate, and difficulty in capturing transient changes. In contrast, first-principles calculations reveal the microscopic mechanism of interactions by computing electronic-level information (e.g., charge distribution, orbital interactions) of the interacting systems. By precalculating key parameters (e.g., HOMO–LUMO energy and binding free energy), they can rapidly screen potential active molecules in silico, reduce experimental costs, shorten the drug development cycle, and identify intermediate configurations by calculating reaction transition states. These advantages make first-principles calculations a powerful tool for studying the antioxidant and antitumor activities of flavonoids.

Compared with ab initio methods (defined as “wave function-based methods that require solving complex multielectron systems with high computational costs”) and semiempirical methods (defined as “methods relying on empirical parameters with relatively low descriptive accuracy”), density functional theory (DFT) determines the ground-state energy and all ground-state properties of multielectron systems by calculating electron density, balancing efficiency, and accuracy, thus exhibiting distinct advantages in electronic structure research. , A reasonable combination of basis sets significantly enhances the computational performance. Currently, DFT is widely used to calculate the electronic structure, optical properties, mechanical properties, and thermodynamic properties of various materials. , It helps researchers understand the properties of existing materials and predict those of new materials. Nowadays, quantum chemistry has been integrated with traditional Chinese medicine research and exhibits a strong momentum in investigating the properties of drug molecules.

At present, research on the electronic structure and spectral properties of luteolin remains limited. A study using the B3LYP/6-311G­(d,p) method identified the hydroxyl group (O20–H30) of luteolin as a key active site for antioxidant activity by calculating BDE; however, this study did not correlate the finding with specific pharmacological activities and focused primarily on single parameters (e.g., BDE, IP), lacking multidimensional collaborative analysis (e.g., Frontier molecular orbital (FMO) analysis, density of states (DOS) interpretation, and the correlation between molecular surface electrostatic potential (MESP) and electron transfer pathways). A study on the chelation of luteolin with Pb­(II) found that luteolin can effectively chelate Pb­(II) via the 5-hydroxy-4-oxo chelating site, providing theoretical support for luteolin as a health supplement for lead cation removal. Nevertheless, this study did not discuss why the 5-hydroxy-4-oxo site can efficiently bind to Pb­(II) from an electronic perspective of luteolin. Another study investigated the interaction mode between luteolin and guanine by using the B3LYP/6-31 + G­(d) basis set. Results showed that the formed complexes are primarily stabilized by hydrogen bonding and that the phenolic hydroxyl groups of luteolin play a crucial role in hydrogen bond formation, providing theoretical support for its antitumor activity. However, the study did not explore the reasons for the reactivity of luteolin’s phenolic hydroxyl groups during hydrogen bond formation. Additionally, the correlation between spectral characteristics and electronic structure was only analyzed at the peak position level, without in-depth discussion on how vibrational modes regulate reaction activity (e.g., the relationship between hydroxyl stretching vibrations and hydrogen transfer efficiency). In view of the above limitations, this study improved the computational method by adding a dispersion correction term to describe noncovalent interactions (NCIs)including hydrogen bonds and π–π-conjugated structures. Beyond analyzing FMO and BDE values, this study integrated analyses of MESP, electron affinity (EA), IP, proton affinity (PA), DOS, infrared (IR) spectroscopy, and nuclear magnetic resonance (NMR) spectroscopy. Specifically, this study systematically analyzed (1) electronic structure, (2) spectral characteristics, and (3) the correlation between electron-donating capacity and antioxidant/antitumor activities. Meanwhile, it provides more in-depth mechanistic explanations to address the fragmentation of existing research, offering key theoretical bases for targeted molecular engineering guided by electronic structure regulation.

2. Methods

As PubChem is a well-recognized biochemical database, the 3D structure of luteolin (Compound ID: 5280445) was retrieved from PubChem and imported into ChemDraw software for construction. This structure, as the predominant conformer of luteolin, was selected as the research object for this study. The initial model was directly imported via the “Import from Database” function of GaussView 16W to ensure the experimental basis of the structure, and the other five conformers of luteolin are discussed in the Supporting Information (S6-Conformational Selection). This study compared three functionals and pointed out that B3LYP can usually reproduce vibrational characteristics well with minimal errors in spectral description. Moreover, the B3LYP algorithm can impartially reflect thermodynamic properties and accurate bond energies, thus being widely used in numerous calculations. Therefore, the hybrid density functional B3LYP was selected as the research functional. Studies have shown that the B3LYP functional poorly describes weak interactions dominated by dispersion forces; adding the EM = gd3bj dispersion correction term improves the average calculation error of weak interactions by 80%, reducing it to 2.94 kcal/mol. Since luteolin exhibits NCIs such as intramolecular hydrogen bonds and π–π stacking between aromatic rings (dominated by dispersion forces), the dispersion correction term EM = gd3bj was adopted to compensate for the shortcomings of the B3LYP hybrid density functional in describing NCIs. A benchmark test of over 10 common functionals for optimizing weak interaction systems revealed that B3LYP-D3­(BJ) achieves nearly the highest optimization accuracy, verifying the reliability of the selected functional. Three basis sets were compared at the same level, and the most cost-effective basis set for subsequent studies was determined by calculating the internal energy and HOMO–LUMO gap. Since optimization calculations ignore the vibrational energy of molecules at 0 K, which is non-negligible due to its significant magnitude, the zero-point energy (ZPE) correction was applied. The frequency and ZPE of the structure were calculated at the same level, and the absence of imaginary frequencies in the optimized structure confirmed that it is located at the minimum point on the potential energy surface, thereby obtaining the stable structure of luteolin. The optimized frequency data are provided in the Supporting Information (S5-Vibration Frequency). The correction method for virtual frequency is provided in the Supporting Information (S7-Correction method of virtual frequency). The Gaussian16 program package was used for the plotting and analysis of HOMO, LUMO, and MESP, as well as the calculation of EA, PA, IP, and BDE. Multiwfn software was employed to calculate NMR chemical shifts, plot IR and DOS spectra, and conduct comprehensive identification and detailed assignment of the calculation results. All calculations in this study were performed on a personal computer (PC) by using the Gaussian16W program package.

Unless otherwise specified, all calculations in this study were carried out under standard conditions (1 atm, 273.15 K) and in the gas phase. The convergence criteria for DFT calculations were set as follows: root-mean-square (RMS) displacement gradient = 12 × 10^–4 radian, maximum displacement = 18 × 10^–4 Bohr, RMS force = 3 × 10^–4 Hartree/radian, and maximum force = 45 × 10^–5 Hartree/Bohr. Additionally, the convergence criteria for self-consistent field (SCF) calculations were RMS density matrix = 1 × 10^–8 and maximum density matrix = 1 × 10^–6. Vibrational frequency calculations confirmed the absence of imaginary frequencies in the optimized structure, indicating that the Hessian matrix had no negative eigenvalues. This verifies the thermodynamic stability of the optimized structure.

