In this study the quantitative analysis of delocalization of electrons acceptor and electrons donor substituent lone pairs on (E)-2-(1H-benzo[d]imidazol-2-yl)-3-phenylacrylonitrile structure and its derivatives and the effects of the substituents on the strength of intramolecular hydrogen bond have been investigated. NBO analysis revealed two types of interactions with the lone pair of substituents 
The stabilization energies 
of 
interactions are generally greater than that of 
interactions. The insertion of -NO2 on the imidazole heterocycle leads to increase of its stabilization energy and induces a greater intramolecular charge transfer in these molecules. The positive values of interaction energies 
of the substituents -CH3, -N (CH3)2, -OH, -OCH3, -Cl and -Br show that they have electron-donating properties with respect to the title molecule. QTAIM analysis was also used to evaluate the strength and nature of intramolecular interactions. For types of intramolecular interactions have been observed 
The highest intramolecular interaction energy has been observed in A16 and A6 molecules at BCPs of 
with an interaction energy of 4.48945 and 4.38873 kcal/mol. Geometrical parameters and QTAIM result showed that these interactions are closed-shell interaction in nature.
Benzimidazole is a heterocyclic aromatic organic compound. It is an important pharmacophore and a favored structure in medicinal chemistry 1, 2, 3. The benzimidazole ring is one of bioactive heterocyclic compounds that have a variety of biological activities such as antivirals (anti-HIV), anticancer drugs, antibacterials, antifungals and many others 4, 5, 6, 7, 8, 9. Benzimidazole derivatives are combined with various types of pharmacokinetic and pharmacodynamic properties. The most important benzimidazole compound in nature is N-ribosyldimethylbenzimidazole, which is used as an axial ligand of cobalt in vitamin B12 10. In addition, some benzimidazoles are used in coordination chemistry 11, 12, 13, 14, optoelectronics 15.
Hydrogen bond is one of fundamental interactions that plays a key role in many fields of chemistry, physics and biology 16, 17, 18, 19. It affects the stability of many important molecular structures such as water 20, 21 and DNA 22. Knowledge of hydrogen bonding strength is essential for physical, chemical and biological applications 23. In addition, a subtle difference in molecular structure may play a role in the strength of hydrogen bonds 24, 25.
The present study reports on the electronic properties and chemical reactivity of the (E)-2-(1H-benzo[d]imidazol-2-yl)-3-phenylacrylonitrile structure as well as its substituted structures. This study aims to study the effect of electron donor and acceptor substituents on the title molecule from NBO analysis and the effect of substituents on the strength of intramolecular hydrogen bonds. QTAIM analysis was used to evaluate the strength and nature of intramolecular hydrogen bonds. We also performed the NBO analyzes that underlie the presence of intramolecular hydrogen bonds in the systems studied.
The A1-A20 molecules (Figure 1) were optimized using the B3LYP calculation level 26, 27 with a 6-31+G(d, p) basis set. The optimization was performed with Gaussian 09 28 software. In addition, the topological analysis of electron density was performed from the file''formatted checkpoint file'' obtained by DFT calculation with the AIMALL software 29. The NBO 30 orbital analysis method (NBO: Natural bond orbital) incorporated in the Gaussian 09 software was used for NBO analysis.
The mutual influences of electronic substituents on the conjugated rings are still relevant due to the variation of reactivity of the resulting chemical system after substitution. NBO analysis provides an efficient method for studying intra- and intermolecular bonds, interactions between bonds, and a practical basis for studying charge transfer or conjugative interactions in molecular systems 31. The NBO analysis is based on an approach to transform the multi-electronic wave functions of molecules into a localized form that corresponds to single-center elements (single pair LP) and two centered orbitals (natural bonding σ π and anti-bonding σ* π* respectively). It provides an in-depth insight into intra- and intermolecular orbital interactions in molecules between the NBOs of filled donors and the NBOs of empty acceptors 32. For each donor NBO (i) and acceptor NBO (j), the stabilization energy associated with delocalization i → j can be estimated as follows:
 | (1) |
Where qi is the electron density in the donor's orbital, F (i, j) is the non-diagonal element of the Fock matrix and εi and εj are the energies of the occupied orbitals i and vacant j. By analyzing the interactions between different NBO acceptors and donors and the resulting stabilization energy, we obtain clear information on the origin of stabilization of a molecule. If the stabilization energy E(2) associated with an interaction is high, the extent of stabilization will be greater.
