Fukui Function Analysis and Optical, Electronic, and Vibrational Properties of Tetrahydrofuran and Its Derivatives: A Complete Quantum Chemical Study

The spectroscopic, optical, and electronic properties of tetrahydrofuran and its derivatives were investigated by FTIR techniques. Wehave done a comparative study of tetrahydrofuran and its derivatives with B3LYPwith 6-311G (d, p) as the basis set. Herewe have done a relative study of their structures, vibrational assignments, and thermal, electronic, and optical properties of ttetrahydrofuran and its derivatives.We have plotted frontier orbitalHOMO-LUMOsurfaces andmolecular electrostatic potential surfaces to explain the reactive nature of tetrahydrofuran and its derivatives.


Introduction
Tetrahydrofuran (THF) is an organic compound with the formula (CH 2 ) 4 O.The compound is classified as heterocyclic compound, specifically a cyclic ether.It is a colorless, watermiscible organic liquid with low viscosity.THF has an odor similar to acetone.Being polar and having a wide liquid range, THF is a versatile solvent.THF is often used in polymer science.For example, it can be used to dissolve polymers prior to determining their molecular mass using gel permeation chromatography.THF is also a starting material for the preparation of tetrahydrothiophene.In the presence of a solid acid catalyst, it reacts with hydrogen sulfide.THF is frequently utilized as a solvent in many pharmaceutical synthetic procedures because of its good solvency for polar and nonpolar compounds.THF is particularly capable of dissolving many ionic species and organometallics which are commonly used in specialty syntheses.In many cases, THF makes higher yields and faster reaction rates possible.In addition, THF's high volatility and very high purity facilitate solvent removal and recovery without leaving residues in the desired product [1,2].Tetrahydrofuran (THF) is a synthesized organic compound that is not found in the natural environment.THF is highly flammable and upon thermal decomposition may form carbon monoxide and carbon dioxide.Under certain conditions, such as prolonged storage in contact with air, THF can decompose into explosive peroxides [3].THF can also be synthesized by catalytic hydrogenation of furan [4,5].THF has been explored as a water-based cosolvent to aid in the deconstruction and delignification of plant lignocellulosic biomass, which are relevant to the production of renewable platform chemicals and sugars.THF is used as a component in mobile phases for reversed-phase liquid chromatography.It has a greater elution strength than methanol or acetonitrile but is less commonly used than these solvents [6].
As a part of our ongoing research work [7][8][9], we report the comparative study of tetrahydrofuran (THF) and its derivatives by DFT study.To the best of our knowledge no comparative quantum chemical calculations of these molecules have been reported so far in the literature.We have taken the infrared spectrum of tetrahydrofuran (THF) from literature which was recorded with FTIR Perkin Elmer spectrometer in KBr dispersion in the range of 500 to 4000 cm −1 for the title molecule as shown in Figure 3 [10].

Results and Discussion
Here we are discussing only important modes.Vibrational frequencies, calculated for tetrahydrofuran and experimental frequencies (FTIR), have been compared in Table 2.We are also discussing the assignments for tetrahydrofuran derivatives which are useful for the experimentalists in absence of its experimental data.2. In vibrational assignments, the C-H stretching vibrations are in the same range for all derivatives of tetrahydrofuran listed in Tables 3, 4, 5, and 6.

N-H Vibrations.
There is no NH 2 group added to tetrahydrofuran but they are presented in all derivatives of tetrahydrofuran.The N-H stretching vibrations are normally viewed in the region 3300-3600 cm −1 .For amino tetrahydrofuran, the N-H stretching vibration is calculated at 3462 cm −1 while it is 3446 cm −1 for 1,2-diamino tetrahydrofuran.A strong scissoring vibration of H-N-H is found at 1586 and 1584 cm −1 for amino tetrahydrofuran and 1,2-diamino tetrahydrofuran, respectively.In case of 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran, the N-H vibration is at 3447 and 3354 cm −1 in calculated spectra.There are also strong scissoring vibrations at 1587 and 1588 cm −1 for 1,2,3-triamino tetrahydrofuran and 1,2,3,4-tetra-amino tetrahydrofuran.Some strong rocking and twisting vibrations of NH 2 are also seen in the assignment of all derivatives of tetrahydrofuran.We see that scissoring modes in THF are lower than all the derivatives of THF.This is due to the addition of amino group (charge transfer) to THF molecule.The interpretation of vibrational spectra of THF is in good agreement with the literature [18] as given in Table 2.

