3.1. Geometrical Parameters

The optimized structures, bond lengths, bond angles, and dihedral angles calculated using Gaussian 09 at B3LYP 6-31+G (d, p) are presented in Figure 1 and Table 1, Table 2 and Table 3. The results show that the geometrical parameters (bond lengths, bond angles, and dihedral angles) of INH were altered by the alcohol group, which could be the reason for the changes observed in its properties. C1-C2, which was calculated to be 1.394 Å in INH, was 1.403 Å, 1.412 Å, 1.391 Å, 1.392 Å, and 1.364 Å in INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, respectively. A similar trend was observed in the bond angles, where C1-C2-C3 (118.82°) for INH was calculated as 118.39°, 118.36°, 120.62°, 118.05°, and 121.45° for INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, respectively. C1-C2-C3-C10 was 179.40° for INH, and for INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, it was 179.9°, −178.58°, −179.99°, 179.37°, and −179.35°, respectively. The details of the changes in geometrical parameters are provided in the tables stated above.

3.2. Frontier Molecular Orbitals

The atomic orbital composition of the frontier molecular orbital for the studied molecules is shown in Figure 2. The frontier orbital, HOMO, and LUMO, determine the way the molecule interacts with other species. It is observed from the figure that HOMOs with high electron density are found to be close to the pyridyl ring nitrogen atom, the two ring carbon atoms meta to the nitrogen atom, and the secondary amine nitrogen atom. Whereas LUMOs are seen near all atoms except the primary amine nitrogen atom. The HOMO→LUMO transition shows that electrons were transferred to the aromatic part of the molecule. In the INHOH molecules, the HOMO orbitals, which are electron dense, are located near all the aromatic ring carbon atoms, the second-degree and third-degree amine nitrogen atoms, as well as the carbonyl oxygen atom. The LUMO orbitals are located at the second and third-degree amine nitrogen atoms, the carbon atoms of the aromatic ring where the cyano groups are attached, and the cyano nitrogen atoms. This shows that there is electronic interaction between the carbonyl oxygen atom and the aromatic ring directed towards the cyano nitrogen atoms, which represents HOMO→LUMO electronic transfers.

3.3. Quantum Chemical Descriptors

The energies of frontier molecular orbital (eHOMO, eLUMO), energy band gap (eHOMO - eLUMO), electronegativity (χ = (IP + EA)/2.), chemical potential (μ = −(IP + EA)/2 ), global hardness (η = (IP − EA)/2), global softness (S = 1/2η) and global electrophilicity index (ω = μ/2η) of the studied molecules were calculated using the famous Koopmans [39] equations above and results are presented in Table 4. Our result showed that the HOMO and LUMO energies were small, ranging from −0.26 and −0.16 and −0.07 and −0.03 eV, respectively, which highlights the existence of weak electron bonds in the molecules. Due to a small energy gap, rapid electron transfers and exchange occurred to the same degree, making these molecules very reactive. The energy gap for the studied molecules was observed in the following order: INHOHN (0.131 eV) ˂ INHOH2 (0.171 eV) ˂ INHOH1 (0.190 eV) ˂ INHOH5 (0.191 eV) ˂ INHOH4 (0.195 eV) ˂ INH (0.198 eV). From our result, the interaction of alcohol with INH lowered its energy gap in all molecules, with the lowest energy gap (0.131 eV) observed in INH OHN, which shows that the highest change in reactivity of INH is when the OH group of alcohol attacks the nitrogen atom of the pyridyl ring. Lower kinetic stability is a function of a small energy gap due to the low activation energy of the system. Consequently, such molecules may experience adjustments in the charge density distribution via radical electron movements between the HOMO and LUMO orbitals and so react rapidly [40]. This could be the reason for the quick metabolism of INH in alcoholics and eventually decreased drug effectiveness. The calculated global quantum descriptors play a vital role in giving useful information about the electronic network and charge transfer behaviour of molecules. Chemical hardness (η) represents the resistance of atoms or atom groups to charge transfer [41]. From our results, alcohol lowered the resistance of INH to charge transfer. This could affect drug absorption and distribution, which is a major cause of treatment failure in INH—alcohol interaction. Electronegativity (χ) defines the ability of an atom group to attract electrons [42]. From our results, alcohol decreased the ability of INH to attract electrons, which could lead to delayed culture conversion. The measure of the ability of an atom or set of atoms to escape their ground/non-excited state is known as chemical potential (μ). It is an effective technique for studying molecules because it provides information about their solvation and transport properties. From our results, alcohol reduced the chemical potential of INH, which suggests that the ease of solvation and transport of INH may be hampered, which could be the reason for delayed absorption, distribution, and metabolism of INH in alcoholic patients. The electrophilicity index (ω) is a measure of a chemical species’ ability to function as an electrophile, that is, to accept an electron pair from a nucleophile. From our result, the electrophilicity index of INH was increased in INHOH2, which means that its propensity to accept an electron pair from a nucleophile was increased. Chemical softness ( $\sigma$ ) characterizes an atom’s propensity to accept an electron or electrons. The chemical softness of INH was increased in all molecules, which suggests an increase in reactivity upon interaction with alcohol.

