Mycolactone A/B possesses nine (09) heteroatoms, all those are sp² or sp³ hybridized oxygen atoms, shown in red color at a 3D molecular structure of mycolactone A/B (Figure 2). Heteroatoms are numbered from 1 to 9 and these numbers will also correspond respectively to the names of the different hydrogen bond complexes.

ONIOM method, developed by Morokuma et al. [11] , is used because of the

high number of atoms in mycolactone A/B. It consists of cutting the studied system into several layers, each of the layers being treated at a different calculation level. It therefore allows to describe precisely the part of the system which has particular interest for the study, called the internal layer, and to describe in a less precise manner the rest of the system, called the outer layer or the environment. ONIOM method permits to obtain the energy of the real system at a high level of computation called high level, , by means of extrapolation according Equation (1), where is the energy of the real system at the low calculation level, the energy of the model system at the higher calculation level, and the energy of the model system at the low calculation level. An example of description of the ONIOM two layers in mycolactone A/B is shown in Figure 3.

All calculations were performed, using Gaussian 03 software [12] at the ONIOM (HF/6-311+G(d,p):AM1) and ONIOM(B3LYP/6-311+G(d,p):AM1). The presence of diffuse and polarization functions in the basis sets is important in order to take into account the lone pairs of the heteroatoms, as well as intermolecular interactions.

Nine hydrogen bond complexes were constructed on each of the oxygen heteroatoms, a water molecule being the probe, as Hydrogen Bonding Donor. Such hydrogen bond can be characterized by geometric parameters (Figure 4).

Before optimization, for all complexes, the angle of the linearity α has been set at 180˚ and the angle of the directionality β, at 109.5˚ for sp³ hybridized oxygen and 120˚ for sp² hybridized oxygen. According to Gillespie’s V.S.E.P.R (Valence Shell Electron Pair Repulsion) theory (Figure 5), the distance d between an oxygen atom of mycolactone and a hydrogen atom of the probe is set at 2 Å. These values correspond respectively to the angles and the minimum approach distance of the hydrogen bond [14] .

Hydrogen bonding between a donor molecule and an acceptor molecule occurs according reaction 2. The Hydrogen bond complex is the product. The variation in electronic energy, at 0 K, is given by Equation (3):

The internal energy, at 298.15 K, corresponds to the sum of the electronic, rotational, translational and vibrational contributions, so that it’ variation can be written according Equation (4):

Geometry optimization of both reactants and products, gives access to all contributions (including nuclear repulsion energies). In ideal gas approximation, rotational and translational contributions are given according Equation (5):

includes ZPVE (Zero Point Vibrational Energy) energy, i.e. lowest vibrational level energy, due to 3N-6 normal vibrational modes (3N-5 for the linear molecules), each with frequency, up to N kernels at 0 K. Taking into account the extra energy due to vibrational levels population during temperature rising from 0 to 298.15 K, leads to Thus, Equation (6), from which the term can be drawn:

As a result, internal energy variation at 298.15 K is given by Equation (7):

Enthalpy and free enthalpy variations, At 298.15 K, enthalpy and free enthalpy are respectively given by Equations (8) and (9), and entropy variation, by Equation (11):

where

Spectroscopic descriptors can serve as Hydrogen bond scale. The X-H bond linking the donor atom X and the hydrogen atom H increases or decreases according Hydrogen bond’s strength. Therefore the stretch vibration wave-num- ber can be measured. When the donor is a water molecule, the displacement is the scale, and respectively for sp² and sp³ oxygen atoms, this scale is defined according Relations (11) and (12):

At ONIOM(HF/6-311+G(d,p):AM1) and ONIOM(B3LYP/6-311+G(d,p):AM1) levels, frequencies of vibrator equal respectively, 4242.25 cm⁻¹ and 3923.88 cm⁻¹.

All geometry optimizations succeeded at the two levels of computation. Examples of initial guess geometry and then optimized geometries of two hydrogen bond complexes are shown in Figure 6. Geometric parameters are given in Table 1.

At level ONIOM(HF/6-311+G(d,p):AM1), value of the linearity angles α on the O₅sp² heteroatom equals 169.78˚ and is the closest angle to the ideal value of 180˚, the directionality angle β equals 120.10˚ and is the closest to the ideal angle of 120˚, the hydrogen bond length d equals 2.00 Å and is the smallest (Table 1). Indeed, as far as the lengths of the H bonds (distance d) are concerned, the practice is to consider a contact as a real H bond if the distance d is less than the sum of the Van der Waals radius, taking 1.52 Å [15] , and 1.2 Å [16] , respectively for a contact with the oxygen and hydrogen atoms; meaning that d ≤ 2.72 Å. It is also known that the shorter the H bond length is, the stronger it is. So, according geometric parameters, O₅sp² heteroatom is the major hydrogen bonding site. At level ONIOM(B3LYP/6-311+G(d,p):AM1), the closest angle α, 171.40˚, rather concerns the O₈sp³ heteroatom, the closest angle β, 108.40˚, is found on O₂sp³ (the ideal β angle for sp³ oxygen equals 109.5˚), and the shortest length d, 1.86 Å, is found for O₇sp³. Values of geometric parameters computed at ONIOM (B3LYP/6-311+G(d,p):AM1) level don’t allow an undoubtedly conclusion about the major hydrogen bonding site.

All values of enthalpy are negative, whatever the calculation level, meaning that all hydrogen bonding process are exothermic (Table 2). However, the lowest values are computed in the case of heteroatom O₅sp², respectively −62.24 kJ/mol and −37.32 kJ/mol at ONIOM(HF/6-311+G(d,p):AM1) and ONIOM(B3LYP/6-311+G(d,p):AM1) levels. In the same way, negative values of free enthalpy are computed for O₂sp³O₃sp², O₅sp² and O₈sp³ at both two levels. Both at ONIOM(HF/6-311+G(d,p):AM1) and ONIOM(B3LYP/6-311+ G(d,p):AM1), these values equal respectively −3.33 kJ/mol, −18.82 kJ/mol, −19.53 kJ/mol and −13.02 kJ/mol. So, onthesespecificheteroatoms, Hydrogen bonding is spontaneous.

Spontaneity is much greater with the O₅sp² heteroatom, since the corresponding values are the lowest, i.e. −19.53 kJ/mol at both ONIOM (HF/6-311+ G(d,p):AM1) and ONIOM(B3LYP/6-311+G(d,p):AM1) levels. Therefore, the O₅sp² heteroatom gives the most stable complexes. Values of computed for O₃sp² are the closest to those computed for O₅sp². Those two heteroatoms, seem to be subject to mesomerism, which enhances their hydrogen bonding ability. In the other hand, O₁sp³, O₄sp³, O₆sp³, O₇sp³ and O₉sp³ heteroatoms have

positive values of free enthalpies, meaning that there is no possibility of spontaneous reaction for these different sites. It’s noticeable that all the latter heteroatoms are sp³ hybridized. It seems that sp³ hybridized oxygen cannot be hydrogen bond major site.

All frequency shifts are positive (Table 3), corresponding to a decrease in the bond O-H vibration frequency, under hydrogen bonding process. The higher the shift Δν(O-H) is, the stronger the Hydrogen bong will be. Highest values correspond to O₅sp² heteroatom, i.e. 159.68 cm⁻¹ and 233.20 cm⁻¹ respectively at ONIOM(HF/6-311+G(d,p):AM1) and ONIOM(B3LYP/6-311+G(d,p):AM1) levels. Spectroscopic parameters designate then the O₅sp² oxygen atom as the major Hydrogen bonding site.