Other Modes of Vibration.
In tetrahydrofuran, a ring deformation mode is calculated at 1056 cm −1 which is in good agreement with experimental data, that is, 1055 cm −1 , while in all derivatives of tetrahydrofuran (except the last one) ring deformation mode is at 1028, 1028, and 1036 cm −1 having appropriate IR intensity.As expected, torsion modes along with wagging modes appear in the lower frequency range.For tetrahydrofuran, strong torsion mode of C-O-C-C is at 628 cm −1 in calculated spectrum which matches well with the experimental one, that is, 625 cm −1 , while strong torsion modes of C-C-C-C are at 725 and 474 cm −1 in calculated spectrum for 1,2-di-ATHF and 1,2,3-tri-ATHF, respectively.A very strong stretching vibration of C-O is found at 981 cm −1 while there is also a strong torsion mode of C-C-C-O at 731 cm −1 in calculated spectra for 1,2,3,4-tetra-ATHF.There are some frequencies in lower region having appreciable IR intensity.Furthermore, the study of low frequency vibrations is of great significance, because it gives information on weak intermolecular interactions, which take place in enzyme reactions [19].Knowledge of low frequency mode is also essential for the interpretation of the effect of electromagnetic radiation on biological systems [20].The aim of vibrational analysis is to acquire direct information on lower and higher frequency vibrations of such THF and its derivatives.No experimental FTIR spectrum is available for comparison of derivatives of THF so it will provide a suitable path for experimental researchers.7.So it can be concluded that 1,2,3-triamino tetrahydrofuran is the most reactive compound among all.The pictures of HOMO, LUMO, and electrostatic potential (MESP) for tetrahydrofuran and its derivatives are shown in Figure 2. Dipole moment (), polarizability ⟨⟩, and total first static hyperpolarizability  [21,22] can be expressed in terms of , ,  components and are given by the following equations: .
(1) The  components of Gaussian output are reported in atomic units.
Where 1 a.u.= 8.3693 * 10 −33 e.s.u., the calculated dipole moments for tetrahydrofuran and its derivatives are 1.585, 2.855, 1.667, 4.022, and 1.743 Debye, respectively.So, 1,2,3triamino tetrahydrofuran is a better solvent among them all.A greater contribution of   is seen in THF, amino THF, and 1,2,3-triamino THF while   is seen in 1,2-diamino THF and   in 1,2,3,4-tetra-amino THF.For THF and 1,2,3-triamino THF, molecules are elongated more towards  direction and more contracted in the  direction while amino THF molecule is elongated more towards  direction and more contracted in the  direction.For 1,2-diamino THF, molecule is elongated more towards  direction and more contracted in the  direction while 1,2,3,4-tetra-amino THF molecule is elongated more towards  direction and more contracted in the  direction.It is seen that the components   ,   ,   ,   , and   contribute lager part of hyperpolarizability from THF to 1,2,3,4-tetra-amino THF.This shows that     and  planes and and -axes are more optically active in these directions.The values of hyperpolarizability indicate a possible use of these compounds in electrooptical applications.
Internal thermal energy (), constant volume heat capacity  V , and entropy , calculated at B3LYP/6-311 G (d, p) level, are listed in Table 9.We know that conduction band is almost empty at the room temperature, so electronic contribution in total energy is negligible.All the thermodynamic data supplies helpful information for the further study on the THF and its derivatives.They can be used to compute the other thermodynamic energies according to relationships of thermodynamic functions and estimate directions of chemical reactions according to the second law of thermodynamics in the thermochemical field.So thermodynamic properties show that vibrational motion plays an important role.
According to these parameters, the chemical reactivity varies with the structural configuration of molecules.Chemical hardness (softness) value of 1,2,3-amino THF is lesser (greater) among all the three molecules.Thus, 1,2,3-amino THF is found to be most reactive among all, whereas THF configuration is less reactive.THF configuration possesses higher electronegativity while 1,2,3-amino THF possesses lower electrophilicity index among them all as given in Table 10.Correlations have been found between electrophilicity of various chemical compounds and reaction rates in biochemical systems.

Figure 2 :
Figure 2: Pictures of HOMO-LUMO and molecular electrostatic potential of tetrahydrofuran and its derivatives.

3. 6 .
Local Reactivity Descriptors.Fukui function (FF) provides information on the local site reactivity within the molecule and as such it provides a system for understanding of chemical reactions.These values correspond to the
3.3.Vibrational Modes Description3.3.1.C-H Vibrations.We have seen in the literature that the C-H stretching vibrations are usually observed in 2800-3200 cm −1 region.In the study of tetrahydrofuran, the (C-H) functional group is present at 2848, 2854, 2939, 2949, 2968, 2983, and 2995 cm −1 in calculated spectra which is in good agreement with the experimental data as given in Table