3. Results

3.1. Base Group Selection

Given the research focus on luteolin’s antioxidant and antitumor activities, its mechanism of action involves NCIs such as intramolecular and intermolecular hydrogen bonds and π–π stacking. In principle, higher-level basis sets yield higher computational accuracy, but the corresponding computational cost increases significantly. As a general 3-zeta basis set, 6–311G­(d,p) can well describe common computational problems and has been widely used in numerous calculations. The polarization functions (d, p) included in the 6–311G­(d,p) basis set effectively improve the description accuracy of such interactions: the d functions can better depict the distortion of electron clouds around heavy atoms (e.g., C, O) and accurately characterize π-electron delocalization in conjugated systems (which is closely related to luteolin’s electron transfer capacity and antioxidant activity); the p polarization functions enhance the description of electron distribution around hydrogen atoms, thereby more precisely simulating electron density transfer between hydrogen bond donors and acceptors. This is particularly crucial for analyzing intramolecular hydrogen bonds in luteolin and the interactions between phenolic hydroxyl groups and biological targets (e.g., proteins, DNA). As shown in Table , existing studies all selected 3-zeta basis sets, differing only in the inclusion of diffuse functions for heavy atoms and hydrogen atoms, yet yielding consistent quantitative resultsO20–H30 is the optimal site for antioxidant activity. Regarding the selection of diffuse functions, studies have found that adding diffuse functions to hydrogen atoms is meaningless in most cases. Hydrogen has only one electron and low electronegativity; in molecular environments, it usually loses many electrons. Adding diffuse functions obviously does not bring perceptible improvements to the results. Moreover, organic systems typically contain a large number of hydrogen atoms; therefore, adding diffuse functions to hydrogen also significantly increases the computational cost. There is no need to add diffuse functions to C and O elements either, as 3-zeta basis sets possess slight diffuse characteristics and can qualitatively describe diffuse properties. Diffuse functions are used only when calculating anionic systems. To verify the rationality of the basis set selection, this study compared the calculation results of structure optimization and HOMO–LUMO gap of luteolin using 6–31 +G­(d,p), 6–311G­(d,p), and 6–311 +G­(d,p) (Table ). A smaller electronic energy indicates higher basis set accuracy. The comparison shows that the calculation results of 6–311G­(d,p) and 6–311 +G­(d,p) have a small deviation (percentage difference in electronic energy = 0.0025%, energy gap difference <0.02 eV), but the computational time of the latter increases by approximately 83%; in contrast, the deviation between 6 and 31 +G­(d,p) and 6–311G­(d,p) is large (percentage difference in electronic energy = 0.021%, energy gap difference <0.02 eV). Combined with the computational analysis in Tables and , from the perspective of balancing computational efficiency and accuracy, unless otherwise specified, the 6-311G­(d,p) basis set is used for neutral and cationic systems and the 6-311+ G­(d,p) basis set is adopted for anionic systems in this study.

2. Research on Related Flavonoids.

item	1	2	3	4	5
object	quercetin	isoliquiritigenin	curcumin	luteolin	apigenin
method	B3LYP/6–311++G(d,p)	B3LYP/6-31 + G(d,p)	B3LYP/6-311G(d,p)	B3LYP-D3/6-311G(d,p)	B3LYP/6-311G(d)
E gap (eV)	3.66	3.96	-	4.37	4.19
E (HOMO) (eV)	–5.97	-	-	–5.99	–6.15
BDE (kJ/mol)	347.35	361.08	337.69	304.27	358.59
IP (kJ/mol)	-	679.44	638.90	724.44	-

1. Base Group Comparison Study .

item	6–311 +G(d,p)	6–311g(d,p)	6–31 +g(d,p)
EE + ZPE (a.u.)	–1029.069699	–1029.043539	–1028.853995
E gap (eV)	4.3598	4.3693	4.3448
time (h)	5.5 h	3 h	4.3 h

^aNote: “E _gap” refers to the HOMO–LUMO gap.

Table summarizes the DFT research on related flavonoid compounds. Studies have found that the order of antioxidant activity of flavonoids in Glycyrrhiza uralensis is isoliquiritigenin > isoliquiritin > liquiritigenin > liquiritin, which is consistent with the experimental activity order. Relevant data for isoliquiritigenin are given in Table (Item-2), where the BDE value corresponds to the 7-OH group. Second, studies on four flavonoids in Medicago sativa have shown that their antioxidant activity follows the order: quercetin > luteolin > genistein > formononetin. Relevant data for quercetin are presented in Table (Item-1), with the BDE value corresponding to the 4’-OH group. Third, a study on the antioxidant activity of two flavonoids and one synthetic compound found that curcumin (a flavonoid) has the best antioxidant performance, and luteolin’s antioxidant activity is comparable to that of butylated hydroxytoluene (BHT). Relevant data for curcumin are shown in Table (Item-3), where the BDE value corresponds to the enolic OH group. Additionally, research on five flavonoids in Chrysanthemum boreale revealed their antioxidant activity order: luteolin > cynaroside > apigenin > acacetin > tilianin, which is consistent with the experimental results. Relevant data for apigenin are listed in Table (Item-5), with the BDE value corresponding to the 4-OH group. As indicated in Table , extensive research on the antioxidant properties of flavonoids has been conducted using the B3LYP functional and the 6–311G­(d,p) basis set. Similar computational methods can be adopted for subsequent studies on the antioxidant activity of related flavonoids.

3.2. Geometric Configuration and Structural Parameters

The structure of luteolin after geometric optimization (Figure ) comprises two benzene rings (Rings A and B), one pyrone ring (Ring C), four hydroxyl groups, and one carbonyl functional group. From the partial key bond length data of luteolin after geometric optimization (Table ), the hydrogen atom of the phenolic hydroxyl group on the C16 carbon atom of Ring B forms an intramolecular hydrogen bond with the oxygen atom of the phenolic hydroxyl group at position 17, with an R (O–H···O) distance of 2.13 Å. The dihedral angle data (Table ) show that the dihedral angle D (2, 3, 4, 5) is −179.1° and D (8, 9, 4, 3) is −179.8°, indicating that Ring A and Ring C of luteolin are essentially coplanar; the dihedral angle D (10, 1, 14, 19) is −163.8°, and D (10, 1, 14, 15) is 16.3°, revealing that Ring C and Ring B of the luteolin molecule are noncoplanar. The bond length, bond angle, and dihedral angle data all indicate that the molecule possesses a highly conjugated system, which facilitates electron delocalization, suggesting that luteolin exhibits potent antioxidant and antitumor activities.

1.

Geometric configuration of optimized luteolin molecule. Note: (a) optimized planar structure diagram; (b) optimized stereoscopic configuration diagram.

3. Main Structural Parameters of Optimized Luteolin Molecules .

key length	value/Å	key length	value/Å	angle	value/(°)
R (21,31)	0.966	R (12,23)	2.544	A (5,13,26)	108.5
R (13,26)	0.964	R (31,20)	2.132	A (7,12,25)	109.3
R (12,25)	0.963	R (3,11)	1.223	A (16,21,31)	107.8
R (20,30)	0.962	R (22,11)	2.579	A (17,20,30)	110.2
R (7,12)	1.359	R (1,14)	1.469	D (2,3,4,5)	–179.1
R (17,20)	1.372			D (8,9,4,3)	–179.8
R (16,21)	1.360			D (10,1,14,15)	16.3
R (5,13)	1.350			D (10,1,14,19)	–163.8

^aNote: The bond length, bond angle, and carbon atom parameters associated with the functional group are selected, while the dihedral angle is determined from the atoms connected to the A and C rings, as well as the C and B rings. The letters R, A, and D represent the key length, key angle, and dihedral angle parameters, respectively. All data on bond lengths, bond angles, and dihedral angles are provided in the supplementary files (S1-Bond length; S2-Bond angle; S3-Dihedral angle). The Cartesian coordinates and total energy of luteolin after molecular optimization are available in the supplementary file (S4-Molecular coordinates).

3.3. FMO

The diagrams of the HOMO (Figure a) and LUMO (Figure b) orbitals of luteolin after geometric optimization are almost identical. Most atoms are involved in orbital composition, with only the atoms H23, H24, H25, H26, and H28 not participating. FMO analysis of luteolin (Table ) shows that its HOMO has an energy of −5.99 eV and the LUMO has an energy of −1.62 eV. The calculated HOMO–LUMO energy gap is 4.37 eV. This narrow energy gap, combined with the relatively high HOMO energy, means the molecule is more prone to electron transfer in chemical reactions and thus exhibits high reactivity. These results lead to the inference that luteolin possesses potential antioxidant and antitumor activities.

2.

Frontline orbitals of luteolin molecules. Note: (a) HOMO orbitals; (b) LUMO orbitals.

4. HOMO and LUMO Energies and Their Energy Range of Luteolin Molecules .

energy level	energy (eV)
E (LUMO)	–1.62
E (HOMO)	–5.99
E gap	4.37

^aNote: E (LUMO) is the LUMO energy, E (HOMO) is the HOMO energy, and E _gap is the HOMO–LUMO gap.

