Theoretical Studies on Molecular Structure and Vibrational Spectra of 2,4-Difluoro-1-Methoxy Benzene and 1-Chloro-3-Methoxy Benzene

Received: 02/May/2019, Accepted: 07/Jun/2019, Online: 30/Jun/2019 Abstract: -In this paper, we have studied the numerical analysis of the effect of Grashof number , modified Grashof number and chemical reaction on the non-Darcy MHD flow of a Casson fluid over a nonlinearly stretching sheet in a porous medium. In the mathematical model, using similarity variables, the momentum , energy and concentration equations are transformed to non-dimensional ordinary differential equations.. And then these are solved numerically using bvp4c method, a Matlab inbuilt bvp4c-programm. A discussion for the effects of the parameters involved on the boundary layer regions and the magnitude of the velocity, temperature and concentration and Local skin friction , Local Nusselt Number and Local Sherwood Number have been done graphically and numerically using figures and tables.


I. INTRODUCTION
Molecular organic compounds with one or more aromatic systems in conjugated positions leading to charge transfer systems, are intensely studied for the past two decades. Now-a-days organic crystals are highly recognized as the materials of the future because of their molecular nature, combined with versatility of synthetic chemistry can be used to alter their structure in order to maximize the non-linear properties [1][2][3]. The substituted benzene derivatives with high optical non-linearities are very promising materials for future optoelectronic and non-linear optical applications. Particularly, the new non-linear optical crystal of chloro and nitro substituted benzene are grown by low temperature solution growth technique. The optical transparency of this crystal is quite good and hence it can be a potential material for frequency doubling of non-linear optics [4]. Moreover, benzene derivatives are widely used to manufacture therapeutic chemicals, dyes, artificial leather and detergent

II. EXPERIMENTAL DETAILS
The fine samples of DFMB and CMB were purchased from Lancaster chemical company, UK and they were used as such without any further purification to record FT-IR and FT-Raman spectra. The FT-IR spectrum of DFMB and CMB has been recorded in the region 4000-400 cm -1 at a resolution of  1 cm -1 using BRUKER IFS 66V model FT-IR spectrometer equipped with an MCT detector, a KBr beam splitter and globar arc source.
The FT-Raman spectrum of DFMB and CMB has been recorded using 1064 nm line of Nd:YAG laser as excitation wavelength in the Stokes region 3500-50 cm -1 on a BRUKER IFS-66V model interferometer equipped with an FRA-106 FT-Raman accessory operating at 200 mW power. The calibrated wave numbers are expected to be accurate within  1 cm -1 .

III. COMPUTATIONAL DETAILS
In order to meet the requirements of both accuracy and computing economy, theoretical methods and basis sets should be considered. DFT has proved to be extremely useful in treating electronic structure of molecules. The DFT calculations were carried out for DFMB and CMB with GAUSSIAN 09W program package [6]. Initial geometry, generated from the standard geometrical parameters was minimized without any constraint on the potential energy surface at DFT level adopting the standard 6-311++G(d,p) basis set. All the parameters were allowed to relax and all the calculations converged to an optimized geometry, which corresponds to a true minimum, as revealed by the lack of imaginary values in the wavenumber calculations. The Cartesian representation of the theoretical force constants are computed at the fully optimized geometry. The multiple scaling of the force constants were performed according to the SQM procedure [7,8] using selective scaling in the natural internal coordinate representation [9,10]. The transformation of force field, the subsequent normal coordinate analysis including the least square refinement of the scale factors and calculation of the Total energy distribution (TED) were done on a PC with the MOLVIB program (version V7.0-G77) written by Sundius [11,12]. The systematic comparison of the results from DFT theory with results of experiments has shown that the method using B3LYP functional is the most promising in providing correct vibrational wave numbers.

Molecular Geometry
The optimized molecular structures of DFMB and CMB along with numbering of atoms are shown in Figs. 1 and 2 respectively. The optimized geometrical parameters calculated at B3LYP/6-311++G(d,p) levels for both the compounds are presented in Tables 1and 2 for DFMB and CMB respectively. The calculated geometric parameters can be used as a foundation to calculate the other parameters for the compounds. The optimized molecular structure of DFMB and CMB, the bonding properties of the molecules are influenced by the rearrangement of electrons during substitutions and addition reactions. Normal coordinate analyses are carried out for DFMB and CMB to provide a complete assignment of fundamental frequencies.
For this purpose, a full set of 55 standard internal coordinates (containing 13 redundancies) for both DFMB and CMB are defined as given in Tables.3 and 4 respectively. From these, a non-redundant set of local symmetry coordinates are constructed by suitable linear combinations of internal coordinates following the recommendations of Fogarasi et al. [10,13] and are summarized in Tables 5 and 6 for DFMB and CMB respectively. The theoretically calculated force fields are transformed to this set of vibrational coordinates and used in all subsequent calculations.

