Spectroscopic (FT-IR, FT-Raman), first order hyperpolarizability, NBO analysis, HOMO and LUMO analysis of N-[(4-(trifluoromethyl)phenyl]pyrazine-2-carboxamide by density functional methods

4.1 IR and Raman spectra

The observed IR, Raman bands and calculated wavenumbers (scaled) and assignments are given in Table 2. The phenyl CH stretching modes occur above 3000 cm⁻¹ and are typically exhibited as multiplicity of weak to moderate bands compared with the aliphatic CH stretching (Coates, 2000). In the present case, the SDD calculations give υCH modes of the phenyl rings in the range 3149–3076 cm⁻¹ and the bands are observed at 3023 cm⁻¹ in the IR spectrum and 3116 and 3039 cm⁻¹ in the Raman spectrum The benzene ring possesses six ring stretching vibrations, of which the four with the highest wavenumbers (occurring near 1600, 1580, 1490 and 1440 cm⁻¹) are good group vibrations (Roeges, 1994). With heavy substituents, the bands tend to shift to somewhat lower wavenumbers. In the absence of ring conjugation, the band at 1580 cm⁻¹ is usually weaker than that at 1600 cm⁻¹. In the case of C⚌O substitution, the band near 1490 cm⁻¹ can be very weak. The fifth ring stretching vibration is active near 1315 ± 65 cm⁻¹, a region that overlaps strongly with that of the CH in-plane deformation. The sixth ring stretching vibration, or the ring breathing mode, appears as a weak band near 1000 cm⁻¹, in mono-, 1,3-di- and 1,3,5-trisubstituted benzenes. In the otherwise substituted benzenes, however, this vibration is substituent sensitive and difficult to distinguish from the ring in-plane deformation (Roeges, 1994; Varsanyi, 1974). The υPh modes are expected in the region 1280–1630 cm⁻¹ for para substituted benzene rings (Roeges, 1994). The SDD calculations give the Ph stretching modes in the range 1334–1598 cm⁻¹ for the title compound. The bands observed at 1599, 1580, 1401, and 1328 cm⁻¹ in the IR spectrum and 1580, 1387, and 1323 cm⁻¹ in the Raman spectrum are assigned as the phenyl ring stretching modes for the title compound. Most of the modes are not pure but contain significant contributions from other modes also. The ring breathing mode of the para-substituted benzenes with entirely different substituents (Varsanyi, 1974) has been reported in the interval 780–880 cm⁻¹. For the title compound, the ring breathing mode Ph is observed at 771 cm⁻¹ in the IR spectrum, and 765 cm⁻¹ in the Raman spectrum, which is supported by the computational result at 771 cm⁻¹. For para-substituted benzene, the ring breathing mode was reported at 804 and 792 cm⁻¹ experimentally and 782 and 795 cm⁻¹ theoretically (Mary et al., 2008; Ambujakshan et al., 2007). The in-plane and out-of-plane CH deformations of the phenyl ring are expected above and below 1000 cm⁻¹, respectively (Roeges, 1994). The in-plane CH deformation bands are assigned at 1308, 1189, 1137, and 1010 cm⁻¹ for the phenyl ring theoretically (SDD) and bands are observed at 1188 and 1153 cm⁻¹ in the Raman spectrum. Generally, the CH out-of-plane deformations with the highest wavenumbers have a weaker intensity than those absorbing at lower wavenumbers (Roeges, 1994). The strong γCH occurring at 840 ± 50 cm⁻¹ is typical for 1,4-disubstituted benzenes and the band observed at 839 cm⁻¹ in the IR spectrum is assigned to this mode which finds supports from the computation value 845 cm⁻¹ (Roeges, 1994). Again according to the literature (Roeges, 1994; Varsanyi, 1974) a lower γCH absorbs in the neighborhood 820 ± 45 cm⁻¹, but is much weaker or infrared inactive. The SDD calculations give a γCH at 816 cm⁻¹ and no band is experimentally observed for this mode. The out-of-plane CH deformation bands of the phenyl ring are assigned at 976, 959, 845, and 816 cm⁻¹ for Phenyl ring theoretically. Most of the modes are not pure according to PED calculations, but contain significant contributions from other modes also. The substituent sensitive modes of the phenyl rings and other modes are also identified and assigned.

