Fourteen (14) Manzamenones have been listed in the literature. These molecules are heterocyclic atypical fatty acids. According to the similarities or differences presented by these different structures, groupings were made. Three sets or groups have been constituted. The first set consists of seven Manzamenones whose reference codes (Refcodes) are A, B, C, D, E, F and H. These seven Manzamenones are six- and five-membered bicyclic compounds. Their basic skeleton, bicyclo [4, 3, 0] nonane, is given in Figure 1.

Manzamenones A and B differ only in the configuration of carbon C₅. They are thus said to be epimers. Manzamenones C, F and D are obtained from Manzamenone A by replacing in position 5 the carboxylic acid function respectively by ethyl ester, n-butyl ester and amide functions. As for Manzamenones E and H, their structures are obtained from that of Manzamenone A by replacing the hydroxyl group of the carboxylic acid function in position 5 with N-valinyl (E) and 4-ethylamine phenol (H).

Three Manzamenones of refcodes L, M and N compose a second group. They have the same basic skeleton as the Manzamenones of the first group. The hydroxyl group in position 1 distinguishes these molecules. The structure of Manzamenone L contains a methyl ester function at positions 2, 5 and 8. Manzamenone M is obtained by replacing the methyl ester function in position 5 by a carboxylic acid function. Concerning manzamenone N, its structure does not contain a hydroxyl group in position 1 on the bicyclo. It contains on the one hand the three esters functions like Manzamenone L and on the other hand two double bonds between C2-C3 and C1-C6. These two double bonds are conjugated with the carbonyl group.

Four Manzamenones of refcodes G, J, K and O form the third set. These molecules do not have a common skeleton structure.

The structures of the fourteen Manzamenones are shown in Figure 2, and those of Quinine and Artemisinin are in Figure 3.

The chemical potential µ_pot is the tendency of the electronic cloud to escape from the molecule. It is an overall property of the molecular system. The chemical potential is also equal to the opposite of the electronegativity χ as defined by Paulin and Mulliken [26] - [32].

μ pot = ( ∂ E ∂ N ) V ( r ) = − χ (5)

It can be expressed by the ionization potential PI and the electronic affinity AE.

μ pot = − P I + A E 2 = − χ (6)

The first derivative of the chemical potential regarding the electron number N leads to the chemical hardness η and are inverse the softness S [33] [34] [35].

η = ( ∂ μ ∂ N ) V ( r ) = ( ∂ 2 E ∂ N 2 ) V ( r ) = 1 σ (7)

According to the theory of acids and bases, developed by Pearson [28], these quantities can be expressed in terms of ionization potential (PI) and electronic affinity (AE).

η = 1 S = P I − A E 2 (8)

The ionization potential (PI) and electronic affinity (AE) are easily obtained in the Koopmans approximation [36] by:

P I = − ε HOMO et A E = − ε LUMO (9)

ε_HOMO and ε_LUMO are the energies of the highest occupied orbital (HOMO) and the lowest vacant orbital (LUMO), respectively. This is the theory of frontier molecular orbitals [37].

The electrophilia index ω [38] is a descriptor developed to evaluate the ability of a molecule to enhance electron transfer. It is calculated from the following relationship.

ω = μ 2 2 η (10)

The intermolecular interactions have a mainly an electrostatic nature [39]. This quantity is very often used to reveal molecular interaction sites [40] [41] [42]. The electrostatic potential (ESP) is defined by Equation (11) below.

V ( r ) = ∑ A Noyaux Z A | R A − r | − ∫ ρ ( r ′ ) d r ′ | r ′ − r | (11)

where Z_A is the charge of nuclei A, R A − r and r ′ − r are respectively the proton-nuclei and proton-electron distances, and ρ ( r ′ ) is the electronic density.

In this work, we selected the electrostatic potential extrema calculated at the molecular surface, Vs_max and Vs_min, to identify and analyze the respective HB donor and acceptor sites in Manzamenones. Indeed, several previous studies carried out on molecules of biological interest (nicotine and derivatives, progesterone) [43] [44] [45] have shown the interest of Vs_min for the study of HB acceptor sites.

The ONIOM 2 method, formulated as indicated, was applied to the fourteen Manzamenones in Figure 2. The different energies of the real and model systems as well as the extrapolated energy E ONIOM2 were estimated. The error resulting from the compatibility of the calculation levels was also evaluated. The results are shown in Table 1.

The analysis of the values for the fourteen Manzamenones shows that the error is zero or very close to zero. This means that the two levels are compatible and should lead to results with good approximations. The ONIOM calculations (B3LYP/6-311++G(d, p): AM1) can be used to study the structures of Manzamenones.

The variations of enthalpies of formation, entropies of formation and free enthalpies of formation are calculated for the fourteen Manzamenones, Quinine and Artemisinin. These values are obtained at the B3LYP/6-311++G(d, p) level of theory in the gas phase at 273.15 K. They are reported in Table 2. Examples of optimized structures of Manzamenones (A, E, L and J), Quinine and Artemisinin are shown in Figure 5.

The values of the enthalpies of formation Δ f H and free enthalpies of formation Δ f G for each of the molecules studied are all negative. The formation processes of these different molecules are therefore spontaneous and exothermic. The results show that the entropy (disorder) increases during the formation processes of the molecules.