V. FIRST HYPERPOLARIZABILITY
The potential application of DFMB and CMB in the field of nonlinear optics demands the investigation of its structural and bonding features contributing to the hyperpolarizability enhancement, by analyzing the vibrational modes using IR and Raman spectroscopies. Many organic molecules, containing conjugated π electrons are characterized by large values of molecular first hyperpolarizabilities, were analyzed by means of vibrational spectroscopy [14,15]. In most of the cases, even in the absence of inversion symmetry, the strongest band in the Raman spectrum is weak in the IR spectrum and vice-versa. But the intramolecular charge from the donor to acceptor group, through a πbond conjugated path can induce large variations of both the molecular dipole moment and the molecular polarizability, making IR and Raman activity strong at the same time. The experimental spectroscopic behavior described above is well accounted for calculations in π conjugated systems that predict exceptionally infrared intensities for the same normal modes [15]. The first hyperpolarizabilities (β) of these novel molecular systems are calculated using ab initio quantum mechanical method, 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. The first hyperpolarizability is a third-rank tensor that can be described by a 3 × 3 × 3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to the Kleinman symmetry [16].
The components of β are defined as the coefficients in the Taylor series expansion of the energy in the external electric field. When the electric field is weak and homogeneous, this expansion becomes where E 0 is the energy of the unperturbed molecule; F i is the field at the origin; and μ i , α ij , β ijk and γ ijkl are the components of dipole moment, polarizability, the first hyperpolarizabilities and second hyperpolarizibilites, respectively. The calculated total dipole moment (μ) and mean first hyperpolarizability (β) of DFMB are 1.8077 Debye and 0.6007 × 10 −30 esu, respectively, which is comparable with the reported values of similar derivatives [4,17]. Similarly, the total dipole moment (μ) and mean first hyperpolarizability (β) of CMB are found to be 1.6071 Debye and 0.7848 × 10 −30 esu, respectively. The large value of hyperpolarizability, β which is a measure of the non-linear optical activity of these molecular systems, are associated with the intramolecular charge transfer, resulting from the electron cloud movement through π conjugated frame work from electron donor to electron acceptor groups. The physical properties of these conjugated molecules are governed by the high degree of electronic charge delocalization, along with the charge transfer axis and by the low band gaps. So, DFMB and CMB are an attractive objects for future studies of nonlinear optical properties.

VI. HOMO-LUMO ANALYSIS
The electronic absorption corresponds to the transition from the ground to the first excited state and is mainly described by one electron excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). The atomic orbital HOMO and LUMO compositions of the frontier molecular orbital for DFMB are shown in Figs.3. For CMB, the atomic orbital HOMO and LUMO compositions of the frontier molecular orbital are shown in Fig.4. The HOMO-LUMO energy gap of DFMB and CMB are calculated at B3LYP/6-311++G(d,p) levels and are shown in Table 7 and 8 respectively. It reveals that the energy gap reflects the chemical activity of the molecules. The LUMO, as an electron acceptor, represents the ability to obtain an electron, and HOMO represents the ability to donate an electron. Moreover, a lower HOMO-LUMO energy gap explains the fact that eventual charge transfer interaction is taking place within the molecules.

VII. OTHER MOLECULAR PROPERTIES
The thermodynamic properties like heat capacity, zero point energy, entropy along with the global minimum energy of DFMB and CMB are obtained by density functional method using 6-311++G(d,p) basis set calculations are presented in Tables 9 and  10 respectively. The difference in the values calculated by both the methods are marginal. Scale factors are recommended [17] for an accurate prediction in determining the zero-point vibration energy (ZPVE), and the entropy (S vib ). The variation in the ZPVE seems to be insignificant. The total energy and the change in the total entropy of the compounds at room temperature are also presented.