2.3. QTAIM AnalysisBader's Quantum Theory of Atoms in Molecules (QTAIM) is a useful tool for characterizing topological properties of chemical bonds 33. The presence of chemical bonds between atoms and interatomic interactions is revealed by the presence of bond critical points (BCPs). QTAIM method provides information on electron density of a system that governs properties at BCPs. QTAIM theory provides information on variations in electron density due to the formation of bonds or complexes 33. There are several parameters within the QTAIM theory, among others the electron density 
its laplacian 
the local potential energy density
the local kinetic energy density
and the total kinetic energy density 
at bonds critical points (BCPs). In general, the parameter values of the QTAIM analysis at BCPs can describe the covalent or electrostatic nature of interactions. According to Rozas et al. 34 the interactions with the different BCPs can be classified as follows: for strong hydrogen bonds 
for medium hydrogen bonds 
for weak hydrogen bonds 
Also, the ratio 
provides a better understanding of the nature of interactions at the different BCPs 35. If 
the bond is considered non-covalent. If 
we have a partially covalent character of the bond. If 
we have a closed-shell interaction. Espinosa 36 proposed a relationship between the energy of the hydrogen bond E_HB and the potential energy density at BCPs (VBCP): EHB = ½ (VBCP). In addition, the ellipticity ε at different BCPs is defined as 
and 
are eigenvalues of the Hessian of the electron density at the BCP. This quantity estimates the extent to which the electron density is deformed in one direction relative to another. Ellipticity provides a measure of the π or σ characters of chemical bonds. A high value of ellipticity (ε>0.1) indicates a π character of the bond while a lower value reflects a σ character of the bond 33. It reflects the stability of the bonds 35, 37.
The NBO method was used for the quantitative analysis of the delocalization of the lone pairs of nitrogen, oxygen, chlorine and bromine atoms of the substituents. We have analyzed the second order interactions 
between the donor orbitals (lone pair on the heteroatom X = N, O, Br, Cl) and the acceptors orbitals (π*, σ * of the title molecule Figure 1). In Table 1 we presented two types of interaction as well as the second-order stabilization energy resulting from intermolecular transitions:
a) 
which designates the transition from the lone pairs of atom X to the atomic orbitals π* of the title molecule.
b) 
which refers to the transition from the lone pairs of atom X to the antibonding orbitals σ* of the title molecule.
For type (a) interactions, the NBO analysis revealed the presence of a strong LP(X)→π*(Figure 2) interaction in the studied molecules. These interactions have a stabilization energy of 47. 91; 32. 48; 23. 35; 29. 13; 11. 53; 12. 30; 4.70 kcal/mol in molecules A3, A4, A5, A6, A7, A8 and A9 respectively (see Table 1). An absence of this type of interaction is observed in the A2, A10 and A11 molecules. The interactions observed in A3-A9 molecules allow intramolecular charge transfer that stabilize these systems. These interactions allow an increase of the electron density in the antibonding orbitals which weakens these respective bonds. The electron density (ED) of the lone pair of the heteroatoms X (O, Br, N, Cl) involved in type (a) interactions between 1.51399 e and 1.97817 e and that of the bonds π* between 0.39290 e and 0.445e indicates a strong delocalization of these lone pairs in the studied molecules. Moreover, the electron density observed in the NBOs highlights a deviation from the ideal LEWIS structures. The hybrid atomic orbitals and their percentages are summarized in Table 1. For type (a) interactions the atomic orbitals of lone pairs on X are hybridized 
with 
(0.83-1). Most of these hybrid atomic orbitals are formed from the s, p, d shell. For example, the lone pair involved in 
interaction of A3 molecule is hybridized 
(with 54.59% s ;45 ,34 %p ;0.07% d). It can be noted that this doublet has a marked s character (54.59% s) which differs from the other doublets involved in this type of interaction which have a significant p character (99.9%p). Except for A10, the insertion of -NO2 on the imidazole heterocycle of A1-A10 molecules (see Table 2) leads to the appearance of type (a) interactions in the A12 molecule and to the increase of its stabilization energy in the resulting A12-A19 molecules. The increase of the stabilizing energies of the type (a) interactions 
in the A12-A19 molecules induces a greater intramolecular charge transfer in these molecules.
c) result of the interaction between the two orbitals which denote type (a) interaction
c) result of the interaction between the two orbitals which denote type (b) interaction The most significant intramolecular charge transfer is obtained for A18 molecule with 
interaction and stabilization energy of 352.28 kcal/mol. The lone pair involved in this interaction is hybridized 
and has an electron density of 1.980095 e and a marked S character (% s = 75.59).
For type (b) interactions (Figure 3), the stabilization energies obtained are generally lower than that of type (a) interactions. The value of electron density observed in lone pairs (LP) and antibonding orbitals 
also indicates the presence of delocalization in the studied molecules. All orbitals involved in type (b) interactions are hybrid (see Table 1) and are formed from the subshell s, p, d. the highest stabilization energy 
is obtained for the 
interaction in A12 molecule.
The interaction between the atomic orbitals of the substituents and those of the homocycle and heterocycle rings leads to two major effects 38, 39:
Ÿ Inductive effect I
Ÿ Mesomeric effect M.
