Vibrational Spectroscopic Investigations, Electronic Properties, Molecular Structure and Quantum Mechanical Study of an Antifolate Drug: Pyrimethamine

Pélagie Manwal A Mekoung^1,2, Bel Youssouf G. Mountessou², Maraf B. Mbah², Martin Signe¹, Auguste Abouem A Zintchem², Charles P. N. Nanseu¹, Ibrahim N. Mbouombouo^2*

¹Department of Inorganic Chemistry, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.
²Computational Chemistry Laboratory, Department of Chemistry, Higher Teacher Training College, University of Yaoundé I, Yaoundé, Cameroon.

DOI: 10.4236/cc.2022.104008                

Abstract

The computational modelling supported by experimental results can explain the molecular structure, vibrational assignments, reactive sites and several structural properties. In this context, the spectroscopic (FT-IR, FT-Raman and NMR) analysis, electronic properties (HOMO and LUMO energies) and molecular structure of pyrimethamine (Pyr) were investigated by density functional theory (DFT) method associated with three levels of theory viz., B3LYP, MN15 and wB97XD with 6-311++G(d,p) and def2TZVPP as basis sets, respectively in the Gaussian 16 programs. The ¹H and ¹³C NMR chemical shifts were calculated with a gauge-independent atomic orbital (GIAO) approach by also applying the same levels of theory and basis sets. All experimental results were compared with theoretical data. Although the results revealed high degrees of correlation between the theoretical and experimental values for spectroscopic properties using the three methods. Furthermore, the atomic and natural charges, energy band gap and chemical reactivity were determined, while the frontier molecular orbital (FMO) and molecular electrostatic potential (MEP) surfaces were plotted to explain the reactive nature of the title molecule.

Keywords

Electronic Property, NMR, Pyrimethamine, Vibrational Spectrum

1. Introduction

Antifolate drugs (also known as folate antagonists or folic acid antagonists) constitute an important class of chemotherapeutic agents used in the treatment of cancer and microbial infections, including those of bacterial and protozoal origins [1]. Among the protozoan infectious diseases, malaria is the most important one against which antifolate drugs are administrated [2] [3]. Pyrimethamine (Pyr) [5-(4-chlorophenyl)-6-ethylpyrimidine-2,4-diamine] has been a popular antifolate drug used for the prevention and treatment of malaria as it inhibits the enzyme dihydrofolate reductase [4] [5], but the bacteria resistance with this drug has been noted. Like most antifolates, pyrimethamine contains a 2,4-diaminopy-rimidine group and a phenyl ring, separated by one rotatable bond [6]. Previous theoretical and structural studies revealed that the relative orientation of the two rings and the protonation state of the 2,4-diaminopyrimidine group play a key role in drug binding [7] [8]. It is noteworthy that investigations on the antimalarial drug Pyr and its derivatives have been carried out in recent years [9] - [14]. In these investigations, the knowledge of the nature of interaction between the drugs with proteins in order to determine active sites of the template molecule has been carried out using computational methods. One of these methods includes the density functional theory (DFT) which has seen explosive growth in its application to molecular systems that are of interest in a variety of scientific fields [15]. DFT plays particularly useful roles in biological molecules as it finds application in the form of hybrid quantum mechanics and molecular mechanics [16]. Moreover, owing to its balanced accuracy and efficiency, the reliability of DFT methods [17] is helpful to economically predict compound properties and to insightfully clarify some experimental phenomena [18] [19].

As the X-ray crystallography of Pyr has been elucidated by Sethuraman et al. [20] [21], the present study aimed to compare DFT results with the experimental data of bond lengths, angles, torsion, NMR and to characterize its structure using energetic data. However, the experimental ¹H NMR data [9] were found in the literature. The structure of Pyr was optimized in gas phase using DFT under B3LYP [22] [23] /6-311++G(d,p), MN15 [24] /def2TZVPP [25] and wB97X-D [26] /def2TZVPP levels. The results were compared with their corresponding experimental values. We further extended our theoretical calculations on the molecular electrostatic potential (MEP) and Mulliken charges of Pyr.

