Vibrational Spectroscopy Investigation Using Ab Initio and Density Functional Theory Analysis on the Structure of tert-Butyl 3 a-Chloroperhydro-2 , 6 a-epoxyoxireno [ e ] isoindole-5-carboxylate

e molecular structure, vibrational frequencies, and infrared intensities of the tert-butyl 3a-chloroperhydro-2,6a-epoxyoxireno[e]isoindole-5-carboxylate were calculated by the HF and DFT (BLYP and B3LYP) methods using 6-31G(d) and 6-31G(d,p) basis sets. e FT infrared spectrum of the solid sample was measured under standard condition. We obtained two stable conformers for the title compound; however Conformer 1 is approximately 0.2 kcal/mol more stable than the Conformer 2. e comparison of the theoretical and experimental geometry of the title compound shows that the X-ray parameters fairly well reproduce the geometry of Conformer 2. Comparison of the observed fundamental vibrational frequencies of the title molecule and calculated results by HF and DFTmethods indicates that B3LYP is superior for molecular vibrational problems.e harmonic vibrations computed by the B3LYP/6-31G(d,p) method are in a good agreement with the observed IR spectral data. eoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions (PEDs) using VEDA 4 program.


Introduction
Epoxides are used as an important intermediate tool in organic synthesis of �ne chemicals and pharmaceuticals [1].Intramolecular Diels-Alder (IMDA) reactions and epoxidation of its cycloadduct have also been of great interest in synthetic pathway of natural products, like conduritols [2], z-isomeric insect sex pheromone components [3], dihydrophenanthroline derivatives [4], vitamin D total synthesis [5], and so on.We have previously prepared a variety of key precursors to the intramolecular Diels-Alder reaction of furan (IMDAF) diene via facile alkylation of furan compounds and its protection.Subsequently IMDAF reaction carried out under thermal condition provided �ve-and sixmembered heterocycles fused to an easily cleavable oxabicycloheptene moiety [6][7][8][9].
e crystal structure of tert-butyl 3a-chloroperhydro-2,6a-epoxyoxireno[e]isoindole-5-carboxylate (TBCEIC) has been determined by X-ray diffraction [10], however so far no ab initio studies have been made on the conformation and vibrational spectra of the title compound in the gas phase.
In the present study, we have synthesized and calculated the vibrational frequencies and geometric parameters of TBCEIC in the ground state to distinguish the fundamentals from the experimental vibrational frequencies and geometric parameters, by using the Hartree-Fock [11] and density functional using B3LYP [12,13] and Becke's exchange functional in combination with the Lee, Yang, and Parr correlation functional methods [13,14] (BLYP) with the standard 6-31G(d) and 6-31G(d,p) basis sets.In continuation of our theoretical studies, in the present work, we checked the relative performance of B3LYP and BLYP methods, as well as of HF for comparison, at the 6-31G(d) and 6-31G(d,p) levels taking as a test compound tert-butyl 3a-chloroperhydro-2,6a-epoxyoxireno[e]isoindole-5-carboxylate.

Results and Discussion
2.1.Conformational Stability.We performed full geometry optimization of the title compound.To establish the most stable conformation as the initial point for further calculations, the molecule was submitted to a rigorous conformation analysis around all bonds having free rotation.is study was performed with the soware Spartan 06 [15,16].e structure of the title compound has two conformations which are shown in Figure 1.For comparison, the total energy and the relative energies of both conformer of the title compound are given in Table 1.Energetics show that Conformer 1 is the most stable.But comparison of the theoretical and experimental geometry of the title compound shows that the X-ray parameters fairly well reproduce the geometry of Conformer 2. erefore, we will focus on this particular form (Conformer 2) of the title compound in this paper.