Analysis of the enthalpies of formation Δ f H show that the Artemisnin formation process is the least energetic, −602,898.25 kcal·mol⁻¹. The heats of formation

of Quinine, Manzamenones K, J and D are quite close in values. They are respectively −650,320.69 kcal·mol⁻¹, −646,217.05 kcal·mol⁻¹, −657,637.67 kcal·mol⁻¹ and −657,649.81 kcal·mol⁻¹. According to the study conditions of this work, each of the presented molecules is obtained according to a spontaneous and exothermic process. The heats of formation of Manzamenones are between −646,217.05 kcal·mol⁻¹ and −899,152.30 kcal·mol⁻¹. Their formation reactions are globally more energetic than those leading to the formation of Artemisinin and Quinine whose heats of formation are respectively −602,898.25 kcal·mol⁻¹ and −650,320.69 kcal·mol⁻¹.

The reactivity parameters considered in this list of compounds are all global descriptors of molecular structures. They are HOMO (E_HOMO), LUMO (E_LUMO), chemical potential (µ_pot), electrophilia index (ω), chemical hardness (η), chemical softness (S), frontier orbital energy gap (ΔE), and dipole moment (µ_D). The energy values of the frontier orbitals and those of some global descriptors are shown in Table 3.

The total energies of Quinine, Artemisinin and the 14 Manzamenones are between −603,134.92 kcal·mol⁻¹ and −900,039.00 kcal·mol⁻¹. They are therefore very stable molecules. Except for Artemisinin, the least stable of the described molecules is the Manzamenone K with a total energy of −646,996.83 kcal·mol⁻¹. Therefore, it was used as a reference to establish relative stability (∆E_tot). According to our calculations, Quinine is more stable than this Manzamenone by

about 3594 kcal·mol⁻¹. As for Artemisinin, it is less stable by about 43862 kcal·mol⁻¹. Compared to the reference, four Manzamenones are distinguished by a very high stability. These are Manzamenones H, O, E and F; they are more stable by 253,042.17 kcal·mol⁻¹, 241,041.25 kcal·mol⁻¹, 228,523.81 kcal·mol⁻¹ and 147,293.13 kcal·mol⁻¹ respectively.

The optimal structures of Manzamenones have HOMO energies between −8 eV and −11 eV. These energies do not vary according to the order of stability of these molecules. Artemisinin and Quinine have their highest HOMO; −7.11 eV and −5.88 eV respectively. However, Quinine has the lowest LUMO (−1.77 eV) of all the molecules in Table 3. Artemisinin has its LUMO (−1.17 eV) located in the energy range of the Manzamenone LUMO (−0.80 eV to −1.43 eV). With the lowest energy gap (4.12 eV), Quinine is more reactive than all other molecules, it is followed by Artemisinin (5.94 eV). The Manzamenones described have larger energy gaps that vary little between 7.84 eV and 10.06 eV. Manzamenones B and E have potent enzymatic activities [46]; M and N have antimicrobial activities [47]; A, F, and L have considerable anti-oxidant activities [48]; and A and O have anticancer activities [49]. These results indicate that the biological activities of these Manzamenones do not depend on the energy gap value.

The dipole moment is the descriptor resulting from the distance between the barycenters of the positive and negative charges. It depends, for a molecule, on its geometry. This explains the remarkable differences between the values of the dipole moment of Manzamenones. All the Manzamenones studied in this work have their dipole moments between 2.38 D and 8.49 D.

They are all more polar than Quinine (2.19 D). The dipole moment of Artemisinin is 4.16 D. Being a parameter that reflects intermolecular interactions [50], these results show that all these molecules would have stronger intermolecular interactions than Quinine. Some Manzamenones (J, G, A, B, L, K, F, O and M) with higher dipole moments than Artemisinin would lead to stronger interamolecular interactions than this molecule. For the other Manzamenones (C, D, E, H and N), their molecular interactions would be weaker.

For the analysis of the electrostatic potential at the molecular surface, a numbering of the heteroatoms of all carbon atoms carrying hydrogen(s) is always adopted. When a carbon carries two or three hydrogens, an average value of the potential is calculated. The numbering adopted for the Vs_min and Vs_max assignments of Artemisinin and Quinine are shown in following Figure 6.

The different numbering of the atoms in the Manzamenone structures are made according to their similarities or differences. Figure 7 shows these numberings.

Some examples of maps of the electrostatic potential calculated at the B3LYP/ 6-31++G(d, p) level are shown in Figure 8.

The electrostatic potential maps of Artemisinin, Quinine, and thirteen Manzamenones were explored. Sites with Vs_min or Vs_max values were identified. These sites are reported in Table 4. They constitute, for Vs_max, the electron-rich regions thus hydrogen bond acceptors. The sites of Vs_max are poor in electrons; thus donors of hydrogen bonds.

The results in Table 4 show that the Manzamenones classified in the first two sets (A, B, C, D, E, H, L, M and N) have three (3) preferred acceptor sites. The other molecules each have two (2) sites. The molecules with the lowest Vsmin values are the Manzamenones F, D, C, and L. For these Manzamenones, the acceptor power of said sites decreases in the following order: L > F > D and C.

However, among these molecules, Artemisinin has the strongest O₁₃ LH acceptor site. All other (oxygen) acceptor sites of the studied molecules (Artemisinin, Quinine and Manzamenones) have little different acceptor powers.

The donor sites attached to the hydrogens of the OH and NH groups are the strongest. This is the case in Quinine and in the Manzamenones A(B), D, E, H, L, M, J and K. The OH donor site always has the strongest donor capacity. Manzamenone M contains two OH donors. This molecule could establish strong intermolecular interactions from these OH groups. The Manzamenones E and H each have an OH donor and an NH donor.