The CF₃ group possesses as many normal vibrations as methyl and as, halogen atoms are much heavier than hydrogen, CF₃ modes are expected at considerably lower values. According to Roeges (1994) the absorption regions of –CF₃ in substituted benzene are: υCF 1300–1100; δCF 720–440; ρCF 470–260 and τCF below 100 cm⁻¹. In the present case the bands at 1052 and 1020 cm⁻¹ in the IR spectrum, 1022 cm⁻¹ in the Raman spectrum and 1249, 1028, and 1016 cm⁻¹ (SDD) are assigned as the stretching modes of CF₃ group. The deformation bands are assigned at 675, 576, and 515 cm⁻¹ in the IR spectrum, 664, 529, and 351 cm⁻¹ in the Raman spectrum and 674, 585, 515, 394, 379, and 355 cm⁻¹ theoretically. Iriarte et al. (2008) reported the CF₃ stretching values at 1244, 1213, 1140, and 1128, (DFT), 1218, 1176, 1136, and 1127 (experimental), deformation bands of CF₃ at 729 cm⁻¹ (experimental), 743 cm⁻¹ (DFT). The CF modes are reported at 1317, 1270, 1143, 643, 632, and 574 cm⁻¹ in the IR spectrum, 1275, 1150, 640, 582, 416, 379, 336, 331, and 234 cm⁻¹ in the Raman spectrum and 1270, 1135, 643, 590, 588, 410, 372, 368, 326, 228, and 118 cm⁻¹ theoretically (Anbarasu and Arivazhagan, 2011; Krishnakumar and Xavier, 2005).

The carbonyl group vibrations give rise to characteristic bands in the vibrational spectra. The intensity of these bands can increase owing to conjugation or formation of hydrogen bonds. In the present case the stretching mode of C⚌O is assigned at 1616 cm⁻¹ in the Raman spectrum, 1617 cm⁻¹ in the IR spectrum and the SDD calculations give this mode at 1610 cm⁻¹. The deformation bands are observed at 870 cm⁻¹ in the IR spectrum, 873 and 689 cm⁻¹ in the Raman spectrum and 870 and 696 cm⁻¹ theoretically. In the case of 2-aminopyrazine-3-carboxylic acid (Pawlukojc et al., 2000) the vibrational modes of carboxylic group were assigned as follows: torsional C⚌O 101 cm⁻¹ (Raman), 111 (HF); rocking C⚌O 537 (Raman), 571 (HF); wagging C⚌O 723 (Raman), 736 (HF); bending C⚌O 912 (Raman), 886 (HF); stretching mode C⚌O 1718 (Raman), 1786 cm⁻¹ (HF).

The N–H stretching vibrations generally give rise to bands (Spire et al., 2000; Bellamy, 1975) at 3500–3300 cm⁻¹. In the present study, the NH stretching band is observed at 3343 cm⁻¹ in the IR spectrum and at 3349 cm⁻¹ in the Raman spectrum. The SDD calculations give this mode at 3388 cm⁻¹. In mono-substituted amides, the in-plane bending frequency and the resonance stiffened CN band stretching frequency fall close together and therefore interact. The CNH vibration where the nitrogen and the hydrogen move in opposite directions relative to the carbon atom involves both NH bend and CN stretching and absorbs (Colthup et al., 1975) near 1500 cm⁻¹. The CNH vibration where N and H atoms move in the same direction relative to the carbon atom gives rise to a weaker band (Colthup et al., 1975) near 1250 cm⁻¹. In the present case the bands observed at 1276 cm⁻¹ in the Raman spectrum, 1273 cm⁻¹ in the IR spectrum and 1511 and 1275 cm⁻¹ (SDD) are assigned as CNH bending modes. The out-of-plane NH wag absorbs at 795 cm⁻¹ in the Raman spectrum and 795 cm⁻¹ theoretically. Mary et al. (2008) reported the NH bands at 1537, 1250, and 650 cm⁻¹ in the IR spectrum and 1580, 1227, and 652 cm⁻¹ theoretically, for a similar derivative.

