The molecular structures of these antibiotics were studied previously as isolated molecules by means of computational chemistry methods, exploring conformational analysis, tautomerism and spectroscopic properties [36]. However, most of the infrared and Raman spectroscopic analyses are performed experimentally at solid state, mainly at crystalline state. Hence, our studies should be performed with the crystal structures of these compounds.

In the case of sulfamethazine (SMT), three crystal forms have been claimed based on X-ray diffraction, CCDC num.1260687, code: SLFNMD01 [24]; CCDC num. 126,088, code: SLFNMD02 [26]; and CCDC num. 126,089, code: SLFNMD10 [25, 37] claimed two polymorphs I and II based on IR spectroscopy. The form II was obtained from form I by trituration. However, their IR spectra, thermograms and X-ray diffractograms were too similar and the distinction was not clear [23]. Nevertheless, Kuhnert-Brandstatter et al. [38] reported four forms of sulfamethazine by thermomicroscopic methods without solid characterizations. However, Maury et al. [26] reported the existence of only one polymorph and different crystal habits. Our previous work clarified these controversies finding that all these claimed crystal polymorphs are actually the same crystal form [36], and hence only one polymorph should be considered. Nevertheless, our previous calculations were performed at the Γ point of the irreducible Brillouin zone of the crystal structure. Exploring with more detail the Brillouin zone sampling with several k points grids along the crystallographic axes, we found that the energy of the crystal structure is 5.325 kcal/mol lower with 1 × 1×3 k points grid than with the Γ point (Table S1). Hence, we reoptimized the crystal structure of the SMT with 1 × 1× 3 k points matching closer to the experimental cell parameters than the previous one calculated with only the Γ point (Table 1 and Fig. 2). Nevertheless, the differences are small and the packing energy is similar in both calculations. In this work, we extend this study to the rest of the sulfonamides series in a similar way.

The optimized crystal structures show a similar XRD pattern that the experimental one with the same 2θ values and relative intensities (Fig. S2). It is remarkable, that in SMT the amino groups of aminobencenic rings do not form hydrogen bonds with sulfonic O atoms in contrast with the rest of the sulfonamides and polymorphs studied (see below). The heterocycle rings are parallel. The aminobencenic rings are parallel to each other being perpendicular with respect to the heterocyclic rings (Fig. 2). Each amino group joins 3 molecules, where each amino H atom forms hydrogen bonding with the heterocyclic N atoms of different molecules d(NH…N) = 2.081–2.232 Å (Fig. 2b). Only the sulfonamidic NH groups form hydrogen bonds with the sulfonic O atoms d(SO…HN) = 1.925 Å. According to the hydrogen bond topology [39], this hydrogen bond between the amido H atom and sulfonic O atom forms C(8) chains and those between the amino H atoms and the heterocyclic N atoms form chains C(10) and rings R22(20) patterns.

Optimized crystal form of sulfamethazine (a), indicating some intermolecular interaction motifs (b) (distances in Å). The C, S, N, Cl, and H atoms are represented in grey, yellow, blue, green, red, and white colours. This format is extended to the rest of the figures of this work.

Nine crystal polymorphs of sulfamethoxazole have been claimed previously based on X-ray diffraction reporting 8 crystal structures: CCDC num. 1,260,679, CSD_code: SLFNMB01; CCDC num. 1,260,680, CSD_code: SLFNMB02; CCDC num. 1,260,681, CSD_code: SLFNMB03; CCDC num. 1,260,682, CSD_code: SLFNMB04 [28]; CCDC num. 270,106, CSD_code: smaIII [16]; CCDC num. 270,107, CSD_code: smaIV [16]; CCDC num. 930,472, CSD_code: BnzSO2NOCH3a [15]; CCDC num. 978,497, CSD_code: datos_0m [9]. Recently a new structure of this polymorphic antibiotic sulfamethoxazole has been claimed [27] (CCDC num. 1,979,417, CSD code SLFNMB09). Three of these polymorphs (I, II, and III) were identified previously based on thermoanalysis and spectroscopy studies [23]. Besides, there is no agreement related with the nomenclature of these polymorphs. Therefore, a preliminary exploration of all these polymorphs claimed is performed comparing all these crystal forms in this work.

