Thermodynamic Functions Molecular Polarizability of 2 , 6-dichloro-4-fluoro Phenol

The Laser-Raman and FT-IR spectra of 2,6-dichloro-4-fluoro phenol (2,6,4-DCFP) have been recorded. The thermodynamic functions, namely, the enthalpy, the heat capacity, the free energy and entropy of 2,6,4-DCFP have been calculated at a pressure of 1 atmosphere in the temperature range 200-1500 K under rigid rotor harmonic oscillator. The one-dimensional semi-empirical delta-function model of chemical binding has been used to evaluate the average molecular polarizability of 2,6,4-DCFP.


INTRODUCTION
Phenol has been the subject of numerous studies, since it is a good model for the investigation of hydrogen bonding and proton transfer in enzymes and other systems containing aryl alcohols [1].Phenol and its derivatives have been widely used as starting material in a vast amount of pharmaceutical, agriculture and many other industrial processes.The understanding of their molecular properties as well as nature of reaction mechanism they undergo has great importance.Hence, the investigation on structures, and the vibrations of phenol and substituted phenols are still being carried out, increasingly.The inclusion of a substituent group in phenol leads to the variation of change distribution in molecule, and consequently, this greatly affects the structural, electronic and vibrational parameters [2,3].
Due to the great biochemical importance the vibrational spectral studies of 2,6,4-DCFP have been carried out in present investigation.Knowledge of the thermodynamic functions is of great importance to study the chemical kinetics and chemical equilibrium of the system.The direct experimental measurement of these quantities is usually tedious and may not be reliable.Molecular polarizability are important for the evaluation of several kinetic aspects of positive ion chemistry.Semi-empirical approaches are of considerable interest for studying the molecular structure and properties of organic compounds [4].Molecular polarizability is considered to be one of the important properties of hydrocarbons in view of the structural application [5].The survey of literature indicates that no work have been reported on, thermodynamic functions and molecular polarizability of title compound.

EXPERIMENTAL SECTION
The spec-pure compound 2,6,4-DCFP was obtained from M/s Aldrich Chemie, West Germany and used as such.The purity of the compound was confirmed by elemental analysis and melting point determination.The FTIR absorption spectrum of the compound was recorded at room temperature in the region 400-4000 cm -1 , at a resolution of 4 cm -1 with scanning speed 2 mm per second using Perkin Elmer spectrophotometer model FT/IR-4100 type A, equipped with TGS detector using KBr pellet and Nujol Mull.Laser-Raman spectrum was recorded on spex Rama Lab spectrophotometer using 52 MW argon-krypton laser of wavelength 488 nm.

RESULT AND DISCUSSION
The molecular structure of 2,6,4-DCFP is shown in  The corrected wave numbers together with their probable assignments are presented in Table 1.The structure parameters and statistically computed thermodynamic functions viz the enthalpy, the free energy, the heat capacity and entropy are presented in Table 2 and Table 3 respectively 4.

Thermodynamic Functions Analysis
The total energy (E) of a system of molecules is given as And total partition function (Q) can be expressed as the product of the individual partition function. Hence, Where the subscripts trans, rot, vib and elect stands for translation, rotational, vibrational and electronic respectively.Also Where gi is the statistical weight of the i-th energy level [21], k is the Boltzmann constant and T is the absolute temperature.Contribution of each partition function may be evaluated separately and then added to the corresponding thermodynamic functions to obtain the total values.The electronic contribution is small and hence ignored.This is because elec is large in comparison to kT at ordinary temperature.The various equations used in computation of various partition functions and their contribution to different thermodynamic functions are given by Heizberg [22].The entropy function represents the total energy stored in a system and the entropy is regarded as a measure of randomness in a system.
Thermodynamic functions viz enthalpy, heat capacity, frequency and entropy of the said compound have been computed using the standard expression [20] by z-axis perpendicular to the molecular plane and y-axis to pass through the para position.For determining the rotational contribution the following structural parameters are given in Table (2) were used [22][23][24].Where C1 to C6 are carbon atoms of phenol ring.O is the atom of phenol.Cl1 and Cl2 are chlorine atoms.
The thermodynamic functions have been calculated with the help of computer program at different temperatures 200-1500 K using fundamental frequencies and assuming the rigid rotor-harmonic oscillator approximation.The symmetry number for overall rotation is three.The principal moments of inertia are found to be, 0.8189, 1.0799 and 1.8988 x 10 -37 gm cm 2 respectively.
The various thermodynamic functions computed for 2,6,4-DCFP have been given in Table (3).It is found that the thermodynamic functions rise more rapidly in the low temperature range and less rapidly in the high temperature range.The variation of these thermodynamic functions with temperature is in good agreement with the trend reported in literature [24][25][26].