2. Materials and Methods

2.1. Sample and Experimental Details

The pure sample (pyrimethamine) was sourced from the European directorate for the quality of medicines & healthcare (EDQM) with a degree of purity of 99.5%. The FT-IR spectrum of the title molecule was measured in the 4000 - 400 cm⁻¹ region at a resolution of 1 cm⁻¹, using a PerkinElmer 2000 FT-IR spectrophotometer, vacuum in KBr pellet technique (solid phase). The FT-Raman spectrum of the molecule was also recorded using 1064 nm as excitation wavelength in the region 4000 - 100 cm⁻¹ on a Bruker FT-Raman instrument. The sample was dissolved in the hexadeteurated dimethyl sulfoxide (DMSO-d₆) solvent and, the ¹³C NMR spectrum was recorded on a Bruker Advance 600 MHz spectrometer.

2.2. Computational Details

In the present study, we used the following functionals of the density functional theory (DFT) associated with 6-311++G(d,p) and def2TZVPP [25] basis sets:

● Hybrid density functional named Becke’s three-parameter hybrid model with the Lee-Yang-Parr correlation functional (B3LYP [22] [23]);

● A Kohn-Sham global-hybrid exchange-correlation density functional viz., MN15 [24];

● The long-range corrected (LC) hybrid density functional [27] [28] [29] namely wB97X-D [26].

All calculations were performed using Gaussian 16 software package [30] and GaussView visualization program [31]; their output files were analysed with GaussSum program [32]. The optimized structural parameters were used in the vibrational frequencies (IR, Raman), isotropic chemical shifts (NMR). The vibrational frequencies, IR and Raman intensities for pyrimethamine were calculated at B3LYP/6-311++G(d,p), wB97XD/def2TZVPP and MN15/def2TZVPP methods. Computed harmonic frequencies were scaled by a factor of 0.967 (B3LYP) [33], 0.955 (wB97XD) [34] and 0.977 (MN15) obtained from the following formula as reported by Malloum et al. [35] in order to improve the agreement with the experimental results:

$\lambda =\frac{{\displaystyle {\sum }_{i=1}^N{\omega }_i^h{\nu }_i^{\exp }}}{{\displaystyle {\sum }_{i=1}^N{\left({\omega }_i^h\right)}^2}}$

(where ${\nu }_i^{\exp }$ stands for the i^th experimental frequency corresponding to the harmonic calculated ${\omega }_i^h$ frequency. N is the number of frequencies investigated).

The total energy distribution (TED) was calculated using VEDA program [36] in order to characterize the fundamental vibrational modes. ¹H and ¹³C NMR chemical shifts were evaluated using the gauge-independent atomic orbital (GIAO) approach [37] by applying the three corresponding methods used in this work. In addition, the frontier molecular orbitals (FMOs), the molecular electrostatic potential (MEP), and the Mulliken population analysis of pyrimethamine were also theoretically investigated.

3. Results and Discussion

3.1. Potential Energy Surface (PES) Scan

The pyrimethamine (Pyr) molecule has one ethyl group and two amino substituents attached to the pyrimidine ring. The ethyl (C₂H₅), methyl (CH₃) and amino (NH₂) groups were chosen to examine the possible conformers of the molecule under investigation. Sethuraman et al. [20] study shows that pyr has two conformers (A and B). In order to determine conformational flexibility of Pyr, the potential energy surface scans was achieved with B3LYP/6-311++G(d,p) method by varying the dihedral angle D1 (C12-C13-C16-C19), D2 (C13-C16-C19-H22) and D3 (N30-C15-N26-H27) in 36 steps of size 10˚. The resultant energy profiles are shown in Figures 1-3, respectively. The structures of the possible conformers and their energies are given in Table 1. It can be seen from Table 1 that structures S3, C2 and M3 have the same minimum energy (−1144.567789 a.u) for the different selected dihedral angles, suggesting that they represent the same conformer. It corresponds to the most stable conformer. According to X-ray crystallographic study, it is the molecule A. In this study, calculations were done for the most stable conformer.

