Protonation Sites in Benzimidazolyl-Chalcones Molecules : An ab Initio and DFT Investigation

In this work, we have focused our investigations on the protonation sites predilection in the benzimidazolyl-chalcones (BZC) derivatives. Particularly, we are interested in the study of geometrical and energetical parameters. BZC are well known for their particularly nematicidal activity. Ten (10) BZC derivatives coded BZC-1 to BZC-10, with various larvicidal concentrations, have been selected for this work. They all are different one from another by the phenyl ring which is substituted by electron modulators such as alkyl, hydroxyl, alkoxy, aminoalkyl, halogen and nitro or replaced by the furan. Quantum chemical methods, namely HF/6-311 + G(d,p) and MPW1PW91/6311 + G(d,p) theory levels have been used to determine the geometrical and energetical parameters by the protonation on each heteroatom of the BZC derivative. An accuracy results with relatively less time consuming has been obtained using Hartree-Fock (HF) and Density Functional Theory methods (DFT/MPW1PW91). The calculations results allow identifying the sp2 nitrogen as the preferential site of protonation in BZC derivative compounds.


Introduction
The derivatives of the benzimidazolyl present a pharmacological interest significantly due to their therapeutic * Corresponding author.
virtues in many diseases.Several studies have demonstrated that the derivatives of benzimidazolyl are antihistaminic [1], antifungal [2], antiallergic [3], antibacterial [4]- [6], analgesic [7], antiplasmodial [8] and antiviral [9].In recent years, it has been documented and reported that the main cause of gastro-intestinal infections of small ruminants as well as loss and reduction in productivity of the livestock is due to the effect of nematodes [10] [11].Nematodes (worm from hearth, freshwater or sea) are also being the origin of most human parasitic diseases [12] [13].The development of an "ideal" anthelmintic seems to be possible with the benzimidazoles, imidazothiazoles, tetrahydropyrimidines and organophosphate compounds.Such ananthelmintic should possess a broad spectrum of action, a high degree of efficiency, a good safety margin and aflexibility of use.However, all reported studies related to benzimidazolyl-chalcones are limited to the synthesis, structural characterization and the investigation of the activity properties.Till date, researches have led to synthesize several hundred of compound.A few have been selected for their effective anthelmintic activity at broad spectrum, and among them, the benzimidazolyl-chalcones (BZC) kernel.
These different molecules have been synthesized by Ouattara et al. [14].The numerous therapeutic properties of BZC could be related to the conformation of molecules and the interactions they can establish with other molecules.Among the different properties of a biological molecule, the proton-transfer reactions play a very important role in the molecular interactionsand biologicalsystems [15] [16].The BZC ability to protonate is likely to affect its fate in the environment, both as regards its transport, his stay, its reactivity in the surrounding environment until the target molecule and as regards its recognition by the receiver.Protonation or deprotonation is the first step in many fundamental chemical rearrangements and in most of the enzymatic reactions [16].Two quantities are used to characterize the ability of a molecule in the gas phase or phase condensed to accept a proton.The gas phase basicity (GB) which is the opposite of the variation of free energy associated with the protonation reaction ( 0 298 ) and the proton affinity ( 0 298 ) [17]- [19].The gas phase basicity and the proton affinity (PA) can inform us on the capacity of a site to accept a proton.A recently work [20] has tried to determine the preferential site of protonation between nitrogen atoms and oxygen.The aim of our present work is to characterize the preferential site of protonation in benzimidazolyl-chalcones by using different quantum chemical methods.

The Calculation Level
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 mechanical 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 Optimization
Geometry initialization of the protonated molecules has been carried out by utilizing the valence angles around the concerned heteroatoms (carbonyl oxygen, sp 2 and sp 3 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 sp 2 and sp 3

Energetic Parameters
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 ν 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 nRT ∆ (∆n being the variation in the number of gaseous moles of the reaction): The entropic contributions of translation trans S , of rotation rot S and of vibration vib S 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 ⋅ .Therefore, the proton affinity in the gas phase (PA) and the gas phase basicity (GB), are easily determined according the above equations.

Geometrical Parameters
The descriptors selected for this study are related to the average valence angles around the potential protonated sites sp2 N , sp2 O and sp3 N .It is assumed that in sp 2 hybridization state, each of the lone pairs of the oxygen atom forms with the carbonyl bond C O = 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 sp 3 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, θ 1 Nsp 2 equals the average of the angles 1 τ and 2 τ , when θ 3 Nsp 3 equals the average of the angles  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 θ 1 Nsp 2 , from 125.37˚ to 125.40˚ and from 125.13˚ to 125.14˚; for θ 2 Osp 2 , from 114.70˚ to 115.56˚ and from 112.36˚ to 113.18˚ and for θ 3 Nsp 3 , 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 θ 1 Nsp 2 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 θ 2 Osp 2 and θ 3 Nsp 3 are respectively 7.64˚ and 0.66˚.And finally, the form sp3 N -H + corresponding to the angle θ 3 Nsp 3 , shows theclosestvalue to the theoretical one.Which confirms the tetragonalisation of sp 3 nitrogen under the effect of protonation.It is thus established, following the criterion to the optimality of the valence angles, that sp 3 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.

Energetic Parameters
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-  3 .means that oxygen atom and sp 3 nitrogen atoms are bothlessbasic sitesandthereforehave thelowestproton affinities.All the values trend to show that the sp 2 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 Nsp [ ] [ ] x is the fraction of the amount of BZC protonated with Nsp 2 , 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 Nsp 3 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, GB , to calculate the average values of equi- x (%) 100 0 0 100 0 0 librium constants according Equation (14).Further, we'll get the average protonation percentages, x of each site using Equations (( 13), ( 15) and ( 16)).Results are given in Table 4.
With the above average values of GB reported in Table 4, all the fractions 2 1 K K , 3 1 K K and 2 3 K K tend toward 0, whereas 2 1 K K 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 sp 2 surrounds 100% when it surrounds 0% on both carbonyl oxygen and sp 3 nitrogen.Thus, according the energetic analysis, the major protonation site is strongly the sp 2 nitogen.

Conclusion
The aim of this work was to determine the protonation major site in benzimidazolyl-chalcone (BZC) kernel as well as its energetic characteristics.Interpreting the valence average angles around each of the three heteroatoms, it has been noticed that the sp 3 nitrogen atom is slightly the major site since the gap from ideal valence angle is the lowest.In the contrary, interpretation of energetic parameters, meaning proton affinity (PA) and gas phase basicity (GB), leads to design sp 2 nitrogen as, strongly, the major site.These conclusions are available whatever the calculation level, meaning HF/6-311 + G(d,p) or MPW1PW91/6-311 + G(d,p).Therefore, the protonation percentage on each site has been calculated.Results show that the protonation percentage surrounds 100% on sp 2 nitrogen.The conclusion is that, taking into account thermodynamic analysis, the sp 2 nitrogen is the unique protonation site in BZC.From the whole results, one can also state that BZC kernel substituents have no effect on protonation properties of the kernel, since, for a kind of heteroatom, geometric or energetic values do not really vary, although substituents vary.

Figure 2 .
Figure 2. Definition of geometrical parameters describing the protonation sites.

Table 4 .
Average gas phase basicity and protonation percentages on sp 2 nitrogen atom, carbonyl oxygen and sp 3 nitrogen atom.