Theoretical Investigations of Hydrogen Bonding Interactions of (E)-1-(1H-Benzo[d]imidazol-2-yl)-3- Phenylprop-2-en-1-one Momoners and Dimers: NBO, QTAIM and NCI Study

Hydrogen bonding is an essential interaction in nature and plays a crucial role in many formations of materials and biological processes, requiring a deeper understanding of its formation. Benzimidazole is an important structural unit found in a large number of natural and pharmacologically active molecules. In the present work, the electronic structures and properties and relatives stabilities of a series of (E)-1-(1H-benzo[d]imidazol-2-yl)-3-phenylprop-2-en-1-one monomers and dimers have been studied by density functional theory using B3LYP 6-31+G (d, p) calculation level. the strengths of the noncovalent interactions have been analyzed in terms of the QTAIM analysis, NCI analysis and natural bond orbital approaches. It was found that the dimers are formed by double N-H⋯O hydrogen bond. QTAIM analysis proved the presence of intramolecular hydrogen bond in monomers and coexistence of intramolecular and intermolecular hydrogen bond in dimers. Frequency analysis show that intermolecular N-H⋯O interactions are proper hydrogen bond while intramolecular C-H⋯N, CH⋯O, C-H⋯H-C interactions are improper hydrogen bond. NBO and NCI analyses confirm the existence of hydrogen bonds in the studied monomers and dimers. The presence of weakly electron acceptor group on benzene ring favor the total interaction energy of dimerization.


Introduction
Benzimidazole (BZim) is a heterocyclic aromatic organic compound. It is an important drug and a preferred structure in medicinal chemistry [1][2][3]. The benzimidazole ring is one of the bioactive heterocyclic compounds that have a range of biological activities such as antivirals (anti-HIV), anticancer drugs, antibacterials, antifungals and many others [4][5][6][7][8][9]. Benzimidazole derivatives are associated with various types of pharmacokinetics and pharmacodynamics properties. The most important benzimidazole compound in nature is Nribosyldimethylbenzimidazole, which serves 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].
The hydrogen bond is one of the 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 slight difference in molecular structure may play a role in the strength of hydrogen bonds [24,25]. In most cases, the formation of − ⋯ bonds leads to a weakening of the X-H bond, accompanied by an elongation of the bond and a concomitant decrease of the vibrational stretching frequency of the X-H bond relative to the noninteractive bond, these bonds are called proper or Red shifted hydrogen bond. However, there are also many examples in which the stretching frequency of the X-H bond increases with the contraction of the bond length during the formation of the hydrogen bond, these are improper or Blue shifted hydrogen bond [26].
The electronic foundations of the improper hydrogen bond were analyzed by Alabugin et al [27]. The structural reorganization of the X-H bond observed for proper and improper hydrogen bonds results from the balance between hyperconjugation ( → * ) which weakens the X-H bond and rehybridization which strengthens X-H bond [27]. Improper hydrogen bonds are observed when the hyperconjugative interaction is relatively low. When the hyperconjugative interaction is low and the hybrid orbital of the X atom of the X-H bond is able to undergo hybridization, rehybridization prevails, resulting in a shortening of the X-H bond and a blue shift of the X-H vibrational stretching frequency. The presence of electron-rich centers (N, O) and hydrogen atoms linked by a covalent bond to nitrogen and carbon atoms offers the possibility of different types of noncovalent bonds such as − ⋯ , − ⋯ , − ⋯ ( Figure 1). In this study, we applied quantum chemistry methods to determine the interaction energies and understand the nature of the different hydrogen bonds of BZims monomers and dimers. The topological properties, hyperconjugative interactions between donor and proton acceptor of different − ⋯ hydrogen bonds formed have been determined. The QTAIM analysis was used to assess the strength and nature of intramolecular and intermolecular hydrogen bonds. We also performed the NBO (natural bond orbital) and NCI (non-covalent interaction) analyses that suggest the existence of hydrogen bonds in the studied systems. Our calculations will give a theoretical overview on the possibility of dimerization of BZims.

Computational Methods and Materials
The monomers M1-M5 and dimers D1-D5 ( Figure 1) were optimized using B3LYP [28,29] calculation level with a 6-31+G (d, p) basis set. The optimization was performed with Gaussian 09 [30] software on Intel i7 2600 processors. In a further step, the topological analysis of the electron density was performed from the ''formatted checkpoint file'' obtained by the DFT calculation with AIMALL software [31]. The NBO orbital analysis method [32] (NBO: Natural orbital bond) incorporated in the Gaussian 09 software was used for NBO analyses. NCI analysis was performed with Multiwfn software [33] and NCI analysis surfaces were represented with Chemcraft software [34].