Molecular Polarizability
Molecular polarizability is composed of bond parallel and perpendicular components.The bond parallel component is obtained from the contribution of two sources, namely the bond region and non-bond region electron.The contribution by the bond region electrons is calculated by -function wave functions, represented by the two nuclei in the bond.This is the expectation value of the electronic position squared along the bond axis and is used to compute the bond parallel components of the polarizability IIb from the expression; where n is the bond order and Aij is the root mean square -function strength of the nuclei i and j involved in the bond ij .The expectation value <X 2 > is evaluated from the relation; where Rij is the internuclear distance and CRij=(ni nj Ni Nj) 1/4 (AiAj) 1/2 .Here ni, Ni and nj , Nj represent the principal quantum number and the number of electrons contributing to the bonding in atoms i and j respectively.where Ai and Aj are deltafunction strengths for atoms i and j respectively.For a heteronuclear bond, a polarity correction is introduced using Pauling's scale [27] of electronegatively to determine the percent covalent character; accordingly, the expression with polarity correction is given as; Where Xi and Xj are electronegativities of the atoms i and j respectively on the Pauling's scale.
The contribution of the non-bond region electrons to the bond parallel component of the polarizabilities is calculated from the fraction of remaining electrons not involved in the bonding and the electronic polarizabilities of the atom concerned.This is analytically expressed as where fi is the fraction of electrons in the i th atom not involved in the bonding and i the atomic polarizability of the atom i, obtainable from the -function strength Ai.
The sum of the bond perpendicular components of the bond polarizability is obtained by an empirical approach made by Lippincott and Stutman [28], which is given by the expression : Where N is the number of atoms in the molecule and nb the number of bonds in the molecule.The term (3N-2nb) gives the number of residual atomic polarizability degrees of freedom, denoted by ndf.This is obtained by the knowledge of the symmetry of the geometry of the molecular system.Now the analytical expression for the mean polarizabilities for a polyatomic molecule with polarity correction is given by: The bond parallel component of molecular polarizability of 2,6,4-DCFP is calculated by using equation ( 6) and the bond lengths in the molecule presented in Table 2.The contribution of the nonbond region electrons to the bond parallel component of polarizability of said molecule and bond perpendicular component are calculated by using equation ( 7) and (8).Molecular polarizability of the title compound is presented in Table 4.The result have been compared with the experimental values wherever available and discussed.It has been observed that the model is good for computation of such data and definite trend exists in the variation of M for the molecule of particular series [29,30].

CONCLUSION
A satisfactory vibrational band assignment of 2,6,4-DCFP was made with FT-IR in KBr pellet, Nujol Mull solution and Laser-Raman spectra.The observed vibrational frequencies are used to compute the thermodynamic functions in temperature range 200-1500 K at an increment of 100 K.The calculated values of thermodynamical function indicate that the stability of the molecule decreases as the temperature increases.The result of present study show that the deltafunction model can be used for the calculations of average molecular polarizabilities for a wide variety of inorganic and organic molecules and complex metal carbonyls, etc.
The fundamental vibrational frequencies have been utilized to calculate the various thermodynamic function, namely the enthalpy function [H0-E 0 0] ,the heat capacity [Cp0] ,the free energy function [-(F0-E 0 0)] and entropy function (S0) in the temperature range 200-1500K at 1 atmospheric pressure.

Fig 1 .
Laser-Raman spectrum of 2,6,4-DCFP is shown in Fig 2 while FT-IR absorption spectra using KBr pellets technique and using Nujol mull is shown in Fig 3 and Fig 4 respectively .
. The variation of enthalpy function and heat capacity function with absolute temperature is shown in Fig 5, while the variation of the free energy and entropy with absolute temperature is shown in Fig 6.The calculated values of molecular polarizabilities of 2,6,4-DCFP have been presented in Table According to the theoretical calculations, title molecule belong to Cs point group symmetry, and its 26 fundamentals are distributed amongst the symmetry species as T=19 A I +7 A I I A I are in plane and A I I are out of plane vibrations The vibrational assignments have been made essentially on the basis of magnitude and relative intensities of the Laser-Raman, FT-IR bands and available for similar molecules.