The ¹H and ¹³C NMR chemical shifts (δ) for the NMP compounds were calculated to compare with those experimental values reported in the literature [10,11]. The values of δ obtained with the level of theory BP86/cc-pVTZ are in good agreement with the experimental data. Tables S1 and S2 show the main ¹H and ¹³C NMR δ values, respectively, obtained for the three NMP compounds.

For ¹H NMR, similar δ for H_ring of the carbazole group are observed for NMP-7 and NMP-181 with values of 7.51–9.00 ppm, while for NMP-4, the values decrease to 6.98–8.18 ppm due to the presence of the methoxy group. δ for H_R-CH2-N, H_CH2, and H_CH3 of the pentyl group are 4.24–4.43, 1.40–1.87, and 0.93–1.22 ppm, respectively, for the three NMP compounds. The methoxy group in NMP-4 shows a δ in H_CH3O 3.89–4.11 ppm and the amine and ester groups in NMP-181 for H_CH3-N and H_CH2-O have δ values of 1.73–2.83 and 4.15–4.71 ppm, respectively; see Table S1.

For ¹³C NMR, δ values for C_ring at the carbazole group are 121.0–131.1 ppm. In the pentyl group, δ values for C_CH2-N, C_CH2-C, C_CH3-C are obtained at 47.4–62.8, 29.4–35.3, and 16.5–16.6 ppm, respectively. δ value for C_C-OCH3 at the methoxy group in NMP-4 is 164.4 ppm. δ values for C_CH3-N and C_CH2-O of the amine and ester groups in NMP-181 are 47.0–51.7 and 69.0 ppm; see Table S2. All the calculated δ values agree with the experimental data reported. The major difference in the calculated data for ¹H and ¹³C NMR are 1.49 and 14.73 ppm, respectively, regarding the experimental data in chloroform [10,11]. Some of the major differences of calculated chemical displacements with respect to the experimental data [10,11] were those H or C that were close to electronegative atoms (N or O) and, therefore, were more deshielded and susceptible to interaction with the solvent. Several factors could be involved in addition to the electronegativity, such as the molecular geometry, the inductive effect, electron delocalization, etc. [13]. For example, in NMP-4 and NMP-7 compounds, the protons bonded at C8 near the carbonyl oxygen had a difference of 1.32 ppm, while in NMP-181 the proton bonded in C10 and C8 had a major difference of 0.63 ppm. Further, the C20, C9, C4 had a difference of 4.97, 4.01, and 10.88 ppm for NMP-4, NMP-7, and NMP-181, respectively (see Figure 1 for labelling). Figure 2 presents the correlation graphs of calculated δ values obtained at BP86/cc-pVTZ level of theory with the experimental δ values for NMP compounds. Figure 2a shows R² values of 0.974–0.992 for ¹H and Figure 2b shows R² values of 0.973–0.997 for ¹³C NMR. In general, the results are satisfactorily obtained for δ ¹H and ¹³C NMR in NMP compounds.

The IR characterization was carried out at the same level of theory, BP86/cc-pVTZ. Table S3 collects the most representative frequencies, intensities, scaled frequencies with 1.014 factor, and the Potential Energy Distribution (PED ≥ 10%). Table S3 shows the characteristic bands for NMP compounds. The most intense vibration is assigned to the C=O stretching located at 1623.2, 1619.5, and 1692.1 cm⁻¹ for NMP-4, NMP-7, and NMP-181, respectively. This last value is modified by the ester group in NMP-181 causing that the absorption band increases at a higher frequency. The reported value for C=O stretching of the amide group is in the range 1680–1630 cm⁻¹ [14] and of the ester group in 1730–1715 cm⁻¹ [15]. The asymmetric and symmetric C-H stretching of the pentyl group is in 3054.3 and 2980.5 cm⁻¹, 3055.7 and 2980.9 cm⁻¹, and 3055.6 and 2981 cm⁻¹, for NMP-4, NMP-7, and NMP-181, respectively. These values are similar to 2926 and 2853 cm⁻¹, reported for asymmetric and symmetric stretching of a methylene group, respectively [13]. The symmetric C-H stretching for the methyl group is located at 2992 cm⁻¹ for NMP-7 according to the 2872 cm⁻¹ reported value for this group [13]. The asymmetric and symmetric C-H stretching for the piperidine group are 3039.3 and 2991.0 cm⁻¹ for NMP-4, and 3039.3 and 2989.0 cm⁻¹ for NMP-7. The reported value in literature for asymmetric C-H stretching is 3000–2800 cm⁻¹ and for the symmetric C-H stretching is 2870–2850 cm⁻¹ [15,16,17].

