Quantum Chemical Studies of Some Hydrazone Derivatives

By the functional B3LYP and M05-2X of DFT and in two bases set, more and more extended (6-311G and 6-311G (d, p)), theoretical study of antioxidant properties of four hydrazones was carried out. The calculations made concern the geometrical, spectroscopic and electronic parameters of the molecules. Analysis of the results relating to the geometrical parameters was carried out by calculating interatomic distances, relative errors between calculated values and those obtained experimentally by X-ray diffraction found in the literature. The C NMR spectra were calculated by GIAO (Gauge Including Atomic Orbitals) methods, and the results were subjected to statistical analysis by calculating Mean Absolute Deviation (MAD), Root Mean. Square (RMS) and the correlation coefficient (R), in comparison with experimental spectra. The analysis of the results of calculations of various electronic parameters (hardness (η), softness (S), electronegativity (χ), electrophile index (ω), energy gap (HOMO-LUMO)) reveals that, overall, the methods M05-2X/6-311G (d, p) and B3LYP/6-311G (d, p) found that (R) (−) carvone salicylhydrazone (N2) is the most antioxidant molecule of the four molecules and also classify them according to their stability. This confirms the results obtained on the antitrypanosomal activity, the toxicity, the cytotoxicity and the selectivity of the synthesized compounds.


Introduction
Nowadays, hydrazones are an important class of biologically active compounds [1].They have a large number of interesting pharmaceutical derivatives and are also important because of their use as reaction intermediates in organic synthesis [2].In addition, these compounds have [3] [4] [5] antitripanosomal [6] [7], antiplasmodic [8] [9] antibacterial properties and are potential inhibitors for several enzymes [10] and DNA synthesis for cell growth [11].Because of these different properties, they have acquired important places in medecinal chemistry.Some derivatives of hydrazones are marketed.For example, nifurtimox is used for the treatment of Chagas' disease [12] and nifuroxazide (D) as an intestinal antiseptic [13].Hydrazones can act as polydentate ligands depending on the nature of the substitution attached to the hydrazone unit.It should also be noted that the complexing properties of hydrazones enhance the potency of drug candidates for these molecules.Indeed, ligands (hydrazones) act synergistically with transition metals to enhance their biological activities [14].Hydrazones are also used as analytical reagents, for a coating of ink polymer, pigment, and fluorescent materials [15].
Numerous biological activities of hydrazones are well known.Among them are antibacterial [16], anticonvulsant [17], antifungal [18] and antipyretic activities [19].Thanks to their very high bioactivity and the biological importance of the hydrazone group and these derivatives, it therefore appears necessary to design and synthetize new derivatives with the hydrazone pharmacophore and to evaluate their pharmacological activity.
The main objective of this work is to study theoretically the biological activities of hydrazones.It will specifically study the antioxidant properties of these molecules and compare the theoretical results with those published in the literature.The studied molecules constituting systems of more than four atoms, the implementation of the DFT with functional ones such as B3LYP and MO5-2X will make it possible to calculate the spectroscopic, electronic and thermodynamic quantities of our molecules with a good precision.

Material and Methods
In the case of this work, the studied molecules being of large size, we chose to use the base of Pople [20], the 6-311G (d, p).The structures of these molecules are as follows (Figure 1 and Figure 2).All theoretical calculations were

Structural Study of Molecules
For molecule with several degrees of freedom, the potential energy surface is a hyper-surface with several minima and maxima.Also the relative error associated with the calculation of each parameter was evaluated.The lower this relative error, the closer the calculated theoretical value is to the experimental data.
The experimental data considered to evaluate the relative errors related to the calculation of the geometrical parameters of the molecules are those of hydrazide (see Figure 3).

