Molecular structure and vibrational spectra of phenobaraitone by density functional theory and ab initio hartree-Fock calculations

Abstract

Quantum chemistry calculations have been performed using Gaussian03 program to compute optimized geometry, harmonic vibrational frequency along with intensities in IR and Raman spectra at RHF/6-31++G** and B3LYP/6-31++G** levels for phenobarbitone (C₁₂H₁₂N₂O₃) in the ground state. The scaled harmonic vibrational frequencies have been compared with experimental FT-IR and FT-Raman spectra. Theoretical vibrational spectra of the title compound were interpreted by means of potential energy distributions (PEDs) using MOLVIB program. A detailed interpretation of the infrared spectra of the title compound is reported. On the basis of the agreement between the calculated and observed results, the assignments of fundamental vibrational modes of phenobarbitone were examined and some assignments were proposed. The theoretical spectrograms for FT-IR and FT-Raman spectra of the title compound have been constructed.

Keywords

phenobarbitone / vibrational spectra / HF ab initio calculation / density functional theory (DFT)

Introduction

Phenobarbitone, a barbiturate, is used to control epilepsy and as a sedative to relieve anxiety. Phenobarbitone is 5-ethyl-5-phenylbarbituric acid and its molecular formula is C₁₂H₁₂N₂O₃. A general model compound with anticonvulsant activity proposed in Ref. [1] comprises two aromatic rings or their equivalents in a suitable orientation and a third, heterocyclic region, usually a cyclic imid. Williams [2] has reported the crystal structure of phenobarbitone. Recent spectroscopic studies of benzene and its derivatives have been motivated by their biologic and pharmaceutical importance [3,4]. The vibrational spectroscopic studies on benzene ring fused to five-membered received considerable attention recently [5-7]. The results obtained from these studies reveal that the change of simple constituents on a constant ring system produces only little changes in the spectrum. Gunasekaran et al. [8] recorded the infrared spectra of phenobarbitone in the region 4000-400 cm^-1, and Raman spectra in the region 3500-50 cm^-1. But so far no theoretical work is done on vibrational spectra of phenobarbitone because of the high complexity and low symmetry. Therefore, we made a deep investigation and studied the structure and vibrational frequencies of phenobarbitone.

Density functional theory (DFT) approaches, especially those using hybrid functional, have evolved to a powerful and very reliable tool, being routinely used for the determination of various molecular properties. B3LYP functional has been previously shown to provide an excellent compromise between accuracy and computational efficiency of vibrational spectra for large and medium size molecules [9-12]. It is well known that vibrational frequencies obtained by quantum chemical calculations are typically larger than their experimental counterparts, and thus, empirical scaling factors are usually used to match the experimental vibrational frequencies [13]. These scaling factors depend on both the method and basis sets used in calculations, and they are determined from the mean deviation between the calculated and experimental frequencies [14,15]. On the other hand, B exchange functionals have the advantage of standard frequency scaling factor which is very close to unity, so the B-based procedures can often be used without scaling [14,16-18]. For this reason, by using the DFT (B3LYP) method with B3LYP/6-31++G** basis set, we have calculated the geometric parameters and the vibrational spectrum of phenobarbitone in the ground state and compared with the experimental vibrational frequencies. The 6-31++G** basis set was also used for Hartree–Fock computations. These calculations are expected to provide new insight into the vibrational spectrum and molecular parameters.

The present study was undertaken with the following twofold objectives. One is to predict the IR and Raman spectra of the title compound. The other is to assign all predicted frequencies using normal mode analysis.

Computational details

Calculations of structural parameters, vibrational frequencies, IR and Raman intensities of the title compound (Fig. 1) were carried out using Gaussian03 program package [19] through RHF and DFT approaches.