3.4. DOS

The DOS plot of luteolin (Figure a) decomposes the electronic states of luteolin by “carbonyl group (CO), hydroxyl group (O–H), and six-membered rings (backbones such as benzene rings)” to reflect the differences in contributions of various functional groups to the electronic energy levels. As shown in the figure, the conjugated system dominated by six-membered rings predominates in the distribution of the bonding region and hydroxyl and carbonyl groups are also distributed near the HOMO orbital, indicating that the entire system possesses high reactivity. The DOS plot of luteolin (Figure b) decomposes the electronic states by “s, p, d orbitals” to reflect the dominant role of different orbital types in the electronic structure. It can be observed from the figure that the partial DOS (PDOS) peaks of p orbitals are the strongest across the entire energy range, demonstrating that the p-orbital-dominated conjugated system is the core of its chemical stability and antioxidant activity.

3.

(a,b) DOS diagram of luteolin. Note: “CO” denotes the carbonyl group in luteolin, and “O–H” denotes the phenolic hydroxyl group of luteolin. “Six-membered ring” denotes the molecular structure of luteolin excluding hydroxyl and carbonyl groups.

3.5. EA and IP

From the EA and IP of the luteolin molecule (Table ), it can be seen that the electron affinity (EA = 109.31 kJ/mol) is relatively low, indicating that the molecule is not prone to accepting electrons and further confirming its tendency to act as an electron donor. The ionization potential (IP = 724.44 kJ/mol) is small, meaning that the molecule is more likely to lose electrons, which is consistent with the analysis of the HOMO orbital. These results demonstrate that luteolin possesses potential antioxidant and antitumor activities.

5. Electron Affinity and Ionization Energy of Luteolin Molecules .

Item	energy (kJ/mol)
E (N)	–2702388.81
E (N – 1)	–2701667.50
E (N + 1)	–2702494.98
Ee–	3.14
EA	109.31
IP	724.44

^aNote: E (N) is the electronic energy of the luteolin molecule; E (N – 1) is the electronic energy of the luteolin molecule after losing one electron; E (N + 1) is its electronic energy after gaining one electron; Ee^– is the energy of an electron. The formulas are defined as follows: EA = E (N) + Ee^– – E (N + 1) and IP = E (N – 1) + Ee^– – E (N).

3.6. BDE and PA

Optimization calculations were performed on the phenoxyl radicals of luteolin after dehydrogenation of the phenolic hydroxyl groups at different positions (Figure ), and the corresponding BDE and PA values were obtained (Tables and ). The formula for calculating BDE is as follows: BDE = Er + EH – E, where Er, EH, and E represent the energy of the phenoxyl radical, the energy of the H atom, and the energy of the luteolin molecule, respectively. The formula for calculating PA is as follows: PA = Er1 + EH1 – E1, where Er1, EH1, and E1 represent the energy of the phenoxide anion, the energy of the H⁺ ion, and the energy of the luteolin molecule, respectively.

4.

Stereoscopic configuration of optimized dehydrogenated free radical of luteolin. Note: (a) denotes the molecular structure of luteolin after losing H25 from its phenolic hydroxyl group (O12–H25); (b) denotes the molecular structure of luteolin after losing H26 from its phenolic hydroxyl group (O13–H26); (c) denotes the molecular structure of luteolin after losing H30 from its phenolic hydroxyl group (O20–H30); and (d) denotes the molecular structure of luteolin after losing H31 from its phenolic hydroxyl group (O21–H31).

6. Energy Values of Optimized Structures of Luteolin Molecules and Their Phenoxide Radicals, As Well As the Dissociation Energy of Phenolic Hydroxyl Hydrogen Bonds .

phenoxy radical	enthalpy (a.u.)	BDE (kJ/mol)
Er–O12-	–1028.40562	360.17
Er–O13-	–1028.40491	362.04
Er–O20-	–1028.42691	304.27
Er–O21-	–1028.40904	351.18

^aNote: E denotes the enthalpy of luteolin, which equals −1029.04260 au; EH denotes the enthalpy of the H atom, which equals −0.49980 au; Er–O12- denotes the molecular structure of luteolin after losing H25 from its phenolic hydroxyl group (O12–H25); Er–O13- denotes the molecular structure of luteolin after losing H26 from its phenolic hydroxyl group (O13–H26); Er–O20- denotes the molecular structure of luteolin after losing H30 from its phenolic hydroxyl group (O20–H30); Er–O21- denotes the molecular structure of luteolin after losing H31 from its phenolic hydroxyl group (O21–H31).

7. Energy Value and Proton Affinity of Luteolin Molecule and Its Phenoxy Ion Optimized Structure .

phenoxy ion	enthalpy (a.u.)	PA (kJ/mol)
Er1–O12-	–1028.544673	1313.43
Er1–O13-	–1028.536014	1336.17
Er1–O20-	–1028.56063	1271.54
Er1–O21-	–1028.529725	1352.68

^aNote: E denotes the enthalpy of luteolin, which equals −1029.04260 au; EH denotes the enthalpy of the H⁺ ion, which equals 0.00234 au; Er1–O12- denotes the ionic structure of luteolin after losing H25 from its phenolic hydroxyl group (O12–H25); Er1–O13- denotes the ionic structure of luteolin after losing H26 from its phenolic hydroxyl group (O13–H26); Er1–O20- denotes the ionic structure of luteolin after losing H30 from its phenolic hydroxyl group (O20–H30); Er1–O21- denotes the ionic structure of luteolin after losing H31 from its phenolic hydroxyl group (O21–H31).

As shown in Table , compound Er–O20- has the smallest BDE of 304.27 kJ/mol, followed by Er–O21- (351.18 kJ/mol) and then Er–O12- (360.17 kJ/mol), and the largest BDE is observed for Er–O13- (362.04 kJ/mol). A smaller BDE indicates that the phenolic hydroxyl group at this site is most prone to hydrogen abstraction reactions with free radicals (e.g., ROS). Therefore, the functional group O20–H30 may be the key active site for luteolin to exert its antioxidant and antitumor pharmacological effects. As shown in Table , compound Er1–O20- has the smallest PA of 1271.54 kJ/mol, followed by Er1–O12- (1313.43 kJ/mol), then Er1–O13- (1336.17 kJ/mol), and the largest PA is found for Er1–O21- (1352.68 kJ/mol). A smaller PA indicates that the site is more likely to exert activity via the sequential proton loss electron transfer (SPLET) mechanism. Thus, the functional group O20–H30 may be the key active site for luteolin to exhibit its antioxidant and antitumor pharmacological effects.

To further investigate the antioxidant mechanism and activity of luteolin, BDE, IP, and PA calculations were performed for luteolin and related flavonoid compounds. The thermodynamic data of protons and electrons in the gas phase used in this study were calculated with reference to the method reported by Markovi’c et al. For aromatic phenols (ArOH), the enthalpy values are defined as follows: BDE = H­(ArO•) + H­(H•) – H­(ArOH); IP = H­(ArOH⁺) + H­(e^–) – H­(ArOH); PA = H­(ArO^–) + H­(H⁺) – H­(ArOH); where H denotes the enthalpy of the corresponding substance in the gas phase, with the unit of kJ/mol. The relevant calculation parameters are listed in Table . Based on a comprehensive analysis of these parameters, the order of antioxidant activity is determined as follows: curcumin > quercetin > luteolin > apigenin > isoliquiritigenin.

8. Antioxidant Activity of Related Flavonoids .

item	1	2	3	4	5
object	quercetin	isoliquiritigenin	curcumin	luteolin	apigenin
E gap (eV)	3.69	3.94	3.33	4.37	4.17
E (HOMO) (eV)	–5.72	–5.89	–5.68	–5.99	–6.14
BDE (kJ/mol)	301.33	352.39	307.60	304.27	348.49
IP (kJ/mol)	697.20	718.57	665.890	724.44	740.77
PA (kJ/mol)	1257.64	1327.91	1278.66	1271.54	1296.99

^aNote: The B3LYP-D3/6–311G­(d,p) basis set is used for calculations on neutral and cationic systems, while the B3LYP-D3/6–311 +G­(d,p) basis set is adopted for anionic systems. The BDE and PA values of all substances are calculated targeting the optimal sites identified in the literature review of Section . For isoliquiritigenin, the BDE and PA values correspond to the 7-OH group; for quercetin, they correspond to the 4’-OH group; for curcumin, they correspond to the enolic OH group; and for apigenin, they correspond to the 4-OH group.