3.2. Molecular Geometry

The X-ray study of pyrimethamine whose chemical structure is depicted in Figure 4(a) was elucidated by Sethuraman et al. [20] [21] The structure of pyrimethamine was optimized (Figure 4(b)) at B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97XD/def2TZVPP levels of theory. The results of the selected optimized structure parameters (bond lengths, bond angles, dihedral angle) were compared with their corresponding experimental values in Table 2.

The bond connecting the pyrimidine and phenyl rings namely C4-C12 (b) is predicted at 1.492 Å for B3LYP, 1.484 Å for MN15 and 1.485 Å for wB97XD

Figure 1. Potential energy surface scan for dihedral angle D1 (C12-C13-C16-C19).

Figure 2. Potential energy surface scan for dihedral angle D2 (C13-C16-C19-H22).

Figure 3. Potential energy surface scan for dihedral angle D3 (N30-C15-N26-H27).

Table 1. Theoretical possible structures for selected dihedral angles of pyrimethamine.

Table 2. Selected experimental values and theoretical optimized structure parameters of pyrimethamine under B3LYP/6-311++ G(d,p), MN15/def2TZVPP and wB97X-D/def2TZVPP levels.

*r represents the correlation coefficient between experimental and theoretical data; For numbering of atoms refer to Figure 1; ^aSee reference [21].

methods, respectively. The theoretical torsion angles C12-C13-C16-C19, which represents the deviation of the ethyl group from the benzene plane are 107.0˚ (B3LYP), 83.5˚ (MN15) and 90.7˚ (wB97XD). These values are in close agreement with those observed in the crystal structure of pyr [(C5A-C9A = 1.491 Å), C5A-C6A-C7A-C8A = 97.8˚)].

Figure 4. X-ray molecular (a) and theoretical optimized (b) structure of pyrimethamine.

The correlation coefficients (r) between experimental and theoretical bond lengths were 0.994, 0.994 and 0.995 for bond lengths and 0.97, 0.98 and 0.97 for bond angles for B3LYP, MN15 and wB97XD methods, respectively. It was worth mentioning that from correlation values, the wB97XD/def2TZVPP level gave the most accurate results than other methods for the bond lengths, while for the computations of bond angles, the best results were found by using MN15/ def2TZVPP level. On the other hand, we observed a weak relationship between some experimental and theoretical parameters. It must be noted that the experimental results were obtained from the solid phase, whereas the theoretical calculations were made from the gas phase of the molecule. In the solid-state, intermolecular interactions connected the molecules together, whereas in gaseous phase, these interactions were much weaker than in the solid-state, due to permanent vibrations within the molecule. These observations allowed us to conclude that the differences between the experimental and theoretical values are normal [38] [39].

3.3. Vibrational Assignments

Vibrational frequencies have been shown to be effective in the identification of functional groups of organic compound as well as in the study of molecular conformations and kinetic reactions. The calculated and scaled up by appropriate frequency factor using B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97XD/ def2TZVPP with their relative intensities, probable assignment and total energy distribution (TED) of the title molecule are summarized in Table 3. A complete assignment of fundamental vibrational modes was proposed based on the calculated TED value infrared and Raman intensities.

Table 3. Calculated (unscaled and scaled) frequencies, IR intensity, Raman intensity and probable assignments (characterized by TED) of pyrimethamine using B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97XD/def2TZVPP methods.

ν_s, very strong; s, strong; m, medium; w, weak; vw, very weak; ^aI_IR: IR intensities (Km/Mol), ^bRA: Raman scattering activity (A⁴/ AMU), ν: stretching; β: deformation in the plane; γ: deformation out-of-plane; w: wagging; τ: torsion, βR: deformation ring, τ_R: torsion ring, ρ: rocking, tw: twisting, δ: deformation, R1: phenyl ring, R2: pyrimidine ring.

