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.

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:

λ = ∑ i = 1 N ω i h ν i exp ∑ i = 1 N ( ω i h ) 2

(where ν i exp stands for the i^th experimental frequency corresponding to the harmonic calculated ω 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.

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.

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

*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˚)].

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].

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.

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.

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.

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.

*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.

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.

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

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.

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.