Additionally, the N-C stretching in the amide group is 1416.5 cm⁻¹ and for the pyrrole nitrogen in carbazole group is 1349.9 cm⁻¹ for NMP-7. The reported value for these groups is 1400 cm⁻¹ and 1342–1266 cm⁻¹, respectively [13]. The C=C stretching in the carbazole group is in 1635.0, 1629.5, and 1629.4 cm⁻¹ for NMP-4, NMP-7, and NMP-181, respectively. These values are according to the value of 1625 cm⁻¹ for the aromatic ring. In NMP-4 the band increases at a higher frequency for the presence of the methoxy group [15]. The C-H stretching in the carbazole group is 3162.3 and 3163.6 cm⁻¹ in NMP-7 and NMP-181, respectively. The reported value for alkene C-H stretching is usually observed above 3000 cm⁻¹, in the range of 3050–3000 cm⁻¹ [15]. For NMP-4 the presence of methoxy group in the absorption region at 3106.0 and 2976.5 cm⁻¹ for asymmetric and symmetric stretching of CH₃ group, respectively, is closed to the reported region at 2830–2815 cm⁻¹ [15]. The C-O-C stretching is in 1239.0 cm⁻¹, the reported region for ether group is 1300–1000 cm⁻¹ [16,17,18]. Furthermore, the 585 cm⁻¹ vibration of the O-C-C bending is according to the region 580–505 cm⁻¹ for aromatic compounds with methoxy groups [15]. For the NMP-181 the asymmetric and symmetric C-H stretching of amine are at 3079.3 cm⁻¹ and 2876.6 cm⁻¹, respectively, corresponding to the range of the -N(CH₃)₂ group in 2820 and 2770 cm⁻¹ [15]. Further, the amine C-N stretching vibration of 1263.7 cm⁻¹ is close to the 1270 cm⁻¹ reported value for tertiary dimethyl amine [15]. The ester C-O-C stretching vibration appears in 1207.1 and 1088.5 cm⁻¹ corresponding to the known range at 1210–1173 cm⁻¹ [15,18]. Figure 3 shows the theoretical IR spectra of the NMP compounds with the main characteristic bands assigned.

The FMO are relevant for predicting the relative reactivity based on the electronic structure properties of a molecular system. The chemical properties of a molecule are controlled by the valence orbitals. In this way, nucleophilic attacks are controlled by the HOMO orbital and electrophilic attacks are controlled by the LUMO orbital. The HOMO-LUMO gap energy (ΔE_gap) is considered as a measure of the molecular structure stability [19]. Table S4 contains the HOMO and LUMO energies, E_HOMO and E_LUMO, and gap energies, ΔE_gap, for NMP compounds. The ΔE_gap is ~3.0 eV at BP86/cc-pVTZ level of theory. NMP-4 has higher gap energy (3.17 eV) than the other NMP compounds; see Figure 4.

Table S5 shows the percentage of the contributions of the functional groups to the molecular orbitals from LUMO+3 to HOMO−3. The carbazole group on the NMP-4, NMP-7, and NMP-181 compounds contributes almost entirely (95%, 97%, and 76%) to the LUMO; the difference observed of 2% for NMP-4 and 21% for NMP-181 with respect to NMP-7 is due to the attached methoxy group to the NMP-4 and the ester group to the NMP-181 compounds. The carbazole group greatly contributes to the HOMO orbital (80% and 86%) for NMP-4 and NMP-7 compounds, respectively, while for NMP-181 the amine group has a major percentage (97%) contribution. The carbonyl group contributes to the HOMO in 8 and 7%, for NMP-4 and NMP-7, respectively, while only participating with 1% in the LUMO in both compounds. In the NMP-181, the ester group participates with 23% in LUMO and only 2% in HOMO. The pentyl group has small contributions on the analyzed orbitals, see Table S5.

Figure 4 shows the isosurfaces of the FMO using an isovalue of 0.02 a.u. It was observed that a great contribution for LUMO is from C atoms of carbazole group and a minor contribution from O atoms in the carbonyl group of NMP-4 and NMP-7 and in the ester group for NMP-181. HOMO major contributions of C and N atoms of carbazole group and minor contributions of C22 and C23 of pentyl group are observed for NMP-4 and NMP-7, while for NMP-181 the HOMO have major contributions of atoms of amine of the piperidine group.