The title molecule had 30 atoms, which underwent 84 (3N-6) normal modes of vibrations, 29 modes of vibrations were stretching, 28 modes of vibrations in plane bending and remaining 27 modes of vibrations were torsion. It agreed with C1 point group symmetry, all vibrations were active in Raman and IR absorptions. The experimental FT-IR and FT-Raman spectra are compared with corresponding predicted spectra in Figure5 and Figure6 respectively. The theoretical infrared and Raman spectra of pyrimethamine are presented in FigureS1 and FigureS2 (Supplementary Material), respectively.

Figure 5. Experimental FT-IR spectra of pyrimethamine.

Figure 6. Experimental FT-Raman spectra of pyrimethamine.

The small difference between the experimental and theoretical spectra could be attributed to the fact that experimental results refer to insufficient vibrations in solid phase contrary to gaseous phase.

3.3.1. NH₂ Vibrations

Amino groups are generally known as electron donating groups. They give rise to six internal modes, namely symmetric stretching ν_s(NH₂), anti-symmetric stretching ν_as(NH₂), scissoring or symmetric deformation or simply deformation β(NH₂), anti-symmetric deformations or rocking ρ(NH₂), wagging w(NH₂) and torsion or twist tw(NH₂) modes. For Pyr, the ν_s and ν_as modes are localised as pure group modes, whereas the β, ρ, w and tw modes are sometimes mixed with the other ring modes. The NH₂ stretching typically appears in the region 3500 - 3000 cm^–1 [40]. Two N-H bonds were identified for each NH₂ stretching mode. The experimental N-H stretching vibrations were observed at 3468 and 3310 cm^–1 in the IR spectrum [41], while the anti-symmetric stretching vibration at 3063 cm^–1 in the Raman spectrum corresponded to ν_as(NH₂). The lower frequency is assigned to the symmetric (νs) mode and the higher one to the anti-symmetric (ν_as) mode. The corresponding anti-symmetric (ν_as) stretching vibrations were calculated as 3607 and 3598 cm^–1 for B3LYP/6-311++G(d,p); 3701 and 3672 cm^–1 for MN15/def2TZVPP and; 3617 and 3605 cm^–1 for wB97XD/ def2TZVPP, while the symmetric (ν_s) stretching mode were computed as 3485 and 3478 cm^–1 for B3LYP/6-311++G(d,p); 3562 and 3541 cm^–1 for MN15/ def2TZVPP and, 3491 and 3482 cm^–1 for wB97XD/def2TZVPP, respectively.

The scissoring modes (β) of the NH₂ group is expected in the range 1625 - 1500 cm^–1, which contains a broad and strong IR band with peak at 1628 cm^–1. DFT calculations provided values at 1585 and 1577 cm^–1 for B3LYP/6-311++ G(d,p); 1626 and 1622 cm^–1 for MN15/def2TZVPP and; 1600 and 1592 cm^–1 for wB97XD/def2TZVPP.

The rocking ρ(NH₂) mode usually appears in the region 1150 - 900 cm^–1 [40]. Here, the IR band at 1012 cm^–1 is associated with this mode, were calculated as 1128 and 1067 cm^–1 for B3LYP/6-311++G(d,p); 1134 and 1085 cm^–1 for MN15/ def2TZVPP and 1128 cm^–1, 1592 cm^–1 for wB97XD/def2TZVPP, respectively.

Twisting tw(NH₂) mode have been obtained at 510, 496 and 475 cm^–1 for B3LYP/6-311++G(d,p); 522, 512 and 489 cm^–1 for MN15/def2TZVPP and 515, 502 and 483 cm^–1 for wB97XD/def2TZVPP, respectively.

Theoretically, wagging w(NH₂) mode appeared at 356, 295 and 287 cm^–1 for B3LYP/6-311++G(d,p); 353, 280 and 275 cm^–1 for MN15/def2TZVPP and 350, 291 and 278 cm^–1 for wB97XD/def2TZVPP, respectively.

