Accepted Manuscript Quantum chemical vibrational study,molecular property, FTIR, FT-Raman spectra, NBO, HOMO-LUMO energies and thermodynamic properties of 1methyl-2-phenyl benzimidazole M. Karnan, V. Balachandran, M. Murugan, M.K. Murali PII: DOI: Reference:

S1386-1425(14)00560-5 http://dx.doi.org/10.1016/j.saa.2014.03.128 SAA 11970

To appear in:

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy

Received Date: Revised Date: Accepted Date:

13 January 2014 20 March 2014 29 March 2014

Please cite this article as: M. Karnan, V. Balachandran, M. Murugan, M.K. Murali, Quantum chemical vibrational study,molecular property, FTIR, FT-Raman spectra, NBO, HOMO-LUMO energies and thermodynamic properties of 1-methyl-2-phenyl benzimidazole, Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy (2014), doi: http://dx.doi.org/10.1016/j.saa.2014.03.128

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Quantum chemical vibrational study,molecular property, FTIR, FTRaman spectra, NBO, HOMO-LUMO energies and thermodynamic properties of 1-methyl-2-phenyl benzimidazole M. Karnana, V. Balachandranb,*, M. Muruganc M. K. Muralid a

b

Department of Physics, SrimadAndavan Arts and Science College, Tiruchirappalli 620005,India Centre for Research, Department of Physics, A. A.Government Arts College, Musiri 621211, India c Department of Physics, Government Arts College, Tiruchirappalli 620022, India d

Department of Physics, JJ College of Arts and Science, Pudukkottai 622 404, India

Abstract The solid phase FT-IR and FT-Raman spectra of1-methyl-2-phenyl benzimidazole (MPBZ) have been recorded in the condensed state. In this work, experimental and theoretical study on the molecular structure, quantum chemical calculations of energies and vibrational wavenumbers of MPBZ is presented. The vibrational frequencies of the title compound were obtained theoretically by DFT/B3LYP calculations employing the standard 6-311+G(d,p) and 6-311++G(d,p) basis set for optimized geometry and were compared with Fourier transform infrared spectrum (FTIR) in the region of 4000 – 400 cm−1 and with Fourier transform Raman spectrum in the region of 4000–100 cm−1. Complete vibrational assignments, analysis and correlation of the fundamental modes for the title compound were carried out. The vibrational harmonic frequencies were scaled using scale factor, yielding a good agreement between the experimentally recorded and the theoretically calculated values. The study is extended to calculate the HOMO-LUMO energy gap, NBO, mapped molecular electrostatic potential (MEP) surfaces, polarizability, Mulliken charges and thermodynamic properties of the title compound. Keywords: 1-methyl-2-phenyl benzimidazole , Vibrational spectra, HOMO-LUMO, NBO, MEP surface. ___________________________________________________________________________ *

Corresponding author. Tel.: +91 431 2591338; fax: +91 4326 262630. E–mail address: [email protected]. (V. Balachandran)

1

1

Introduction Benzimidazole is a dicyclic compound having imidazole ring fused to benzene.

Benzimidazole structure is a part of the nucleotide portion of vitamin B12 and the nucleus in some drugs such as proton pump inhibitors and anthelmintic agents. Imidazole has two nitrogen atoms. The one is slightly acidic, while the other is basic. Imidazole and its derivatives are widely used as intermediates in synthesis of organic target compounds including pharmaceuticals, agrochemicals, dyes, photographic chemicals, corrosion inhibitors, epoxy curing agents, adhesives and plastic modifiers. Benzimidazole is produced by heating o-phenylenediamine with 90% formic acid. It is of a considerable interest as a ligand towards transition metal ions with a variety of biological molecules including ionheme systems, Vitamin B12 and its derivatives and several metallo-proteins. The complexes of transition metal salts with benzimidazole derivatives have been extensively studied as models of some important biological molecules [1]. Metal complexes of biologically important ligands are sometimes more effective than free ligands [2]. Benzimidazole and its derivatives occur in vitamin B12 and in other biologically active compounds. The molecule of vitamin B12 contains a large planar group involving four reduced pyrrole rings, which esemble a porphyrin. Recently a number of vitamin B12 compounds have been isolated in which the 1-methyl-2-phenyl benzimidazole part of the vitamin molecule has been replaced by adenine. Benzimidazole is bicyclic hetroatomic molecule. Polycyclic are worth to study for many reasons chief among them being their prevalence among biologically active molecules. At the same time, it is difficult to elucidate an accurate vibrational potential field and the resulting vibrational assignments for a polycyclic hetroatomic molecule, because of extensive coupling of the different modes leading to strong coupling of the force constants associated with the various chemical bonds of the molecule. Moreover, benzimidazole is used as a corrosion inhibitor for metals and alloys.

2

Recently density functional theory (DFT) has emerged as a powerful tool for analyzing vibrational spectra of fairly large molecules. The application of DFT to chemical systems has received much attention because of faster convergence in time than traditional quantum mechanical correlation methods [3–6]. The present work reports a detailed spectroscopic study on 1-methyl-2-phenyl benzimidazole (MPBZ) using IR and Raman spectra followed by normal coordinate analysis (NCA). The natural bond orbital (NBO) analysis is carried out to interpret hyperconjugative interaction and intramolecular charge transfer (ICT). The calculated value of HOMO– LUMO energy gap is used to interpret the biological activity of the molecule.

2

Experimental Techniques The sample 1-methyl-2-phenyl benzimidazole was purchased from Lancaster

Chemical Company, U.K with a stated purity of greater than 97%, and it was used as such for the spectral measurements. The room temperature Fourier transform infrared spectra of 1-methyl-2-phenyl benzimidazole was recorded in the region 4000−400 cm−1 at a resolution of ±1 cm−1, using BRUKER IFS-66V Fourier transform spectrometer, equipped with an MCT detector, a KBr beam splitter and global source. The FT-Raman spectrum was recorded on the same instrument with FRA-106 Raman accessories in the region 3500−100 cm−1. Nd:YAG laser operating at 200 mw power with 1064 nm excitation was used as source. 3

Computational Methods For a supportive evidence to the experimental observations, the density

functional theory (DFT) computations were performed with the aid of GAUSSIAN 09W software package [7] with internally stored B3LYP/6-311+G (d,p) and 6311++G (d,p) basis sets. Subsequently the vibrational normal mode wavenumbers in association with the molecule were derived along with their IR intensity and Raman activity.