The interaction energy between the atomic orbitals of the substituents and that of the title molecule (A1) can be used to evaluate the total electronic effect of substituent. In accordance with the designations, the effects -C and -I indicate the electron accepting characters while the effects +I and +M indicate the electron donating properties of substituents. The various interactions between the atomic orbitals of the substituent and the title molecule obtained from NBO analysis were used to evaluate the total electronic effect of each substituent on the title molecule. The total electronic effect (interaction energy) of each substituent is shown in Table 3. The energies related to the individual components of the + I, -I, + M and -M effects , the total energies 
and 
for the inductive and mesomeric effects, the energy 
is the total electronic effect of the substituent.
If 
the substituent is an electron acceptor and we have a partial transfer of the electron density from the orbitals the title molecule to that of the substituent.
If 
the substituent is an electron donor and the partial transfer of electron density takes place from the orbitals of the substituents to that of the title molecule.
The transfer of electron density of the bonding orbitals σ from the title molecule to the antibonding orbitals σ * of substituent characterizes the electron accepting inductive effect of the substituent and is noted as -I. The Interaction Energy 
is counted negatively. The transfer of electron density of the bonding orbitals σ from the substituent to the antibonding orbitals σ* of the title molecule refers to the inductive donor effect noted +I. The interaction energy 
is counted positively. In molecule A17 the inductive donor effect (+ I) (Figure 4) and the inductive acceptor effect (-I) (Figure 5) correspond to the interactions 
and 
with interaction energies of +2.49kcal/mol and -3.60 kcal/mol respectively. The electron donating mesomeric effect (+M) is characterized by the partial transfer of the electron density of the bonding atomic orbitals π from the substituent to the antibonding atomic orbitals π* of the title molecule. In molecule A17 the (+M) effect corresponds to the transition 
with an interaction energy of +4.01 kcal/mol and the transition 
with an interaction energy of -29.09 kcal/mol (Figure 6) indicates an electron accepting mesomeric effect (-M). To determine the overall effect of the substituents on the title molecule, we took into account all the interactions between the atomic orbitals of the title structure and those of the substituents. This means that the determination of the electron donating inductive effect of -NO2 substituent in A10 is determined from contributions of 5 components.
The groups -CH3, -N(CH3)2, -OH, -OCH3, -Cl and -Br have +I, -I and +M effects with respect to the title structure when they are present on the benzene homocycle, only the group -CH3 has an additional -M effect.
b) natural antibonding orbital 
c) result of the interaction between the two orbitals, modeling the +I effect in A17
b) natural antibonding orbital 
c) result of the interaction between the two orbitals, modeling the -I effect in A17
; b) natural antibonding orbital 
; c) result of the interaction between the two orbitals, modeling the +M effect in A17The positive values of 
of the substituents in the A1-A10 molecules show that they have electron-donating properties with respect to the title molecule. The greatest interaction energy 
is obtained for the electron acceptor substituent NO2 in molecule A10. The insertion of NO2 on the imidazole heterocycle leads to an increase of 
of the substituents -CH3, -N (CH3)2,-OH, -OCH3, -Cl and -Br in molecules A14-A19. This increase shows an improvement in the electron-donor properties of these substituents and a greater charge transfer from the orbitals of the substituents to that of the title molecule. The negative values of 
of the nitro group in molecules A11, A14, A15, A16, A17, A19 and A20 highlight the electro-accepting nature of NO2 in relation to the title molecule. Nevertheless, NO2 has an electro-donor character in the molecules A10, A12, A13, A18 with interaction energies of 58.61, 1590.389 and 884.08 kcal/mol respectively.
The properties of the electron density obtained from the QTAIM analysis are presented in Table 4. This analysis allowed us to detect the presence of non-covalent intramolecular interaction in the systems studied (Figure 7). These interactions are classified into four types:
a. 
b. 
c. 
d. 
The geometrical parameters of the intramolecular interactions of the compounds A1-A20 are shown in Table 5, where X, H, Y denote the donor, the acceptor and the hydrogen atom involved in the bond. It is observed that in all cases the distances 
and 
are between 2.0 - 3.0 Å and 3.0-4.0 Å respectively and in addition all angles are between 90-180 which indicates that we are in the presence of weak intramolecular hydrogen bonds 40. For all the interactions observed, the ratio |V(r)|/G(r) <1 allows us to confirm that we have closed-shell interactions (hydrogen bonding). The type (a) interaction is observed only in the A6 and A16 molecules. The electron density ρ(r) at BCPs of 
is larger than that of the other types of interactions and is of value. and has a value of 0.017930 et 0.018281 
(see Table 4). There is an increase in electron density ρ(r) after insertion of the R-group NO2 on the imidazolic heterocycle 
This increase in electron density makes it possible to strengthen the 
bond in the A16 molecule with an interaction energy that passes 
kcal/mol to
In addition, as shown in Table 5, the interactions between the lone pair of the oxygen atoms O29 and O28 with the anti-bonding orbitals and with stabilization energies =1.57 kcal/mol and =1.69 kcal/mol respectively confirm the presence of a hydrogen bond 
Concerning the interactions of type (b), they are observed in molecules A1, A6, A7, A8, A10, A11, A12, A15, A16, A16, A1, A17, A18, A18, A19, A20 .the electronic densities at the BCPs of the 
bonds are arranged in the following decreasing order: 
.