3.3.2. C-H Vibrations

The characteristic C-H stretching vibrations of the phenyl rings commonly exhibit multiple weak bands in the region 3100 - 3000 cm^–1 [40] [41] [42]. The DFT calculations give values at 3094, 3092, 3071 and 3068 cm^–1 for B3LYP/ 6-311++G(d,p); 3163, 3162, 3135 and 3133 cm^–1 for MN15/def2TZVPP and; 3084, 3083, 3060 and 3059 cm^–1 for wB97XD/def2TZVPP, while the bands were observed at 3150 and 2985 cm^–1 in the IR and Raman spectra, respectively. Because of the interaction (sometimes strongly) with various ring C=C vibrations, many bands in the 1600 - 1000 cm^–1 involve in-plane C-Η bending vibrations and 1000 - 700 cm^–1 in out-plane bending [43], respectively. The C-H in plane bending vibrations of phenyl rings were observed at 1087 cm^–1 (FTIR spectrum) and 1086 cm^–1 (Raman spectrum), while calculated ones appeared at 1471, 1371, 1278, 1160 and 1086 cm^–1 for B3LYP/6-311++G(d,p); 1501, 1393, 1292, 1155 and 1090 cm^–1 for MN15/def2TZVPP and; 1480, 1377, 1273, 1157 and 1085 cm^–1 for wB97XD/def2TZVPP, respectively. The C-H out-of-plane bending vibrations of Pyr were observed at 955, 939, 819, and 815 cm^–1 (B3LYP/6-311++G(d,p)); 974, 972, 849 and 840 cm^–1 for MN15/def2TZVPP and; 967, 954, 833, and 828 cm^–1 (wB97XD/def2TZVPP).

3.3.3. CH₂ and CH₃ Vibrations

The vibrations of the CH₂ group, the asymmetric stretch ν_asCH₂, the symmetric stretch ν_sCH₂ and bending vibrations βCH₂, appear in the region 3000 - 2900 cm^–1, 2900 - 2800 cm^–1 and 1410 - 1480 cm^–1, respectively [44] [45]. The νCH₂ stretching vibrations were found at 2977 cm^–1 in IR spectrum. The DFT calculations gave ν_asCH₂ at 3010, 3084 and 3004 cm^–1 for B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97XD/def2TZVPP methods, respectively; while ν_sCH₂ were found at 2943 (B3LYP), 3026 (MN15) and 2946 cm^–1 (wB97XD). In the present work, the predicted wavenumbers at 1438 cm^–1 (B3LYP/6-311++G(d,p)), 1446 cm^–1 (MN15/def2TZVPP) and 1436 cm^–1 (wB97XD/def2TZVPP) were identified as CH₂ bending vibrations. For the title molecule, the CH₂ bending mode was observed at 1439 cm^–1 in FT-IR spectrum. Theoretically, wagging wCH₂ of Pyr was identified at 1306 cm^–1 (B3LYP/6-311++G(d,p)), 1303 cm^–1 (MN15/ def2TZVPP) and 1297 cm^–1 (wB97XD/def2TZVPP), while twisting twCH₂ were observed at 1221 cm^–1 (B3LYP/6-311++G(d,p)), 1227 cm^–1 (MN15/def2TZVPP) and 1217 cm^–1 (wB97XD/def2TZVPP). The rocking ρCH₂ appeared at 1093 and 774 cm^–1 (B3LYP/6-311++G(d,p)), 1101 and 770 cm^–1 (MN15/def2TZVPP) and 1089 and 777 cm^–1 (wB97XD/def2TZVPP).

The stretching vibrations of the CH₃ group are expected in the range of 2900 - 3050 cm^–1 [44] [45]. In the present case, the calculated asymmetric stretching modes of the methyl group were found to be: 3010, 2991 and 2985 cm^–1 for B3LYP/6-311++G(d,p), 3084, 3076 and 3059 cm^–1 for MN15/def2TZVPP, 3004, 2994 and 2982 cm^–1 for wB97XD/def2TZVPP while, the symmetric modes were at 2928 cm^–1 (B3LYP), 2992 cm^–1 (MN15) and 2917 cm⁻¹ (wB97XD). Experimental bands were observed at 2977 cm^–1 in the IR spectrum and 2985 cm^–1 for Raman spectrum. The asymmetric and symmetric bending vibrations of the methyl group normally appear in the region of 1400 - 1485 and 1420 - 1380 cm^–1 [45] [46]. The bands observed at 1479 and 1439 cm^–1 in the IR spectrum were assigned as CH₃ bending modes. The DFT/B3LYP/wB97XD/MN15 calculations gave the following modes: 1460, 1447 and 1351 cm^–1 [B3LYP/6-311++G(d,p)]; 1461, 1451 and 1356 cm^–1 (MN15/def2TZVPP) and; 1447, 1437 and 1356 cm^–1 (wB97XD/def2TZVPP).