3.4. Vibrational Analysis

The infrared spectra of the studied molecules are presented in Figure 3, while the frequencies, intensities, and locations are listed in Table S1. C-C vibration occurred at 1300 cm⁻¹, 1334 cm⁻¹, 1357 cm⁻¹, 1325 cm⁻¹, 1329 cm⁻¹ and 1323 cm⁻¹ for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. C=C stretching vibrations was observed at 1604.88 cm⁻¹, 1618.98 cm⁻¹, 1601.69 cm⁻¹, 1607.23 cm⁻¹, 1621.00 cm⁻¹ and 1652.89cm⁻¹ for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. NH₂ bending vibrations was observed at 1686.55 cm⁻¹, 1686.55 cm⁻¹, 1683.04 cm⁻¹, 1688.49 cm⁻¹, 1685.26 cm⁻¹ and 1676.35 cm⁻¹ for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. C=O stretching vibrations for INH was observed at 1778 91 cm⁻¹ while for INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN it was observed at 1777.07 cm⁻¹, 1732.58 cm⁻¹, 1769.27 cm⁻¹, 1781.81 cm⁻¹, 1732.57 cm⁻¹, respectively. C-H stretch is observed at 3171.21cm⁻¹, 3174.84 cm⁻¹, 3178.63 cm⁻¹, 3126.87 cm⁻¹, 3180.12 cm⁻¹, 3207.26 cm⁻¹, for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. NH₂ symmetric stretching vibrations occurred at 3505.31 cm⁻¹, 3505.20 cm⁻¹, 3508.25 cm⁻¹, 3500.83 cm⁻¹, 3505.00 cm⁻¹ and 3490.89 cm⁻¹, for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. N-H stretch was observed at 3564.99 cm⁻¹, 3570.42 cm⁻¹, 3600.75 cm⁻¹, 3583.45 cm⁻¹, 3555.42 cm⁻¹ and 3537.94 cm⁻¹ for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. NH2 asymmetric stretch was observed at 3614.16 cm⁻¹, 3612.39 cm⁻¹, 3613.64 cm⁻¹, 3601.12 cm⁻¹ and 3616.01 cm⁻¹, 3616.87 cm⁻¹ for INH, INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively. While O-H stretch was observed at 3827 37 cm⁻¹, 3291. 51 cm⁻¹, 3812.46 cm⁻¹, 3831.46 cm⁻¹ and 3775.37 cm⁻¹ for INHOH1, INHOH2, INHOH4, INHOH5 and INHOHN respectively.

3.5. UV-vis Spectroscopic Analysis

The UV-vis analysis was studied by TD-SCF/IEF-PCM/B3LYP 6-311+G (d,p). The resulting UV-visible spectra of the studied molecules in aqueous medium are shown in Figure 4, while the wavelengths (λ_max), excitation energy (E), and oscillator strengths are listed in Table S2. From our result, INH was observed to have an oscillator strength of 0.0045 and a wavelength of 279 nm, while INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN had 0.0554 and 275 nm, 0.1443 and 295 nm, 0.1047 and 273 nm, 0.0636 and 274 nm, 0.0015 and 547 nm, respectively. These transitions corresponding to π→π^* transition are governed by HOMO→LUMO excitation. From our results, we observe that the absorption wavelength of INH was extended remarkably from 278 nm to 295 nm and 547 nm in INHOH2 and INHOHN, respectively. On the other hand, it was lowered in others. The red and blue shift observed shows that the optical property of INH was altered by alcohol interaction with the N atom of the pyridyl ring and the carbon atoms of INH. These extensions increase as the band gap decreases.

3.6. Natural Bonding Orbital (NBO) Analysis

Natural bond orbital (NBO) analysis is a suitable method for understanding the nature of intra- and intermolecular bonding interactions existing in bonds. It also establishes a fair ground for studying charge transfer or closed-shell interactions in molecules [43]. The greater the perturbation energy value, the stronger the interaction between the electron donors and the more the conjugation of the system [44]. The second-order perturbation energy values of INH, INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN were identified from the second-order Fock matrix perturbation theory using DFT/B3LYP/6-31+G (d, p) functional. The most interacting NBOs are presented in Tables S3–S8 for INH, INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, respectively. From our result, the transition from π*-π* had a major contribution to the electron transition. Hyper intra-molecular conjugative interactions in the molecules are formed by the orbital overlap between π*C5-N6 and π*C3-C4 for INH, π*C1-N6 and π*C2-C3 for INHOH1, π*C10-O11 and π*C2-C3 for INHOH2, π*C5-N6 and π*C3-C4 for INHOH4 and INHOH5, LP (1) C3 and π*C11-O12 for INH OH1. Perturbation energies of 236.93 kcal/mol, 180.40 kcal/mol, 141.83 kcal/mol, 282.82 kcal/mol, 245.78 kcal/mol, and 31.23 kcal/mol were obtained for INH, INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, respectively. This shows that donor-acceptor interaction was strongest in INHOH4 and lowest in INHOHN.

3.7. Binding Energy and Dipole Moment

The binding energies are 317. 988 kcal/mol, 315.633 kcal/mol, 321.002 kcal/mol, 319.036 kcal/mol, and 2.0877 kcal/mol were calculated for INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, respectively (Table S9). These positive binding energies suggest that alcohol binding to INH is less favourable. Dipole moments were calculated as 6.128 debye, 5.512 debye, 5.972 debye, 5.911 debye, and 4.622 debye for INHOH1, INHOH2, INHOH4, INHOH5, and INHOHN, respectively (Table S10). High binding energies, small energy gaps, and large dipole moments favour active interactions. This correlates with the narrow band gaps calculated for the molecules, which all suggest high interactions and reactivity between alcohol and isoniazid.