All the calculations have been carried out, on ten BZC compounds (Figure 1), with the software GAUSSIAN 03 [21] , in vacuo, at the HF/6-311 + G(d,p) and MPW1PW91/6-311 + G(d,p) theories levels. Choosing Hartree- Fock (HF) and Density Functional Theory methods (DFT/MPW1PW91) allows accuracy results with relatively

less time consuming. Usually, it’s highly recommended to use at least two different methods in quantum mecha- nical calcultions, so that consistency of results can be, in some way, verified. The choice of split-valence and triple-dzeta basis sets is justified by the need of sufficiently extended levels. Diffuse and polarization functions are important, whenever the matter is intermolecular interactions. Each of the protonation complexes has been fully optimized, with a frequencies calculation at the same levels of theories.

Geometry initialization of the protonated molecules has been carried out by utilizing the valence angles around the concerned heteroatoms (carbonyl oxygen, sp² and sp³ nitrogens) of the benzimidazolyl-chalcones (BZC) kernel. According to Gillespie method or V.S.E.P.R (Valence Schell Electron Pair Repulsion) method, the average values of valence angles around sp² and sp³ atoms equal and respectively. Figure 2 shows the initial geometries of protonation.

The protonation is a process in which a Lewis base B fixed a proton to give a protonated molecule BH⁺ according Equation (1):

Knowing the variations of energy contributions to the internal energy at 0 K and at 298.15 K between the products and reactants contributes to the energy characterization of a chemical reaction. For a given energy parameter X, its variation is determined according Equation (2):

The geometrical optimization and the calculation of the frequencies of the free molecules allow us to determine the variation of the internal energy at 0 K (ΔE_0K) and at 298.15 K (ΔE_298K) with respect to the reaction studied. The variation of the internal energy to 298.15 K, ΔE_298K, constitutes a sum of different electronic, translation, rotation and vibration contributions and the internal energy at 0 K given in Equation (3):

ZPVE (Zero Point Vibrational Energy) contribution, i.e. lowest vibrational level energy, due to 3N − 6 normal vibrational modes (3N − 5 for the linear molecules), each with frequency n_i, up to N kernels at 0 K, is defined according Equation (4):

k is the Boltzmann constant; h Planck’s constant; R the constant of perfect gases. To obtain the corresponding energy at 298.15 K, it is necessary to take into account the extra energy due to vibrational levels population during temperature rising from 0 to 298.15 K. Thus, Equation (4) becomes Equation (5):

As regards the contributions of rotation and translation, they are drawn from the approximation of perfect gases according relationship (6):

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

From this relationship, it is deducted the enthalpy of the reaction at 298.15 K. It corresponds to the variation of the internal energy corrected by the term ∆(PV), either (∆n being the variation in the number of gaseous moles of the reaction):

The entropic contributions of translation, of rotation and of vibration of given species at 298.15 K are regrouped in the total entropy term S and the Gibbs energy, at 298.15 K, linked to the reaction is simply obtained by the relationship (9):

The electronic energy of an isolated proton equals zero, therefore it doesn’t appear in the calculation of the variation of the electronic energy. Again, for the proton, the translational energy is different from zero

(at 298.15 K and the entropy of translation equals

. Therefore, the proton affinity in the gas phase (PA) and the gas phase basicity

(GB), are easily determined according the above equations.

The descriptors selected for this study are related to the average valence angles around the potential protonated sites, and. It is assumed that in sp² hybridization state, each of the lone pairs of the oxygen atom forms with the carbonyl bond an angle of 120.0˚, and that the lone pair of the nitrogen atom also points out with an angle of 120.0˚ with each adjacent bond. In the case of sp³ nitrogen, the optimal angle is assumed to be 109.5˚. It is clear from these observations that the binding geometry, the more probable, which can be formed between hydrogen and each basic site, will be the one measuring the average valence angles θ_m, which better approaches the optimal angles. The values measured of the valence angles θ_m are shown in Table 1. In this table, θ₁Nsp² equals the average of the angles and, when θ₃Nsp³ equals the average of the angles

, and. θ₂Osp² stands for describing the angle (Figure 2).