Interaction Energy
The interaction energies of the complexes were determined by the difference between the total energy of the complex and the energies of the isolated monomers, then corrected by taking account the basic set superposition error (BSSE) using the Boys-Bernardi counterpoise procedure [35] and the ZPE:

NBO Analysis
NBO analysis is based on an approach of transformation of the multielectronic wave functions of the molecules in a localized form that corresponds to the elements with single center (single lone pair LP) and two centered orbitals (natural bonding σ π and antiboning σ * π * respectively). It provides an in-depth understanding of intra-and intermolecular orbital interactions in molecules between the NBOs of filled donors and the NBOs of empty acceptors [36]. For each donor NBO (i) and acceptor NBO (j), the stabilization energy associated with delocalization i → j can be estimated as follows: 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 the different acceptor and donor NBOs as well as the resulting stabilizing energy, clear information is obtained on the origin of the stabilization of a molecule. If the stabilization energy E (2) associated with an interaction is high, the extent of stabilization will be greater.

QTAIM Analysis
Bader's Quantum Theory of Atoms in Molecules (QTAIM) is a useful tool for characterizing topological properties of chemical bonds [37]. The presence of chemical bonds between atoms and interatomic interactions is revealed by the presence of bond critical points (BCPs). The QTAIM method provides information on the electron density of a system that governs properties at BCPs. The QTAIM theory gives information on variations of electron density due to the formation of bonds or complexes [37]. Several parameters exist within the framework of the QTAIM theory, we have among others the electron density -. , its Laplacian / & -. , the potential local energy density 0 . , the local kinetic energy density 1 . and the total kinetic energy density . at bond critical points (BCPs). In general, the parameter values of the QTAIM analysis at BCPs can describe the covalent or electrostatic nature of non-covalent interactions. According to Rozas et al [38] the interactions at the different BCPs can be classified as follows: for strong hydrogen bonds / & -234 ≺ 0, 234 ≺ 0; for medium hydrogen bonds / & -234 ≻ 0, 234 ≺ 0 ;; for weak hydrogen bonds / & -234 ≻ 0, 234 ≻ 0. Also, the ratio − 8 9 also allows a better understanding of the nature of the interaction at the different BCPs [39][40][41]. If − ≺ 0,5 we have a closed-shell interaction. Espinosa [42] proposed a relationship between the energy of the hydrogen bond 2 and the potential energy density (V BCP ) at BCPs: 2 = < & |0 234 |.
In addition, the ellipticity ε to the different BCPs is defined as , = > ? > @ − 1 : A < and A & are eigenvalues of the Hessian of the electron density at BCP. This quantity estimates the extent to which the electron density is deformed in one direction relative to another. Ellipticity provides a measure of π or σ character 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 [37]. Ellipticity reflects the stability of the bonds [39.43].

NCI Analysis
NCI (Non covalent interaction) analysis based on the correlation between the Reduced Gradient Density (RDG) and electron density ρ(r) was recently developed by Yang et al [44,45]. The reduced gradient density is a fundamental dimensionless quantity of DFT, which is used to describe the deviation from a homogeneous distribution of electron density [44,46]. To some degree, the NCI analysis method can be considered as an extension of the AIM analysis [45]. The non-covalent interaction analysis method provides graphical visualization of molecule regions where noncovalent interactions occur and has demonstrated its ability to distinguish hydrogen bonds, van der Waals interactions and repulsive interactions [47]. Recently, the NCI-RDG analysis detected a low interaction compared to the AIM analysis [48]. To determine the presence of low interactions, BC1 = DE *F A & × -. H graphs were generated, where *F A & × -. is the product of the electronic density ρ(r) by the sign of the second eigenvalue of the hessian. The sign value *F A & × -. is useful for predicting the nature of non-covalent interaction. For an attractive interaction *F A & × -. < 0 (hydrogen bond) and for repulsive interactions *F A & × -. > 0 (steric hindrance). For Van Der Walls interactions *F A & × -. = 0.