3

In our calculations, there were some deviations persist between the observed and calculated wavenumbers due to the neglect of anharmonic effect at the beginning of frequency calculation and basis set deficiencies. In the present study, these deviations were overcome by a selective scaling procedure in the natural internal coordinate representation followed by the reference [8, 9]. Transformations of the force field and the subsequent normal coordinate analysis including the least squares refinement of the scaling factors, calculation of PED, IR and Raman intensities were done on a PC with the MOLVIB program (Version V7.0-G77) written by Sundius [10,12]. The PED elements provide a measure of each internal coordinate’s contribution to the normal coordinate. For the plots of simulated IR and Raman spectra, pure Lorentzian band shapes were used with a bandwidth of 10 cm−1 and the modified Raman activities during scaling procedure with MOLVIB were converted to relative Raman intensities using the following relationship derived from the basic theory of Raman scattering [11,12]. I Ra =

f (ν 0 − ν i ) 4 S Ra

ν i 1 − exp − hcν i kT  





where  is the exciting wavenumber (1064 nm = 9398 cm−1) of laser light source used while recording Raman spectra,  the vibrational wavenumber of the ith normal mode. h, c and kb fundamental constants, and f is a suitably chosen common normalization factor for all peak intensities of the Raman spectrum of the title molecule. Finally, the converted Raman intensities and the calculated infrared intensities were modified by assigning the highest intensity peak to 100%. In order to predict the reactive behaviour of a molecule, we have plotted MEP surface and derived electrostatic potential values and point charges at B3LYP/6-311+G (d,p)and 6-311++G (d,p) basis sets. The population of atomic charges on the individual atoms and the distribution of atomic charges in core and valance were also derived using NBO calculations in GAUSSIAN 09W. From the computed NBO results, the stabilization energies of molecular species which are most responsible for the stability of molecule were identified. Furthermore, the highest occupied molecular orbital

4

(HOMO) and the lowest unoccupied molecular orbital (LUMO) energies were predicted to interpret the orbital overlapping and the possibility of charge transfer within the molecule using B3LYP/6-311++G (d,p)method and basis set combination. Apart from the aforesaid calculations, certain thermodynamic properties were computed at B3LYP/6-311++G (d,p)method to examine the intensity of molecular vibrations at different temperatures.

4

Results and Discussion

4.1

Optimized geometry The optimized molecular structure of the isolated MPBZ molecule calculated

using DFT theory at B3LYP/6-311+G (d,p) and 6-311++G (d,p) basis sets level is shown in Fig.1. The optimized geometrical parameters of MPBZ in DFT level are shown in Table1. The dihedral angle [13] (N1–C2–C18–C23) between the two ring systems is 32.857°. In benzimidazole, the bond length C6–C7 = 1.412/C4–C5 = 1.404/C4–C9 = 1.417˚A are appreciably greater than the other C–C bonds (C5– C6/C7–C8/C8–C9 = 1.39A˚) in the ring. The internal bond angles C3–C4–C5 = 116.914°and C2–C1–C6 = 118.005°are consistently smaller than the normal bond angle of the phenyl ring.

4.2

Molecular electrostatic potential (MEP) analysis The molecular electrostatic potential, V(r), at a given point r (x, y, z) in the

vicinity of a molecule, is defined in terms of the interaction energy between the electrical charge generated from the molecule electrons and nuclei and a positive test charge (a proton) located at r. The molecular electrostatic potential (MEP) is related to the electronic density and is a very useful descriptor for determining sites for electrophilic attack and nucleophilic reactions as well as hydrogen-bonding interactions [14,15]. To predict reactive sites for electrophilic and nucleophilic attack for the title molecule, MEP was calculated at the B3LYP/ 6-311++G (d,p) basis set optimized geometry.

5

The negative (red) regions of MEP were related to electrophilic reactivity and the positive (white) regions to nucleophilic reactivity shown in Fig. 2 the negative regions are mainly localized on the nitrogen atom N3. A maximum positive region is localized on the hydrogen atoms indicating a possible site for nucleophilic attack. The MEP map shows that the negative potential sites are on electronegative atoms as well as the positive potential sites are around the hydrogen atoms. These sites give information about the region from where the compound can have noncovalent interactions.

4.3

Natural bond orbital analysis The NBO approach of Weinhold and co-workers [16] has been frequently used

in the evaluation of the anomeric effect [17-20]and the origin of internal rotation barrier [21,22]. The NBO analysis allows estimating the energy of the molecule with the samegeometry in the absence of electronic delocalization. In order to investigate the various second order interaction between the filled orbital of one subsystem and vacant orbital of another subsystem the DFT/B3LYP level is used, and it predicts the hyperconjugation. The hyperconjugative interaction energy was deduced from the second-order perturbation approach [23].The most important interactions between ‘filled’ (donors) Lewis-type NBOs and ‘empty’ (acceptors) non-Lewis NBOs arereported in Table S1 (Supporting Material). The hyperconjugative interactions are formed by the orbital overlap between π(C–C) bond orbital to π*(C–C) anti bonding orbital, which results in ICT causing stabilization of the system. These interactions can be identified by finding the increase in electron density (ED) in anti bonding orbital. The hybrid directionality and bond bending analysis of the benzene ring in the title molecule provide excellent evidence to the substituent effect and steric effect. The angular properties of the natural hybrid orbitals are very much influenced by the type of substituent that causes conjugative effect or steric effect [24]. In Table S2 (Supporting Material), the bending angles of different bonds are expressed as the

6

angle of deviation from the direction of the line joining two nuclear centers. The σ∗(C5−C6) bond is more bent away from the line of C4−C9 centers by 0.7° results. According to the results, we can say that the degree of pyramidalization has affected by CH3 substituents.

5

Vibrational Analysis The vibrational spectra of MPBZ have not been described in detail in any

literature. Therefore, we focused on MPBZ. The observed and simulated FT-IR and FT-Raman spectra of the title compound are shown in Figs. 3 and 4, respectively. We have calculated the theoretical vibrational spectra of MPBZ by using B3LYP method with 6-311+G(d,p) and 6-311++G(d,p) basis sets. None of the predicted vibrational spectra has any imaginary frequency, implying the optimized geometry is located at the local lowest point on the potential energy surface. It is known that DFT potentials systematically overestimate the vibrational wavenumbers. These discrepancies can be corrected either by computing anharmonic corrections explicitly or by introducing a scaled field [25] or directly scaling the calculated wavenumbers with the proper scaling factor [9]. Considering systematic errors with scaling factor of 0.9574, 0.9631 and 0.9663, we calibrated the vibrational wavenumbers calculated by B3LYP. After scaled with a scaling factor, the deviation from experiments is less than 10 cm−1 with a few exceptions. Theoretical and experimental frequencies of the title compound are shown in Table 2. The vibrational bands’ assignments have been made by using both the animation option of Gauss View 5.0 graphical interface for Gaussian programs [7] and version V7.0-G77 of the MOLVIB program written by Sundius [10]. The B3LYP/6311++G (d,p) basis set is superior to other basis sets in terms of realistic reproduction of both band intensity distribution and general spectral features. C–H vibrations The aromatic C–H ring stretching vibrations are normally found between 3100 and 3000cm−1 [26]. C–H stretching of MPBZ ring is observed in Raman spectra at 7

3068cm−1with aPED 95%. The C–H in-plane bending vibrations of MPBZ are coupled with ring C–C and C–N stretching modes (Table 2). IR active C–H in-plane bending of MPBZ appears at 1266, 1223, 1138 cm−1 (1, 2substituted benzene ring) and1160, 1085 cm−1 (mono substituted benzene ring) with significant PED (>60%). The Raman active bands at 1181, 1159, 1102, cm−1 and 1125 cm−1(1, 2substituted benzene ring) are corresponding to C–H in-plane bending mode of MPBZ. The IR active C–H out-of-plane bending modes of MPBZ appears at 984, 904,841 cm−1 (1, 2 substituted benzene ring) 996, ,947, and 777(mono substituted benzene ring) with significant PED (>60%). The Raman active bands at 909,854,837 (1, 2substituted benzene ring) and 782 cm−1 (mono substituted benzene ring) are corresponding to C– H out-of-plane bending modes of MPBZ. The experimental values are good agreement with theoretical values [8,27].