Primary aromatic amines with nitrogen directly on the ring absorb at 1330–1260 cm⁻¹ because of the stretching of the phenyl C–N bond (Colthup et al., 1975). For the title compound, the υC₁₀–N₁₉ mode is observed at 1244 experimentally and 1246 cm⁻¹ theoretically. The C₉–N₁₉ stretching band is reported in the range 1050–1150 cm⁻¹ (Kundoo et al., 2003). In the present case υC₉–N₁₉ is observed at 1071 cm⁻¹ in the IR spectrum, 1103 cm⁻¹ in the Raman spectrum and 1097 cm⁻¹ theoretically.

The CH stretching modes of pyrazinecarboxamide are reported in the range 3050–3088 cm⁻¹ and the in-plane CH deformations at 1316, 1188, and 1062 cm⁻¹ and out-of-plane CH deformations at 970, 922, and 792 cm⁻¹ (Kalkar et al., 1989; Schettino et al., 1972). The ring stretching modes of pyrazinecarboxamide are reported at 1589, 1530, 1480, 1443, 1175, and 1035 cm⁻¹ (Kalkar et al., 1989), 1581, 1525, 1479, 1437, 1166, and 1025 cm⁻¹ (Akyuz, 2003). For the title compound the pyrazine CH stretching modes are assigned at 3133, 3122, and 3099 cm⁻¹ theoretically and experimentally bands are observed at 3127 and 3090 cm⁻¹ in the IR spectrum and 3139 and 3080 cm⁻¹ in the Raman spectrum. The CH stretching band of pyrazine was reported in the range 3100–3000 cm⁻¹ (Schettino et al., 1972; Sbrana et al., 1973; Arenas et al., 1985). These modes are observed at 3057, 3070, and 3086 cm⁻¹ (IR), 3060, 3070, and 3087 (Raman) and 3061, 3074, and 3079 cm⁻¹ (theoretical) for 2-chloropyrazine and 3099 and 3104 (IR), 3078 and 3103 (Raman), 3096 and 3100 cm⁻¹ (calculated) for 2,6-dichloropyrazine (Ngo et al., 2007). For 2-aminopyrazine-3-carboxylic acid (Pawlukojc et al., 2000) the pyrazine ring stretching modes are observed at 1564, 1536, 1468, 1458, 1360, 1258, and 1083 cm⁻¹ (Raman) and 1567, 1565, 1457, 1415, 1373, 1231, and 1068 cm⁻¹ (ab initio). For pyrazine, the ring stretching modes are reported at 1411, 1485, 1128, and 1065 (IR), 1579, 1522, and 1015 (Raman) and 1597, 1543, 1482, 1412, 1140, 1063, and 1009 cm⁻¹ theoretically (Endredi et al., 2003). For 2-chloropyrazine the pyrazine ring stretching modes are reported at 1561, 1515, 1198, 1176, 1133, and 1047 (IR), 1562, 1518, 1197, 1177, 1135, and 1049 (Raman) and 1563, 1533, 1210, 1167, 1128, and 1042 (DFT) and for 2,6-dichloropyrazine these values are reported at 1550, 1540, 1412, 1230, 1189, 1151, and 1136 (IR), 1551, 1407, 1172, 1152, and 1138 (Raman) and 1547, 1541, 1407, 1229, 1170, 1167, and 1143 cm⁻¹ (DFT) (Endredi et al., 2003). For the title compound, the pyrazine ring stretching modes are observed at 1533, 1475, and 1416 cm⁻¹ in the IR spectrum, 1528, 1417, 1188, and 1000 cm⁻¹ in the Raman spectrum and 1526, 1489, 1424, 1183, 1002, and 977 cm⁻¹ theoretically. The ring breathing mode of pyrazine is reported at 1015 cm⁻¹ (Endredi et al., 2003). In the Raman spectrum of 2,6-dichloropyrazine and 2-chloropyrazine the ring breathing mode is reported at 1131 and 1049 cm⁻¹ (Endredi et al., 2003). The band at 1002 cm⁻¹ (DFT) is assigned as the ring breathing mode of the pyrazine ring, for the title compound. The δCH bending modes in 2,6-dichloropyrazine are reported at 1189 and 1151 cm⁻¹ in the IR spectrum (Endredi et al., 2003). For 2-chloropyrazine these modes are reported at 1455, 1380, 1280, and 1179 cm⁻¹ in the IR spectrum and 1457, 1380, 1289, and 1167 cm⁻¹ theoretically (Endredi et al., 2003). For pyrazine, the δCH modes are observed at 1485, 1413, and 1065 cm⁻¹ in the IR spectrum and 1482, 1412, 1227, and 1063 cm⁻¹ theoretically (Endredi et al., 2003). In the present case the CH in-plane bending modes are observed at 1417 and 1367 cm⁻¹ in the Raman spectrum, 1416 and 1365 in the IR spectrum and 1424, 1371, and 1269 cm⁻¹ theoretically (SDD). For the title compound the out-of-plane CH modes are assigned at 967, 966, and 859 cm⁻¹ theoretically. For pyrazine γCH modes are observed at 790 cm⁻¹ in the IR spectrum, 976 and 925 cm⁻¹ in the Raman spectrum and 985, 972, 930, and 790 cm⁻¹ by DFT calculations (Endredi et al., 2003). For 2-chloropyrazine the γCH modes are reported at 954, 929, and 844 cm⁻¹ in the IR spectrum, 960, 928, and 847 cm⁻¹ in the Raman spectrum and 960, 923, and 837 cm⁻¹ theoretically (Endredi et al., 2003). In the case of 2,6-dichloropyrazine these bands are reported at 897 and 875 cm⁻¹ in the IR spectrum, 896 cm⁻¹ in the Raman spectrum and 919 and 869 cm⁻¹ theoretically (Endredi et al., 2003). For 2-aminopyrazine-3-carboxylic acid γCH modes are reported at 1006 and 850 cm⁻¹ in the Raman spectrum and 987 and 852 cm⁻¹ by HF calculations (Pawlukojc et al., 2000). The substituent sensitive modes and other deformation bands of the phenyl and pyrazine ring are also identified and assigned (Table 2). Most of the modes are not pure, but contain significant contributions from other modes.