3.7. MESP

After geometric optimization, the MESP of luteolin was mapped onto its molecular surface (Figure ), where the order of electron density is blue < green < red. Red regions have negative electrostatic potential values and high electron cloud density; these regions are more prone to donating electrons, exhibit higher nucleophilicity, and are susceptible to nucleophilic substitution reactions. In contrast, blue regions have positive electrostatic potential values and low electron cloud density; these regions tend to accept electrons, show higher electrophilicity, and are liable to undergo electrophilic substitution reactions. The deeper the color, the stronger the corresponding electrophilicity or nucleophilicity. The three red regions correspond to the carbonyl group region (C3O11) and two phenolic hydroxyl group regions ((C7–O12), (C16–O21)). Among them, the C3O11 region has the deepest color, indicating that C3O11 is the strongest nucleophilic group. The four blue regions correspond to the four phenolic hydroxyl groups ((O20–H30), (O12–H25), (O13–H26), (O21–H31)), with the O20–H30 region having the deepest color, thus identifying O20–H30 as the strongest electrophilic group. In summary, luteolin contains nucleophilic groups in three regions and electrophilic groups in four regions, thereby inferring that luteolin possesses potent potential antioxidant and antitumor activities.

5.

Surface electrostatic potential of luteolin molecule.

3.8. IR Spectrum

The IR spectrum (Figure ) and vibrational frequencies (Table ) of the luteolin molecule are presented. The calculated vibrational frequencies were corrected with a scaling factor of 0.9613. The spectral peaks between 3660 and 3610 cm^–1 mainly correspond to the stretching vibrations of hydroxyl groups. Combined with the bond length R (31,20) = 2.1 Å, bond angle A (21,31,20) = 115°, and the hydroxyl group at 3615.14 cm^–1 (red-shifted by approximately 32 cm^–1), it can be inferred that weak intramolecular hydrogen bonds are formed in the molecule, which is consistent with the bond length and BDE studies. The peak at 1624 cm^–1 corresponds to the stretching vibration of the carbonyl group. This functional group may participate in nucleophilic addition reactions, which align with the MESP analysis. The peaks at 1607, 1594, 1582, and 1567 cm^–1 are primarily attributed to the skeletal vibrations of benzene rings, confirming the presence of aromatic rings and supporting the conjugated stability of the molecule. The range of 1340–1150 cm^–1 mainly involves the in-plane bending vibrations of C–H and O–H bonds. These results indicate that the luteolin molecule forms intramolecular hydrogen bonds and possesses a conjugated structure, leading to the conclusion that luteolin exhibits potent antioxidant and antitumor activities.

6.

Infrared absorption spectrum of the luteolin molecule.

9. Vibration Frequencies of Optimized Luteolin Molecules .

calculated frequency (cm–1)	revised frequency (cm–1)
1672.03	1605.15
1672.03	1605.15
1691.70	1624.03
3170.66	3043.83
3185.25	3057.84
3194.45	3066.68
3207.04	3078.75
3217.82	3089.11
3223.78	3094.83
3765.78	3615.14
3777.04	3625.96
3788.57	3637.02
3799.27	3647.30

^aNote: The vibration frequency is selected from the functional group region, the benzene ring region, and the hydrogen bond region. The experimental comparison data of luteolin’s vibrational spectrum are provided in the supplementary file (S9-Vibration spectrum comparison).

3.9. NMR Spectrum

The ¹³C NMR spectrum (Figure ), the ¹H NMR spectrum (Figure ), and the chemical shifts of ¹³C and ¹H nuclei of the luteolin molecule are summarized in Table . Since the chemical shift of C3 is 178 ppm, which matches the characteristic downfield shift of carbonyl carbons, C3 is identified as the carbonyl carbon. The chemical shifts of benzene ring carbons (100–170 ppm) fall within the typical range of sp²-hybridized carbons. A peak appears around 5 ppm, which is assigned to the hydrogen atom of the phenolic hydroxyl group. The slight upfield shift of this phenolic hydroxyl H atom is attributed to hydrogen-bonding interactions, confirming the formation of intramolecular hydrogen bonds. A peak is observed in the range of 6–7 ppm, consistent with the chemical shift of aromatic hydrogen atoms. Thus, this peak is assigned to the H atoms on the benzene rings, which aligns with the presence of the conjugated system. These results indicate that luteolin can enhance its biological activity through the construction of a conjugated system and the formation of intramolecular hydrogen bonds, thereby exerting its antioxidant and antitumor pharmacological effects.

7.

Chemical-shift of ¹³C molecule of luteolin.

8.

Chemical shift of ¹H molecule of luteolin.

10. NMR Calculation Data of Optimized Luteolin Molecules .

atom	chemical shift (ppm)	atom	chemical shift (ppm)
1(C)	165.935	22(H)	6.659
2(C)	111.368	23(H)	6.386
3(C)	178.879	24(H)	6.629
4(C)	114.909	25(H)	5.123
5(C)	165.085	26(H)	5.427
6(C)	101.309	27(H)	7.898
7(C)	166.808	28(H)	7.081
8(C)	96.897	29(H)	7.639
9(C)	164.826	30(H)	4.976
14(C)	131.144	31(H)	5.431
15(C)	116.588
16(C)	151.425
17(C)	151.898
18(C)	118.584
19(C)	122.992

^aNote: “C” represents ¹³C, and “H” represents ¹H.

4. Discussion

Luteolin is a natural drug molecule with antioxidant and antitumor activities. Currently, extensive research has been conducted on its pharmacological properties, but studies of its electronic structure and spectral properties are rarely reported. This study employed DFT calculations combined with multidimensional analysis to systematically reveal the electronic structure and spectral properties: Data on bond lengths, bond angles, and dihedral angles indicate that the molecule possesses a highly conjugated system and forms intramolecular hydrogen bonds; E _gap, BDE, EA, IP, and PA demonstrate that the molecule efficiently scavenges free radicals primarily through HAT-dominated mechanism, synergistically assisted by SPLET and single electron transfer followed by proton transfer (SET-PT), thereby exerting its antioxidant and antitumor activities; BDE and MESP analyses identified O20–H30 and C3O11 as the key active sites of luteolin; the calculated results of IR and NMR spectroscopy verified the enhancing effect of luteolin’s conjugated system and intramolecular hydrogen bonds on its biological activity.

Data from the geometrically optimized structure of luteolin reveal the structural basis for its antioxidant activity. The bond length of the phenolic hydroxyl group on the C16 atom of Ring B (R (21,31) = 0.966 Å) is slightly longer than that of other phenolic hydroxyl groups (e.g., R (13,26) = 0.964 Å and R (12,25) = 0.963 Å). This is attributed to the formation of an intramolecular hydrogen bond (bond distance: 2.13 Å) between the hydrogen atom of this hydroxyl group and the oxygen atom of the hydroxyl group at position 17. This hydrogen bond enhances the polarity of the O–H bond and reduces its bond energy, making the hydrogen atom more prone to homolysis via the HAT mechanism to generate a hydrogen radical. Meanwhile, this hydrogen bond stabilizes the phenoxide anion formed after deprotonation: the lone pair electrons of the phenoxide anion can delocalize through the conjugated system, reducing the energy of the radical intermediate. This enables luteolin to efficiently scavenge free radicals via the “hydrogen bond-assisted proton–electron synergistic transfer” mechanism. Dihedral angle data indicate that Ring B and Ring C are noncoplanar (D (10,1,14,19) = −163.8°; D (10,1,14,15) = 16.3°), resulting in weakened π-conjugation. However, the hydrogen bond forms a bridging effect between the rings, providing an electron coupling pathwaywhich explains the uniform distribution of electrons in the Frontier orbitals. In contrast, Ring A and Ring C are highly coplanar (D (2,3,4,5) = −179.1°; D (8,9,4,3) = −179.8°), forming an extended large π-conjugated system. This significantly enhances the electron delocalization ability, allowing electrons to delocalize on the A–C ring skeleton and providing a channel for the SET-PT mechanism. These characteristics collectively explain the uniform distribution of electrons in the Frontier orbitals. In summary, the antioxidant activity of luteolin stems from a synergistic dual mechanism: (1) the large π-conjugated system of the A–C rings dominates the SET-PT mechanism, enabling rapid reduction of free radicals; (2) the phenolic hydroxyl group of Ring B and its hydrogen bond network dominate the HAT mechanism, promoting efficient hydrogen atom donation. These two mechanisms complement each other, improving the scavenging efficiency against various free radicals. Furthermore, the molecular planarity of luteolin interferes with the function of biomacromolecules through NCIs, which may be one of the potential mechanisms underlying its antitumor activity.