Methyl group vibrations For the assignments of CH3 group frequencies, basically nine fundamentals can be associated to each CH3 [28], group namely, CH3ss: symmetric stretch; CH3ips: inplane stretch (i.e. in-plane hydrogen stretching modes); CH3ipb: in-plane-bending (i.e., hydrogen deformation modes); CH3sb: symmetric bending; CH3ipr: in-plane rocking; CH3opr: out-of-plane rocking and tCH3: twisting hydrogen bending modes. In addition to that, CH3ops: out-of-plane stretching and CH3opb: out-of-plane bending modes of the CH3 group would be expected to be depolarised for A" symmetry species. The CH3ss frequencies are established at 2417 cm−1in FT-IR. We have observed the symmetrical methyl deformation mode at 1366 cm−1in FT-Raman and at 1500 cm−1in FT-IR. The band at 1034 in FT-Raman 1043 cm−1in infrared are attributed to out-of-plane bending of CH3. C–N, C= N vibrations The identification of wavenumber for C–N stretching in the side chains is rather difficult since there are problems in differentiating those wavenumber from

8

others. James et al. [29] assigned1370cm−1for 1-benzyl-1-H-imidazole for C–N vibration. Pinchaset al. [30] assigned the C–N stretching at 1368cm−1in benzamide.Kahovec and Kohlreusch [31] identified the stretching wavenumber of C=N

band

in

salicylicaldoxinne

at

1616cm−1.

For

1-methyl-2-phenyl

benzimidazolemolecule the observed bands at 1563,1543,1436,1338 and 1245 cm−1in IR are assigned to C–N stretching, in which 1563cm−1have PED of 73%.The corresponding Raman active bands are observed at 1537,1443,1239 and1205 cm−1.The C=N stretching is assigned to the wavenumber 1537cm−1in FT-Raman with70% PED. These values support the reported results [29, 30].

C–C vibrations The (C–C) vibrations are more interesting if the double bonds are in conjugation with the ring. The actual positions are determined not so much by the nature of the substituent but by the form of substitution around the ring [32]. For MPBZ ring IR bands at 1660, 1585, 1471 cm−1 (1, 2substituted benzene ring) and 1457 1596 cm−1 (mono substituted benzene ring) are assigned to C–C stretching and the counterpart in Raman are 1602 and 1580 cm−1( mono substituted benzene ring) in which the mode corresponding to 1580cm−1have a PED of66%. The strong bands at 1340 and 1297 cm−1 (1, 2substituted benzene ring) in IR and bands at 1341 and 1294 cm−1 (1, 2substituted benzene ring) in Raman for C–C stretching correspond to the MPBZ. The band at 1585 cm−1(mono substituted benzene ring) inIR represents C–C stretch in MPBZ ring with a PED 66%.Most of the C–C stretching modes in this region are coupled with C–H in-plane bending modes.

Ring modes The ring modes are usually appears in IR and weakor absent in Raman. In IR spectra the ring mode occurs at482 cm−1for MPBZ.The ring deformation is active in IR. Small changes in wavenumbers observed for ring modes are due to the changes in force constant/reduced mass ratio resulting mainly due to the extents of mixing between

9

ring and substituent group vibrations. The C–C bond ring in-plane bending mode which is active at251 and 156cm−1in Raman with a PED of 55% and C–C out-of-plane bending is active in Raman at 411cm−1with a PED of 62%. 6

Other molecular properties

6.1

HOMO and LUMO analysis Many organic molecules, containing conjugated π electrons are characterized

by large values of molecular first hyperpolarizabilities, were analyzed by means of vibrational spectroscopy [33, 34]. In most cases, even in the absence of inversion symmetry, the strongest band in the FT-Raman spectrum is weak in the FTIR spectrum and vice-versa. But the intramolecular charge transfer from the donor to acceptor group through a single-double bond conjugated path can induce large variations of both the molecular dipole moment and the molecular polarizability, making FTIR and FT-Raman activity strong at the same time. The experimental spectroscopic behavior described above is well accounted by ab initio calculations is π conjugated systems that predict exceptionally FTIR intensities for the same normal modes [34]. It is also observed in our title molecule the bands in FTIR spectrum have their counterparts in FT Raman shows that the relative intensities in FTIR and FT Raman spectra are comparable resulting from the electron cloud movement through π conjugated frame work from electron donor to electron accepter groups. The analysis of the wave function indicates that the electron absorption corresponds to the transition from the ground to the first excited state and is mainly described by oneelectron excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). The HOMO of π nature, (i.e., benezene ring) is delocalized over the whole C–C bond. The HOMO and LUMO transition implies an electron density transfer to aromatic part and propionic acid of π conjugated system from methyl group. Moreover, these orbital significantly overlap in their position for MPBZ. The atomic orbital composition of the frontier molecular orbital is shown in Fig. S1 (Supporting Material) for MPBZ.

10

Commonly, the atom occupied by more densities of HOMO should have stronger ability for detaching electrons, whereas the atom with more occupation of LUMO should be easier to gain electron. For MPBZ, the highest occupied molecular orbital (HOMO) lying at 0.21535 eV, is a delocalized π orbital. The HOMO-1, lying 0.22505eV below the HOMO, is a delocalized π orbital over C6-C7. While, the HOMO-2 lying 0.26078 eV above the HOMO, respectively, are π orbitals that localized in benzene ring. Whereas, the lowest unoccupied molecular orbital (LUMO), lying at 0.04431 eV, is π* orbital that localised for MPBZ. The LUMO+1, lying about 0.01499 eV below the LUMO, is also a π* that is similar to LUMO. The HOMOLUMO energy gap of MPBZ was calculated at the B3LYP/6-311++G (d,p) basis set is −0.17104 eV, reveals that the energy gap reflects the chemical activity of the molecule. The calculated self-consistent field (SCF) energy of MPBZ is −650.217a.u moreover; the lower in the HOMO and LUMO energy gap explains the eventual charge transfer interactions taking place within the MPBZ molecule.