Initially, the geometry optimization and calculation of other parameters were performed at restricted Hartree-Fock (RHF) level using 6-31++G** basis set. Electron correlations were included using Becke3-Lee-Yang-Parr (B3LYP) procedure [20-22]. This includes Becke’s gradient exchange corrections, Lee, Yang and Parr correlation functional and/or Vosko, Wilk and Nusair correlation functional [23]. The optimized geometry at RHF/6-31++G** level was taken as the input structure for the density functional calculation at B3LYP/6-31++G** level. All the parameters were allowed to relax and all the calculations converged to an optimized geometry which corresponds to a true energy minimum revealed by the lack of imaginary frequencies. The vibrational frequencies for this molecule were calculated with the RHF and B3LYP methods with 6-31++G** basis set and then were scaled [24] by 0.8992 and 0.9614, respectively.

Furthermore, theoretical vibrational spectra of the title compound were interpreted by means of potential energy distribution (PED) with the version V7.0-G77 of the MOLVIB program written by Sundius [25,26].

The calculated Raman activity (S_i) have been converted to relative intensities (I_i) using the following relationship derived from the basis theory of Raman scattering [27,28]:

(1)I_i={\displaystyle \frac{f{(v_{\mathrm{0}}-v_i)}^{\mathrm{4}}{S}_i}{v_i\left[\mathrm{1}-\exp \left({\displaystyle \frac{-hc{v}_i}{kT}}\right)\right]}}

where v_{\mathrm{0}} is the exciting frequency (in cm^-1 units); v_i is the vibrational wavenumber of the ith normal mode; h, c and k are universal constants, and f is the suitably chosen common scaling factor for all the peak intensities.

Results and discussion

Williams [2] determined the crystal structure of the title compound. The title compound, C₁₂H₁₂N₂O₃, is monoclinic crystal system with the space group P2₁/c. The lattice parameters of the title compound are a = 9.534 Å, b = 11.855 Å, c = 10.794 Å, β = 111.56°, and Z = 4, D_c = 1.38.

Molecular geometry

The atom numbering scheme of the title compound is shown in Fig. 1 and the optimized geometrical parameters, namely, bond lengths and angles at RHF/6-31++G** and B3LYP/6-31++G** levels are given in Table 1. The experimental data obtained by S. Gunasekaran et al. [8] and Williams [2] are also included. It is noted from Table 1 that the bond lengths obtained by S. Gunasekaran et al. [8] and Williams [2] are not the same. The largest difference between them is 0.018 Å, while the bond angles obtained by them are nearly the same. Considering the different experimental methods, here, we adopted the experimental parameters obtained by S. Gunasekaran et al. [8].

The largest difference between experimental and calculated bond length by B3LYP method is about 0.031 Å. The RHF method leads to geometry parameters which are much closer to experimental data [2,8]. Optimized structure yields identical bond lengths for the N₁–C₂ and C₂–N₂, C₁–N₁ and C₃–N₂ bonds at the two levels of calculations RHF/6-31++G** and B3LYP/6-31++G**, respectively. These bond lengths increase from RHF/6-31++G** to B3LYP/6-31++G** level and are found to be about 1.372 Å at RHF/6-31++G** level for phenobarbitone, which is between double bond length (C=N, 1.28 Å) and single (C–N, 1.47 Å) bond lengths.

Similarly, calculated C–O bond length increases from RHF to B3LYP level. The C–O bond lengths calculated by B3LYP level are closer to the experimental data [2,8]. The C₂–O₂ bond length is slightly shorter than the C₁–O₁ and C₃–O₃ bond lengths, which is probably due to the participation of O₁ and O₃ in intermolecular hydrogen bonds. The three C–O bond lengths are found to have a magnitude of about 1.213 Å between double (C=O, 1.20 Å) and single (C–O, 1.43 Å) bond length at B3LYP/6-31++G** level, which indicates its involvement in conjugation. The N–H bond lengths increase with the increase of the level of calculation refinements. The two N–H bond lengths are similar.