Study of Monomers
The electronic properties obtained from QTAIM analysis, the geometrical parameters as well as the hyperconjugative interactions between the orbitals involved in the intramolecular hydrogen bonds of the M1-M5 monomers are presented in Tables 1 and 2. The interactions − ⋯ , − ⋯ − and − ⋯ K were revealed by the QTAIM analysis ( Figure 2). From the data in Table 1, it can be seen that the distances L ⋯ and L ⋯ are between 2.20881-2.27482 Å and 3.03051-3.05551Å respectively. Also, the linearity angles ∠ are between 127.080-130.636°. These geometrical parameters indicate the presence of weak intramolecular hydrogen bond [18,49,50] [51][52][53][54]. In addition, for all − ⋯ bond, the ratio − 8 9 ≻ 1 implies that the − ⋯ hydrogen bonds are non-covalent character [40,41]. The interaction energies obtained for the − ⋯ bonds are in the order of 3.3414375-3.8873625 kcal/mol, these values confirm that these hydrogen bonds are weak [42]. Nevertheless, these interactions are stable because we have a low ellipticity value at the different BCPs.
The − ⋯ K hydrogen bond is observed in the M4 molecule. At the Bcp of − ⋯ K bond we have an electron density -.    Table 2. NBO analysis revealed the presence of − ⋯ and − ⋯ K interactions. Hyperconjugative interactions → * with stabilization energy ranging from 2.57-4.91 kcal/mol and corresponding transferred charges ranging from 5-9.096 me were obtained confirming the presence of weak intramolecular hydrogen bonds − ⋯ and − ⋯ K [27].

Stability, Geometrical Parameters and NBO Analysis of Complexes
D2 dimer with an interaction energy of -13.0604 kcal/mol is the most stable of the series. It is characterized by the presence of a hydrogen bond pair − ⋯ (figure 3). The intermolecular distances L ⋯ and L ⋯ are in 2.87592 and 1.88814 Å respectively. The ∠ angle of the − ⋯ bond is separated by 18.849° from linearity. The variation in the length of the − bond "L − >0 implies an elongation its length during complexation. The vibrational stretching frequency s f of the monomer is 3646.9195 tu < while that of the dimer is 3435.3275 tu < .
As a result, the variations in the vibrational stretch frequencies are negative. Based on the findings, we can say that the elongation of the N-H bonds in the dimer is done in concert with a decrease in the elongation vibration frequencies of "s f =-211.5919 tu < to the low frequencies (red shift). Thus in the D2 dimer the − ⋯ bonds are proper hydrogen bonds [26,55]. In Table 5 we have presented the non-covalent interactions observed in the dimers as well as the stabilization energy, the charge transferred and the variation of charges of the atoms X, H and Y involved in the interactions − ⋯ . The NBO analysis detected the presence of the − ⋯ hydrogen bond characterized by the transfer of the lone pair of oxygen atom to the antibonding orbital * of the − bond. on the other hand with stabilization energies & of 10.12 and 6.12 kcal/mol and charges transferred CT of 13.75 and 12.552 me respectively prove the presence of − ⋯ hydrogen bonds [27].
The second stable complex in the series is the D5 dimer with an interaction energy =-11.94 kcal/mol. This value is slightly lower than that of D2 dimer ( =-13.0604 kcal/mol). The  (Table 4). These observations allow us to conclude that we have two types of non-covalent interactions in the D5 dimer; The − ⋯ interaction characterized by an elongation of the − bond ("L − > 0) and a large red displacement of the vibrational stretching frequency is a proper hydrogen bond. The − ⋯ , − ⋯ and − ⋯ − interactions characterized by a blue shift of the vibrational stretching frequencies are improper hydrogen bonds [26,55] The NBO analysis of D5 dimer and the NBO descriptors of hydrogen bond are recorded in Table 4 Table 4. Geometrical parameters of − ⋯ , − ⋯ − interactions (distances en Å, angle ∠ (deg), change in bond length "L (mÅ) and stretching frequencies s (cm -1 ) and its shifts "s (cm -1 ) for − and − bond.    [26,55].
The elongation of the − bond in the − ⋯ interaction is generally attributed to the charge transferred of the interaction " → * between the lone pair of the proton acceptor and the anti-bonding orbital * of the donor [24]. The consequence of these charges transferred are measured by the second-order stabilization energy & obtained by the NBO analysis presented in Table 5. We observe that the largest stabilization energies & and charge transferred are obtained for the interaction << − <& ⋯ wj ( vwj < → f<< <& * , & = 11.31 kcal/mol, y =15.52 e) followed by ww − wQ ⋯ <x interaction ( v<x < → fww wQ *  [26,55].
The NBO analysis was performed and the stabilization energy due to hyperconjugative interactions " → * of the − ⋯ interactions are recorded in Table 5 [27]. These observed interactions due to the overlap between the free doublet of the atom " and the antibonding orbital * have as total stabilization energies " & equal to 44.24 kcal/mol for the ww − wQ ⋯ <x , << − <& ⋯ wj and <g − &O ⋯ <P interactions, therefore there is a strong charge transfer in the D3 dimer which contributes to its stability.
The least stable complex is D1 dimer. It has an interaction energy =-10.0422 kcal/mol significantly lower than that of D2-D5 dimers. It is stabilized by a − ⋯ hydrogen bond  Table 5. Apart from QO − Q& ⋯ K xP D4 and <g − &O ⋯ <P D Q hydrogen bonds, the atomic charges of hydrogen in the − ⋯ interactions of the D1-D5 dimers increase ("( ≺ 0) while that of the N, O and C atoms decrease "( v ≻ 0, "( 3 ≻ 0, "( f ≻ 0 with complexation. Nevertheless, in the intramolecular bonds of the D1 and D4 dimers, the increase in the positive charge of the hydrogen atom H is combined with an increase of the charge of the nitrogen atom. In the interactions − ⋯ of the D1-D5 dimers, the increase of positive charge of the hydrogen atom H and that of the negative charge of X atom observed is a signature of the hydrogen bond [27,56]. The lone pairs of the Y atoms ≡ , , K involved in hyperconjugative interactions " → * are hybridized š u ∈ 0.74 − 99.99 with electron densities ranging from 1.90394 to 1.99144 e. These electron densities less than 2 show that these lone pairs are delocalized, particularly in the antibonding orbital * , which have an electron density between 0.01378 e and 0.04825 e. the electron densities of the antibonding orbitals of the N-H, C-H bonds and the S character of the nitrogen and carbon atoms (( − , ( − ) ( Table 7) increase with complexity. this increase in the S character of nitrogen and carbon atoms indicates a rehybridization of the orbitals of the latter during the formation of the hydrogen bonds − ⋯ , − ⋯ and − ⋯ [27]. Table 6. Lone pairs( " ) and antibonding orbitals ( * ) hybridization states, their respective electronic densities as well as the variation of the electronic density of the antibonding orbitals * upon complexation.