6.2

Hyperpolarizability calculations The first hyperpolarizabilities (β0) of this molecular system, and related

properties (β, α0 and α) of MPBZ were calculated using B3LYP/6-311+G (d,p) and 6311++G (d,p) basis sets, based on the finite-field approach. In the presence of an applied electric field, the energy of a system is a function of the electric field. Polarizabilities and hyperpolarizabilities characterize the response of a system in an applied electric field [35]. They determine not only the strength of molecular interactions (long-range inter induction, dispersion force, etc.) as well as the cross sections of different scattering and collision process. First hyperpolarizability is a third rank tensor that can be described by 3×3×3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to the Kleinman symmetry [36]. It can be given in the lower tetrahedral format. It is obvious that the lower part of the 3×3×3 matrixes is a tetrahedral. The components of β are defined as the coefficients in the

11

Taylor series expansion of the energy in the external electric field. When the external electric field is weak and homogeneous, this expansion becomes:

E = E 0 − µα Fα − 1 ααβ Fα Fβ − 1 βαβγ Fα Fβ Fγ + ...... 2 6 where E0 is the energy of the unperturbed molecules, Fα the field at the origin µα, ααβ and βαβγ are the components of dipole moments, polarizability and the first hyperpolarizabilities, respectively. The total static dipole moments µ, the mean polarizabilities α0, the anisotropy of the polarizabilities α and the mean first hyperpolarizabilities β0, using the x, y and z components they are defined as: [37,38]

µ = (µx2 + µ y2 + µz2 ) 2 1

The total static dipole moment is The isotropic polarizability is

α0 =

α xx + α yy + α zz 3

The polarizability anisotropy invariant is

α = 2−

1

2

[(α

− α yy ) + (α yy − α zz ) + (α zz − α xx ) + 6α xx 2

xx

2

2

2

]

1

2

and the average hyperpolarizability is

(

β 0 = β x 2 + β y2 + β z2

)

1

2

β x = β xxx + β xyy + β xzz

β y = β yyy + β xxy + β yzz β z = β zzz + β xxz + β yyz

The total static dipole moment, polarizabilities and first hyperpolarizabilities of MPBZ were calculated. Table 3 lists the values of the electric dipole moment (Debye) and dipole moment components, polarizabilities and hyperpolarizabilities of the MPBZ. In addition to the isotropic polarizabilities and polarizabilities anisotropy invariant were also calculated. The polarizabilities and first hyperpolarizabilities of

12

MPBZare −89.5533, −88.2654 a.u and 2.32793x10−30, 2.18798 x10−30 esu, by and B3LYP/6-311+G(d,p)and 6-311++G(d,p)

levels, which are comparable with the

reported values of similar derivatives [39, 40].

6.3

Natural population analysis The natural population analysis [41] performed on the title molecule clearly

describes the distribution of charges in the various sub-shells (core, valence, Rydberg) in the molecular orbital. The accumulation of natural charges on individual atom of the title molecule is given in Table 4.

It shows that an atom C9 has the most

electronegative charge of −5.8645e and N3 has the most electropositive charge of 7.4963e. Likewise, C4 and C2 atoms have considerable electro negativity and they are tending to donate an electron. Conversely, the C8 and C10atoms have considerable electropositive and they are tending to acquire an electron. Further, the natural population analysis showed that 110 electrons in the title molecule are distributed on the sub shell as follows: Core

: 31.98527 (99.9540% of 32)

Valence : 77.78745 (99.7275% of 78) Rydberg : 0.22728 (0.2066% of 110)

6.4

Mulliken atomic charge Mulliken atomic charge calculation has an important role in the application of

quantum chemical calculation to molecular system because of atomic charges effect dipole moment, molecular polarizability and electronic structure. The calculated Mulliken charge values of MPBZ are listed in Table S3 (Supporting Material). The Mulliken charge distribution of the MPBZ in B3LYP/6-311++G(d,p) basis set are shown in Fig. S2 (Supporting Material). The charge distribution of the title molecule shows all the hydrogen atoms, N1, N3, C8 and C18 are negatively charged whereas the other carbon atoms are positive. The influence of electronic effect resulting from the hyperconjugation and induction of methylene group in the aromatic ring causes a large

13

negatively charged value in the carbon atom C9 in MPBZ. The charge changes with basis set presumably occurs due to polarization. The charge distribution of nitrogen atom is increasing trend inB3LYP methods in MPBZ.

6.5

Thermodynamic function analysis On the basis of vibrational analysis, the statically thermodynamic functions:

heat capacity (C0p,m), entropy (S0m), Gibb’s free energy (G0m) and enthalpy changes (H0m) for the title molecule were obtained from the theoretical harmonic frequencies and listed in Table S4 (Supporting Material). From the Table S4 (Supporting Material), it can be observed that these thermodynamic functions are increasing with temperature ranging from 100 to 1000 K due to the fact that the molecular vibrational intensities increase with temperature. The correlation equations between heat capacity, entropy, Gibb’s free energy, enthalpy changes and temperatures were fitted by quadratic formulas and the corresponding fitting factors (R2) for these thermodynamic properties are 0.998, 1.000, 0.999 and 0.999 respectively. The corresponding fitting equations are as follows and the correlation graphics of those shows in Fig. S3 (Supporting Material) C p0 ,m = 2.191 + 0.207T − 8.0 × 10 −5 T 2 ( R 2 = 0.998) S m0 = 57.45 + 0.171T − 3.0 × 10 −5 T 2 ( R 2 = 1.000) G m0 = −55.16 − 0.104T − 2.0 × 10 −5 T 2 ( R 2 = 0.999) H m0 = 2.289 + 0.066T − 5.0 × 10 −5 T 2 ( R 2 = 0.999)

7

Conclusion Molecular structure and vibrational wavenumbers of MPBZ is studied using

vibrational spectra and density functional method. The DFT based calculations for MPBZ reproduced its experimental geometry and vibrational wavenumbers excellently. A complete vibrational analysis of MPBZ was performed on the basis of the SQM force field obtained by DFT calculation.

14

The wavenumbers proposed by PED calculations are in fair agreement with the observed wavenumbers. Lower in the HOMO and LUMO energy gap reveals the significant degree of charge transfer interactions taking place within the molecule. The NBO analysis reveals the reasons for hyperconjugative interaction, ICT and stabilization of the molecule. Furthermore, the thermodynamic and electronic absorption properties of the compounds have been calculated. The correlations between the statistical thermodynamics and temperature are also obtained.