In order to investigate the performance of vibrational wavenumbers of the title compound, the root mean square (RMS) value between the calculated and observed wavenumbers were calculated. The RMS values of wavenumbers were calculated using the following expression (Joseph et al., 2012). $$\mathit{RMS}=\sqrt{\frac{1}{n-1}{\displaystyle \sum _i^n}{({\upsilon }_i^{\mathit{calc}}-{\upsilon }_i^{\exp })}^2}\text{.}$$

The RMS error of the observed IR and Raman bands are found to be 30.70 and 25.28 for B3PW91/6-31G^∗, 24.46 and 19.35 for B3LYP/6-31G^∗ and 14.93 and 11.46 for B3LYP/SDD methods, respectively. The small differences between experimental and calculated vibrational modes are observed. This is due to the fact that experimental results belong to solid phase and theoretical calculations belong to gaseous phase.

4.2 Geometrical parameters

To the best of our knowledge, no X-ray crystallographic data of the title compound has yet been established. However, the theoretical results obtained are almost comparable with the reported structural parameters of similar molecules. For pyrazine ring (Bormans et al., 1997) the CN bond lengths are 1.339 and 1.331 Ǻ. For 2-chloropyrazine (Endredi et al., 2003) CN bond lengths are in the range 1.335–1.312 Ǻ. For the title compound the pyrazine bond lengths C₁–C₂, C₁–N₆, C₅–N₆, C₅–C₄, C₄–N₃ and C₂–N₃ are 1.4121, 1.3517, 1.3608, 1.4104, 1.3577, and 1.3577 Ǻ, respectively. For a similar derivative Mary et al. (2008) reported the corresponding values as 1.3917, 1.2996, 1.3229, 1.3840, 1.322 and 1.3116 Ǻ. For 2-aminopyrazine-3-carboxylic acid (Pawlukojc et al., 2000; Ptasiewicz-Bak and Leciejewicz, 1997), the bond lengths C₅–C₉, C₉–O₂₀, C₅–N₆ and C₅–C₄ are1.479, 1.212, 1.333, and 1.4079 (XRD) and 1.492, 1.186, 1.315, and 1.4092 Ǻ (ab initio calculations), respectively. In the present case, the corresponding values are 1.5079, 1.2580, 1.3608 and 1.4104 Ǻ. Endredi et al. (2004) reported the bond lengths C₂–C₁, C₁–N₆, C₅–N₆, C₅–C₄ and C₄–N₃ as 1.391, 1.331, 1.331, 1.331, and 1.331 for pyrazine, 1.4, 1.327, 1.333, 1.387, and 1.334 for 2-methylpyrazine, 1.41, 1.331, 1.33, 1.385, and 1.331 Ǻ for 2,3-dimthylpyrazine, 1.396, 1.327, 1.335, 1.396, and 1.335 for 2,5-dimethylpyrazine, and 1.399, 1.326, 1.332, 1.399, and 1.332 Ǻ for 2,6-dimethylpyrazine. For pyrazinamide, Chis et al. (2005) reported bond lengths, C₅–N₆, C₄–C₅, C₄–N₃, C₂–N₃, C₁–C₂, C₁–N₆, C₅–C₉, C₉–N₁₉, C₉–O₂₀, C₄–H₈, and N₁₉–H₂₁ as 1.341, 1.4, 1.337, 1.338, 1.397, 1.336, 1.510, 1.357, 1.226, 1.086, and 1.010 Ǻ and these results are in agreement with the present study.

The CN bond length in the pyrazine ring of the title compound C₁–N₆ = 1.3517, C₅–N₆ = 1.3608, C₂–N₃ = 1.3577 and C₄–N₃ = 1.3577 Ǻ is much shorter than the normal C–N single bond that is referred to 1.49 Ǻ. The same results are shown for the bond lengths of the two C–C bonds, C₂–C₁ = 1.4121 and C₅–C₄ = 1.4104 Ǻ in the pyrazine ring and are also smaller than that of the normal C–C single bond of 1.54 (He et al., 2004). The C–N bond lengths C₉–N₁₉ = 1.3782 and C₁₀–N₁₉ = 1.4120 are also shorter than the normal C–N single bond of 1.49, which confirms this bond to have some character of a double or conjugated bond (Bakalova et al., 2004). The CF bond lengths are reported as 1.4068, 1.3284, 1.3251, and 1.3284 Ǻ theoretically (Anbarasu and Arivazhagan, 2011; Krishnakumar and Xavier, 2005) and for the title compound the CF lengths are in the range 1.4025–1.4163 Ǻ. For the title compound, the CCF angles lie in the range 112.9–113.1° and the FCF angles in the range 105.1–106.7°, which are in agreement with the reported literature (Iriarte et al., 2008).

For benzamide derivatives, Noveron et al. (2003)) reported the bond lengths C₁₀–N₁₉, C₉–O₂₀, C₉–N19, C₉–C₅ and N₁₉–H₂₁ as 1.3953, 1.2253, 1.3703, 1.4943, and 0.733, whereas the corresponding values for the title compound are 1.4120, 1.2580, 1.3789, 1.5079, and 1.0209Ǻ. The C⚌O and CN bond lengths (Takeuchi et al., 1999) in benzamide, acetamide and formamide are respectively, 1.2253, 1.2203, and 1.2123 and 1.3801, 1.3804, and 1.3683 Ǻ. According to the literature (Stevens, 1978; Gao et al., 1991) the changes in bond lengths in C⚌O and CN are consistent with the following interpretation: that is, hydrogen bond decreases the double bond character of C⚌O bond and increases the double bond character of C–N bond.

