Multitask Quantum Study of the Curcumin-Based Complex Physicochemical and Biological Properties

Density functional theory (DFT), time-dependent density functional theory (TDDFT), quantum theory of atoms in molecules (QTAIM), and extended transition state natural orbitals for chemical valence (ETS-NOCV) have all been used to investigate the physicochemical and biological properties of curcumin and three complexes, i.e., Cur-M (M = Ni, Cu, and Mg). Based on DFT calculations, the enolic form (Cur-Enol) is more stable than the anti-diketone form (Cur-Anti diketone) favored for complexation. This enolic form stability was explained by the presence of three intramolecular hydrogen bonds according to the QTAIM analysis. Furthermore, the ETS-NOCV technique revealed that the enolic form had more significant antioxidant activity compared with the anti-diketone form. The calculations from the COnductor-like Screening MOdel for Realistic Solvents (COSMO-RS) showed that the dimethyl sulfoxide (DMSO) solvent could dissolve all the curcumin tautomers Cur-Enol, Cur-Anti-diketone and Cur-Cu, Cur-Mg, and Cur-Ni complexes in contrast to benzene, acetone, octanol, ethanol, methanol, and water. Furthermore, except for Cur-Mg, which had a relatively low solubility (14 g/L), all complexes were insoluble in water. Cur-Anti-diketone was considerably more soluble than Cur-Enol in the examined solvents.


Introduction
Curcumin, a major active component of Turmeric, has long been used as a spice, and it possess a wide range of biological activities, including antibacterial and antifungal [1], antioxidant, anticancer [2,3], antimicrobial [4], and inflammatory properties [5]. Curcumin has piqued the interest of many academics since then, and numerous papers have been published on the subject [6][7][8]. It was first discovered by Vogel and Pelletier as a powder "yellow coloring matter" from rhizomes of C. longa (Zingiberaceae family) [9], and characterized and first synthesized by Milobedeska, Lampe et al. [10,11].
Polyphenols have gained attention essentially due to their antioxidant capabilities. They can trap free radicals and prevent lipid peroxidation by scavenging free radicals. They can also capture metal ions due to their chelating capabilities. Nevertheless, curcumin complexes remain little explored despite their promising properties particularly for Alzheimer's disease [14]. In general, the experimental identification of therapeutic characteristics of specific natural compounds requires a prior deep understanding, specifically for computational investigations. Examples include the solubility in water and other liquids of interest, especially when dealing with chemicals intended for human consumption. The insoluble nature of curcumin, for example, makes it challenging to utilize in medicinal applications.
The complexation of a chemical with other metals can drastically alter certain molecular features, resulting in new compounds with distinct properties that are potentially suitable for desired purposes. This is the case of curcumin and its complexes. Hence, the main purpose of this investigation is the study of the complexation behavior and the antioxidant properties of curcumin-metal complexes based on Nickel, Copper, and Magnesium transition metals by density functional theory (DFT) techniques, i.e., time-dependent density functional theory (TDDFT) to simulate the absorption and emission spectra; quantum theory of atoms in molecules (QTAIM) to simultaneously explore the electron density and hydrogen bond interactions; extended transition state natural orbitals for chemical valence (ETS-NOCV) to evaluate the antioxidant activity; and COSMO-RS to calculate and analyze the solubility of curcumin and molecular interactions in various solvents. The results will be helpful to the experimentalists to synthesize curcumin complexes with more reliable properties.