15

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12. G. Keresztury, S. Holly, J. Varga, G. Besenyei, A.V. Wang, J.R. Durig, Spectrochim. Acta 49 (1993) 2007-2017. 13. N. Rashid, M. Hasan, M. Tahir, M.K. Yusof, NM. Yasmin, ActaCryst. 63 (2007) 1260-1261. 14. Y. Shyma Mary P.J. Jojob, C. Yohannan Panickerc, Christian Van Alsenoyd, Sanaz Ataeie, Ilkay Yildizf Spectrochim. Acta 122 (2014) 499–511. 15. M. Karnan, V. Balachandran, M. Murugan, J. Mol. Struct. 1039 (2013) 197–206. 16. A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899-926. 17. A.J. Kirby, TheAnomeric Effect and Related Stereoelectronic Effects at Oxygen, Springer Verlag, Berlin, 1983. 18. U. Salzner, P.V.R. Schleyer, J. Am. Chem. Soc. 115 (1993) 10231-10236. 19. U. Salzner, P.V.R. Schleyer, J. Org. Chem. 59 (1994) 2138-2155. 20. H. Roohi, A. Ebrahimi, J. Mol. Struct. (Theochem) 726 (2005) 141–148. 21. L. Godman, V. Pophristic, P.V.R. Schleyer (Eds.), Rotational Barrier Origins, Encyclopedia of Computational Chemistry, Vol. 4, Wiley, New York, 1998. 22. H. Roohi, A. Ebrahimi, F. Alirezapoor, M. Hajealirezahi, Chem. Phys. Lett. 409 (2005) 212–218. 23. C. Ravikumar, I. Hubert Joe, V.S. Jayakumar, Chem. Phys. Lett. 460 (2008) 552–558. 24. A. Ebrahimi, F. Deyhimi, H. Roohi, J. Mol. Struct. (Theochem) 626 (2003) 223– 229.

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18

Fig. 1 Geometrical structure of 1-methyl-2-phenyl benzimidazole

Fig. 2 3D-Molecular electrostatic potential map of 1-methyl-2-phenyl benzimidazole

a) Observed

Transmittance (%)

b) B3LYP/6-311G+(d,p)

c) B3LYP/6-311G++(d,p)

4000

3500

3000

2500

2000

1500

1000

500

Wavenumber (cm-1)

Fig. 3 Observed FT-IR and simulated spectrum of 1-methyl-2-phenyl benzimidazole (a) Observed (b) B3LYP /6-311+G(d,p) (c) B3LYP/6-311++G(d,p)

a) Observed

Raman Intensity (kmmol1)

b) B3LYP/6-311G+(d,p)

c) B3LYP/6-311G++(d,p)

3500

3000

2500

2000

1500

1000

500

100

-1

Wavenumber (cm ) Fig. 4 Observed FT-Raman and simulated spectrum of 1-methyl-2-phenyl benzimidazole (a) Observed (b) B3LYP /6-311+G(d,p) (c) B3LYP/6-311++G(d,p)

HOMO –2 HOMO –1 HOMO E = 0.17104 eV

E = 0.21006 eV

E = 0.2572 eV

LUMO LUMO +1

LUMO +2

Fig. S1 (Supporting Materials) The atomic orbital composition of the frontier molecular orbital for 1-methyl-2-phenyl benzimidazole

0.14 0.12

B3LYP/6-311++G(d,p)

0.10

0.06 0.04 0.02 0.00 -0.02

C 4 C 5 C 6 C 7 C 8 C C9 1 H0 1 H1 1 H2 1 H3 1 H4 1 H5 1 H6 1 C7 1 C8 1 C9 2 C0 2 C1 2 C2 2 H3 2 H4 2 H5 2 H6 2 H7 28

Atomic Charges

0.08

-0.04

Atomic Number

Fig. S2 (Supporting Materials) Fig.6 Mulliken atomic charges with 6-311++G(d,p) level of 1-methyl-2-phenyl benzimidazole

Thermodynamic Parameter (Kcal/mol)

250

Cp S o o (H -E )/T o o (G -E )/T

200 150 100 50 0 -50 -100 -150 0

200

400

600

800

1000

Temperature (Kelvin)

Fig. S3 (Supporting Materials) Correlation graph of Gibb’s energy, entropy and enthalpy with temperature of 1-methyl-2-phenyl benzimidazole

Table 1 Optimized structural parameters of 1-methyl-2-phenyl benzimidazole utilizing B3LYP/6-311+G(d,p) and 6-311++G(d,p) density functional calculation. Bond length N1-C2 N1-C9 N1-C10 C2-N3 C2-C18 N3-C4 C4-C5 C4-C9 C5-C6 C5-H14 C6-C7 C6-H15 C7-C8 C7-H16 C8-C9 C8-H17 C10-H11 C10-H12 C10-H13 C18-C19 C18-C23 C19-C20 C19-H24 C20-C21 C20-H25 C21-C22 C21-H26 C22-C23 C22-H27 C23-H28

Value(Å) 6-311+G(d,p) 1.406 1.396 1.460 1.334 1.468 1.397 1.401 1.419 1.394 1.084 1.414 1.085 1.397 1.085 1.399 1.085 1.094 1.096 1.091 1.409 1.410 1.399 1.084 1.399 1.085 1.402 1.085 1.395 1.085 1.084

6-311++G(d,p) 1.394 1.387 1.453 1.321 1.474 1.381 1.404 1.417 1.393 1.092 1.412 1.092 1.395 1.092 1.400 1.092 1.101 1.103 1.097 1.407 1.408 1.397 1.091 1.397 1.092 1.400 1.092 1.394 1.092 1.090

Bond angle C2-N1-C9 C2-N1-C10 C9-N1-C10 N1-C2-N3 N1-C2-C18 N3-C2-C18 C2-N3-C4 N3-C4-C5 N3-C4-C9 C5-C4-C9 C4-C5-C6 C4-C5-H14 C6-C5-H14 C5-C6-C7 C5-C6-H15 C7-C6-H15 C6-C7-C8 C6-C7-H16 C8-C7-H16 C7-C8-C9 C7-C8-H17 C9-C8-H17 N1-C9-C4 N1-C9-C8 C4-C9-C8 N1-C10-H11 N1-C10-H12 N1-C10-H13 H11-C10-H12 H11-C10-H13

Value(°) 6-311+G(d,p) 106.586 128.889 124.091 111.892 125.211 122.896 106.013 129.979 109.816 120.205 118.005 120.119 121.876 121.248 119.661 119.091 121.534 119.235 119.231 116.914 120.908 122.175 105.687 132.217 122.094 109.017 111.854 109.853 108.624 108.428

6-311++G(d,p) 106.187 129.132 124.123 112.765 124.681 122.553 105.506 129.997 110.155 119.848 118.082 120.082 121.836 121.351 119.597 119.052 121.522 119.273 119.205 116.784 121.042 122.172 105.385 132.201 122.412 109.155 111.910 109.956 108.459 108.366

Dihedral angle C9-N1-C2-N3 C9-N1-C2-C18 C10-N1-C2-N3 C10-N1-C2-C18 C2-N1-C9-C4 C2-N1-C9-C8 C10-N1-C9-C4 C10-N1-C9-C8 C2-N1-C10-H11 C2-N1-C10-H12 C2-N1-C10-H13 C9-N1-C10-H11 C9-N1-C10-H12 C9-N1-C10-H13 N1-C2-N3-C4 C18-C2-N3-C4 N1-C2-C18-C19 N1-C2-C18-C23 N3-C2-C18-C19 N3-C2-C18-C23 C2-N3-C4-C5 C2-N3-C4-C9 N3-C4-C5-C6 N3-C4-C5-H14 C9-C4-C5-C6 C9-C4-C5-H14 N3-C4-C9-N1 N3-C4-C9-C8 C5-C4-C9-N1 C5-C4-C9-C8