VIII. VIBRATIONAL SPECTRA
From the structural point of view, the molecules DFMB and CMB are assumed to have C s and C 1 point group symmetries, respectively. The 42 fundamental modes of vibrations, arising for DFMB are classified into 29A' and 13A" species. The A' and A" species represent the in-plane and out-of-plane vibrations, respectively. From the structural point of view, the molecule CMB is assumed to have C 1 point group symmetry and hence all the calculated frequency transforming to the same symmetry species (A). The molecule CMB consists of 16 atoms and expected to have 42 normal modes of vibrations. These modes are found to be IR and Raman active suggesting that the molecule possesses a non-centrosymmetric structure, which recommends the compound for non-linear optical applications. The observed FT-IR and FT-Raman spectra of DFMB and CMB are shown in Figs. 5-8. The detailed Vibrational assignment of fundamental modes of DFMB and CMB along with the calculated IR and Raman frequencies and normal mode descriptions (characterized by TED) are reported in Tables.11 and 12 respectively. The vibrational analysis obtained for DFMB and CMB with the unscaled B3LYP/6-31+G(d,p) force field are generally greater than the experimental values due to neglect of anharmonicity in real system. These discrepancies can be corrected either by computing anharmonic corrections explicitly or by introducing a scaled field or directly scaling the calculated wave numbers with proper factor [18]. A tentative assignment is often made on the basis of the unscaled frequencies by assuming the observed frequencies, so that they are in the same order as the calculated ones. Then, for an easier comparison to the observed values, the calculated frequencies are scaled by the scale to less than 1, to minimize the overall deviation. A better agreement between the computed and experimental frequencies can be obtained by using different scale factors for different regions of vibrations. For that purpose, different scaling factors for all fundamental modes are utilized to obtain the scaled frequencies of the compounds. The resultant scaled frequencies are also listed in Table 11 and 12.

C-H Vibrations
The C-H Stretching vibrations of benzene derivatives generally occur in the range 3100-3000 cm -1 . The in-plane C-H bending vibrations appear in the range 1300-1000 cm -1 in the substituted benzenes and the out-of-plane bending vibrations in the range 1000-750 cm -1 [19].  Tables 11 and 12.

C-C Vibrations
The C-C aromatic Stretching vibrations gives rise to characteristic bands in both the observed IR and Raman spectra, covering the spectral range from 1600 to 1400 cm -1 [19,20]. Therefore  Table 11. Further, the ring in-plane and out-of-plane bending vibrations are made for CMB by careful consideration of their qualitative descriptions and are reported in Table 12. The reductions in the frequencies of these modes are due to the change in force constant and the vibrations of the functional groups present in the molecules. The theoretically computed values for C-C vibrational modes of the compounds by B3LYP/6-311++G(d,p) method gives excellent agreement with experimental data.

C-F Vibrations
In the vibrational spectra of related compounds, the bands due to C-F Stretching vibrations [21] may be found over a wide frequency range 1360-1000 cm -1 since the vibration is easily affected by adjacent atoms or groups. In the present investigation, the FT-IR band observed at 1286, 1261 cm -1 is assigned to C-F Stretching mode of vibration for DFMB. The C-F in-plane vibrations of DFMB is found at 801 and 761 cm -1 in FT-IR and 810 cm -1 in Raman spectrum. The C-F out-of-plane deformation is also reported in the Table 11.

C-Cl Vibrations
The C-Cl Stretching vibrations generally yield strong bands in the region 760-505 cm -1 [22]. The FT-IR band observed at 768 cm -1 is assigned to C-Cl Stretching vibrations. Most of the aromatic chloro compounds have a band of strong-to-medium intensity in the region 385-265 cm -1 due to C-Cl in-plane bending vibrations. Accordingly, the FT-Raman band identified at 490 cm -1 is assigned to the C-Cl in-plane bending mode. The C-Cl out-of-plane deformation vibration is established at 410 cm -1 in FT-Raman spectrum.

CO Vibrations
The interaction of the carbonyl group with a hydrogen donor group does not produce drastic and characteristic changes in the frequency of the C=O stretch as done by OH stretch. A great deal of structural information can be derived from the exact position of the carbonyl Stretching absorption peak. Susi and Ard [23] identified the C=O Stretching mode at 1645 and 1614 cm -1 . On referring to the above findings and on the basis of the results of the normal coordinate analysis, the present investigation, the CO Stretching vibrations are found at 1318, 1298 cm 1 in FT-IR and 1320, 1290 cm 1 in FT-Raman for DFMB and for CMB, the FT-IR peaks observed at 1432, 1424 cm 1 are assigned for CO Stretching vibrations are confirmed by their TED values. The CO in-plane and out-of-plane bending vibrations level are also identified and presented in Tables 11 and 12 respectively for DFMB and CMB.