Spectroscopic Study of Molecules
The 1 H NMR and 13 C NMR spectra of molecules were calculated with respect to DMSO (dimethylsulfoxide) taken as a reference molecule by the [23] approach.
In order to appreciate the functional and the most suitable basis for carrying out the study of the biological properties of molecules, the calculated values of various parameters studied were compared with the corresponding experimental data.For this purpose, error discrepancies were calculated for some of the base 6-311G (d, p).Calculations were made using the GIAO method.
1) Mean Absolute Deviation (MAD) These three statistical quantities must build us on suitability of the combination Method/Base judicious for the study carried out.More lowly the values of MAD and RMS are, closer the theoretical results are to the experimental data, and the more convenient are the functional and the base.And, a value of the correlation coefficient (R 2 ) close to 1, indicates a good quality of the theoretical results.

Study of Electronic Properties
For each of the molecules denoted ArOH, the calculated electronic parameters were: • The energy of the highest occupied molecular orbital (Ehomo).
• The energy of the lowest molecular orbital vacant (Elumo).
• The hardness (η) which expresses the resistance of a molecule to the change of its number of electrons or to the charge transfer.The harder the hardness, the less reactive the molecule is [25]: • Softness (S), defined as the inverse of hardness [26]: • Electronegativity (χ), which measures the tendency of a chemical species to attract electrons [27]: ( ) • The electrophilic index (ω), which represents the stabilizing energy of a molecule saturated by electrons coming from its surroundings [28]: The dipole moment (μ) of a molecule expresses the value of its great polarity.
It constitutes a very important index of reactivity which makes it possible to define the biological properties related to the interaction with the active sites of the molecule.In fact, the polar molecules are defined by a non-zero dipole moment whereas the apolar ones are defined by a zero dipole moment [29].

Results and Discussions
The results from this section constitute a theoretical tool for geometric, spectroscopic and electronic characterization of four hydrazones by quantum chemistry methods.It consisted in calculating the geomeric, spectroscopic, and electronic parameters relating to transformations to which they can lend themselves.Analysis of the results in Table 1 shows that, in general, the calculated values of the interatomic distances are very close to the experimental data for the two functional ones when we consider the (R) -(−) -carvone benzohydrazone.

Structural Study of Each Molecule
The analysis of the results in Table 2 shows that, in general, the calculated values of the interatomic distances are very close to the experimental data for the two functional ones when we consider the (S) -(+) -carvone benzohydrazone.
At the end of the results of The analysis of results of Table 4 shows that, in general, calculated values of the interatomic distances are very close to the experimental data for the two functional ones by considering (S) -(+) -carvone salicylhydrazone.
At this stage of the calculations, we do not find any significant difference between structural results given by the two functional ones.Since the theoretical calculations are carried out in the gaseous phase and taking into account the effects of solvents on the atoms, the comparison of certain theoretical results with those of the experimental ones will be made on the basis of the statistical parameters obtained.

Spectroscopic Study: Case of the 13 C NMR Spectra of the Molecules
In Table 5 and Table 6 are grouped the chemical shift values (δ in ppm) of carbon atoms at the approximation levels M05-2X/6311G (d, p) and B3LYP/ 6311G (d, p) for each of the four molecules and the corresponding experimental values.
Since the theoretical calculations are carried out in the gaseous phase and do not take into account the effects of solvents on the atoms, the comparison of theoretical results of Table 5 and Table 6 with those of the experimental ones will be done on the basis of the statistical parameters obtained (Table 7).
The values of absolute mean deviation (MAD), standard deviation (RMS) and correlation coefficient (R 2 ), relative to the 13 C experimental and theoretical NMR spectra of each of the molecules, were calculated by functional B3LYP and M05-2X using the GIAO method.The results are shown in Table 7.