In bond angle calculation of phenobarbitone, the bond angles of C₁–N₁–C₂ and C₂–N₂–C₃ increase from RHF to DFT method and are 127.4° and 127.1° at RHF/6-31++G** level, respectively. Interestingly, bond angles of N₁–C₁–O₁ and C₄–C₁–O₁ are 119.7° and 123.8° at RHF/6-31++G** level, respectively, which indicates that the C₁=O₁ bond is not symmetrically disposed on C₁, rather, it is tilted toward the H₁ atom of the N₁–H₁ bond due to the propensity of O₁ atom to form H-bonding with the H₁ atom. Similarly, bond angles of N₂–C₃–O₃ and C₄–C₃–O₃ are 120.0° and 123.5° at RHF/6-31++G** level, respectively, which indicates that the C₃=O₃ bond is not symmetrically disposed on C₃, but tilted toward the H₂ atom of the N₂–H₂ bond due to the propensity of O₃ atom to form H-bonding with the H₂ atom.

Further, the bond angles of C₂–N₁–H₁ and C₁–N₁–H₁ are 119.5° and 116.5° at RHF/6-31++G** level, respectively. The magnitudes of these angles conform with the tilting of the N₁–H₁ bond toward oxygen atom of the C₁=O₁ bond to form H-bonding. While the bond angles of C₂–N₂–H₂ and C₃–N₂–H₂ are 119.7° and 116.6° at RHF/6-31++G** level, respectively, which conforms with the tilting of the N₂–H₂ bond toward oxygen atom of the C₃=O₃ bond to form H-bonding. The hydrogen bond lengths and bond angles are listed in Table 2.

All the dihedral angles on the benzene ring are either 0° or 180° with±1.0° at RHF/6-31++G** level, which indicates that the hydrogen atoms are in the plane of the benzene ring. The dihedral angles of C₈–C₇–C₄–C₁ and C₁₂–C₇–C₄–C₁ are 0° and 180°, respectively. The dihedral angles of C₈–C₇–C₄–C₃ and C₁₂–C₇–C₄–C₃ are -118.65° and 61.38°, respectively. The N₁, N₂, C₂, O₂ atoms are the planar part of the heterocyclic ring of the molecule. If the normal to the planar part of the heterocyclic ring is defined as the base vector of a spherical coordinate system, then the coordinate of the normal to the phenyl ring is ϕ = 83.07°, θ = 32.5°.

In addition, the heterocyclic ring of the molecule is markedly non-planar. It is noted that the dihedral angles of O₂–C₂–N₁–C₁, C₂–N₁–C₁–O₁, O₂–C₂–N₂–C₃ and C₂–N₂–C₃–O₃ are 172.3°, -167.4°, -172.3° and 167.4°. The dihedral angles of C₂–N₂–C₃–C₄ and C₂–N₁–C₁–C₄ are 12.6° and -12.7°, respectively. The above analysis shows that the heterocyclic ring of the molecule assumes the characteristic “envelop” conformation.

Atomic charges

Mullican atomic charges at heterocyclic ring of phenobarbitone calculated at RHF/6-31++G** and B3LYP/6-31++G** levels are collected in Table 3. The magnitudes of charges calculated on N₁ and N₂ atoms increase from RHF to DFT level of calculation. Their values are found to be -0.66 and -0.67 at the B3LYP/6-31++G** level of calculation, respectively. The charges on H₁ and H₂ atoms exhibit positive charges and their magnitudes decrease from RHF to DFT method and are all 0.36 at DFT level of calculation.

The charge distribution listed in Table 3 shows that the double bond carbon atoms are negative except C₇ atom, whereas the remaining carbons are positively charged. The nitrogen atoms have more negative charges whereas all hydrogen atoms have positive charges. The result suggests that the atoms bonded nitrogen atoms are the electron acceptor, and also indicates that the charge transfers from H to N.