Value(°) 6-311+G(d,p) 0.826 -179.446 -171.749 7.979 -0.620 -179.955 172.404 -6.932 140.285 -99.571 21.604 -31.114 89.030 -149.795 -0.658 179.606 33.281 -149.379 -147.019 30.320 -179.897 0.244 -179.659 0.276 0.187 -179.877 0.249 179.668 -179.626 -0.207

6-311++G(d,p) 0.541 -179.450 -171.029 8.980 -0.376 -179.872 171.729 -7.767 137.017 -102.919 18.267 -33.192 86.873 -151.942 -0.457 179.534 35.756 -147.153 -144.234 32.857 -179.829 0.199 -179.702 0.150 0.268 -179.881 0.121 179.678 -179.854 -0.297

Table 2 Experimental and Calculated DFT-B3LYP/6-311++G(d,p)levels of vibrational frequencies (cm1), IR intensity (kmmol1) and Raman activity (Å4 amu1) of 1-methyl-2-phenyl benzimidazole No

Spe.

Observed frequencies (cm1)

IR 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A A A A A A A A A A A A A A A A A A A A A A A A A A A

Raman 3068

3041 3020 2951 2917 2875 2834 2792 2480 2417

1660 1602 1596 1585 1563 1543

1580

1537 1500 1471 1457 1436

1340 1338

1433 1386 1366 1341

Calculated frequencies (cm1) DFT-B3LYP 6-311+G(d,p) 6-311++G(d,p)

IR Intensity (kmmol1)

Un scaled

Scaled

Un scaled

Scaled

6-311+G (d,p)

6-311++G (d,p)

3282 3234 3229 3220 3218 3207 3205 3195 3194 3172 3123 3052 1674 1665 1641 1635 1574 1555 1542 1537 1524 1519 1498 1494 1416 1403 1388

3074 3046 3028 2955 2923 2880 2839 2798 2485 2424 2404 2382 1668 1623 1599 1594 1568 1544 1541 1516 1480 1475 1455 1451 1397 1362 1348

3216 3205 3204 3197 3196 3185 3184 3177 3174 3155 3100 3029 1665 1656 1632 1628 1559 1518 1510 1494 1481 1470 1464 1449 1407 1401 1359

3072 3042 3025 2954 3020 2279 2838 2794 2480 2420 2401 2371 1661 1609 1598 1590 1563 1544 1440 1507 1471 1460 1436 1489 1361 1341 1339

4.898 20.728 20.197 31.503 40.426 14.982 12.365 0.299 0.875 6.977 20.688 41.674 1.552 3.040 0.117 0.617 0.814 11.766 10.395 13.772 37.591 23.698 4.851 45.200 13.415 40.407 15.615

2.985 13.770 17.395 22.707 27.531 9.751 9.182 0.197 1.086 4.236 16.017 42.731 4.543 4.590 0.124 0.466 5.957 5.643 41.554 28.019 19.974 21.252 16.819 16.457 45.263 20.523 25.283

Raman Intensity (kmmol1) 6-311+G (d,p)

2.780 5.680 3.468 4.179 3.384 3.348 3.469 1.260 1.066 1.027 1.888 3.984 4.227 100.000 9.950 1.855 70.408 3.636 3.392 1.528 49.765 0.816 13.122 54.996 18.932 4.755 0.849

6-311++G (d,p)

2.760 9.354 3.379 3.960 3.922 4.095 3.958 1.555 0.943 1.116 2.270 4.606 1.955 100.000 6.933 3.112 89.227 0.749 14.611 11.143 11.928 29.716 15.939 7.140 18.503 13.353 9.400

Vibrational assignments /PED (≥ 10%) νCH(95) νCH(96) νCH(96) νCH(95) νCH(96) νCH(96) νCH(94) νCH(95) νCH(93) νCH3(72), νCH(23) νCH3(88), νCH(11) νCH3(72), νCH(23) νCC(70), βCH(19), γCH3(10) νCC(66), βCH(18), γCH3(9) νCC(65), βCH(19), γCH3(12) νCC(66), βCH(18), γCH3(11) νCN(73), νCC(15), γCH3(11) νCN(72), νCC(14), γCH3(11) νCN(70), νCC(16), γCH3(12) β CH3(62), νCN(14), νCC(16) νCC(82), tCH3(11) νCC(71), βCH(16), νCH3(12) νCN(58), βCH(18), νCC(11) γCH3(60),βCH(20), νCC(10) β CH3(72),βCH(12), νCC(16) νCC(50),βCH(20), νCN(12), γCH3(11) νCN(52), tCH3(13),νCC(12),βCH(11)

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A

1297 1266 1245 1223

1160 1138

1294 1239 1205 1181 1159 1125

1116 1102 1085 1059 1043

1068 1034

996 984 947 904 873 841 809 777 766 755 735 710 702 617 596 585 553 532 482 436

909 854 837 782 750 716 681 621 591 546

1366 1357 1314 1287 1245 1240 1224 1213 1172 1169 1132 1126 1087 1069 1054 1036 1032 1009 1008 964 963 923 884 883 842 809 787 778 753 729 721 709 651 618 606 601 560 515 453

1308 1278 1276 1250 1209 1204 1189 1178 1138 1135 1109 1093 1065 1048 1044 1008 1002 1000 989 956 915 896 868 857 818 786 771 755 741 718 709 688 632 600 591 564 548 500 444

1358 1325 1309 1280 1226 1194 1172 1166 1139 1133 1113 1102 1070 1063 1054 1014 1013 992 988 945 944 908 865 864 838 794 783 757 748 715 711 691 629 602 593 592 552 502 447

1304 1266 1243 1221 1207 1186 1164 1138 1131 1115 1105 1083 1063 1046 1031 1006 1001 998 989 948 907 874 859 848 802 773 769 755 739 713 706 686 625 598 589 558 534 488 440

10.247 7.339 30.175 16.066 0.991 3.390 0.030 4.035 2.163 6.925 4.464 7.161 5.401 14.881 7.882 0.673 1.226 0.033 0.857 4.574 1.606 0.326 0.544 0.134 13.865 17.755 10.438 85.281 2.405 42.592 1.358 2.861 0.035 3.471 2.740 1.150 3.424 2.657 2.063

12.080 8.275 21.365 6.218 2.287 1.821 0.012 5.479 5.582 2.206 1.399 6.902 5.286 14.531 9.279 0.480 0.195 1.056 0.055 2.719 1.018 0.971 0.418 0.538 11.666 11.668 4.941 54.591 4.889 30.520 0.803 2.845 0.051 5.087 0.535 3.313 3.104 3.433 1.806