Initially, preliminary calculations were performed at the Γ point of the irreducible Brillouin zone of the crystal structure. However, the optimization of some polymorphs gave structures far from experimental ones, except the structures belonging to forms II and III that matched the experimental cell parameters. Exploring with more detail the Brillouin zone sampling with several k points grids along the crystallographic axes we found that the energy of the crystal structures belonging to form I was -61.761 kcal/mol lower with 1 × 3 × 1 k points grid than with the Γ point (Table S1). Analogously, the energy of the polymorph IV was 34.182 kcal/mol lower with 3 × 1 × 1 k points than with the Γ point (Table S1). A higher number of k points did not yield lower energy and demanded higher computational effort. Hence, we reoptimized the crystal structures of the polymorphs I with 1 × 1 ×  3 k points and the form IV with 3 × 1 × 1 k points.

All these polymorphs were fully optimized including atomic positions and cell parameters reproducing the experimental data (Table 2). In Fig. 3, these optimized structures are described. Our calculations reproduced the experimental crystal structures in all polymorphs. Actually, only 4 crystal forms should be considered as different polymorphs, instead of the initial 9 forms previously claimed. The crystal forms, 1,260,679, 1,260,681, 930,472, and 1,979,417, have very similar cell parameters, and the same space group, C2/c, belonging to the same type of polymorph, previously named as Form I. The cell parameters of the crystal ‘1,979,417’ are slightly smaller than the rest because it was measured at 100 K whereas the rest were measured at 295 K. Analogously, the crystal forms, 1,260,680, 1,260,682, and 978,497, have also similar cell parameters, the same space group, C2/c, and can be considered as the same polymorph, previously named as Form II. The crystal ‘978,497’ shows smaller cell parameters because was measured at 100 K being the rest analysed at 295 K. The other polymorphs are ‘270,106’ (Form III) and ‘270,107’ (form IV). The Form II has the highest packing energy. This behaviour is consistent with previous experimental results, where the Form II was more stable than Form I with a transition energy of ~ 1 kcal/mol [23, 39]. The packing energy follows the sequence: form II > III > IV > I (Table 2). Nevertheless, the energy differences are not important and hence, the formation of one polymorph of SMX will depend more on experimental conditions than the thermodynamic control.

Optimized crystal structure of SMX polymorph I (a) indicating some intermolecular interaction motifs (b and c)

The powder X-ray diffraction patterns of these optimized SMX polymorphs were simulated and compared with the experimental ones (Fig. S3). The optimized crystal structures show similar XRD patterns to the experimental structures with the same 2θ values of the reflections and only changing the relative intensities of the peaks. The four crystal structures of the polymorph I show a similar XRD pattern with only differences in the relative intensities of the peaks confirming that all belong to the same polymorph. Analogously, the three optimized crystal forms of polymorph II show similar XRD patterns to the experimental structures and all these show similar XRD patterns each other, indicating that they belong to the same polymorph II. On the contrary, the forms I, II, III, and IV show different XRD patterns corresponding to different crystal polymorphs.

In all polymorphs of SMX, the molecule has a syn conformation, where the N–H group is oriented to the same side as the heterocyclic N atom. This is consistent with our previous calculations, where the syn conformer was the most stable one [36]. The crystal structure of form I shows the heterocyclic rings alternating in opposite orientations and bridging the amino-benzenic rings (Fig. 3a). A motif with three hydrogen bonds is observed between the heterocyclic moieties: one between the sulfonic O atom and the H atom of the NH group d(SO…HN) = 2.191 Å forming a chain C(4) pattern, one between the heterocyclic N atom and the heterocyclic CH H atom d(N…HC) = 2.165 Å, and another one between the heterocyclic O atom and the methyl H atom d(NO…HCH2) = 2.617 Å (Fig. 3b). These hydrogen bonds form a ring pattern R22(7) of 7 atoms attached to another ring R22(10) of 10 atoms (Fig. 3a). The sulfonic O atoms also forms hydrogen bonds with the amino H atoms forming a chain C(8) motif SO…HNH…O…HNH…OS, d(SO…HN) = 2.248, 2.387 Å, and at the same time form a ring R33(10) pattern (Fig. 3c).