Vibrational analysis

The goal of the vibrational analysis is to find vibrational modes connected with specific molecular structures of calculated compound. To obtain the spectroscopic signature of phenobarbitone, vibrational frequencies were calculated by using RHF/6-31++G** and B3LYP/6-31++G** methods. The theoretically calculated DFT force fields were transformed to the latter set of vibrational coordinates and used in all subsequent calculations. Table 4 presents the calculated vibrational frequencies, IR intensities and Raman activity of phenobarbitone. The vibrational frequencies reported by S.Gunasekaran et al. [8] are listed in Table 4. The difference between experimental and calculated vibrational modes is observed. Any discrepancy noted between the observed and the calculated frequencies may be due to three facts: one is that hydrogen bond vibrations present in crystal lead to strong perturbation of the infrared frequencies (and intensities) of many other modes; one is that the experimental results belong to solid phase, and theoretical calculations belong to gaseous phase; the other is that the calculations have been actually done on a single molecule contrary to the experimental values recorded in the presence of intermolecular interactions.

Table 4 shows that the theoretical frequencies obtained with B3LYP method are in good agreement with their experimental data. While almost all the vibrations at RHF method deviate enormously even after scaling because of the single determinant wave function and the neglect of electron correlation. So discussions are being performed with the results at DFT level calculation with 6-31++G** basis set. Figs. 2 and 3 give the experimental and theoretical FT-IR and FT-Raman vibrational spectra of the title compound, respectively. Calculated Raman activities and IR intensities help us to distinguish and more precisely assign those fundamentals which are close in frequency.

C–H vibrations

The existence of one or more aromatic rings in a structure is normally readily determined from the C–H and C=C–C ring related vibrations. The C–H stretching occurs above 3000 cm^-1 and is typically exhibited as a multiplicity of weak to moderate bands, compared with the aliphatic C–H stretch [29]. According to Roeges [30], the CH stretching vibrations of the phenyl ring are expected in the region of 3120-3000 cm^-1. The calculated values of these modes for phenobarbitone are 3069, 3079, 3091, 3103, 3105 cm^-1 at B3LYP level. Experimentally, no bands are observed in the IR spectrum for phenobarbitone.

The C–H out of plane deformation is observed between 1000 and 700 cm^-1 [30]. These δ(C–H) out of plane modes and δ(C–H) in-plane deformation vibration are not observed for phenobarbitone in the IR spectrum. The DFT calculations give δ(C–H)_oop at 689, 706, 742, 769, 834, 897, 905, 945, 956, 969 cm^-1 and δ(C–H)_ip at 1080, 1084, 1120, 1146, 1154, 1188, 1331, 1440 cm^-1 at B3LYP/6-31++G** method.

C–C stretching vibrations

The ring carbon-carbon stretching vibrations occur in the region 1625-1430 cm^-1. For aromatic six-membered rings, e.g., benzenes and pyridines, there are two or three bands in this region due to skeletal vibrations, the strongest usually being at about 1500 cm^-1. For substituted benzenes with identical atoms or groups on all para-pairs of ring carbon atoms, the vibrations causing the band at 1625-1590 cm^-1 are infrared-inactive due to symmetry consideration; the compound has a center of symmetry at the ring center. If there is no center of symmetry, the vibrations are infrared-active [31]. Chithambarathau et al. [32] have observed the FT-IR bands at 1574, 1498 and 1468 cm^-1 in 1,3,5-triphenyl-4,5-dihydro pyrazole. In the present work, the CC stretching is observed at 1236 cm^-1 for phenobarbitone in the IR spectrum [8]. The DFT calculations give the aromatic CC stretching modes at 1281, 1290, 1303, 1488, 1579, 1598 cm^-1.

C–N vibrations

The weak absorption bands for the C–N linkages in amines appear in the region 1200-1020 cm^-1. It is a difficult task to identify the C–N stretching in the side chain from other vibrations [33]. The ring C=C and C=N stretching vibrations occur in the region 1615-1575 cm^-1 and 1520-1465 cm^-1 [34]. Krishnakumar and John Xavier [35] have observed the C–N stretching vibration at 1375 cm^-1 in pyrimidines. Mohan et al. [36] have identified the stretching frequency of C=N bond in benzimidazole at 1617 cm^-1. For phenobarbitone, C–N stretching vibrations are observed at 1315, 1350, 1368 cm^-1 [8]. DFT calculations give the C–N stretching vibrations at 994, 1290, 1303, 1350, 1377, 1396 cm^-1.