Molecular
Geometry.e optimized structure parameters of the title compound calculated by ab initio and DFT method listed in Table 2 are in accordance with atom numbering scheme given in Figure 2(a).e crystal and molecular structure of the title compound have been reported previously [10].e geometric structure is monoclinic, the space group P2 1 /c, with the cell dimensions:   111 Å,    Å,   1 Å,   1 ∘ , and   1 Å  (Figure 2(b)).e structure parameters obtained by X-ray single-crystal diffraction method are given in Table 2. Also, Table 2 compares the calculated geometric parameters with the experimental data.
Based on this comparison, the bond lengths and angles calculated for the title compound show good agreement with experiment.However, according to our calculations, the optimized both bond lengths and bond angles obtained by DFT methods show the best agreement with the experimental values.e large difference between experimental and calculated DFT/B3LYP-6-31G(d,p) bond length and bond angle is 0.065 Å and 1.65 ∘ , respectively.compound are gathered in Table 3. e last column of Table 3 shows the detailed vibrational assignment obtained from the calculated potential energy distribution (PED).

Vibrational Assignments.
Comparison of the frequencies calculated at HF, BLYP, and B3LYP with experimental values reveals the overestimation of the calculated vibrational modes due to neglect of anharmonicity in real system.Inclusion of electron correlation in density functional theory to a certain extent makes the frequency values lower in comparison with the Hartree-Fock frequency data [17][18][19][20].Reductions in the computed harmonic vibrations, though basis set sensitives are only marginal as observed in the DFT values using 6-31G(d) and 6-31G(d,p).Any way notwithstanding the level of calculations, it is customary to scale down the calculated harmonic frequencies in order to improve the agreement with the experiment [17][18][19][20].erefore, the scaling factor values of 0.8953/0.8992,0.9614/0.9614,and 0.9945/1.0072for HF, B3LYP, and BLYP (6-31G (d)/6-31G(d,p)), respectively, are used in our study [17,[21][22][23][24][25].Experimental fundamentals are in better agreement with the scaled fundamentals which are found to have a good correlation for DFT/B3LYP/6-31G(d,p) (  ) than HF method.e calculated frequencies (scaled) do not differ so much from the experimental ones that the maximum difference between two spectra is not more than 27 cm −1 for DFT/B3LYP/6-31G(d,p) method.Also, the average absolute error of the calculated frequencies was found less than 0.86% for DFT/B3LYP/6-31G(d,p) method.
A general better performance of B3LYP and BLYP versus HF can be quantitatively characterized by using the mean deviation, mean absolute deviation, average absolute error, root mean square values, and coefficients of correlation () between the calculated and observed vibration frequencies and given in Table 3.All these values were calculated in this study by the PAVF 1.0 program [26] according to Scott and Radom [21].e root mean square (RMS) values were obtained in this study using the following expression [21]: e  values for both DFT methods were greater than 0.9998, whereas for HF it was 0.9997.ese values are very     close to those reported in the literature [27][28][29][30][31][32][33].ese results indicate that the B3LYP calculations approximate the observed fundamental frequencies much be better than the HF results.e small difference between experimental and calculated vibrational modes is observed.It must be due to the fact that hydrogen bond vibrations present in crystal lead to strong perturbation of the infrared frequencies (and intensities) of many other modes.Also, we state that the experimental results belong to solid phase and theoretical calculations belong to gaseous phase [17,19,20,[23][24][25][30][31][32][33][34].
Finally, we calculated the optimal scaling factors, which are crucial for IR spectral predictions, using the PAVF 1.0 program [26].Without accounting for different vibrations, only single-uniform scaling factors were calculated.e values obtained are 0.8974/0.9024,0.9587/0.9612,and 0.9891/0.9906for the HF, B3LYP, and BLYP (6-31G(d)/6-31G(d,p)) methods, respectively.ey are very close to those recommended by Scott and Radom [21] for the same levels of theory and increase in the same order of the HF, B3LYP and BLYP methods.us, for future IR spectral predictions for unknown derivatives of the title compound, one can recommend scaling factors of 0.897/0.902,0.959/0.961,and 0.989/0.991for the HF, B3LYP, and BLYP (6-31G(d)/6-31G(d,p)) methods, respectively.