CH 3 group Vibrations
The investigated molecule under consideration possesses CH 3 groups in first position of DFMB and CMB third position of the ring. For the assignments of CH 3 group frequencies, one can expect that nine fundamentals can be associated to each CH 3 group, namely three Stretching, three bending, two rocking modes and a single torsional mode describe the motion of methyl group. The CH 3 symmetric Stretching frequency is identified at 2940 cm 1 in the FT-IR spectrum and 2935 cm 1 in the FT-Raman spectrum for DFMB and 2940 cm 1 in the FTIR spectrum for CMB. The CH 3 in-plane bending vibrations are identified at 2912 cm 1 in the FTIR spectrum for DFMB and 2960 cm 1 in FT-Raman spectrum and 2963cm 1 in the FT-IR spectrum for CMB. The CH 3 symmetric bending and CH 3 in-plane bending frequencies are attributed at 1205 cm -1 in FT-Raman and 1219 cm 1 in the FT-IR spectrum for DFMB respectively and 1183 cm -1 and 1232 cm 1 in the FT-IR spectrum and 1240 cm 1 FT-Raman spectrum for CMB respectively. These assignments are supported by literature [24]. The in-plane rocking and out-ofplane rocking modes of CH 3 group are found at 761 cm -1 and 718 cm -1 in the FTIR spectrum for DFMB respectively, and the peaks observed at 846cm -1 in the FTIR and 740 cm -1 in FT-Raman spectrum for CMB. The bands obtained at 2844 cm -1 and 2850 cm 1 in the FTIR and FT Raman spectrum and 1190 in FT-Raman spectrum for DFMB and at 2908 cm -1 and 1168 cm -1 in the FTIR for CMB are assigned to CH 3 out-of-plane stretching and CH 3 out-of-plane bending modes, respectively. The assignment of the bands at 250 cm 1 in the FT Raman spectrum for DFMB and 203 cm -1 FT-Raman spectrum for CMB are attributed to methyl twisting mode.

IX. CONCLUSION
The optimized geometries, harmonic vibrational wave numbers and intensities of vibrational bands of 2,4-difluoro-1-methoxybenzene (DFMB) and 1-chloro-3-methoxy benzene (CMB) are determined using DFT/B3LYP method with 6-311++G(d,p) level calculations. The normal modes of the compounds have been studied by FT-IR and FT-Raman spectroscopies based on scaled quantum chemical calculations. The systematic comparison of the results from DFT theory with results of experiments has shown that the method using B3LYP functional is the most promising in providing correct vibrational wavenumbers. On the basis of the agreement between the calculated and experimental results, assignments of all the fundamental vibrational modes of DFMB and CMB are made in this investigation. The difference between the observed and scaled wave number values of most of the fundamentals are very small. The TED calculation regarding the normal modes of vibration provides a strong support for the frequency assignment. Furthermore, the thermodynamic, nonlinear optical, first-order hyperpolarizability and total dipole moment properties of the compounds are calculated in order to get insight into the compounds. These results will be of assistance in the quest of the experimental and theoretical evidence for DFMB and CMB in reaction intermediates, nonlinear optical and photoelectric materials.    C-C  C1-C2, C2-C3, C3-C4, C4-C5, C5-C6, C6-C1   7-8  R i  C-O  C1-O7, C8-  a These symbols are used for description of normal modes by TED in Table 11 b The internal co-ordinate used here are defined in Table 3. a These symbols are used for description of normal modes by TED in Table 12 b The internal co-ordinate used here are defined in Table 4.     Abbreviations: stretching; sssymmetric stretching; assasymmetric stretching; bbending; out-of-plane bending; Rring; trigdtrigonal deformation; symdsymmetric deformation; asymdantisymmetric deformation. Abbreviations: stretching; sssymmetric stretching; assasymmetric stretching; bbending; out-of-plane bending; Rring; trigd -trigonal deformation; symdsymmetric deformation; asymdantisymmetric deformation.