C=O vibration

The carbonyl group is important and its characteristic frequency has been extensively used to study a wide range of compounds. The carbonyl group vibrations give rise to characteristic bands in vibrational spectra. The intensity of these bands can increase owing to conjugation or formation of hydrogen bonds. The increase in conjugation, therefore, leads to intensification of IR bands. If a compound contains a carbonyl group, the absorption caused by C=O stretching is generally the strongest peak [33]. The C=O stretching frequency appears strongly in the infrared spectrum in the range 1600-1850 cm^-1. The C=O stretching modes reported by S.Gunasekaran et al. [8] are 1678 and 1712 cm^-1. DFT calculation gives C=O stretching modes at 1722, 1753, 1785 cm^-1. The deviation of the calculated wavenumber for this mode can be attributed to the underestimation of the large degree of π-electron delocalization due to the conjugation in the molecule [37].

N–H vibration

The NH stretching vibration [30] appears strongly and broadly in the region of (3390±60) cm^-1. For the title compound, the N–H symmetric stretching reported by Gunasekaran et al. [8] is at 3207 cm^-1, and the N–H asymmetric stretching reported is at 3308 cm^-1 in the IR spectrum. The calculated value for N–H symmetric stretching is 3460 cm^-1, and the N-H asymmetric stretching obtained is at 3463 cm^-1. The NH stretching wavenumber is red shifted by 155-253 cm^-1 in the IR with a strong intensity from the computed wavenumber, which indicates that the weakening of the N₂–H₂ bond results in proton transfer to the neighboring oxygen [38].

Deformation vibrations

In benzene, six ring deformation frequencies are observed. Of these, three arise from in-plane bending vibrations corresponding to 606 and 1010 cm^-1 mode, and the remaining three are derived from out-of-plane bending vibrations corresponding to 404 and 711 cm^-1 mode of vibrations. The in-plane bending mode of benzene splits into two components in substituted benzenes while both of these components are reducing heavily in metal isomers of di-substituted benzenes [39,40]. The aromatic ring vibration is not reported by S.Gunasekaran et al. [8]; the ν(ring) mode is calculated at 1024 cm^-1 for phenobarbitone. DFT calculations give the α(ring) vibrational modes at 609, 613, 693, 980 cm^-1 and Φ(ring) vibrational modes at 401, 432, 482, 491, 536 cm^-1.

Hydrogen bonding

Generally, a hydrogen bond is formed when the hydrogen atom of a covalent A-H bond of a proton donor molecule interacts with a lone electron pair of an atom of X of a proton acceptor. In the title compound, there exist some hydrogen bonds. Among these, there is one hydrogen bond of the N–H…O type. The intramolecular H…O distances of H₁–O₁ is found to be 2.45 Å. These distances are much shorter than that of the van der Waals separation between the O atom and H atom (2.72 Å) [41] indicating the existence of the N–H…O interaction in the title compound. The DFT calculation predicts the shortening of N₁–H₁ bond, and the bond length is 0.999 Å, which leads to red shift in their observed band in IR spectra.

Other molecular properties

Several calculated thermodynamic parameters are presented in Table 5. Scale factors have been recommended for an accurate prediction in determining the zero-point vibration energies (ZPVE), and the entropy, S_vib(T). The variations in the ZPVEs seem to be insignificant. The total energies and the change in the total entropy of the title compound at room temperature at different methods are also presented.

Conclusions

The optimized molecular structures, vibrational frequencies and corresponding vibrational assignments of phenobarbitone have been calculated using RHF/6-31++G** and B3LYP/6-31++G**. The analysis of the bond distance for the title compound shows that there exists the strong H-bonding between H₁ and O₁ atoms, and H₂ and O₃ atoms. A same conclusion is obtained from the analysis of the bond angle. The comparison of the experimental and calculated spectra of the molecules showed that DFT B3LYP method is in good agreement with experimental ones. Following the agreement between the calculated and experimental results, all the fundamental vibrational modes of the title compound were assigned based on the results of the PED output obtained from normal coordinate analysis.

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