At N₁₉ position, the angles C₉–N₁₉–H₂₁ is 113.5°, C₁₀–N₁₉–H₂₁ is 118.9° and C₉–N₁₉–C₁₀ is 128.6°. This asymmetry of angles at N₁₉ position indicates the weakening of N₁₉–H₂₁ bond resulting in proton transfer to the oxygen atom O₂₀ (Barthes et al., 1996). At C₁₀ position the angel C₁₁–C₁₀–N₁₉ is increased by 3.0° and C₁₅–C₁₀–N₁₉ is reduced by 2.7° from 120° and this asymmetry reveals the interaction between the amide moiety and the phenyl ring. The CC bond lengths in the phenyl ring lie between 1.3980–1.4171 Ǻ and the CH bond lengths lie between 1.0819–1.0878 Ǻ. The CC bond length of benzene (Tamagawa et al., 1976) is 1.3993 Ǻ and benzaldehyde (Borizenko et al., 1996) is 1.3973 Ǻ.

4.3 First hyperpolarizability

Non-linear optical (NLO) is at the forefront of current research because of its importance in providing key functions of optical modulation, optical switching, optical logic and optical memory for the emerging technologies in areas such as telecommunications, optical interconnections and signal processing (Andraud et al., 1994). The first hyperpolarizability (β₀) of this novel molecular system is calculated using the B3LYP/6-31G^∗ method, based on the finite field approach. In the presence of an applied electric field, the energy of a system is a function of the electric field. First hyperpolarizability is a third rank tensor that can be described by a 3 × 3 × 3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to the Kleinman symmetry (Kleinman, 1962). The components of β are defined as the coefficients in the Taylor series expansion of the energy in the external electric field. When the electric field is weak and homogeneous, this expansion becomes. $$E=E_0-{\displaystyle \sum _i}{\mu }_i{F}^i-\frac{1}{2}{\displaystyle \sum _{\mathit{ij}}}{\alpha }_{\mathit{ij}}{F}^i{F}^j-\frac{1}{6}{\displaystyle \sum _{\mathit{ijk}}}{\beta }_{\mathit{ijk}}{F}^i{F}^j{F}^k-\frac{1}{24}{\displaystyle \sum _{\mathit{ijkl}}}{\gamma }_{\mathit{ijkl}}{F}^i{F}^j{F}^k{F}^l+..\text{.}$$

where $E_0$ is the energy of the unperturbed molecule, $F^i$ is the field at the origin, ${\mu }_i$ , ${\alpha }_{\mathit{ij}}$ , ${\beta }_{\mathit{ijk}}$ and ${\gamma }_{\mathit{ijkl}}$ are the components of dipole moment, polarizability, the first hyper polarizabilities, and second hyperpolarizibilites, respectively. The calculated first hyperpolarizability of the title compound is 9.77 × 10⁻³⁰ esu (Table 3). The C–N distances in the calculated molecular structure vary from 1.3517–1.4120 Ǻ which are intermediate between those of a C–N single bond (1.48 Ǻ) and a C⚌N double bond (1.28 Ǻ). Therefore, the calculated data suggest an extended π-electron delocalization over the pyrazine ring and carboxamide moiety (Tain et al., 2002) which is responsible for the nonlinearity of the molecule. We conclude that the title compound is an attractive object for future studies of non linear optical properties.

4.4 NBO analysis

The natural bond orbitals’ (NBO) calculations were performed using a NBO 3.1 program (Glendening et al., 2003) as implemented in the Gaussian 09 package at the DFT/B3LYP level in order to understand various second-order interactions between the filled orbitals of one subsystem and vacant orbitals of another subsystem, which is a measure of the intermolecular delocalization or hyper conjugation. NBO analysis provides the most accurate possible ‘natural Lewis structure’ picture of ‘j’ because all orbital details are mathematically chosen to include the highest possible percentage of the electron density. A useful aspect of the NBO method is that it gives information about interactions of both filled and virtual orbital spaces that could enhance the analysis of intra and inter molecular interactions. The second-order Fock- matrix was carried out to evaluate the donor–acceptor interactions in the NBO basis. The interactions result in a loss of occupancy from the localized NBO of the idealized Lewis structure into an empty non-Lewis orbital. For each donor (i) and acceptor (j) the stabilization energy (E2) associated with the delocalization i → j is determined as. $$E(2)=\mathrm{\Delta }{E}_{\mathit{ij}}=q_i\frac{{(F_{i\text{,}j})}^2}{(E_j-E_i)}$$