e IR bands at 3082, 3067, and 3010 cm −1 in FT-IR spectrum of the title compound have been designated to CH stretching fundamentals of C20, C25, and C19 atoms, respectively [23,35,36].e wavenumbers corresponding to the aliphatic CH stretching are listed in Table 3.All the calculated values in each method are overestimated, as well known in theoretical quantum mechanic assignment concerning hydrocarbons.Aer we applied the scale factor both calculated in this research and given by Scott and Radom [21] for all the methods, we observed a good concordance between the experimental and the calculated values.e vibrational spectra show six bands in the aliphatic CH stretching region and evident overlap between the different C-H stretching modes.e asymmetric and the symmetric C-H stretching bands for -CH 2 -group are listed in Table 3. ese assignments were also supported by the literature [20,23,35,37].e in-plane and out-of-plane bending vibrations of C-H group have also been identi�ed for the title compound and they are presented in Table 3.
e carbonyl stretching vibrations are found in the region 1780-1700 cm −1 [38,39].e sharp intense band in IR spectrum at 1686 cm −1 can be assigned to the carbonyl group C=O stretching vibration.
e vibrational modes concerning the bond angle bending (-CH 2 -), scissoring, wagging, twisting, and rocking are well de�ned in all the calculations.As seen from Table 3, the bands observed at 1460, 1451, and 1431 cm −1 in FT-IR spectrum correspond to scissoring deformation of -C(18)H 2 -, -C(22)H 2 -and -C(24)H 2 -group in the title compound, respectively [37,40].e theoretically computed values of scissoring deformation vibration modes show a good agreement with the experimental values.e wagging, twisting, and rocking vibrational modes are distributed in a wide range [36,37,40,41].Twisting and wagging vibrational modes of the -CH 2 -groups were assigned in the range of 1350-1163 cm −1 .e above result is in close agreement with the literature values [36,37,[40][41][42]. ese vibrational modes are described in the tables by mean of the general symbol CH 2 .e rocking -CH 2 -is assigned in the wavenumber range of 1109-852 cm −1 , and the wavenumber shi of these bands is due to the atom nature in which the -CH 2 -group is bonded.e -CH 2 -rocking vibrational modes are generally intensive bands which can be appreciating the vibrational coupling with other vibrational modes [36,37].ese bands are assigned using calculated potential energy distribution.
For the assignments of CH 3 group frequencies, 15 fundamental vibrations can be associated to CH 3 groups.Nine stretching, three umbrella, and three rocking vibration modes are designated the motion of the methyl group.e CH 3 asymmetric and symmetric stretching frequencies are established at 3067, 3010, 3003, and 2923 cm −1 in infrared spectrum.e three methyl hydrogen deformation modes are also well established in the spectrum.We have observed the methyl deformation mode at 1474, 1451, 1431, and 1409 cm −1 in the infrared spectrum.
e C-C stretching vibrations in cyclic alkanes appeared as weak bands, so these vibrations are of little importance for structural study [43].e IR bands appearing at 1360, 1247, 1222, 1211, 1180, 1163, 1128, 1109 1089, 1045, 993, 947, and 928 cm −1 were assigned to CC vibrations coupled with the CCH for the title compound.So, in our study, the C-C stretching vibrations are observed as medium-intensity bands.ese results were con�rmed by Gunasekaran et al. [44].
e identi�cation of CN vibrations is a di�cult task, since the mixing of vibrations is possible in CN stretching vibration frequencies region.However, with the help of both the animation option of Gaussian programs and theoretical calculations (VE�A 4), the CN vibrations are identi�ed and assigned in this study.e IR bands appearing at 1409, 1282 and 1211 cm −1 are assigned to CN vibrations.ese results agree with Sundaraganesan et al. [45].
Epoxide group could be identi�ed via its characteristic C-O stretching bands which gives two different absorption bands in the �ngerprint region around ∼800-950 and ∼1250 cm −1 , respectively [46,47].ere is also a third band in the range 750-850 cm −1 .e IR bands appearing at 1180, 993, and 883 cm −1 are assigned to C-O stretching vibrations.ese results agree with Evtushenko et al. [47].e difference between observed and literature values is coming from the effects of the aromatic rings.
e C-Cl stretching vibrations give generally strong bands in the region of 710-505 cm −1 .e band observed at 685 cm −1 in FT-IR spectrum has been assigned to C-Cl stretching vibration in the present investigation [37].