IR analysis of luteolin: the spectral range 3660–3610 cm^–1 corresponds to the hydroxyl stretching vibrations. The typical wavenumber of the free O–H stretching vibration is approximately 3650 cm^–1: the vibration of O20–H30 is located at 3647.30 cm^–1, exhibiting the characteristic of a free hydroxyl group. For hydrogen bonds, the typical R(O–H···O) distance ranges from 1.5 to 2.2 Å, with a hydrogen bond angle close to 180°. The vibration of O21–H31 is red-shifted to 3615.14 cm^–1; combined with its geometric parameters (R(31,20) = 2.1 Å, bond angle A(21,31,20) = 115°), this indicates the formation of an intramolecular hydrogen bondhowever, the bond angle deviates from linearity and the distance is relatively large, making this hydrogen bond relatively weak. This hydrogen bond induces an electron cloud migration of the O20–H30 bond, reducing its BDE to 304.27 kJ/mol (the lowest among all phenolic hydroxyl groups). This renders O20–H30 prone to donating hydrogen via the HAT mechanism, thereby scavenging hydrophobic free radicals. The carbonyl stretching vibration appears at 1626 cm^–1, which is significantly lower than the typical wavenumber of ketone carbonyl groups (∼1715 cm^–1). This is attributed to the strong conjugation between the carbonyl group and the A/C rings (the dihedral angle of the A/C rings is close to 180°), leading to electron delocalization and enhancement of the positive charge of the carbonyl carbon. This region is the main distribution area of LUMO, enabling it to accept electrons and assist the SET-PT mechanism in scavenging electron-rich free radicals. In summary, luteolin exerts synergistic antioxidant and antitumor effects through the hydrogen-bond-enhanced phenolic hydroxyl group (dominating the HAT mechanism) and the conjugated carbonyl group (dominating the SET-PT mechanism and nucleophilic binding).

NMR analysis: structural optimization of luteolin and tetramethylsilane (TMS) was performed in a chloroform solvent at the B97–2/def2-TZVP level using Gaussian software. The calculated ¹³C and ¹H magnetic shielding constants of TMS were 195.7234 and 31.7118 ppm, respectively, which were used to determine the chemical shifts of luteolin. The chemical shift of the carbonyl carbon (C3) is approximately 178 ppm, attributed to the deshielding effect caused by carbonyl magnetic anisotropya characteristic signal of carbonyl groups. The chemical shifts of Ring A carbons fall within the range of 100–130 ppm. The coplanarity of Ring A and Ring C (dihedral angle ≈180°) enhances conjugation and electron density, leading to an upfield shift of chemical shifts, which facilitates electron transfer. Ring B carbons are in the range of 140–160 ppm. The torsion between Ring B and Ring C (dihedral angle = −163.8°) weakens conjugation, and the intramolecular hydrogen bond (O21–H31···O20, 2.13 Å) further reduces electron density, resulting in a downfield shift of chemical shifts. This is favorable for trapping free radicals through π–π stacking. The hydrogen chemical shift of the phenolic hydroxyl group of groups O20 and H30 is approximately 5 ppm. As a hydrogen bond acceptor, its electron density increases, enhancing the shielding effect. The hydrogen of the complex of O21–H31 is expected to appear at around 5.5 ppm. As a hydrogen bond donor, it undergoes electron cloud migration, reducing the shielding effect; however, due to its relatively high bond dissociation energy (BDE = 351.18 kJ/mol), the signal may be broadened. Aromatic hydrogens of Ring B are located at 6–7 ppm, showing an upfield shift due to weakened conjugation. Aromatic hydrogens of Ring A are in the range of 7.5–8 ppm, exhibiting a downfield shift due to the strong conjugative deshielding effectthis supports its π–π stacking interaction with DNA. These results confirm that luteolin exerts synergistic antioxidant effects through the HAT mechanism of the hydroxyl group on Ring B (BDE = 304.27 kJ/mol) and the SET-PT mechanism of the large π system in the A–C rings, capable of scavenging both hydrophobic and hydrophilic free radicals. Furthermore, the nucleophilicity of its carbonyl group and planar conjugated structure support nucleophilic addition and π–π stacking interactions with biological targets, interfering with DNA and protein functions, thereby exerting antitumor activity.

Studies have shown that conjugated structures play a key role in antioxidant activity. , BDE is a critical factor affecting antioxidant activity; optimization of the conjugated system can significantly reduce BDE while enhancing antioxidant capacity. In tumor-related research, conjugated structures have been confirmed to be crucial for the antitumor activity of paclitaxel and its analogs. By exerting antioxidant effects, conjugated structures can reduce ROS levels in tumor cells, thereby inhibiting their growth and proliferation.

In summary, conjugated structures play an important role in antioxidant and antitumor activities by influencing electron delocalization and stabilizing free radicals. Through geometric optimization and spectral analysis, this study reveals that luteolin possesses hydrogen bonds and conjugated structures. This indicates that the presence of these hydrogen bonds and conjugated structures is an important reason for the potent antioxidant and antitumor effects of the luteolin molecule.

According to the FMO theory, the HOMO energy level characterizes the electron-donating capacity: the higher the energy level, the lower the electron stability and the more prone to oxidation. The LUMO energy level reflects the electron-accepting capacity: the lower the energy level, the stronger the EA. Overall, the electron cloud distribution of HOMO and LUMO covers almost the entire molecular skeleton of luteolin, indicating a favorable conjugated effectbenefiting from the coplanar structure of the A–C rings and the hydrogen-bonding interaction between the B–C rings. This provides a structural basis for efficient electron transfer and endows luteolin with an inherent application potential in photoelectric conversion and biomedical intervention. The electron cloud of HOMO is concentrated on the 16,17-dihydroxyl groups of Ring B, the aromatic ring of Ring A, and the conjugated double bond region of Ring C, highlighting its strong electron-donating potential. Phenolic hydroxyl groups (−OH) donate electrons to the aromatic rings through the p–π conjugation, making these regions electron-rich. They can efficiently scavenge free radicals by releasing hydrogen radical via the HAT mechanism or e^– via the SET-PT mechanism. The HOMO orbital energy of luteolin is −5.99 eV, which is significantly higher than that of common antioxidants (e.g., the HOMO orbital energy of phenol is approximately −9.01 eV). This indicates that the HOMO electrons of luteolin are easily detached and exhibit high reactivity. This characteristic enables luteolin to not only release electrons to oxidants to exert antioxidant effects but also donate electrons to electron-deficient metal atoms (e.g., Fe³⁺) at the active center of tumor targets to form stable complexes. Furthermore, it inhibits the activity of metal-dependent tumor enzymes (e.g., matrix metalloproteinases), providing a structural basis for antitumor drug design. The electron cloud of LUMO is mainly distributed in the carbonyl group (C4O) of Ring C, the adjacent conjugated bridge (C1–C2–C3), and extends to the conjugated systems of Rings A and B, showing a clear electron-accepting potential. The carbonyl group (C O) attracts electrons through π–π conjugation to form an electron-deficient region. The E _gap is a key balancing indicator of molecular stability and reactivity. The E _gap of luteolin is 4.37 eV, which falls within the typical range of flavonoids (4–5 eV): it not only ensures the reactivity of electron transfer but also avoids self-oxidative degradation after electron transfer, balancing the effectiveness and stability of pharmaceutical applications.