The contribution of the LUMO orbital is located at >75% on the NMP carbazole group, it can be speculated that this molecular region possesses the major participation during the ligand-receptor interaction for both CB1/CB2 receptors and T-type calcium channel. The energies of the FMO can be related to the experimental measurements of compounds determining their biological activity. For example, for ethosuximide, another T-type calcium channel blocker, its gap energies obtained at the HF/6-311+G(d,p) level of theory were correlated with the anticonvulsive activity determined by the logED50 parameter (effective dose 50%) obtaining R² = 0.97 [20]. Here, it is obtained the correlation between ΔE_gap energies and the logIC₅₀ (maximum inhibitory concentration to the 50%) values of the T-type calcium channel blocker activity reported for the NMP-4, NMP-7, NMP-181 [10,11,12], NMP-144 [11], and N-tert-butyl-2-[4-(9-pentyl-9H-carbazole-3-carbo nyl)piperazin-1-yl] acetamide (Compound 10 in reference [21]) blockers. Figure S1 shows the correlation result obtaining ~R² = 0.90. The ΔE_gap energy with respect to logIC₅₀ follows the trend: NMP-144 (2.971) < NMP-181 (3.002) < Compound 10 (3.031) < NMP-7 (3.142) < NMP-4 (3.169), which correspond to the IC₅₀ values: 5.59 µM > 4.60 µM > 3.68 µM > 1.84 µM y 2.47µM, respectively.

The Molecular Electrostatic Potential (MEP) is useful for determining different nucleophilic and electrophilic regions in molecular systems. Figure 5 shows the MEP maps in a range between −3.0 × 10⁻² and 3.0 × 10⁻² e a.u.⁻³ for the NMP compounds obtained at BP86/cc-pVTZ level of theory using an isovalue of 0.004 a.u. The major electronic density charge (red region) is located around the O1 in the carbonyl group spread toward the carbazole group in the three NMP compounds; additionally N6 of amine in NMP-181 concentrates major electronic density charge; see Figure 1 for labeling. The deficient electronic density charge (blue region) is on the region where the pentyl group is bonded to N17 of the carbazole group in the three NMP compounds. Furthermore, in the NMP-4 structure deficient electronic density charge region it is observed around H atoms on the methoxy group. In addition, the major electronic density region in the NMP-4 compound extends longitudinally almost 10.14 Å reaching the oxygen in the methoxy group. In the case of the NMP-7, this region measures 8.77 Å in the absence of the methoxy group, and 8.94 Å for NMP-181, similar to the NMP-7 compound. However, a region is located on the N6 atom of the amine group at 5.05 Å (measured from O1 atom of the carbonyl group to N6 of the amine group). It can be proposed as functional similarity of the ligand-receptor electrostatic recognizing and binding pocket coupling for the NMP compounds with the CB1/CB2 receptors and T-type calcium channel [22].

The NBO calculations for the NMP compounds were carried out to define a stability measure through the stabilization energy, E (2) parameter. The interaction between donor and acceptor of electrons is larger when the E (2) value increases. The delocalization of electronic density between Lewis-type NBO orbitals (donor) and non-Lewis NBO orbitals (acceptor) corresponds to one stabilizing donor-acceptor interaction [23]. The NMP-7 compound has three hydrogen bond acceptors (O1, N3, and N17), while NMP-4 (O1, N3, N17, and O27) and NMP-181 (O1, O3, N17, and N6) have four of them. Due to the absence of any hydrogen bond donors, in all the NMP compounds, the molecular structure stability cannot be well established by intramolecular hydrogen bond formation. In this case, the NBO analysis is useful to determine relevant interactions between Lewis-type NBO orbitals (donor) and non-Lewis NBO orbitals (acceptor), and to define electronic density delocalization. Table S6 lists the highest stabilization energies E (2) of donors and acceptors for the NMP compounds. The bond (donor) and anti-bond (acceptor) orbitals, π → π*, are found on the carbazole ring carbons in the range at ~11–24 kcal mol⁻¹. The bond (donor) and anti-bond (acceptor) orbitals, π (C9–C13) → π* (O1–C2), have larger stabilization energy on the ester group of NMP-181 than on the amide group of NMP-4 and NMP-7. The electronegative atoms O and N interact, through their lone pair electrons, with the antibonding π orbitals of carbon neighbor, LP→ π*, with stabilization energy at ~16–40 kcal mol⁻¹, and with the antibonding σ orbital of NMP-181, LP(N6) → σ* (C8–H53), with the energy of 7 kcal mol⁻¹. Finally, the anti-bond/anti-bond interaction, π* → π*, corresponds to ~23–84 kcal mol⁻¹. The electronic delocalization is observed on the conjugated bonds of the carbazole ring, and it is extended to the region of the lone pairs (LP) of the p orbitals of the electronegative neighbor atoms to carbazole moiety. Specifically, in NMP-4 and NMP-7, the electronic delocalization spreads out the amide group (O1 and N3 atoms) and the carbazole group (N17); additionally, on methoxy group (O27 atom) in NMP-4. In NMP-181, the electronic delocalization is observed on the ester group (O1 and O3) and the carbazole group (N17). In this case, in NMP-181, the tertiary amine (N6) contributes to a lesser extent to the delocalization, then it is observed a hyperconjugation interaction. The results state that the stability of the minima energy structures of the NMP compounds is mainly due to the electronic delocalization effect, where the major E (2) values are localized on electronegative atoms and carbazole moiety.

