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. We have done a comparative study of tetrahydrofuran and its derivatives with B3LYP with 6-311 G (d, p) as the basis set. Here we 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 orbital HOMO-LUMO surfaces and molecular electrostatic potential surfaces to explain the reactive nature of tetrahydrofuran and its derivatives.
Tetrahydrofuran (THF) is an organic compound with the formula (CH2)4O. The compound is classified as heterocyclic compound, specifically a cyclic ether. It is a colorless, water-miscible 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 . 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 .
As a part of our ongoing research work [7–9], 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.
2. Experimental and Computational Methods
2.1. Structure and Spectra
The molecular structures of the tetrahydrofuran (THF) and its derivatives are made by molecular modeling. The model molecular structures of tetrahydrofuran (THF) and its derivatives are given in Figure 1. 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 .
2.2. Computational Methods
All the calculations were performed by the B3LYP [11, 12] method using the 6-311 G (d, p) basis set of density functional theory . All computations were carried out with the GAUSSIAN 09 package . By combining the results of the GAUSSVIEW’S program  with symmetry considerations, vibrational frequency assignments were made with a high degree of accuracy. Vibrational frequencies for these molecules were calculated with these methods and then scaled by 0.9613 .
3. Results and Discussion
3.1. Geometry Optimization
Alternate dispositions of amino groups have been studied, but finally we get these five optimized structures of THF derivatives. Optimized parameters of tetrahydrofuran (THF) and its derivatives (amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran) calculated by B3LYP method with 6-311 G (d, p) basis set are listed in Table 1 in accordance with the atom numbering scheme as shown in Figure 1. Local minimum energies are −232.5134 a.u, −287.8832 a.u, −343.2555 a.u, −398.6109 a.u, and −453.9997 a.u., for tetrahydrofuran (THF), amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran, respectively. Tetrahydrofuran (THF) and all its derivatives have C1 point group symmetry. The amino groups attached to all derivatives do not lie in the plane of ring and alternatively they are in the opposite direction to each other.
For tetrahydrofuran (THF) and its derivatives, C–C bond distances are found to be in the range of 1.542–1.553 Å, 1.529–1.543 Å, 1.529–1.552 Å, 1.540–1.542 Å, and 1.532–1.549 Å while, for C–N (except THF), these values are 1.443 Å, 1.438–1.467 Å, 1.435–1.461 Å, and 1.428–1.462 Å, respectively, for amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran. For C–O, these values are 1.423 Å, 1.434 Å, 1.429 Å, 1.431 Å, and 1.435–1.462 Å, respectively, for THF, amino tetrahydrofuran, 1,2-diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran. In case of C–H bond distances, they lie in the range of 1.091–1.101, 1.093, 1.092–1.094, 1.097–1.102, and 1.096–1.101, respectively. In the literature, bond lengths for THF-water complex  have a little bit lower values of 1.527–1.537 Å (for (C–C)) and a little bit higher values of 1.443–1.446 Å (for (C–O)). This may be due to shifting of charge in interaction of THF with water molecule. Optimized structures of tetrahydrofuran and its derivatives by B3LYP/6-311 G (d, p) method are shown in Figure 1.
3.2. Assignment of Fundamentals
Tetrahydrofuran has 13 atoms with 33 normal modes of vibration while amino tetrahydrofuran has 15 atoms with 39 normal modes of vibration. 1,2-Diamino tetrahydrofuran, 1,2,3-triamino tetrahydrofuran, and 1,2,3,4-tetra-amino tetrahydrofuran have 17, 19, and 21 atoms with 45, 51, and 57 normal modes of vibration, respectively. From our calculated data and experimental FTIR spectra, we observe similarities and differences between the experimental and the calculated frequencies by DFT/B3LYP method. Assignments are done using the animated view of normal mode description. A good agreement is found between the theoretical and experimental data. 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.
3.3. Vibrational Modes Description
3.3.1. 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 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.
3.3.2. N–H Vibrations
There is no NH2 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 NH2 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  as given in Table 2.
3.3.3. 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 . Knowledge of low frequency mode is also essential for the interpretation of the effect of electromagnetic radiation on biological systems . 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.
3.4. Electrical, Optical, Dipole Moment and Thermodynamical Properties
Frontier orbital energy gap, that is, the gap between HOMO and LUMO, shows the interaction of that molecule with other species. Frontier orbital energy gap helps to differentiate the chemical reactivity of the molecules. In case of tetrahydrofuran and its derivatives, frontier orbital energy gap is 7.9402, 6.9066, 6.8312, 6.4991, and 6.8870 eV, respectively, and is given in Table 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: The components of Gaussian output are reported in atomic units.
Where 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, 1,2,3-triamino 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 , 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.
3.5. Reactivity Descriptors
3.5.1. Global Reactivity Descriptors
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.
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 qualitative descriptors of reactivity of different atoms in the molecule. A study by Ayers and Parr  has shown that FF is larger when attacked by soft reagents and in places where the FF is smaller when attacked by hard reagents. Fukui functions for electrophilic and nucleophilic attacks have been made with the basis of B3LYP/6-311 G (d, p) level of theory. With the help of Mulliken atomic charges of cationic and anionic states, local Fukui functions , local softness values , and local electrophilicity indices have been calculated using the following equation: Local softness values and electrophilicity indices are calculated using where + and − signs show nucleophilic and electrophilic attack, respectively.
Fukui functions, local softness values, and local electrophilicity indices for selected atomic sites in tetrahydrofuran and its derivatives have been listed in Tables 7 and 8. For amino hydrofuran, the maximum value for local nucleophilic reactivity descriptors at N13 indicates that this site is more prone to electrophilic attack. But in comparison with N16 of 1,2,3,4-tetra-amino hydrofuran it is found that the N16 of 1,2,3,4-tetra-amino hydrofuran has lower affinity towards electrophile as given in Table 11. This situation changes because of change of position of the nitrogen of 1,2,3,4-tetra-amino hydrofuran, and hence the charge density around N16 decreased.
All calculated wave numbers are real in nature for all the molecules and thus all the compounds are stable. We have done density functional calculations on tetrahydrofuran and its derivatives. The calculated parameters (bond lengths and band angles) and wave numbers show a good agreement with the corresponding experimental data showing the strength of density functional calculations. Normal modes are discussed in detail with the help of Gauss view program. The chemical reactivity of molecules shows the supremacy of 1,2,3-triamino tetrahydrofuran over the remaining molecules. A possible use of these compounds in electrooptical applications is discussed with the help of hyperpolarizability. In addition, to assess the utility of global reactivity descriptors, the relationships between the reactivity and electrophilicity have been discussed. THF configuration possesses higher electronegativity while 1,2,3-amino THF possesses lower electrophilicity index among them all. Correlations have been found between electrophilicity of various chemical compounds and reaction rates in biochemical systems.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Abhishek Bajpai is thankful to University Grants Commissions, New Delhi, for its financial assistance. The corresponding author is also grateful to Professor Neeraj Misra for providing valuable suggestions.
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