The analysis of HOMO–LUMO energy levels and their energy gap plays a crucial role in the optoelectronic field. By regulating the energy positions of HOMO and LUMO and the energy gap between them, the performance of materials in devices such as solar cells, organic light-emitting diodes (OLEDs), and photodetectors can be systematically predicted and improved. , Luteolin has potential application advantages in the field of solar cells: its high HOMO energy level (−5.99 eV) facilitates electron detachment, enabling it to act as an electron donor; its low LUMO energy level confers EA, allowing it to serve as an electron acceptor. This “donor–acceptor” characteristic enables it to form a donor–acceptor heterojunction in organic photovoltaic devices, promoting the separation and transport of photogenerated carriers. Additionally, the electron cloud of HOMO–LUMO covers almost the entire molecular skeleton with a strong conjugated effect, enabling light absorption in the visible region. Thus, luteolin is suitable as a photosensitive active layer material for solar cells to absorb sunlight and convert it into electrical energy. In the field of biomedical applications, HOMO–LUMO analysis helps to predict the reactivity and biological activity of drug molecules. A smaller E _gap usually indicates higher chemical reactivity of the molecule, which may be more likely to participate in redox processes or undergo electron transfer interactions with biological targets. Studies have found that after doping with Cd­(II), the E _gap of luteolin is significantly reduced (from 4.32 to 0.49 eV). This indicates that metal coordination significantly decreases the E _gap and enhances the electron mobility of the molecule. It can be used as a metal ion sensor or an intracellular ion imaging probe and also as an anticancer agent by penetrating cell membranes and interacting with DNA or other targets. In summary, the HOMO–LUMO characteristics of luteolin not only reveal the core mechanisms of its antioxidant and antitumor activities at the molecular level but also clarify its application potential in optoelectronic materials and biomedicine.

The main mechanisms by which ArOH exert antioxidant activity are the HAT mechanism, SET-PT mechanism, and SPLET mechanism. In the HAT mechanism, ArOH transfers one hydrogen atom to ROS (R•) via the cleavage of the O–H bond, generating nontoxic RH and phenoxyl radicals (ArO•). BDE is a parameter associated with this mechanism; the lower the BDE, the stronger the antioxidant activity. From the BDE data, compound Er–O20- exhibits the smallest BDE (304.27 kJ/mol). A smaller BDE indicates that the phenolic hydroxyl group at this site is most prone to hydrogen abstraction reactions with free radicals (e.g., ROS). Thus, the functional group O20–H30 may be the key active site for luteolin to exert its antioxidant and antitumor pharmacological effects. The SET-PT mechanism involves two steps. In the first step, an electron is transferred from ArOH to the free radical, forming a cation radical (ArOH•⁺); in the second step, a proton is transferred from ArOH•⁺ to ArO•. IP is a parameter related to the first step; the lower the IP, the easier the single electron transfer and the higher the antioxidant activity. By comparison of BDE values, it is found that luteolin is more likely to exert antioxidant activity through the HAT mechanism. The SPLET mechanism consists of two steps. In the first step, ArOH dissociates into an anion (ArO^–) and a proton; in the second step, an electron is transferred from ArO^– to ArO•. PA is a parameter associated with the first step; the lower the PA, the easier the proton loss and the higher the antioxidant activity. By comparing IP values, the primary antioxidant mechanism of luteolin is determined to be HAT, followed by the SET-PT mechanism and finally the SPLET mechanism. O20–H30 is confirmed as the key active site for luteolin’s antioxidant and antitumor activities. Among all of the phenolic hydroxyl groups, Er–O20- has the lowest BDE, indicating that its O–H bond is most easily cleaved and exhibits the strongest hydrogen transfer activity. This phenomenon is closely related to intramolecular hydrogen bonding: the formation of the O20–H30···O21 hydrogen bond makes O20 act as an electron acceptor. The deviation of its lone pair electron cloud enhances the polarity of the O20–H30 bond, weakens its bond energy, and significantly reduces the BDErendering it the most easily dissociated hydrogen-donating site in the HAT mechanism. Although the BDE of the hydrogen-donating group O21–H31 is slightly higher (still lower than that of non-hydrogen-bonded hydroxyl groups), it is more conducive to stabilizing the radicals generated during the reaction through conjugative effects. When the hydrogen bond of the O20–H30 species undergoes homolysis to form a semiquinone radical (Lut-O20•), the original hydrogen bond promotes the delocalization of unpaired electrons to the O20–O21 region via the π-conjugated system, greatly enhancing radical stability. This synergistic effect of “low BDE” and “high radical stability” significantly improves the efficiency of luteolin in scavenging free radicals through the HAT mechanism, enabling it to continuously eliminate ROS, regulate redox balance, and thereby indirectly contribute to antitumor activity. In conclusion, hydrogen bonds and conjugated structures play a crucial role in luteolin’s antioxidant and antitumor effects.

Through calculations of the antioxidant activity of related flavonoid compounds, the following findings are obtained. Antioxidant activity regulated by single mechanism: order of antioxidant activity via the HAT mechanism: quercetin (301.33 kJ/mol) > luteolin (304.27 kJ/mol) > curcumin (307.60 kJ/mol) > apigenin (348.49 kJ/mol) > isoliquiritigenin (352.39 kJ/mol); Order of antioxidant activity via the SET-PT mechanism: curcumin (665.890 kJ/mol) > quercetin (697.20 kJ/mol) > isoliquiritigenin (718.57 kJ/mol) > luteolin (724.44 kJ/mol) > apigenin (740.77 kJ/mol); order of antioxidant activity via the SPLET mechanism: quercetin (1257.64 kJ/mol) > luteolin (1271.54 kJ/mol) > curcumin (1278.66 kJ/mol) > apigenin (1296.99 kJ/mol) > isoliquiritigenin (1327.91 kJ/mol). A smaller E _gap indicates a lower energy barrier for electron transition from HOMO to LUMO, leading to higher molecular reactivity and stronger antioxidant activity. Based on this principle, the antioxidant activity of the flavonoid compounds is ranked as follows: curcumin (3.33 eV) > quercetin (3.69 eV) > isoliquiritigenin (3.94 eV) > apigenin (4.17 eV) > luteolin (4.37 eV). Antioxidant activity regulated by synergistic multiple mechanisms: HAT reflects “hydrogen-donating capacity”, SPLET reflects “proton–electron synergistic transfer capacity”, and SET-PT reflects “single electron transfer capacity”these three mechanisms collectively constitute the core pathways of flavonoid antioxidant activity. E _gap explains the difference in reactivity from the perspective of electronic structure, forming a “microstructure–macroscopic activity” correlation with mechanism parameters. Curcumin exhibits the optimal SET-PT mechanism (lowest IP) and the smallest E _gap, with good performance in the HAT mechanism (BDE only higher than quercetin and luteolin). Thus, it shows prominent reactivity in electron transfer reactions and is the most comprehensively reactive substance. Quercetin performs excellently in both HAT and SPLET mechanisms (lowest BDE and PA) and maintains a high level in the SET-PT mechanism. This enables quercetin to easily donate hydrogen atoms via HAT and transfer electrons after proton loss via SPLET, making it a classic “dual-mechanism-dominated” antioxidant. Luteolin’s HAT mechanism is second only to quercetin, with good SPLET performance, but moderate SET-PT and Frontier orbital E _gap. This indicates that luteolin takes HAT and SPLET as core mechanisms, with stable activity but lacking advantages in electron transfer reactions. Apigenin’s parameters are all at a moderately low level, with no obvious advantages in HAT (high BDE), SET-PT (high IP), or SPLET (high PA) mechanisms, meaning its antioxidant activity is mediocre, only superior to isoliquiritigenin. Isoliquiritigenin shows the worst performance in HAT (highest BDE) and SPLET (highest PA) mechanisms, with no competitiveness in the SET-PT mechanism, resulting in the weakest antioxidant activity. This ranking is consistent with the antioxidant activity order reported in the relevant literature. − In summary, the comprehensive antioxidant activity is ranked as follows: curcumin > quercetin > luteolin > apigenin > isoliquiritigenin.