q_i → donor orbital occupancy

E_i, E_j → diagonal elements

F_ij → the off diagonal NBO Fock matrix element

In NBO analysis a large E(2) value shows the intensive interaction between electron-donors and electron-acceptors and greater the extent of conjugation of the whole system, the possible intensive interactions are given in Table 4. The second-order perturbation theory analysis of Fock matrix in NBO basis shows strong intra-molecular hyper-conjugative interactions of π electrons. The intra-molecular hyper-conjugative interactions are formed by the orbital overlap between n (N) and σ^∗ (C–O) bond orbitals which results in ICT causing stabilization of the system. The strong intra-molecular hyper-conjugative interaction of C₉–O₂₀ from n1(N₁₉) → π^∗ (C₉–O₂₀) which increases ED (0.32646e) that weakens the respective bonds leading to stabilization of 68.38 kcal mol⁻¹. Also the strong intra-molecular hyper-conjugative interaction of C₉–N₁₉ from n2(O₂₀) → σ^∗ (C₉–N₁₉) which increases ED (0.06813 e) that weakens the respective bonds leading to stabilization of 22.08 kcal mol⁻¹. These interactions are observed as an increase in electron density (ED) in C–O and C–N anti-bonding orbitals that weaken the respective bonds. The increased electron density at the nitrogen and carbon atoms leads to the elongation of their respective bond lengths and a lowering of the corresponding stretching wavenumbers. The electron density (ED) is transferred from the n(O), and n(N) to the anti-bonding π^∗ orbital of the C–N, and C–O explaining both the elongation and the red shift (Choo et al., 2002). The –NH, and –C⚌O stretching modes can be used as a good probe for evaluating the bonding configuration around the corresponding atoms and the electronic distribution of the molecule. Hence the above structure is stabilized by these orbital interactions.

The NBO analysis also describes the bonding in terms of the natural hybrid orbital n2(F₂₄), which occupies a higher energy orbital (−0.43933 a.u.) with considerable p-character (99.98%) and low occupation number (1.96168 a.u.) and the other n1(F₂₄) occupies a lower energy orbital (−1.10579) with p-character (21.75%) and high occupation number (1.98878 a.u.). Also n2(F₂₅), which occupies a higher energy orbital (−0.43722 a.u.) with considerable p-character (100.0%) and low occupation number (1.96256 a.u.) and the other n1(F₂₅) occupies a lower energy orbital (−1.10735 a.u.) with p-character (21.43%) and high occupation number (1.98884 a.u.). Again n2(F₂₆), which occupies a higher energy orbital (−0.43166 a.u.) with considerable p-character (99.74%) and low occupation number (1.96233 a.u.) and the other n1(F₂₆) occupies a lower energy orbital (−1.10750 a.u.) with p-character (20.75%) and high occupation number (1.98905 a.u.). Also n2(O₂₀), which occupies a higher energy orbital (−0.28291 a.u.) with considerable p-character (100.0%) and low occupation number (1.88796a.u.) and the other n1(O₂₀) occupies a lower energy orbital (−0.71130 a.u.) with p-character (35.25%) and high occupation number (1.97577 a.u.).Thus, a very close to pure p-type lone pair orbital participates in the electron donation to the σ^∗(C–N), π^∗(C–O), and σ^∗(C–F) orbital interactions in the compound. The results are tabulated in Table 5.