3.3.4. C=N and C=C Vibrations

The C=N and C=C ring stretching vibrations bands for pyrimidine compounds are often observed with strong absorptions in the region 1600 - 1500 cm^–1 [47]. In the literature, the vibration bands of C=N and C=C are found at 1650 - 1620 cm^–1 and 1600 - 1450 cm^–1, respectively [48]. In this work, experimental C=N stretching bands at 1560 cm⁻¹, were computed to be 1556 and 1533 cm⁻¹ (B3LYP/6-311++G(d,p)), 1589 and 1556 cm⁻¹ (MN15/def2TZVPP) and, 1562 and 1551 cm⁻¹ (wB97XD/def2TZVPP).

Occurrence of conjugation especially in aromatic rings tends to decrease the frequency of the bond [48]. The C=C stretching vibrations at the α-position of the C=N bond and aromatic ring were observed at 1560 cm^–1. The calculated values corresponded to 1575, 1544 and 1533 cm^–1 (B3LYP/6-311++G(d,p)); 1597, 1589 and 1556 cm⁻¹ (MN15/def2TZVPP) and; 1581, 1562 and 1551 cm^–1 (wB97XD/def2TZVPP).

3.3.5. C-Cl Vibrations

Usually, chlorine present in the molecules has a strong vibration band between 550 and 850 cm^–1 [49] [50] due to the C-Cl stretching vibrations. In this work, the IR and Raman bands observed at 512 and 475.8 cm^–1, respectively, were calculated as 451 cm⁻¹ for B3LYP/6-311++G(d,p), 461 cm⁻¹ for MN15/def2TZVPP and 457 cm⁻¹ for wB97XD/def2TZVPP. The corresponding in-plane deformation modes (bending) appear in the Raman spectrum as a shoulder at 357.3 cm⁻¹ while calculated frequencies are identified at 295 cm⁻¹ for B3LYP/6-311++G(d,p), 280 cm⁻¹ for MN15/def2TZVPP and 291 cm⁻¹ for wB97XD/def2TZVPP.

3.4. ¹H and ¹³C NMR Data

The ¹H and ¹³C NMR chemical shifts of the title molecule have been carried out using the B3LYP, MN15 and wB97XD functionals with 6-311++G(d,p), def2TZVPP and def2TZVPP basis sets for the optimized geometry and the results were given in Table 4 and Table 5 (see Figures S3-S5 and Figures S6-S8 of Supplementary material for calculated ¹H and ¹³C NMR spectra, respectively associated to the three methods). The experimental ¹H and ¹³C NMR spectra in DMSO-d₆ (at 600 and 150 MHz, respectively) of the molecule are shown in FigureS9 and FigureS10 (Supplementary material), respectively. It is noteworthy that the experimental ¹H NMR spectrum of the studied compound has been reported in the literature [9].

In the ¹H NMR spectra, aromatic ring protons have chemical shifts in the region of 6.5 - 8.0 ppm [51]. From experimental spectrum, we observed the aromatic ring protons between 7.464 and 7.180 ppm. The chemical shifts of the protons were calculated in the region 7.877 - 8.235 ppm for B3LYP/6-311++G(d,p), 8.418 - 8.727 ppm for MN15/def2TZVPP and 8.091 - 8.391 ppm for wB97XD/ def2TZVPP. Table 4 shows some correlations between the experimental and calculated ¹H NMR results.

Table 4. Experimental and calculated chemical shifts (in ppm) of isotropic ¹H for pyrimethamine under B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97X-D/def2TZVPP levels.