These results show that all correlation coefficient values are close to unity (1).
This means that approximations taken into account in the calculation methods used are good.However, it can be generally observed that the absolute average deviation values calculated by the functional B3LYP are lower than those calculated by the functional M05-2X.For the calculated standard deviation values, the same trend is observed.The standard deviation values calculated by the functional B3LYP are lower than those calculated by the functional M05-2X.
Finally, the functional M05-2X and the base 6-311G (d, p) seem really suitable for calculating the 13

Study of the Stability of Molecules
It is found that the four molecules do not have the same values of the electronic parameters.
Note that:  hardnes of the four molecules are weak and almost equal, which would mean that it is easy for these molecules to exchange electrons with the environment. Gap (HOMO-LUMO) of the enantiomer (R) -(−) -carvone salicylhydrazone is greater than the Gap (HOMO-LUMO) relative to enantiomer (S) -(+)carvone salicylhydrazone.With B3LYP/6-311G (d), p) method; therefore (R) -(−) -carvone salicylhydrazone is more stable than (S) -(+) -carvone salicylhydrazone.As for the enantiomers of the benzohydrazone, they have the same values of the Gap, so same stability with this method.Similarly, we find that (R) -(−) -carvone benzohydrazone is more stable than (S) -(+)carvone salicylhydrazone and (R) -(−) -carvone salicylhydrazone is more stable than (S) -(+) -carvone benzohydrazone. However, (S) -(+) -carvone salicylhydrazone is less stable than the other three compounds. On the other hand, with the method M05-2X/6-311G (d, p), the enantiomers of the carvone salicylhydrazone have the same stability.It is the same for the enantiomers of carvone benzohydrazone.In addition, the enantiomers of carvone salicylhydrazone are more stable than those of carvone benzohydrazone.

Study of Antioxidant Properties
On the basis of these series of results, the following observations can be made:

Conclusions
Theoretical study of the antioxidant properties of the four hydrazones (R) -(−)carvone benzohydrazone, (S) -(+) -carvonebenzohydrazone, (R) -(−) -carvone salicylhydrazone and ((S) -(+) -carvone salicylhydrazone) was carried out, by the functional groups B3LYP and M05-2X of the DFT, in the bases 6-311G and 6-311G (d, p).For this, different parameters have been calculated.It's about: -Geometric parameters of the molecules.The comparison of the calculated values with experimental X-ray diffraction data from the literature did not tangibly retain one of the functionalities as the most suitable for the study.
-Spectroscopic parameters relating to the 13 C NMR spectra of the three molecules.The statistical analysis of chemical shift values calculated by the GIAO method revealed that the M05-2X functional appears to be the most appropriate for calculating the 13 C NMR spectrum of each molecule.-Electronic parameters such as hardness (η), softness (S), electronegativity (χ), electrophilic index (ω), energy gap (HOMO-LUMO) of the molecules.The theoretical results obtained have shown that (R) -(−) -carvone salicylhydrazone (N 2 ) is the most antioxidant molecule of the four and also classified according to their stability.The experimental results are confirmed by the theoretical results.The method M05-2X/6-311G (d, p) appears best indicated in the calculation of electronic parameters.
In perspective, we plan to: -To enhance the biological activity of the compounds by formation of the metal complexes.-To carry out quantum-chemical studies on the complexes formed.

Tables 1 -
4 show the experimental and calculated values of some geometric parameters (lengths) of the (R) -(−) -carvone benzohydrazone molecule, the (S) -(+) -carvone benzohydrazone, (R) -(−) -carvone salicyldrazone and (S) -(+)carvone salicyldrazone, on the one hand, and related relative errors, on the other hand.Analysis of these tables will make a comparative study of the experimental and calculated values.

Table 3
, in general, the calculated values of the interatomic distances are very close to the experimental data for the two Table1.Experimental and calculated values of some interatomic distances of the (R) -(−) -carvone benzohydrazone and the corresponding relative errors.

Table 2 .
Experimental and calculated values of some interatomic distances of (S) -(+)carvone benzohydrazone and the corresponding relative errors.

Table 3 .
Experimental and calculated values of some interatomic distances of (R) -(−)carvone salicylhydrazone and the corresponding relative errors.

Table 4 .
Experimental and calculated values of some interatomic distances of (S) -(+)carvone salicylhydrazone and the corresponding relative errors.

Table 7 .
Values of the statistical quantities calculated for each of the four molecules by the method GIAO/B3LYP and GIAO/M05-2X.