In the polymorphs II and III the relative orientations of the heterocyclic and aminobenzenic rings are similar with different packing. The heterocyclic rings are parallel each other in alternating orientations bridging the aminobenzenic rings, which are also parallel each other. Layered packing can be observed where the aminobenzenic rings of one layer interact with the homologue ring of the other layer by electrostatic forces between the amine and sulfonic groups (Figs. 4a and b). In both polymorphs, the intermolecular interaction motifs are different that in form I. The sulfonic O atoms forms hydrogen bonds with the amine H atoms forming a C(8) chain OSO…HNH…OSO…HNH…, d(SO…HN) = 1.961, 2.009, 2.103 Å (Fig. 4c). The heterocyclic rings form a R22(8) ring motif with two hydrogen bonds, between the NH H atom and the N atom, d(N…HN) = 1.860, 1.862 Å, that can be considered as pseudotautomeric forms (Fig. 4d). Our previous studies on tautomers of SMX found that the sulfonamide tautomer was 7.07 kcal/mol more stable than the sulfonimide tautomer [36]. However, the cohesive energy for a pair of SMX molecules is -78 kcal/mol (Table 2), being higher than the energy barrier (53 kcal/mol) for the intramolecular transition between both tautomers [36]. This indicates that H atom exchanges can occur between both N atoms for each pair of molecules. Although the exact position of the H atom is difficult to be determined with XRD, this tautomeric consideration is corroborated by some bond lengths, where the SN–C bond length is shorter and the C-NO bond of the heterocycle is longer in the polymorphs II and III than in the form I, indicating a certain tautomeric participation (Table 3). In general, the hydrogen bonds in form II are shorter than in form I justifying the higher packing energy of form II (Table 2) being consistent with the IR spectroscopy study of Yang and Guillory [23].

Optimized crystal structure of SMX polymorphs II (a) and III (b), highlighting some intermolecular motifs (c and d)

On the other hand, the polymorph IV shows a helical configuration of the SMX molecules (Fig. 5a). The main intermolecular interaction motifs (Figs. 5b, c) are similar to those found in the polymorph I (Fig. 3b, c). The amine H atoms form a hydrogen bonds C(8) chain with the sulfonyl O atoms, N–H…O(S)…HNH…OS, d(SO…HN) = 1.987, 2.551 Å forming also a ring R33(10) pattern. The heterocyclic rings form a motif with three H bonds d(SO…HN) = 2.134 Å, d(N…HC) = 2.204 Å, and d(NO…HCH2) = 2.761 Å, forming two ring patterns R22(7) and R22(10) as in form I.

Optimized crystal structure of SMX polymorph IV (a) highlighting some intermolecular motifs (b, c)

The molecular structure of SMX is similar in all crystal polymorphs, only small differences can be detected (Table 3). In form I, the sulfonic groups are asymmetric with different S–O bond lengths, due to the different nature of the hydrogen bonds in which they participate, d(SO…HN) = 2.191 Å and d(SO…HNH) = 2.248, 2.387 Å. The bonds S-C and N–C are slightly longer in form I than in the rest of the polymorphs. The main intermolecular hydrogen bonds are shorter in form II than in form I (Table 3), corroborating previous experimental results specially where the NH group is involved [23, 39]. The conformations of the functional groups are similar with analogous dihedral angles in the SMX molecules of all polymorphs.

In the case of SCP, two polymorphs were considered, which were claimed previously with experimental crystallographic studies: CCDC num. 274,449 Tan et al. [40], and SeethaLekshmi et al. [14] recently showed a crystal form CCDC num. 1,841,485 different that the previously reported. Following a similar procedure to above we explored the Brillouin zone sampling with several k points grids along the crystallographic axes directions finding the best optimization results for the polymorph I, using 3 × 1 × 1 k points grid as in the above form IV of SMX. In the case of the polymorph II, we found that the energy of the crystal structure was -104.296 kcal/mol lower with 1 × 3 × 1 k points grid than with the Γ point (Table S1).

