Electrostatic potential is the interaction energy between a molecule and a positive unit charge (proton) placed at a point of its environment. It is by the electrostatic potential that a molecule is first “seen” or “estimated” by another chemical species that approaches it [24] . It is a real physical property that can be determined theoretically as well as experimentally by X-ray diffraction methods [24] [25] . It is defined by the expression 1 below in atomic unit [24] [25] [26] .

Z_A is the charge of the nucleus A, located at A and the electron density function of the molecule. Molecular electrostatic potential is an important tool for predicting the reactive properties of a molecule and it has been widely used, especially in the case of electrostatic reactions [24] such as hydrogen bonding interactions. Thus an electrophilic attack will tend to occur at the region where the potential is the most negative [27] , the local minima [24] .

Each of the DP derivatives has four heteroatoms. Four hydrogen bonding complexes were constructed, with the hydrogen fluoride molecule (HF) as the hydrogen bond donor (HBD). The characteristic geometric parameters of an hydrogen bond [28] are presented in Figure 2.

α is the HB linearity angle, θ is the directionality angle, d length of Hydrogen bond. Thus, before starting a computation on a complex, the initial values below have been assigned (Figure 3): α = 180˚, θ₁ = θ₂ = 120˚ for sp² nitrogen and oxygen, for the sp³nitrogen and d = 2 Å for all the complexes.

Energetic parameters of the hydrogen bond were calculated considering the

formation of complexes on each heteroatom according Reaction (2):

Hydrogen bonding energy is calculated by subtracting the energies of the isolated fragments from that of the complex [23] [29] [30] [31] according to Equation (3):

stands for BSSE. Calculations are carried out at a temperature of 298.15 K under normal atmospheric pressure (P = 1 atm). Moreover, the total energy E of an isolated molecule is obtained by summing the energies of the electronic movements, translation, rotation and vibration [32] according to Equation (5):

In the perfect gas approximation, the translation and rotation contributions are given by the Relations (6), (7) and (8). For nonlinear molecule A and A ・・・ D:

For the diatomic molecule D (HF):

The contribution of the vibration motion to the total energy is given by Equation (9):

The Zero Point Vibrational Energy (ZPVE) contribution is the lowest vibrational level energy due to the 3N-6 normal vibration modes (3N-5 for linear molecules) of frequencies ν_i of the N kernels at 0 K, and defined by relation 10:

The contribution is the additional energy due to the population of vibration levels during the temperature rise from 0 to T = 298.15 K, and defined by Equation (11):

Finally, the change in the internal energy E upon Reaction (2) to 298 K is given by expression 12:

Frequencies calculations provide these different electronic, vibrational and thermal contributions, as well as entropy. The enthalpy variation at 298.15 K is given by the expression 13:

Free Enthalpy variation, at 298.15 K, is given by Equation (14):

Variation in entropy, , is calculated according to expression 15:

Molecular electrostatic potential maps of studied DP were designed after optimization at B3PW91/6-311+G(d,p). Potential surfaces (Figure 4) are associated

with a color code evolving continuously from red indicating the most negative potentials to blue indicating the most positive potentials [33] . These maps indicate that the heteroatom N6 is favorable to an electrophilic attack given its approaching zone which is the redder. As for the other heteroatoms, O and N8 are disadvantaged for electrophilic attacks because of their approach zones which are in the green whereas N2, whose approach zone is orange, is less favorable than N6. The results are similar for the three molecules. It is thus apparent that N2 and N6 nitrogen atoms of pyrimidine nucleus are the most nucleophilic, thus favorable to hydrogen bonding in these three derivatives.

Geometry optimization of the hydrogen bond complexes on the oxygen atom did not succeed. Indeed, after optimization, migration of the probe from the oxygen atom to the N6 nitrogen atom of the pyrimidine nucleus is observed, whatever the DP molecule.

This phenomenon may be explained by the participation of one of the lone pairs of oxygen atom in the aromatic character of the furan. The commitment of this doublet in electronic delocalization depletes the oxygen atom. Probe migrations have recently been observed in studies conducted by Ziao et al. [34] [35] , both in the case of two imidazopyridinyl-chalcone derivatives and four benzimidazolyl-chalcone derivatives using water molecule as probe. Thus, only energetic parameters of the complexes on the nitrogen atoms of these three DP molecules have been calculated. Geometric parameters of the complexes formed on the three nitrogen atoms are recorded in Table 1 below.

Results of Table 1 show that for the same level of calculation and hydrogen bonding site, values obtained for each parameter are virtually the same from one molecule to another. Thus for the linearity angles α of the complexes formed on the N2 and N6 atoms with sp² hybridization, the mean values are respectively 165.7˚ and 160.5˚ at the DFT level and 165.3˚ and 156.8˚ at the HF level for the

All values of the enthalpies changes are negative (Table 2), expressing exother- mic reactions whereas some values of the free enthalpies changes are negative translating spontaneous complexations, while others are positive, showing non- spontaneous reactions in the conditions of the study. Thus, the two levels of theory predict spontaneous reactions on N6 for the three derivatives and on N2 for the DP-1 and DP-2 derivatives; for DP-3, the HF method predicts a spon- taneous reaction and DFT provides a non-spontaneous reaction as on nitrogen N8 for the two theories levels. A classification in ascending order of the free enthalpy change of complexation gives the following result for each derivative, and also for each computation level: . It appears from this energetic study that on N6 nitrogen atom, the variation of the free enthalpy of complexation is the smallest, values being −4.649 kcal/mol, −4.500 kcal/mol and −0.951 kcal/mol with DFT method and −1.840 kcal/mol, −1.758 kcal/mol and −1.740 kcal/mol with HF method respectively for DP-1, DP-2 and DP-3. Therefore N6 is the preferred hydrogen bonding site in these pyrimidine derivatives.

If we consider and the fractions of the complexes formed on N2 and N6 respectively, then:

The various values of and are summarized in Table 3.

Values in Table 3 show that, whatever the calculation method is, the complexes formed on N2 nitrogen are in a minority compared to those formed on N6 nitrogen. This result indicates that the N6 nitrogen atom in the pyrimidine is the major hydrogen bonding site with the average percentages of 82.98% at the B3PW91/6-311+G(d,p) level and 93.19% at the HF/6-311+G(d,p) level.