Table 5. Experimental and calculated chemical shifts (in ppm) of isotropic 13C for pyrimethamine under B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97X-D/def2TZVPP levels.

*r represents the correlation coefficient between experimental and theoretical data.

In this work, the chemical shifts of the carbon atom in C=N-(C14, C15) found in ¹³C spectrum of pyrimethamine, were observed at 162.15 and 161.96 ppm and calculated values at 170.208 and 171.102 ppm for B3LYP/6-311++G(d,p), 173.641 and 173.851 ppm wB97XD/def2TZVPP, 192.246 and 191.820 ppm for MN15/def2TZVPP. As presented in Table 5, there is a correlation between the experimental and calculated ¹³C NMR results, and the corresponding r values were found to be 0.987, 0.985 and 0.984, respectively for corresponding method/basis sets.

3.5. Frontier Molecular Orbitals (HOMO-LUMO)

The most important orbitals in a molecule are the frontier molecular orbitals (FMOs), called highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). These orbitals play a significant role in the optical and electric properties, as well as in quantum chemistry, chemical reactions and UV-vis spectra [52]. The energies of HOMO (E_H) and LUMO (E_L) characterize the ability of a molecule to donate and accept electrons, respectively. The difference between E_H and E_L is called energy gap (ΔE_G), which enables the determination of the electrical transport and other properties such as kinetic stability, chemical reactivity, optical polarizability and chemical hardness–softness of the molecular system. The energy gap is large for hard molecules and small for soft molecules [53]. Soft molecules are more polarizable than the hard ones because they need small energy for excitation [54] [55]. The HOMO, LUMO and chemical reactivity descriptors for pyrimethamine were calculated by Gaussian 16 program using B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97XD/ def2TZVPP levels and their values were summarized in Table 6.

Calculations indicated that Pyr has 65 occupied sites with high energy gaps found to be 5.015, 6.465 and 8.884 eV (ΔE_HOMO–LUMO gap) with B3LYP/6-311++ G(d,p), MN15/def2TZVPP and wB97XD/def2TZVPP methods, respectively and also has high hardness value [2.508 eV (B3LYP), 3.232 eV (MN15) and 4.442 eV (wB97XD)] and low softness value [0.399 eV (B3LYP), 0.309 eV (MN15) and 0.225 eV (wB97XD)]. These results probably suggested that it is a hard molecule with high stability. The 3D plots of HOMO and LUMO orbitals are illustrated in Figure 7 using B3LYP/6-311++G(d,p) calculation level. The positive and negative phases were represented in red and green colour, respectively.

3.6. Mulliken Atomic Charges

The computation of the reactive atomic charges plays an important role in the application of quantum chemical calculations [56] for the molecular system. The Mulliken atomic charges were calculated by determining the electron population of each atom with DFT using B3LYP, MN15 and wB97XD method at 6-311++ G(d,p), def2TZVPP and def2TZVPP basic functions, respectively. The charge distribution calculated by the natural bond orbital (NBO) and Mulliken methods of pyrimethamine are summarized in Table 7. From Mulliken charges computation, the carbon atom C15 had a high positive charge compared to all other carbon atoms, because of the three-neighbouring electronegative N26, N29 and

Table 6. Calculated energy values for pyrimethamine under B3LYP/6-311++G(d,p), MN15/def2TZVPP and wB97XD/def2TZVPP levels.

Figure 7. Atomic orbital compositions of the frontier molecular orbital for pyrimethamine.

Table 7. Charge distribution calculated by the natural bond orbital (NBO) and Mulliken methods of pyrimethamine.

N30 atoms, respectively. C15 behaves as an acceptor atom and it sustains nucleophilic reactions. The nitrogen atoms N23 and N26 perform as donor atoms, they endure electrophilic reaction. The charge distribution is modified by changing different basis sets as summarized in Table 7. The corresponding Mulliken plots are shown in Figure 8.

3.7. Molecular Electrostatic Potential (MEP) Analysis

The molecular electrostatic potential (MEP) is a very cooperative tool in understanding the relationship between molecular structure and reactivity. MEP mapping is often used for interpretation and prediction of relative reactivity sites for electrophilic and nucleophilic attacks [57] [58], calculations of atomic charges [59], and study of molecular similarity [60].