The optimized crystal structures with our DFT calculations matches the experimental cell parameters with a standard deviation smaller than 1% (Table 4). The simulated XRD patterns of these optimized forms are similar to the simulated from the experimental crystal structures with the only variations in the relative intensities. The XRD patterns of the forms I and II of SCP are clearly different being actually different polymorphs (Fig. S4). The packing energy is similar for both polymorphs (Table 4) being lower than that of SMX crystals (Table 2). This is according with the experimental values of sublimation enthalpy of similar sulphonamides (32.3 kcal/mol) [15]. Nevertheless, the SCP form I is more stable than the SCP form II. This is consistent with experimental behaviour where the more stable is also the form I with a lower heat of fusion [14]. Nevertheless, the energy difference is small and additional kinetic and thermodynamic factors will involve at higher temperatures. The SCP molecules adopt the conformer syn where the heterocyclic N atoms are on the same side as the sulfonamide NH group. This is consistent with our previous calculations of isolated molecules where this syn conformer is more stable than anti [36].

In the polymorph SCP-I, the aminobenzenic rings are parallel each other in alternating orientation. In a similar way the heterocyclic rings are parallel each other. However, in the polymorph SCP-II, the aminobencenic and heterocyclic rings are parallel at a distance of 3.535 Å. In both polymorphs the heterocyclic rings are joined by a motif of three intermolecular hydrogen bonds, d(SO…HN) = 2.343 (form I), 2.317 (form II) Å and d(CH…Nhet) = 2.257–2.561 Å (form I), 2.345–2.507 Å (form II). Besides, the amino H atoms form intermolecular hydrogen bonds with the sulfonic O atoms in both polymorphs (Figs. 6 and 7) as in the above sulfonamides. The Cl atoms interact with the π electron clouds of both aromatic rings, the aminobencenic one and the heterocyclic one, with Cl…π interactions, d(Cl…π) = 3.800 Å (with heterocyclic), 3.480 Å (with aminobencenic ring) in form I, and d(Cl…π) = 3.570 Å (with heterocyclic), 3.449 Å (with aminobencenic ring) in form II. In general, the molecule structure and intermolecular interactions are very similar in both polymorphs and the only difference is in the packing of the crystal lattice. In both forms, the amidic H atom and sulfoxy O atom form a C(4) chain and also a ring R22(10) pattern with the heterocyclic N atoms (Fig. 6b) which form attached a ring R22(6) motif.

Optimized crystal structures of the polymorph I of SCP (a) highlighting some intermolecular motifs (b, c)

Optimized crystal structures of the form II of SCP-II (a), highlighting some intermolecular motifs (b)

The powder X-ray diffraction patterns of the optimized SCP crystal structure were simulated and compared with the simulated from the experimental data (Fig. S4a, b). The optimized crystal structures show a similar XRD pattern that the experimental ones with the same 2θ values and relative intensities. This confirms that both crystal forms are different and both are actual polymorphs.

In the case of SCM, only one crystal form was found CCDC num: 1,260,699 (CSD code: SLFNMG01) [29]. The optimizations of this crystal structure using the Γ point of the Brillouin zone and using 3 × 1 × 1 k points yielded similar structures. The cell parameters of the calculated and optimized crystal structure reproduce the reported experimentally with a standard deviation smaller than 1% (Table 4). The cohesive energy is higher than in SCP but slightly lower than in SMX. In this crystal lattice (Fig. 8), the SCM molecules have a conformation anti with the carbonyl group on the opposite side with respect to the sulfonamide SN–H group. No energetic preference was found in our previous calculations of isolated molecules where both conformers, syn and anti, had the same energy [36]. In this crystal lattice the main intermolecular interactions are the strong hydrogen bonds between the carbonyl O atoms and the SNH H atoms with d(CO…HN) = 1.751 Å forming a C(4) chain, and the hydrogen bonds between the amine H atoms and the sulfonic O atoms forming a C(8) chains, as in the above sulfamides (Fig. 8). The N–C bond length is shorter than in other sulfonamides, due to the participation of the carbonyl π electrons in this bond. The powder X-ray diffraction pattern of the optimized SCM crystal structure was similar that the experimental one with the same 2θ values and relative intensities (Fig. S4c; Table 5).

Optimized crystal structures of SCM