Hyperconjugation and Rehybridization
In − ⋯ interactions, we have a rehybridization of the orbitals of nitrogen atoms with complexation. The orbitals of the nitrogen atoms are hybridized š &.&O in monomers while in dimers they are hybridized š (n∈ 2.01-2.03) ( Table 7). The P character of the orbitals of the nitrogen atoms decreases (the S character increases) with complexation. This observation is also verified by the parameter "%¥ of the nitrogen atoms of the − ⋯ interaction which is between 1.73-2.46. This presence of rehybridization during complexation allows to shorten the − bond [27]. The presence of hyperconjugative interactions v → f * with a stabilization energy between 5.17-11.31 kcal/mol for − ⋯ interactions increases the electron density in the bonding orbitals f * which are all polarized with respect to the hydrogen atom (Table 6), this polarization of the antibonding orbitals f * with respect to the H atom ensures a better overlap v → f * [56]. The observed variation in electron density " * has the effect of weakening the N-H bonds by lengthening them. The elongation of the N-H bond "L − > 0 is clearly demonstrated in the geometry of the complexes where it is between 10.19-11.8 mÅ. Consequently, in the − ⋯ interactions, the presence of the hyperconjugative interaction v → f * with high stabilization energy & masks the hybridization effect, which leads to the elongation of N-H bonds and a red shift in their vibrational stretching frequency [24,27].
Except for the D2 dimer, − ⋯ interactions are observed in the different complexes studied. carbon atoms (C) are hybridized š (m∈ 2.26-2.28) in monomers and š &.&P in dimers. Also the variation in the percentage of the carbon atom "%¥ is between 0.29-0.51. The S character of the carbon atoms involved in − ⋯ interactions increases, so there is a presence of rehybridization with complexation. Hyperconjugative interactions v → f * are also observed in the D1 and D5 complexes with a low stabilization energy value of 0.06 and 0.05 kcal/mol respectively. the interactions v → f * were not observed in D3 and D5 dimers. For − ⋯ interactions, the presence of hyperconjugative interaction with a very low value of & and its absence in certain complexes (D3 and D5) do not allow to mask the effects of rehybridization observed with complexation. As a result, the − bonds are shortened with a blue shift of their vibrational stretching frequency [24,55]. The − ⋯ interactions are observed in D1, D3, D4 and D5 dimers. The hybridization states š of the carbon atoms involved in the − ⋯ interactions reveal the presence of rehybridization with the complexation. We also note the presence of hyperconjugative interactions that allows an increase of the electron density in the antibonding orbital. This electron density " * = 0.000205 e has the effect of lengthening the CH bond of "L − =0.00026 Å in the interaction <g − &O ⋯ <P combined with a red shift "s 3 =-2.7588 cm < of the vibrational stretching frequency of the − bond. However, in the D1, D4 and D5 dimers, the rehybridization which has the effect of lengthening the bonds during the complexation outweighs the hyperconjugative interactions. Therefore, we have an elongation of the C-H bond with a blue shift of the vibrational stretching frequencies [24,55]. Concerning the − ⋯ − interactions, the hybridization states of the carbon atoms vary little with the complexation. In addition, NBO analysis did not detect the presence of interaction between orbitals in different bonds involved in − ⋯ − interactions. Consequently, a blue shift of the vibrational stretching frequencies is observed.