The highest electron density 
is observed in A8. This variation of electron density with respect to A1 
is due to the insertion of chlorine atoms on the benzene homocycle of A1. This density is slightly decreased in A18 after insertion of R-group NO2 on the imidazole ring of A8. Therefore the interaction energies obtained for the 
bonds in A1 (
-2.2649612 kcal/mol are lower than those obtained for A8 and A18 which are substantially equal: 
and 
the NBO analysis presented in Table 5 reveals the presence of 
interaction by the transitions 
and 
observed in the molecules A8 and A18.
The type (c) interactions are observed in A2, A3, A4, A8, A9, A13, A14, A16 molecules. The electronic densities at the BCPs of the 
bonds are arranged in the following descending order: 
The interaction energies at the different BCPs are arranged in the same order:
Except for A8, the presence of transition between the orbitals of the molecules involved in the hydrogen bond obtained from NBO analysis confirms the presence of this 
bond (see Table 5). Note that the second-order stabilizing energies are not arranged in the same order as the hydrogen bond energies 
when we are in presence of transition 
Type (d) interactions are observed in molecules A8 and A18. The electron density at the BCPs of 
bond in A18 is greater than that of A8, resulting in a stronger intramolecular hydrogen binding energy in the A18 molecule than in A8 36. in addition, the presence of interaction 
and 
confirms the presence of these intramolecular hydrogen bonds 42.
The interaction energy of the hydrogen bond and the stabilization energy 
are in the same order in the molecules A8 and A18 
The ellipticity values observed at the different BCPs of the A1-A20 molecules are shown in Table 4.
The ellipticities observed at the various intramolecular hydrogen bonds are between 0.326738 and 3.294540. The greatest values of the ellipticity are observed in the type (c) interactions of the molecules A8, A9, A13, A16 and A18. The non-zero values of the ellipticity confirm that there is delocalization and presence of resonance-assisted intramolecular hydrogen bonding in the systems studied.
In this work, a theoretical study of the intramolecular hydrogen bond, intramolecular interactions with orbital substituents of benzimidazole and its derivatives has been carried out. Some conclusions that can be drawn from this study are as follows:
Ÿ Two types of intramolecular interaction 
highlighting the delocalization of free substituent doublets were observed. The greatest intramolecular interaction was observed in molecules A12 and A18 with stabilization energies of 352.28 kcal/mol and 253.73 respectively. The electronic densities obtained from NBO analysis confirm that we are in the presence of delocalization in the studied molecules.
Ÿ The presence of BCPs obtained by the AIM analysis, the geometrical parameters and the NBO transitions obtained show that we are in the presence of four types of intramolecular hydrogen bonding 
The strongest intramolecular hydrogen bonds are observed in the A6, A16 and A18 molecules.
Ÿ The presence of electron donor and acceptor substituents on the basic structure of benzimidazole makes it possible to increase the strength of the intramolecular hydrogen bonds in the various molecules obtained.
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 and their derivatives){kind=link}
 the lone pair of chlorine atom ; b) natural antibonding orbital c) result of the interaction between the two orbitals which denote type (a) interaction){kind=link}
 the lone pair of chlorine atom; b) natural antibonding orbital c) result of the interaction between the two orbitals which denote type (b) interaction){kind=link}
 for intramolecular transitions in A1-A10 molecules){kind=link}
 for intramolecular transitions in A11-A20 molecules){kind=link}
 From Orbital Interactions According to the Inductive and Mesomeric Effect of substituent){kind=link}
 Natural bonding orbital b) natural antibonding orbital c) result of the interaction between the two orbitals, modeling the +I effect in A17){kind=link}
 Natural bonding orbital b) natural antibonding orbital c) result of the interaction between the two orbitals, modeling the -I effect in A17){kind=link}
 Natural bonding orbital ; b) natural antibonding orbital ; c) result of the interaction between the two orbitals, modeling the +M effect in A17){kind=link}
 (ea0-3)2(r)(ea0-5) G, V, H, L (au) selected at BCPs of intramolecular hydrogen bonds of benzimidazoles and their derivatives){kind=link}
 and observed transitions for intramolecular hydrogen bonds){kind=link}