Computational Methods
As part of the DFT (density functional theory) level computations, the geometric optimization calculations were conducted using Gaussian09 [15] and the functional B3LYP (Becke three-parameter Lee-Yong-Parr) [16]. All the atoms were based on the 6-311G (2d, 2p) basis. The polarizable continuum model (PCM) introduced the DMSO (dimethyl sulfoxide) solvent effect. Casida's method obtained characteristics and absorption spectrum of the excited states [17].
The theoretical study of curcumin-based transition metal compounds performed by Density Functional Theory (DFT) [18,19] using ADF software (Amsterdam Density Functional) [20] was only used for the single-point calculations, the functional GGA: PW91 (Generalized Gradient Approximation) [21], the Slater TZP (Triple zeta polarized) set of atomic bases [22], valence orbitals of all atoms (4s and 3d for Ni, Cu, and Mg; 2s and 2p for O and C; and 1s for H. Relativistic effects were taken into account at the scalar level using the regular approximation of order zero (ZORA) [23].
The integration parameter and the energy convergence criterion are: 6 and 10-6 a.u., respectively. Several DFT approaches can be used to describe the properties of chemical bonds; the quantum theory of atoms in molecules (QTAIM) is one of them. Hydrogen bonds were characterized using QTAIM [24], which was connected with investigating electron density's topology [24][25][26]. Using the NOCV technique [27], the dissociation energy of the phenolic hydrogen atoms could be calculated, allowing the antioxidant activity of the molecule and its complexes to be measured.
According to the relevant research [28,29], the ETS technique was included in the NOCV method [30,31]. Covalent bonds [32], intramolecular agnostic interactions [29,31], and intermolecular hydrogen bonds [33] may all be determined using the combined ETS-NOCV technique. The binding interactions were investigated using a Morokuma-type energy decomposition described by Ziegler and Rauk [34]. According to the stated approach, the total binding energy (∆E) is defined as: ∆E pauli indicates the repulsive four-electron interactions between the occupied orbitals, and ∆E els represents the classical electrostatic interaction between the molecule fragments in the complex in their final locations. Finally, the term ∆E orb stabilizes interactions between occupied and empty molecular orbitals of the two fragments. It should be emphasized that the last term ∆E orb contains the combination of occupied and vacant orbitals in the same fragment (polarization of internal fragments).
The strain density can be expressed as a sum of eigenvectors, ψ −k , ψ +k corresponding to the eigenvalues −ν k and +ν k with the same absolute value: where M denotes the total number of molecular orbitals on the fragments. Specifically, all occupied and empty molecular orbitals of the two fragments are included in the summation. Its eigenvalue ν k indicates the number of electrons that are moved from the anti-bonding orbitals, ψ − k. As a function of the eigenvalues of NOCV (ν i ), the orbital interaction term (∆E orb ) is represented in the combined ETS-NOCV scheme as follows: The diagonal elements of the Kohn-Sham matrix on NOCVs in the transition state (TS) are T TS −k,−k and T TS k,k . Equations (2) and (3) show that ∆ρ k can be visualized, and its energetic contributions to the overall bond energy are provided [26]. COSMO-RS is a completely predictive model for thermodynamic characteristics of fluids and solutions using statistical thermodynamics and quantum chemistry [35]. Polarization occurs when the charge density is high due to the solvent at the cavity surface. The total energy may be calculated by calculating the forces that result.
COSMO-RS combines statistical thermodynamics with quantum chemistry to provide an utterly predictive model for the thermodynamic characteristics of fluids and solutions. The charge density of the solvent at the cavity's surface expresses its polarization effects. The resulting force was quantified to calculate the total energy. The COSMO-RS model is one of the most outstanding forecasters of solubility, particularly for tiny compounds, despite its lack of popularity [36].

The Antioxidant Property of Curcumin
The antioxidant property of curcumin depends fundamentally on its structure, including methoxylated phenols and the enol form of β-diketone. By Michael's non-enzymatic addition or GST (Glutathione S-transferase) mediated process, curcumin's core β-diketone component is converted from curcumin to glutathione. Curcumin has been found to be ten-times more effective than vitamin E as an antioxidant because of these particular characteristics [37].
Curcumin was studied in two forms, Cur-Enol and Cur-Anti diketone. Both forms were neutral, and it was found that the Cur-Enol form had the best antioxidant properties (see Figure 1). The local antioxidant property was measured using ETS-NOCV and the Bond Dissociation Energy (BDE) (see Table 1 and Figure 2).   The Cur-Enol molecule has the best reducing characteristics (electron or hydrogen atom donor) due to the low dissociation energy value in phenol at the Position β and the low ionization potential (Table 1), which allows it to perform the antioxidant role. Our results agree with previous research findings based on experimental evaluations [38][39][40].