1.419 9.892 13.791 37.012 6.739 11.216 2.035 3.669 17.141 10.418 11.169 0.854 1.361 0.954 7.575 5.029 27.014 0.083 0.984 0.716 0.189 0.529 4.898 1.273 0.703 0.298 0.787 0.900 8.844 1.870 2.507 1.741 3.173 0.681 3.946 1.430 3.341 0.665 0.126

0.811 12.792 43.058 3.032 8.970 4.877 1.938 1.036 25.232 0.898 12.893 0.295 1.768 11.019 5.940 8.118 14.558 1.168 0.083 0.520 0.236 0.541 4.520 1.409 1.496 0.574 0.773 0.694 7.805 1.322 2.683 2.129 3.228 0.198 1.766 5.333 2.475 0.864 0.043

νCC (58),βCH(24), νCN(13) βCH(65), νCN(21), νCC(11) νCN(63), βCH(21), νCC(15) βCH(66), νCN(18), νCC(12) νCN(67), βCH(16), νCC(12) βCH(66), νCC (20) βCH(78), νCC (10) βCH(78), βCH3(16) βCH(74), βCH3(21) β CN(69), βCH(17) βCH(56), βCH3(21), νCN(12) βCH(68), νCC(21) νCN(61),β CH3(12), βCH(17) CH3(65), βCC(30), νCN(13) CH3(71), βCC(23) βCH(66), βCC(21) γCH(66), νCC(13) γCH(67), νCC(12) γCH(66), νCC(11) γCH(68), νCC(10) γCH(67), νCC(11) βCC(64), βCH3(20), νCN(13) γCH(68), νCC(21) γCH(68), νCC(20) νCC (64), βCH3(20), νCN(13) γCH(67), νCC(12) γCH(66), νCC(16) νCN(68), νCC(13) νCN(64), βCH(20), νCC(15) γCN(67), νCC(11) γCN(71), βCH(17), νCC (11) νCC(71), βCH(17) νCC(64), βCH3(20) βCN(71), βCH(17), νCC(11) νCC(76), γCH(11), νCC(77), γCH(12), γCC(74), βCH3(18) γRing(60), βCH3(18), νCC(11) γRing(62), βCH3(15), νCC(10)

67 68 69 70 71 72 73 74 75 76 77 78

A A A A A A A A A A A A

411 289

251 156

429 373 308 303 295 280 202 180 142 103 64 52

417 365 290 280 268 262 199 165 132 100 62 50

419 368 302 293 286 271 198 166 130 98 62 50

416 362 288 271 264 259 197 156 129 97 62 50

0.137 1.755 1.448 0.983 1.028 0.723 0.048 1.040 3.303 0.426 1.129 0.788

0.122 0.899 1.330 0.296 1.431 0.567 0.045 1.154 1.815 0.366 0.775 0.727

3.994 0.867 5.446 3.516 12.899 1.383 20.096 13.900 14.695 36.233 46.450 343.304

5.256 1.224 3.165 1.258 16.193 6.181 21.250 11.874 10.059 38.997 51.980 426.793

γRing(62), βCH3(16), νCC(12) βRing(61), βCH3(12) βCN(61), βRing(11) βRing(52), βCH3(11) tCH3(51), γRing(12) βRing(52), tCH3(12) βRing(50), tCH3(11) βRing(55), tCH3(16) γRing(42), tCH3(13) βRing(61), βCH3(12) γRing(52), νCC(16) γRing(52), tCH3(11)

-stretching, νsym-sym stretching, νasym-asym stretching, β-in-plane bending, γ-out-of-plane bending, -scissoring, wagging,-rocking, ρip-in-plane rocking, ρop-out-of-plane rocking, t-twisting,sd-symmetric deformation, ad-asymmetric deformation, Rtrigd-Ring trigonal deformation, βRing-in-plane ring, γRing-out-of -plane ring τ-torsion.

Table 3 The Ab initio B3LYP/6-311+G (d,p) and 6-311++G (d,p) calculated electric dipole moments (Debye), Dipole moments compound, polarizability (in a.u), β components and βtot (1030 esu) value of 1-methyl-2-phenyl benzimidazole B3LYP/ B3LYP/ B3LYP/ B3LYP/ Parameters 6-311++G Parameters 6-311+G (d,p) 6-311+G (d,p) 6-311++G (d,p) (d,p) x

-1.3051

-1.2921

xxx

-23.7637

-22.9307

y

3.2796

3.0988

yyy

16.5559

15.0827

z

0.7699

0.7157

zzz

2.0622

1.8815



3.6127

3.4328

xyy

3.4764

2.293

xx

-83.4589

-83.1608

xxy

-5.6787

-4.6449

yy

-87.0678

-85.3927

xxz

-1.8783

-1.0565

zz

-98.1331

-96.2426

xzz

-6.2667

-4.3548

xy

0.8337

0.8627

yzz

4.681

4.035



-89.55326667

-88.26536667

YYZ

4.8029

4.1342

Δ(esu)

18.9450×1025

15.5773×1025

tot(esu)

2.32793x1030

2.18798 x1030

Table 4 Accumulation of natural charges and electron population of atoms in core, valance, Rydberg orbitals of 1-methyl-2-phenyl benzimidazole. Natural population (e)

Atomsa

Charge (e)

Core

C2 C4 C9 H11 H12 H13 H14 H15 H16 H17 H24 H25 H26 H27 H28

0.4032 0.1136 0.1355 0.2389 0.2389 0.2050 0.2577 0.2472 0.2468 0.2447 0.2038 0.2465 0.2469 0.2505 0.2755

1.9993 1.9988 1.9988 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

a b

Valence 3.5773 3.8713 3.8522 0.7593 0.7593 0.7937 0.7409 0.7519 0.7522 0.7541 0.7942 0.7525 0.7521 0.7486 0.7230

Atoms containing negative charges Atoms containing positive charges

Rydberg

Total (e)

0.0202 0.0163 0.0135 0.0018 0.0018 0.0013 0.0015 0.0009 0.0010 0.0012 0.0020 0.0010 0.0010 0.0010 0.0015

5.5968 5.8864 5.8645 0.7611 0.7611 0.7951 0.7423 0.7528 0.7532 0.7553 0.7962 0.7535 0.7532 0.7496 0.7245

Atoms N1 N3 C5 C6 C7 C8 C10 C18 C19 C20 C21 C22 C23

b

Natural population (e)

Charge (e)

Core

-0.3997 -0.4963 -0.2429 -0.2527 -0.2480 -0.2765 -0.4361 -0.0949 -0.1959 -0.2363 -0.2366 -0.2364 -0.2023

1.9991 1.9995 1.9989 1.9990 1.9990 1.9989 1.9992 1.9988 1.9989 1.9990 1.9990 1.9990 1.9989

Valence 5.3934 5.4902 4.2327 4.2421 4.2371 4.2675 4.4301 4.0850 4.1873 4.2254 4.2260 4.2257 4.1921

Rydberg

Total (e)

0.0071 0.0067 0.0113 0.0116 0.0120 0.0102 0.0067 0.0110 0.0097 0.0120 0.0116 0.0117 0.0113