Global reactivity descriptors for the NMP compounds were evaluated: chemical potential (μ), electronegativity (χ), hardness (η), softness (s), and electrophilicity index (ω), according to the conceptual DFT approach [24]. Table 2 summarizes the global reactivity descriptors for NMP compounds. The values of the HOMO and LUMO energies are reported in Table S4. In Table 2 it is observed that global reactivity descriptors values in NMP compounds are similar with no significant changes. The methoxy group in NMP-4 slightly decreases the electronegativity and increases the chemical potential by 3.7%, while amine and ester groups in the NMP-181 have an inverse change on those parameters in 1.57% with respect to NMP-7. The hardness is larger in NMP-4, followed by NMP-7 and NMP-181, with values of 3.17 > 3.14 > 3.00 eV, respectively, then NMP-181 decreases the hardness by 4.6% while the NMP-4 increases it by 0.86%, both with respect to NMP-7. The softness keeps a similar value of 0.3 eV in the three compounds. Finally, the NMP-181 has the largest electrophilic behavior, followed by NMP-7 and NMP-4. The methoxy group in NMP-4 decreases the electrophilicity index, while the amine and ester groups of NMP-181 increase this value by ~8% with respect to NMP-7, which does not contain these functional groups; see Figure 1. The electrophilicity index results to be well correlated to the receptor affinity properties and biological activity [25].

Table S7 shows the condensed Fukui functions, f+(r) and f−(r), the dual descriptor, f(2)(r), and the Parr functions, P−(r) and P+(r), for the NMP compounds. The Fukui functions values are in the ranges of f⁺ = 0.025−0.072 and f^– = 0.011−0.070 for NMP-4, f⁺= 0.031−0.072 and f⁻ = 0.012−0.074 for NMP-7, and f⁺ = 0.014−0.086 and f⁻ = 0.002−0.10 for NMP-181. Values of the Fukui functions for relevant functional groups in NMP compounds are f⁺ = 0.048 in the methoxy group O27 (NMP-4) and f⁺ = 0.086 in the amine group N6 (NMP-181). The maxima values indicate the most probable zone for local electrophilic and nucleophilic attacks. The C21, N17, and N6 are the more prone to nucleophilic attack for NMP-4, NMP-7, and NMP-181, respectively, while the C20 is more prone to electrophilic attack for NMP-7, and C13 for NMP-4, and NMP-181. For Parr functions, it is found that the same sites for nucleophilic and electrophilic attack for all compounds; however, the results indicate that C13 is the most probable site for electrophilic attack.

Figure 6 presents the isosurfaces for Fukui functions with the major value for f⁺ and f⁻ for NMP compounds, using an isovalue of 0.002 a.u. In this figure, it is observed that f⁺ is located mainly in the carbazol nitrogen N17, in the carbonyl oxygen O1 for NMP-4 and NMP-7, in the methoxy oxygen O27 in NMP-4, and the amide nitrogen N6 in NMP-181. For f⁻ the distribution is located on the carbazol carbons in the NMP compounds and the carbonyl oxygen O1 in NMP-181. In summary, the carbazole group is an important region of electronic density accumulation for the NMP compounds. The calculated distance along this region is 6.6 Å in C9–C20 for NMP-7. It can be proposed functional similarity of the electrostatic recognizing and binding pocket coupling for the NMP compounds with the CB1/CB2 receptors and T-type calcium channel [22].