Absorption and Emission Wavelengths
Cur-enol form characterization has been the subject of research. The TD/B3LYP/6-311G (2d,2p) technique was used to theoretically compute absorption and emission wavelengths of curcumin in various solvents (DMSO, water, methanol, ethanol, THF, acetonitrile, and cyclohexane). Table 2 summarizes all the acquired findings, including the     The Cur-Enol molecule has the best reducing characteristics (electron or hydroge atom donor) due to the low dissociation energy value in phenol at the Position β and th low ionization potential (Table 1), which allows it to perform the antioxidant role. O results agree with previous research findings based on experimental evaluations [38-40

Absorption and Emission Wavelengths
Cur-enol form characterization has been the subject of research. The TD/B3LYP/ 311G (2d,2p) technique was used to theoretically compute absorption and emission wav lengths of curcumin in various solvents (DMSO, water, methanol, ethanol, THF, aceton trile, and cyclohexane). Table 2 summarizes all the acquired findings, including th The Cur-Enol molecule has the best reducing characteristics (electron or hydrogen atom donor) due to the low dissociation energy value in phenol at the Position β and the low ionization potential (Table 1), which allows it to perform the antioxidant role. Our results agree with previous research findings based on experimental evaluations [38][39][40].

Absorption and Emission Wavelengths
Cur-enol form characterization has been the subject of research. The TD/B3LYP/6-311G (2d,2p) technique was used to theoretically compute absorption and emission wavelengths of curcumin in various solvents (DMSO, water, methanol, ethanol, THF, acetonitrile, and cyclohexane). Table 2 summarizes all the acquired findings, including the absorption/emission wavelength (λ max ), oscillator strength f, and the Stokes shift (∆λ). Figure 2 shows the spectra of epsilon (ε) as a function of the wavelength. The solvent DMSO produced the maximum absorption wavelength for curcumin enol ( Table 2). The absorption wavelength is shorter in apolar solvents particularly cyclohexane, (λ abs = 445.46 nm). The curcumin enol-form absorbs light in the following order: DMSO > ethanol > acetonitrile > water > THF > methanol > cyclohexane.
The results of Table 2 were further supported by Figure 2 demonstrates that the absorption spectra in all the solvents are almost identical. When comparing different solvent emission wavelengths λ em , water has the maximum value. In the enol-form of curcumin, the wavelength of λ em emission decreases from cyclohexane to water (the most polar). In polar solvents, the oscillator force f, which reflects the transition probability, is more significant than in non-polar solvents.
The order of the emission wavelengths in different media is given as: water > DMSO > acetonitrile > methanol > ethanol > THF > cyclohexane. The solvatochromic effect is weak but present in both absorption and emission events. The HOMO-LUMO transition of Cur-Enol in the investigated solvents dominates both the absorption and emission in the UV-vis range.

Curcumin Complexation
Curcumin is an efficient metal ion chelator, the diketone portion of curcumin can bind metals, such as copper, nickel, and magnesium. According to most scientific studies, the oxygen of the diketone part binds metal cations; whereas, other researchers suggested that the non-binding doublets of oxygen in the methoxy group might constitute chelation sites [41]. The chelation capacity of curcumin is particularly noteworthy since it can indirectly attach to proteins by utilizing metal or metalloprotein atoms.
The geometry optimization was carried out by a "single point" calculation with PW91/TZP for curcumin complexes and B3LYP/6-311G (2p, 2d) for the curcumin ligand. The PW91/TZP was the most useful in reproducing the experimental data. The curcumin complex (neutral compounds) theoretical geometric characteristics (Figure 3 and Table 3) are similar to the literature results [42][43][44]. The spin states for the compounds Cur-Ni, Cur-Cu, and Cur-Mg are doublet, triplet, and singlet respectively.    After complexation, the differences in binding lengths of specific molecule segments (C(4)-C(5)) and (C(4)-C(9)) ( Figure 3) for both forms of curcumin allowed us to establish whether the complexation was produced using the enol or diketone form (Table 3). After complexing with the three metals, the bond lengths of Cur-Anti-diketone (C(4)-C(5)) and (C(4)-C(9)) decrease. On the other hand, the Cur-Enol complexation causes an increase in the C(4)-C(5) bond length and a decrease in the C(4)-C(9) bond length ( Table 3). The nodal structure of the HOMO and LUMO orbitals of the two curcumins may explain this variation ( Figure 4). Given that neither C(4), C(5) nor C(9) atoms in Cur-Anti diketone contribute to the HOMO orbitals, the LUMO structure may be the cause of the shift. The reduced length of the two bonds is explained by the binding character of th C(4)-C(5) and C(4)-C(9) in the LUMO (Figure 4), thus, confirming the electronic back donation from the metal fragment to curcumin.
The atomic orbitals of the C(4), C(5), and C(9) atoms participate in both HOMO an LUMO molecular orbitals in Cur-Enol. The C(4)-C(5) and C(4)-C(9) bonds in the HOMO are binding, but the C(4)-C(9) bond in the LUMO is anti-binding (Figure 4). Due to elec The reduced length of the two bonds is explained by the binding character of the C(4)-C(5) and C(4)-C(9) in the LUMO (Figure 4), thus, confirming the electronic back-donation from the metal fragment to curcumin.
The atomic orbitals of the C(4), C(5), and C(9) atoms participate in both HOMO and LUMO molecular orbitals in Cur-Enol. The C(4)-C(5) and C(4)-C(9) bonds in the HOMO are binding, but the C(4)-C(9) bond in the LUMO is anti-binding (Figure 4). Due to electronic transfer through LUMO back-donation or HOMO electronic donation, the bonds C(4)-C(5) and C(4)-C(9) lengthen. This conclusion is insufficient to account for the observed C(4)-C(9) bond shortening.