7.3997 7.4963 6.2429 6.2527 6.2480 6.2765 6.4361 6.0949 6.1959 6.2363 6.2366 6.2364 6.2023

Table S1 (Supporting Materials) Significant second-order interaction energy (E (2), kcal/mol) between donor and acceptor orbitals of 1-methyl-2-phenyl benzimidazole calculated at B3LYP/6-311+G(d,p)level of theory

a

Do Donor (i)

Acceptor (j)

(N1-C2) (N1-C2) (N1-C9) (N1-C9) (N1-C9) (C2-N3) (C2-N3) (C2-C18) (N3-C4) (N3-C4) (N3-C4) (C4-C9) (C4-C9) (C4-C9) (C10-H11) (C10-H12) (C10-H13) (C10-H13) π (N1) π (N1) π (N3) π (N3)

*(N1-C9) *(N1-C10) *(C2-C18) *(C4-C5) *(C8-C9) *(N1-C10) *(C4-C5) *(C18-C23) *(C2-C18) *(C4-C5) *(C8-C9) *(N1-C10) *(C4-C5) *(C8-C9) *(N1-C2) *(N1-C2) *(N1-C9) *(C19-H24) π *(C10 - C4) π *(C10 –H12) π *(N1 – C2) π *(C4 – C9)

E(2)a kcal/mol 1.33 1.05 3.94 2.26 2.02 3.95 3.85 2.13 4.72 2.16 2.97 4.29 3.63 4.40 2.53 2.53 4.63 12.19 4.39 4.39 7.13 4.83

(εi - εj)b a.u 1.14 1.10 1.13 1.34 1.33 1.06 1.36 1.20 1.09 1.30 1.29 0.95 1.25 1.24 0.93 0.93 0.90 1.04 0.65 0.65 0.74 0.83

Fijc a.u 0.04 0.03 0.06 0.05 0.05 0.06 0.07 0.05 0.06 0.05 0.06 0.06 0.06 0.07 0.04 0.04 0.06 0.10 0.05 0.05 0.07 0.06

E(2) means energy of hyperconjugative interactions. Energy difference between donor and acceptor i and j NBO orbitals. c F(i,j) is the Fock matrix element between i and j NBO orbitals. b

Table S2 (Supporting Materials) Natural atomic orbital occupancies and energies of most interacting NBO’s of 1-methyl-2-phenyl benzimidazole along with their hybrid atomic orbitals and hybrid directionality Parametersa (AB)

(N1-C2)

(N1-C9) (N1C10)

(C2-N3) (C2C18)

(N3-C4)

(C4-C9) (C10H11) (C10H12) (C10H13) (C18C19)

Occupancies

Hybrid Sp1.88(N1) Sp2.43(C2)

0.0408

0.3879 Sp2.08(C1) Sp2.77(C7)

0.0374

0.3398 Sp2.05(N1) Sp3.17(C10)

0.0191

0.2930 Sp2.15(C2) Sp2.12(N3)

0.0121

0.4156 sp1.56(C2) sp2.49(C18)

0.0341

0.3796 sp2.27(N3) sp2.63(C4)

0.0239

0.3748 Sp2.19(C4) Sp2.04(C9)

0.0375

0.4834

0.0123

0.3880

Sp3.03

0.0123

0.3880

sp3.03

0.0328

0.4700

Sp2.78 Sp1.83(C18) Sp1.81(C19)

0.0239

0.5504 Sp1.78(C18) Sp1.79(C23)

(C18C23)

0.0225

(N3)

1.9397

a

Energies (a.u)

0.5528 0.34919

Sp1.68

AO(%) b s( 34.71) + p(65.29) s( 29.12) + p(70.88) s( 32.43) + p(67.57) s( 26.50) + p(73.50) s( 32.83) + p(67.17) s( 23.96) + p(76.04) s( 31.77) + p 68.23) s( 32.10) + p(67.90) s( 39.11) + p(60.89) s( 28.67) + p(71.33) s( 30.55) + p(69.45) s( 27.53) + p(72.47) s( 31.33) + p(68.67) s( 32.92) + p(67.08) s( 24.84) + p(75.16) s( 24.84) + p(75.16) s( 26.47) + p(73.53) s( 35.36) + p(64.40) s( 35.60) + p(64.40) s( 35.97) + p(64.03) s( 35.85) + p(64.15) s(37.35)+ p(62.65)

Deviation at A( °)

Deviation at B(°)

7.1

5.4

7.6

8.3

-

-

4.9

5.7

-

-

7.0

9.2

2.3

1.6

1.5

-

1.5

-

2.6

3.3

2.8

-

-

-

For numbering of atoms refer Fig. 9.1 Percentage of s-type and p-type subshell of an atomic orbitals are given in their respective brackets b

Table S3 (Supporting Materials) Mulliken population analysis of 1-methyl-2-phenyl benzimidazole performed at B3LYP/ 6-311++G (d,p) Atomic Atomic Atoms Atoms charges charges N1 -0.278 H15 -0.034 C2 0.205 H16 -0.034 N3 -0.231 H17 -0.039 C4 0.028 C18 -0.034 C5 0.004 C19 0.007 C6 0.038 C20 0.040 C7 0.032 C21 0.037 C8 -0.005 C22 0.043 C9 0.136 C23 0.058 C10 0.074 H24 -0.043 H11 0.045 H25 -0.028 H12 0.044 H26 -0.027 H13 0.052 H27 -0.024 H14 -0.034 H28 -0.031

Table S3 (Supporting Materials) Statistical thermodynamic parameters of 1-methyl-2-phenyl benzimidazole at various temperatures Temp.

(Kelvin)

Thermodynamic parameters (k cal mol–1) CP

S

(Ho −Eoo)/T (Go−Eoo)/T

100

19.8543516 75.12187

10.35396

-64.7679

200

34.0148092 93.14055

17.11071

-76.0298

300

50.7635604 111.4742

25.954

-85.5202

400

67.4249983 130.7043

36.21029

-94.494

500

81.8576688 150.8382

47.59597

-103.242

600

93.665146

171.7356

59.93648

-111.799

700

103.233342 193.2337

73.09359

-120.14

800

111.059452 215.1875

86.94813

-128.239

900

117.545041 237.4787

101.397

-136.082

1000

122.98164

116.3525

-143.662

260.0146

Graphical abstract

HOMO –2 HOMO –1 HOMO E = 0.17104 eV

E = 0.21006 eV

E = 0.2572 eV

LUMO LUMO +1 LUMO +2

Highlights

 The FT-IR and FT-Raman spectra of 1-methyl-2-phenyl benzimidazole were analyzed.  Charge transfer characteristics were examined by HOMO-LUMO and NBO analysis.  Calculations were carried out at B3LYP/6-311+G (d,p) and 6-311++G (d,p) basis

sets  MEP surface provide information about donor and acceptor atoms in the molecule.  Thermodynamic properties were determined at different temperatures.