AIM Analysis
In the D1-D5 dimers, the − ⋯ interactions have an electron density -. between 0.024561-0.026517 N O P and a positive value of the Laplacian / & -. (varying between 0.082075-0.09015 N O Q ) and the total kinetic energy density . (varying between 0.000672-0.001158 ua). The values of -. , / & -. and . indicate a decrease of electronic density in the interatomic bond path characteristic of closedshell interactions such as hydrogen bonds [52,54]. Also for all − ⋯ interactions, the ratio − 8 9 ≻ 1 highlights the electrostatic nature of these hydrogen bonds [39][40][41]. Ellipticity is a measure of the stability of the chemical bond. A chemical bond with a large ellipticity is potentially unstable. The − ⋯ interactions observed in dimers are stable because they have a low ellipticity , . in the range of 0.02064-0.031263. The Espinoza method was used to calculate the − ⋯ interaction energies and the results obtained are shown in Table 8. The energies of the − ⋯ interactions vary between 5.81074-6.29393 kcal/mol. The − ⋯ interactions are weak because the energies obtained are less than 15 kcal/mol [50]. . show that − ⋯ interactions are weak hydrogen bonds [52,54]. Moreover, the ratio − 8 9 >1 for the − ⋯ interactions highlights its electrostatic nature [40,41]. The high value of the ellipticity , . observed (1.512957-11.458266) and the low value of the energy of the hydrogen bond 2 (0.35141-0.36396 kcal/mol) highlight their instabilities and weaknesses with respect to the − ⋯ and − ⋯ hydrogen bonds.
At the Bcps of the − ⋯ − interactions, the electronic density -. is in the range of 0.008995-0.009047 N O P , the corresponding Laplacian is between 0.038854-0.039858 N O Q with a positive energy density . (0.002478-0.002492 au). Also the interaction energy is about 1.49 kcal/mol, thus − ⋯ − interactions are weak hydrogen bonds [50,54]. From more − 8 9 >1 at the Bcps of the different − ⋯ − interaction, thus the − ⋯ − interactions are purely electrostatic [40]. The ellipticity of the − ⋯ − interactions is between 1.145216-2.031056, so we can say that the − ⋯ − interactions are less stable than the − ⋯ and − ⋯ interactions but more stable than the − ⋯ interaction.

NCI-RDG Analysis
In

Conclusion
We carried out a detailed theoretical analysis of the monomers and dimers of BZims. Geometry optimization and harmonic frequency analysis were performed. The results of the frequency calculations show that all the monomers and dimers of the BZims are at least global structures. Our calculations clearly show that the BZims monomers and dimers have intramolecular and intermolecular hydrogen bonds. From the point of view of the interaction energy, the D2 dimer is more stable than the other forms. The stability sequence of dimers BZims is C & ≻ C Q ≻ C w ≻ C P ≻ C < . The presence of weakly electron acceptor group (-Cl) on benzene ring favor the total interaction energy of dimerization. Evidence for the presence of intramolecular and intermolecular hydrogen bonding has been demonstrated by topological, geometrical, NCI and NBO analyzes. Frequency analysis results for BZims monomers and dimers indicate that the intramolecular hydrogen bond shows an increase in stretching frequencies and a blue shift in the IR spectrum, while the intermolecular hydrogen bond shows a decrease in stretching frequencies. and a red shift of the IR spectrum.