Energy Analysis of Cur-M Complexes (M = Ni, Cu, and Mg)
The Ziegler-Rauk energy decomposition method [34] was used to assess the relative importance of the covalent and ionic contributions to the binding energy (BDE). This formal fragmentation treated the curcumin ligand as an organic moiety (L1) and the remaining moiety as an organometallic part (L2). The binding energy BDE was divided into three components using the "single point" calculation with PW91/TZP and the ZORA approximation: the Pauli energy, orbital energy, and electrostatic energy (shown in the Table 4). According to the Ziegler-Rauk method, the degree of covalency in the metal fragment and curcumin bond agrees with Hirshfeld charges. The Cur-Mg boundary orbital nodal characteristics reflect the poor covalency (8%).

ETS-NOCV Analysis
The ETS-NOCV fragmentation analysis was carried out in the same way as before. The total interaction energies of the Cur-M complexes are similar. The interaction may be thought of as an ionic bond. Although the E elec and E orb values are close, the stabilizing electrostatic interaction is more significant than the orbital interaction. The results of energy decomposition obtained according to this method are shown in Table 5. Compared to the other investigated systems, the cur-Mg complex has a lower covalent binding (9%) and a higher electrostatic term (91%). Consequently, the ETS-NOCV approach produces decomposition energies that increase in the same way as the fragmentation of Ziegler-Rauk (Table 4). Figure 5 shows the natural orbitals that have the most significant impact on the metalcurcumin bond, as well as the deformation density. Red represents areas of electronic density depletion, whereas blue represents areas of electronic density accumulation. From the red zones to the blue zones, the electrical density shifts accordingly. The orbital diagram depicts a back-donation of the metal fragment to curcumin ( Figure 5).

QTAIM Topological Analysis
The QTAIM parameters were obtained by a single point calculation on the geome tries optimized with GGA: PW91/TZP. The most important point in this analysis is the

QTAIM Topological Analysis
The QTAIM parameters were obtained by a single point calculation on the geometries optimized with GGA: PW91/TZP. The most important point in this analysis is the presence of an additional critical point between the central portion (β-diketone), the hydroxyl groups on phenyl rings, and the oxygen on methoxy groups. QTAIM descriptors were computed at critical points for each complex, and their values are cited in Table 6. The electron density and its Laplacian for intramolecular hydrogen bonds were included in the study. Curcumin and its complexes have hydrogen bonding properties, including as donor and acceptor.   Figure 6). The chelation of curcumin with the metal pieces created two conformations: pseud tetrahedral for Cur-Ni and Cur-Mg and pseudo-plane square for Cur-Cu. Hydroge   Figure 6). The chelation of curcumin with the metal pieces created two conformations: pseudotetrahedral for Cur-Ni and Cur-Mg and pseudo-plane square for Cur-Cu. Hydrogen bonding (Cl . . . HOH) is enabled by the copper square-planar coordination, which is preferred by Cu(II) compounds in general (Table 6 and Figure 6).