Three MEP diagrams have been plotted for pyrimethamine at B3LYP/6-311++ G(d,p), MN15/def2TZVPP and wB97XD/def2TZVPP levels of calculations as illustrated in Figure 9. This figure provided a visual representation of the chemically active sites and comparative reactivity of atoms. The electrostatic potential increases in the order red < orange < yellow < green < blue, where the blue colour indicates a minimal concentration of electrons (nucleophilic reactivity) and the red indicates a high density of electrons (electrophilic reactivity). In addition, the negative electrostatic potential regions (red) were localized on the carbon atom C15 nearby nitrogen atoms (N26, N29 and N30) indicating possible site for electrophilic attack. However, positive potential regions (blue) were localized around NH₂ groups (N26, N23), indicating possible sites for nucleophilic attack in the drug. This result was also supported by the evidences of charge analysis parts. The docking study by Musa et al. [61] reveals that the NH2 group (N26) is the preferred binding site.

Figure 8. Mulliken atomic charges of pyrimethamine.

Figure 9. 3D plots of the molecular electrostatic potential map of pyrimethamine.

4. Conclusions

The FT-IR and FT-Raman spectra of pyrimethamine were experimentally studied and analysed, while the X-ray and ¹H NMR data were obtained from literature. The molecular geometry and wave numbers were calculated using DFT functionals associated with 6-311++G(d,p) and def2TZVPP basis sets. The optimized geometrical parameters were found to be in good agreement with the XRD results. It is observed that there are no significant differences between the experimental and the theoretical structures. It was noted that some of the experimental results belong to the solid phase, while theoretical calculations were due to gaseous phase. A reasonable agreement was observed between the observed and stimulated spectra (IR and Raman). The TED calculation regarding the normal modes of vibration provides strong support for the frequency assignment. The spectroscopic investigations showed a high degree of approximation between the calculated and experimental results. However, remarkable differences observed between the experimental and theoretical chemical shifts may be due to the fact that DFT calculations have been performed in the gas phase whereas the experimental results were carried out in solid phase.

The HOMO/LUMO analysis was done in order to characterize the electron density of the molecule. Analysis of Mulliken’s charge revealed a concentration of negative charge at the nitrogen atoms of the amino groups, while the carbon atom (C15) is positively charged. The MEP map shows that the negative potential sites are around the carbon atom (C15) and the positive potential sites are on nitrogen atoms of the amino groups. These sites provide information concerning the region from where the molecule can undergo intramolecular and intermolecular interactions.

Overall, the present investigations provide a solid foundation for dealing with diaminopyrimidine compounds.

Acknowledgements

The authors thank the University of Yaoundé I and the Higher Teacher Training College of Yaoundé (Cameroon) for infrastructural facilities.

Supplementary Material

Supporting data have been provided herein.

Figure S1. Theoretical FT-IR spectra of pyrimethamine.

Figure S2. Theoretical FT-Raman spectra of pyrimethamine.

Figure S3. Theoretical ¹H NMR spectrum of pyrimethamine by DFT/B3LYP/6-311++G(d,p).

Figure S4. Theoretical ¹H NMR spectrum of pyrimethamine by DFT/MN15/def2TZVPP.

Figure S5. Theoretical ¹H NMR spectrum of pyrimethamine by DFT/wB97XD/def2TZVPP.

Figure S6. Theoretical ¹³C NMR spectrum of pyrimethamine by DFT/B3LYP/6-311++G(d,p).

Figure S7. Theoretical ¹³C NMR spectrum of pyrimethamine by DFT/MN15/def2TZVPP.

Figure S8. Theoretical ¹³C NMR spectrum of pyrimethamine by DFT/wB97XD/def2TZVPP.

Figure S9. Experimental ¹H NMR spectrum (600 MHz, DMSO) of pyrimethamine.

Figure S10. Experimental ¹³C NMR spectrum (150 MHz, DMSO) of pyrimethamine.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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