Other Molecular Properties.
Several calculated thermodynamic parameters are presented in Table 4. e total energies and the changes in the total entropy of the title compound at room temperature at different methods also presented.Turkey).e room-temperature-attenuated total re�ection Fourier transform infrared (FT-IR ATR) spectrum of the tert-butyl 3a-chloroperhydro-2,6a-epoxyoxireno[e]isoindole-5-carboxylate was recorded using Varian FTS1000 FT-IR spectrometer with Diamond/ZnSe prism (4000-525 cm −1 ; number of scans: 250; resolution: 1 cm −1 ) in the solid (Figure 3).

Calculations Details
. e conformation analysis study was performed by Spartan 06 program package [15,16].All the other calculations were performed with the Gaussian 03W program package on a double xeon/3.2GHz processor with 8 GB Ram [48].e molecular structure of the title compound, in the ground state, is optimized by using HF, BLYP and B3LYP methods with the standard 6-31G(d) and 6-31G(d,p) basis sets.e vibrational frequencies were also calculated with these methods.e frequency values computed at these levels contain known systematic errors [27][28][29][49][50][51][52][53].erefore, we have used the scaling factor for HF, B3LYP, and BLYP methods [17,[21][22][23][24][25].We have also calculated optimal scaling factors for all investigated methods.We have also calculated optimal scaling factors for all investigated methods.e assignment of the calculated wavenumbers is aided by the animation option of GaussView 3.0 graphical interface for gaussian programs, which gives a visual presentation of the shape of the vibrational modes [52].Furthermore, theoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions (PEDs) using VEDA 4 program [54].

Conclusions
e frequency assignment for the tert-butyl 3a-chloroperhydro-2,6a-epoxyoxireno[e]isoindole-5-carboxylate has been done for the �rst time from the FT-IR spectrum recorded.e conformation stability, equilibrium geometries, and harmonic frequencies of the title compound were determined and analyzed both at HF and DFT level of theories utilizing 6-31G(d) and 6-31G(d,p) basis sets.e difference between the observed and scaled wavenumber values of most of the fundamentals is very small.Any discrepancy noted between the observed and the calculated frequencies may be due to the fact that the calculations have been actually done on a single molecule in the gaseous state contrary to the experimental values recorded in the presence of intermolecular interactions.e IR spectrum of the title compound was interpreted in terms of the potential energy distribution (PED) analysis.Optimal uniform scaling factors were calculated for the title compound.Taking into account small variations of the scaling factors for the derivatives of the title compound, for future IR spectral predictions for unknown compounds of this class, one can recommend scaling factors of 0.897/0.902,0.959/0.961,and 0.989/0.991for HF, B3LYP, and BLYP (6-31G(d)/6-31G(d,p)), respectively.

F 2 :
a e atom numbering scheme of the molecular structure is given in Figure 2(a).b r: correlation coefficient between optimized and experimental geometrical parameters.c From [10].e optimized molecular structure (Conformer 2) of the title compound (a), the single crystal structure of the title compound.ermal ellipsoids are shown at the 50% probability level (b).

T 3 :
Vibrational wavenumbers obtained for the title compound a .

Table 3
T 2: Optimized and experimental geometries of the title compound in the ground state.
lists the wavenumbers of the bands observed in the FT-IR spectra of the tert-butyl 3a-chloroperhydro-2,6a-epoxyoxireno[e]isoindole-5-carboxylate.e theoretical frequencies and infrared intensities calculated by HF, BLYP, and B3LYP methods of the title T 4: eoretically computed energies, zero-point vibrational energies, entropies and dipole moment for the title compound.