The review of the values in Table 1 shows that respectively at HF/6-311+G (d,p) and MPW1PW91/6-311 + G(d,p) levels, the average values of the angles extend for θ₁Nsp², from 125.37˚ to 125.40˚ and from 125.13˚ to 125.14˚; for θ₂Osp², from 114.70˚ to 115.56˚ and from 112.36˚ to 113.18˚ and for θ₃Nsp³, from 109.50˚ to 110.16˚ and from 109.91˚ to 110.06˚ respectivelyat the HF/6-311 + G(d,p) and MPW1PW91/6-311 + G(d,p) levels. Now, let’s examine which calculated angles are closer to the theoretical optimal angles according to Figure 2. For bothlevels of theories, the average θ₁Nsp² angles vary from 125.13˚ to 125.40˚ corresponding to a maximum gap of 5.40˚comparing with the ideal angle of 120.0˚. Samely, the maximum gaps obtained for θ₂Osp² and θ₃Nsp³ are respectively 7.64˚ and 0.66˚. And finally, the form corresponding to the angle θ₃Nsp³, shows theclosestvalue to the theoretical one. Which confirms the tetragonalisation of sp³ nitrogen under the effect of protonation. It is thus established, following the criterion to the optimality of the valence angles, that sp³ nitrogen atom is the major protonation site in benzimidazole-chalcone kernels. Now, we’re going to examine energitical criterion to confirm or not the above conclusion.

The values of the proton affinityand those of the gas phase basicity calculated at HF/6-311 + G(d,p) and MPW1PW91/6-311 + G(d,p) levelsare reported respectively in the Table 2 and Table 3.

All the values, of proton affinity and gas phase basicity of the different sites, reported in Table 2 and Table 3, are positive, indicating that protonation reactions on the different sites are exothermic and spontaneous. Further-

more, at level HF/6-311 + G(d,p), the average values (PA and GB) for, and are respectively 221.724 and 214.401 kcal/mol, 207.426 and 199.773 kcal/mol and 188.496 and 180.930 kcal/mol. At MPW1PW91/6-311 + G(d,p), the average values (PA and GB) are respectively 222.063 and 214.236 kcal/mol, 212.991 and 205.061 kcal/moland 186.658 and 178.953 kcal/mol We note greater energy values on the Nsp² nitrogen atom compared to Osp² and Nsp³. This means that oxygen atom and sp³ nitrogen atoms are bothlessbasic sitesandthereforehave thelowestproton affinities. All the values trend to show that the sp² nitrogen is the major protonation site in BZC. Besides, according the energetic values, the following ascending sequence can be made:. Furthermore, the percentage of protonation on each site, can be calculated. The process was the following way, depending on the below protonation reactions ((10)-(12)), respectively, with Nsp², O_carbonyl and Nsp³ leading to the complexes, and, corresponding respectively to thermodynamic equilibrium constants, and:

If is the fraction of the amount of BZC protonated with Nsp², the below calculation process can lead to it:

The different equilibrium constants are calculated from variations of free enthalpies according to the relationship (14):

In the same way, the fraction of the amount of BZC protonated with O_carbonyl is given by the below relation (15) and finally, the fraction of the amount of BZC protonated Nsp³ is drawn according relation (16).

and

From the results in Table 2 and Table 3, one can state that BZC kernel substituents have, in practice, no effet on protonation properties of the BZC kernel, since, for a kind of heteroatom, energetic values do not really vary. So, to simplify, we’ll use the average values of gas phase basicity, , to calculate the average values of equi-

librium constants according Equation (14). Further, we’ll get the average protonation percentages, of each site using Equations ((13), (15) and (16)). Results are given in Table 4.

With the above average values of reported in Table 4, all the fractions, and

tend toward 0, whereas tends toward. Therefore, at level HF/6-311 + G(d,p) as well as at level MPW1PW91/6-311 + G(d,p), the average protonation percentage on sp² surrounds 100% when it surrounds 0% on both carbonyl oxygen and sp³ nitrogen. Thus, according the energetic analysis, the major protonation site is strongly the sp² nitogen.