4.5 Frontier molecular orbitals

To explain several types of reactions and for predicting the most reactive position in conjugated systems, molecular orbitals and their properties such as energy are used (Choudhary et al., 2013). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are the most important orbitals in a molecule. The eigen values of HOMO and LUMO and their energy gap reflect the biological activity of the molecule. A molecule having a small frontier orbitals gap is more polarizable and is generally associated with a high chemical reactivity and low kinetic stability (Sinha et al., 2011; Lewis et al., 1994; Kosar and Albayrak, 2011). HOMO, which can be thought as the outer orbital containing electrons, tends to give these electrons as an electron donor and hence the ionization potential is directly related to the energy of the HOMO. On the other hand LUMO can accept electrons and the LUMO energy is directly related to electron affinity (Gece, 2008; Fukui, 1982). Two important molecular orbitals (MO) were examined for the title compound, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) which are given in Figs. 4 and 5. In the title compound, the HOMO of π nature is delocalized over the whole C–C bonds of the phenyl ring, and CONH and CF₃ groups. By contrast, LUMO is located over the pyrazine ring and CONH group. Accordingly, the HOMO–LUMO transition implies an electron density transfer from the phenyl ring to the pyrazine ring through the CONH group. For understanding various aspects of pharmacological sciences including drug design and the possible ecotoxicological characteristics of the drug molecules, several new chemical reactivity descriptors have been proposed. Conceptual DFT based descriptors have helped in many ways to understand the structure of molecules and their reactivity by calculating the chemical potential, global hardness and electrophilicity. Using HOMO and LUMO orbital energies, the ionization energy and electron affinity can be expressed as: I = −E_HOMO, A = −E_LUMO, η = (−E_HOMO + E_LUMO)/2 and μ = 1/2(E_HOMO + E_LUMO) (Koopmans, 1993). Parr et al. (1999) proposed the global electrophilicity power of a ligand as ω = μ²/2η. This index measures the stabilization in energy when the system acquires an additional electronic charge from the environment. Eelctrophilicity encompasses both the ability of an electrophile to acquire additional electronic charge and the resistance of the system to exchange electronic charge with the environment. It contains information about both electron transfer (chemical potential) and stability (hardness) and is a better descriptor of global chemical reactivity. The hardness η and chemical potential μ are given by the following relations η = (I − A)/2 and μ = −(I + A)/2, where I and A are the first ionization potential and electron affinity of the chemical species (Parr and Pearson, 1983).

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Figure 4

HOMO plot of N-[(4-(trifluoromethyl)phenyl]pyrazine-2-carboxamide.

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Figure 5

LUMO plot of N-[(4-(trifluoromethyl)phenyl]pyrazine-2-carboxamide.

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For the title compound, E_HOMO = −6.984, E_LUMO = −2.925, Energy gap = HOMO–LUMO = 4.059, Ionization potential I = 6.984, Electron affinity A = 2.925, global hardness η = 2.0295, chemical potential μ = −4.9545, and global electrophiliciy = μ²/2η = 6.05. It is seen that the chemical potential of the title compound is negative and it means that the compound is stable. They do not decompose spontaneously into the elements they are made up of. The hardness signifies the resistance toward the deformation of electron cloud of chemical systems under small perturbation encountered during the chemical process. The principle of hardness works in Chemistry and Physics but it is not physically observable. Soft systems are large and highly polarizable, while hard systems are relatively small and much less polarizable.

4.6 ¹H and ¹³C NMR analysis

The calculated values of ¹³C and ¹H NMR chemical shifts by the B3LYP/GIAO model level of theory in the DMSO environment for the title compound are summarized in Table 6. Density functional theory shielding calculations are rapid and applicable to large systems, but the paramagnetic contribution to the shielding tends to be over estimated. In this sense, theoretical calculations of the chemical shifts may be used as an aid for the assignment of the experimental data. The observed NMR data are given as supporting information. The absolute isotropitc chemical shielding of N-[(4-(trifluoromethyl)phenyl]pyrazine-2-carboxamide was calculated by the B3LYP/GIAO model (Wolinski et al., 1990). Relative chemical shifts were then estimated by using the corresponding TMS shielding: σ_calc (TMS) is calculated in advance at the same theoretical level. Numerical values of chemical shift σ_pred = σ_calc(TMS) − σ_calc together with calculated values of σ_calc(TMS), are given in Table 6. It could be seen from Table 6 that the chemical shift was in agreement with the experimental data. Thus, the results showed that the predicted chemical shifts were in good agreement with the experimental data for the title compound.