Effect of Curcumin Complexation on Its Antioxidant Character
The BDE method was used to determine the phenolic hydrogen atoms dissociation energies to better understand the influence of curcumin complexation on its antioxidant properties. The ionization potentials (IP) of the Cur-Ni, Cur-Cu, and Cur-Mg complexes are indicated in Table 7.
In the case of the antioxidant action with hydrogen transfer mechanism, Cur-Enol remained the most active species. The Cur-Mg complex exhibited an IP = 115.45 Kcal mol −1 value for the electron transfer antioxidant mechanism. The Cur-Mg shows the best antioxidant activity explained by its values of HOMO energies (as best electron donor). The BDE and PI energies are lower than those of Cur-Ni and Cur-Cu.

The Solubility of Curcumin and Its Complexes
For an antioxidant compound, high solubility is one of the most important physicochemical and biopharmaceutical criteria for use as an active agent in a drug or food supplement [45].
Curcumin is a lipophilic amphiphilic molecule with therapeutic properties [12]. Its solubility in water must be improved to boost curcumin's bioavailability [46]. The aromatic groups in curcumin structure provide hydrophobicity, which makes it poorly soluble in water, while acetone, ethanol, and benzene are suitable solvents. The most widely used solvent is still DMSO [47]. The solubility of curcumin tautomers and its complexes (Cur-Enol, Cur-Anti-diketone, and Cur-Ni, Cur-Cu, and Cur-Mg) were investigated (Table 8 and Figure 7).  In all solvents except water, Cur-Anti-diketone is the most soluble compound. Cur-Enol dissolves well only in benzene and DMSO but not in other solvents. The Cur-Mg complex is weakly soluble in water (14 g/L) but considerably superior to the other compounds, which are insoluble in water. Consequently, complexation can increase the water solubility of curcumin. In terms of solvents, only DMSO can dissolve all of the molecules (curcumin and its complexes). In all solvents except water, Cur-Anti-diketone is the most soluble compound. Cur-Enol dissolves well only in benzene and DMSO but not in other solvents. The Cur-Mg complex is weakly soluble in water (14 g/L) but considerably superior to the other compounds, which are insoluble in water. Consequently, complexation can increase the water solubility of curcumin. In terms of solvents, only DMSO can dissolve all of the molecules (curcumin and its complexes).

Conclusions
DFT quantum calculations highlighted interesting properties of curcumin and its complexes, i.e., Cur-M (M = Ni, Cu, and Mg). The enolic form of curcumin (Cur-Enol) was found to be energetically more stable and biologically more active compared with its Cur-Anti-diketone tautomer. Furthermore, the antioxidant properties of Cur-Enol calculated by both ETS-NOCV and BDE methods were found to be better compared with Cur-Antidiketone and its complexes. A combined ETS with the NOCV approach was also conducted to study the nature of curcumin-metal (Cur-M) bonding, and the results showed that all Cur-M bonding had a primarily ionic character (Cur-Ni: 71%, Cur-Cu: 57%, and Cur-Mg: 91%). QTAIM results showed the existence of two hydrogen bonds for Cur-Enol and Cur-Cu, which explained their stability compared to Cur-Mg and Cur-Ni.
The TDDFT calculated absorption and emission transitions of curcumin gave peaks that were similar to the published experimental findings with some shifts. The first excitation had the highest probability and was of the HOMO-LUMO type ( π → π * electronic transition). Solvatochromism existed in both absorption and emission and was found to be weak. We concluded that the HOMO-LUMO transition in Cur-Enol in all solvents was the most present in the UV-vis region in absorption and emission.
The theoretical descriptors BDE and PI, for which the antioxidant activity showed that the compound Cur-Mg was the best antioxidant, presented the values of BDE and PI as the lowest on two sites with (143. 36-143.35) and 115.45 kcal/mol, respectively. This result was confirmed by the highest value of the HOMO structure.
Solubility calculations demonstrated that both Cur-Enol and Cur-Anti-diketone tautomers were soluble in DMSO but insoluble in water. Only Cur-Mg had a low water solubility (14 g/L), indicating that complexation promoted curcumin water solubilization and improved the therapeutic effects.