Through the analysis of FMO energy levels, E _gap, BDE, IP, PA, and other parameters, combined with HAT/SET-PT/SPLET mechanisms, it is found that luteolin has a strong conjugative effect with O20–H30 as the key active site. It takes the HAT mechanism as the main antioxidant mechanism and exhibits stable activity, indicating its potential antioxidant and antitumor capabilities.

The DOS represents the number of electrons within a unit energy range (E–E + ΔE). DOS analysis of luteolin shows that PDOS contribution of the carbonyl group (CO) is mainly reflected in its PDOS peaks, which are primarily distributed in the low-energy bonding region (−11.25 to −9.5 eV) and the region near the HOMO orbital (−6.25 to −6 eV). The strong peak in the low-energy bonding region corresponds to the σ bonding orbital of CO, featuring highly localized electron clouds with low energy and high stability; the weak peak near the HOMO orbital corresponds to the π bonding orbital of CO, indicating electron cloud delocalization. This distribution demonstrates that the carbonyl group not only serves as a “stable bonding unit” of the molecule but also readily participates in transitions upon electronic excitation, making it a key site for luteolin’s photochemical properties. PDOS contribution of hydroxyl groups (O–H): the PDOS peaks of hydroxyl groups are widely distributed in the bonding region (−15 to −5.99 eV) with a significant peak near the HOMO orbital. This indicates that hydroxyl groups not only serve as “stable bonding units” of the molecule but also readily participate in transitions upon electronic excitation, making them key sites for the photochemical properties of luteolin. Six-membered rings: their PDOS spectra exhibit strong peaks across the entire energy range. Peaks in the bonding region correspond to the σ skeleton bonds and π bonding orbitals of benzene rings (with highly delocalized electron clouds that stabilize the conjugated system); peaks in the Frontier orbital region correspond to the π-conjugated orbitals of benzene rings. This characteristic explains luteolin’s conjugated stability and electron delocalization ability, which constitute the structural basis for its antioxidant activity (scavenging free radicals through π electron transfer). Decomposing the DOS by “s, p, d orbitals” primarily reflects the dominant role of different orbital types in the electronic structure: absolute dominant contribution of p orbitals: the PDOS peaks of the p orbitals are the strongest across the entire energy range. Strong peaks in the bonding region correspond to the p-orbital hybridization of σ bonds (e.g., C–C and C–O) as well as the π bonding orbitals of benzene rings and carbonyl groups; the strong peak in the HOMO region corresponds to the π-conjugated orbital. Absolute dominant contribution of p orbitals: the PDOS peaks of p orbitals are the strongest across the entire energy range. Strong peaks in the bonding region correspond to the p-orbital hybridization of σ bonds (e.g., C–C and C–O) and the π bonding orbitals of benzene rings and carbonyl groups; the strong peak in the HOMO region corresponds to the π-conjugated orbital. This characteristic directly confirms that luteolin’s electronic structure is dominated by the hybridization and conjugation of p orbitals, which is the root cause of its aromaticity, conjugated stability, and chemical activity. Auxiliary contribution of s orbitals: the PDOS peaks of s orbitals are mainly concentrated in the low-energy bonding region (−15 to −10 eV), corresponding to the s–p hybrid orbitals of σ bonds (e.g., C–H, O–H). Negligible contribution of d orbitals: the PDOS peaks of d orbitals are almost zero. This is because luteolin only contains light atoms (C, H, and O) without the involvement of transition metals; d orbitals only act as “polarization functions” to assist in describing electron cloud deformation, and their contribution to the overall electronic state is negligible. In summary, DOS studies have comprehensively revealed the electronic structure characteristics of luteolin: the p-orbital-dominated conjugated system is the core of its chemical stability and antioxidant activity; functional groups, such as carbonyl and hydroxyl groups, participate in the construction of electronic states through p-orbital hybridization/conjugation, ultimately determining the structure–function relationship of the molecule.

MESP intuitively reflects the distribution of the electrostatic potential on the molecular surface through color gradients. The essence of color differences lies in the quantitative manifestation of the electron density and reactivity: negative potential regions (red series) correspond to electron-rich areas serving as preferential active centers for nucleophilic reactions. The more negative the potential (the darker the color), the higher the electron cloud density and the stronger the nucleophilic attack ability; positive potential regions (blue series) correspond to electron-deficient areas, acting as preferential active centers for electrophilic reactions. The more positive the potential (the darker the color), the lower the electron cloud density and the stronger the electrophilic acceptance capacity (e.g., hydrogen bond donor activity and H atom transfer ability). This color–reactivity correlation provides a quantum chemical basis for accurately predicting the biological targets and reaction mechanisms of luteolin. , In the MESP map of luteolin, among the three red regions, C3O11 exhibits the darkest color (most negative electrostatic potential) and is identified as the strongest nucleophilic center. From a chemical perspective, the lone pair electrons of phenolic hydroxyl oxygen delocalize with the aromatic ring through the p–π conjugation, and the π electron cloud of carbonyl oxygen is highly concentrated due to the conjugated systemboth leading to a significant negative shift in the electrostatic potential of the site. This is consistent with the general rule in natural products that “oxygen-rich functional groups (hydroxyl, carbonyl) are typical nucleophilic sites”. The chemical significance of this nucleophilic center is reflected in two aspects: as a ligand, the lone pair electrons of the oxygen atom can form coordination bonds with the empty orbitals of metal ions (e.g., Fe³⁺, Zn²⁺). Sites with more negative potential exhibit higher coordination stability (C3O11 has the optimal coordination ability), thereby interfering with the activity of metal-dependent tumor enzymes (e.g., topoisomerases); When binding to the aromatic rings of DNA base pairs through π–π stacking, the electron cloud of the nucleophilic site can interact with the π electron cloud of base pairs, enhancing the binding affinity between the molecule and DNA and potentially interfering with DNA replication and transcription. This mechanism is highly consistent with the antitumor mode of natural flavonoids but requires further verification through coordination experiments. Among the four blue regions, O20–H30 shows the darkest color and is the strongest electrophilic site. Its chemical essence is that the O–H bond of the phenolic hydroxyl group exhibits strong polarity due to the electronegativity difference between O and H, resulting in an extremely low electron density of the H atom and a significant positive shift in electrostatic potentialmaking it an efficient hydrogen bond donor and H-transfer site in electrophilic reactions. From the perspective of the reaction mechanism, the strong electrophilicity of this site is directly related to the O–H BDE: O20–H30 has the lowest BDE value (304.27 kJ/mol), indicating that its O–H bond is the most easily cleaved. It can donate hydrogen atoms to ROS via the HAT mechanism, reducing ROS to stable molecules. This is consistent with the rule that the stronger positive potential of MESP correlates with higher H atom transfer activity. Previous studies have confirmed through DPPH and BDE experiments that 7-OH is the key site for luteolin’s antioxidant activity, which is fully consistent with the prediction in this study that “O20–H30 (the hydrogen atom corresponding to 7-OH) is the strongest electrophilic site”further verifying the accurate predictive ability of MESP color coding for reactive active sites. In summary, analyses of parameters such as MESP and BDE demonstrate that electrophilic sites (with O20–H30 as the core) scavenge ROS through the ″high electrophilicity → low BDE → efficient HAT mechanism″ to exert antioxidant and antitumor effects; nucleophilic sites (with C3O11 as the core) bind to biological targets such as metal ions and DNA through “high electron density → strong coordination/π–π stacking ability”, synergistically enhancing biological activity.

This study explores the electronic structure, spectral characteristics, and active sites of the luteolin molecule through theoretical simulations, providing crucial theoretical support for the application and modification of this molecule. Luteolin is a phytochemical with broad application prospects; however, its low solubility and relatively low bioavailability limit its clinical application. Thus, the design of luteolin derivatives is imperative. Studies have shown that compared with luteolin, 5-O-acyl luteolin derivatives exhibit better antitumor cell proliferation activity while retaining free radical scavenging activity. Additionally, studies have indicated that Mannich base luteolin derivatives possess superior anticancer activity compared to luteolin and 5-fluorouracil (5-Fu). Through the analysis of parameters such as MESP and BDE, this study concludes that the O20–H30 and C3O11 regions are reactive active sites, while the C8 and O13 sites are inert. Modifying the inert sites while avoiding the reactive sites retains the drug activity and enhances properties, such as solubility. Therefore, based on luteolin, introducing a Mannich base at the C8 position and an acyl derivative with an aliphatic chain at the O13 position is proposed to improve luteolin’s solubility, bioavailability, and antioxidant/antitumor performance. Drug delivery systems can cross physiological barriers (e.g., intestinal mucosa, blood–brain barrier) and reduce toxic side effects by regulating the release site and rate of drugs, making them a key technology to improve the druggability of low-bioavailability drugs. For natural products like luteolin with poor water solubility and easy metabolism, nanodrug delivery can enhance bioavailability through the “solubilization–protection–targeting” triple effect. Functionalized carbon nanotubes (f-CNTs) have attracted considerable attention in recent years as nanocarriers due to their microscale size (diameter: 1–2 nm, length: 50–200 nm), large specific surface area (>1000 m²/g), and good biocompatibility. Currently, f-CNTs can be used to deliver chemotherapeutic drugs such as doxorubicin and paclitaxel, enabling targeted drug delivery, improving efficacy, and reducing systemic toxicity. Studies have found that chloromethyl (CH₂Cl)-functionalized semiconductor SWCNT­(8,0) enhances the solubility of carbon nanotubes and induces magnetization of the carrier. The adsorption of the anticancer drug 5-Fu by SWCNT­(8,0)-CH₂Cl is exothermic and physical, a characteristic that retains the drug’s activity. Although the drug itself is nonmagnetic, it acquires a net magnetization after adsorption by the carrier and exhibits ferromagnetic bipolar semiconductor properties, allowing magnetic field-targeted drug release. Experiments have obtained carbon nanotubes with a diameter of approximately 4 Å, while the diameters of SWCNT­(4,4) and zigzag SWCNT­(7,0) are 5.42 Å and 5.48 Å, respectively, which can be verified through experiments. MESP analysis in this study reveals that the region of O20–H30 is electrophilic, while the Cl region of the carrier SWCNT-CH₂Cl is electronegative. Thus, theoretically, the carrier can adsorb the drug through electrostatic interactions. Literature research indicates that there are a few studies on luteolin-based nanodrug delivery systems, with most focusing on functionalized carbon nanotube sensors. , Therefore, it is feasible to investigate a luteolin nanodrug delivery system based on f-CNTs through a combination of theoretical research and experimental synthesis.

Due to the limited research on solvation effects in this study, Supporting Information on luteolin’s solvation effects was obtained through literature review. Using the implicit solvation model (SMD) at the M06–2X/6–311++G­(d,p) level, studies have investigated the influence of solvation effects on luteolin’s structure and properties. It was found that in the polar solvent water, the E _gap decreases, enhancing molecular reactivity, whereas in the nonpolar solvent benzene, the E _gap increases. The slight adjustment (±2.6%) of the BDE of hydroxyl groups by water indicates that solvent molecules in the physiological environment do not significantly alter its antioxidant potential, which is consistent with the results in the supplementary file (S8-Solvation Effect). The difference in solvation effects may be attributed to the formation of double hydrogen bonds (O–H···O_solvent, O···H–O_solvent) between water and luteolin’s phenolic hydroxyl groups, which stabilize the electron cloud and render the conformation more “rigid”, thereby enhancing luteolin’s antioxidant properties. In polar solvents, intramolecular electrostatic interactions can be effectively shielded, stabilizing the charge distribution and reducing the system energy. Meanwhile, hydrogen bonding weakens the O–H bond strength, facilitating the SPLET mechanism, and solvation effects stabilize charged intermediates, leading to enhanced antioxidant activity. In nonpolar solvents, intramolecular electrostatic interactions cannot be shielded, and luteolin maintains the planarity of its conjugated system with strong π-electron delocalization, making the HAT mechanism dominant.

Studies have investigated the antioxidant activities of luteolin, BHT, and curcumin via a combination of theoretical and experimental methods. DFT calculations (B3LYP/6-311G­(d,p)) revealed that the antioxidant electronic parameter (BDE) of luteolin was consistent with that of BHT, while the antioxidant electronic parameter (IP) of curcumin was significantly lower than those of BHT and luteolin. These DFT results indicated that curcumin exhibited the strongest antioxidant activity, which was consistent with the outcomes of DPPH assays. In addition, studies have explored the antitumor activities of Evodiamine (EVO) and Rutecarpine (RUT) through integrated theoretical and experimental approaches. DFT calculations (B3LYP/6-311++G­(d,p)) showed that the E _gap of EVO (3.96 eV) was significantly smaller than that of RUT (4.47 eV). These DFT results demonstrated that EVO had remarkably higher activity than RUT, which was in agreement with the results of 3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium Bromide (MTT) assays. These findings consistently demonstrate that the parameters derived from DFT calculations (B3LYP/3-zeta basis set) are consistent with the antioxidant and antitumor activities observed in experiments. Therefore, future studies can verify luteolin’s antioxidant activity via DPPH assays and evaluate its proliferation inhibition or toxic effects on tumor cells through in vitro cell experiments (MTT) combined with molecular dynamic studies.

5. Conclusion

In this study, DFT calculations were employed to conduct a comprehensive multidimensional investigation of the luteolin molecule. The results demonstrate that luteolin possesses a highly conjugated planar structure and an intramolecular hydrogen bond network: Rings A and C are highly coplanar, forming an extended large π-conjugated system that significantly enhances the electron delocalization ability, providing a pathway for free radical scavenging via the SET-PT mechanism. Despite torsion between Rings B and C, electronic coupling is maintained through hydrogen bond bridging; the phenolic hydroxyl groups of luteolin, under the influence of intramolecular hydrogen bonds, exhibit the lowest BDE, making them efficient hydrogen-donating sites in the HAT mechanism. A relatively high HOMO energy level and low IP indicate luteolin’s strong electron-donating capacity, while its E _gap falls within the typical range of flavonoid compoundsensuring reactivity while maintaining molecular stability. IR and NMR analyses further verify the existence of the conjugated system and hydrogen bonds as well as their enhancing effect on biological activity. MESP analysis identified the key nucleophilic and electrophilic sites. BDE, EA, IP, and PA confirm the antioxidant activity and dominant mechanisms, while DOS confirms the orbital types and functional group activity of luteolin.

In summary, the O20–H30 and C3O11 sites of luteolin are the key active sites. Via a p-orbital-dominated conjugated system, luteolin efficiently scavenges free radicals through an HAT-dominated mechanism synergistically assisted by SPLET and SET-PT, thereby exerting its antioxidant and antitumor activities. These results provide a theoretical basis for understanding the structure–activity relationship of flavonoid compounds.

The data that support the findings of this study are available within the article and its Supporting Information.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c06946.

• Bond length data of luteolin after molecular optimization (S1-Bond length); bond angle data of luteolin after molecular optimization (S2-Bond angle); dihedral angle data of luteolin after molecular optimization (S3-Dihedral angle); Cartesian coordinates and total energy of luteolin after molecular optimization (S4-Molecular coordinates); vibrational frequencies of luteolin after molecular optimization (S5-Vibration frequency); conformational selection of luteolin (S6-Conformational selection); correction method for optimized virtual frequency (S7-Correction method of virtual frequency); solvation effect of luteolin (S8-Solvation effect); and experimental comparison of luteolin’s vibrational spectrum (S9-Vibration spectrum comparison) (ZIP)

Yijun Zheng is responsible for data analysis, creating graphs, and writing manuscript text; Yawu Zhang and Zheyuan Wang are responsible for partial data extraction and analysis; Youcheng Zhang provided the article’s ideas, made revisions, and provided funding support. All authors reviewed the manuscript.

This work was supported by the Gansu Province University Industrial Support Plan (grant number: 2023CYZC-05) and the Doctoral Students Training Research Fund of Lanzhou University Second Hospital (grant number: YJS-BD-32).

The authors declare no competing financial interest.