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ISSN: 2414-3146

Metformindiium dibromide

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aFacultad de Ciencias Químicas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur, 72570 Puebla, Pue., Mexico, and bInstituto de Física Luis Rivera Terrazas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur, 72570 Puebla, Pue., Mexico
*Correspondence e-mail: [email protected], [email protected]

Edited by M. Bolte, Goethe-Universität Frankfurt, Germany (Received 31 July 2026; accepted 2 August 2026; online 11 August 2026)

The crystal structure of the title salt, C4H13N52+·2Br, is reported in space group P21/c, with Z = 4. Unexpectedly, this crystal is not isomorphous to the dichloride analogue, which has been reported in space group P21 (Z = 2). This originates from the shift of one halide anion in the asymmetric unit, which modifies the network of N—H⋯halide hydrogen bonds. For the here-reported structure, centrosymmetric R42(8) ring motifs are formed, affording a one-dimensional structure along [100], and the network is further expanded to a three-dimensional structure including larger ring motifs. This report is an example of a routine refinement carried out using now well-established techniques of quantum crystallography.

3D view (loading...)
[Scheme 3D1]
Chemical scheme
[Scheme 1]

Structure description

In a recent article, Hill & Boeré (2025View full citation) argue in favour of wider application of quantum crystallography methods in routine chemical crystallography. Nowadays, experimental data quality is enough, even at room temperature, to fit the observed structure factors against non-spherical features of the electronic density map ρ(r). As a result, refined structures are closer to those expected from neutron diffraction data. Most significantly, accurate positions for H atoms can be obtained, frequently with anisotropic displacement parameters. Such a precision is inherently unachievable in the context of an IAM (Independent Atom Model), since structure factors only include spherical scattering factors. In fact, the default SFAC command in SHELXL still refers to Cromer–Mann scattering factors for neutral atoms, taken from the 1992 edition of the Inter­national Tables (Wilson & Geist, 1992View full citation; Sheldrick, 2015bView full citation). In opposition, the ‘Hirshfeld Atom Refinement' approach (HAR; Capelli et al., 2014View full citation; Kleemiss et al., 2021View full citation) uses non-spherical form factors for each atom in the model. The computed map ρ(r) is then suitable for studying atoms, bonds, and lone pairs, using the concepts devised by Richard Bader in the QTAIM theory (Quantum Theory of Atoms in Mol­ecules; Bader, 2005View full citation). Indeed, some such ‘routine' structures have already been published in repository journals like Acta Cryst. C or IUCrData (e.g. Jones, 2025View full citation; Samson et al., 2025View full citation). We report here the HAR refinement for a new metforminium(2+) salt.

The title compound, abbreviated H2Mf2+·2Br, is the dibromide salt of metformin [IUPAC name: [amino­(di­methyl­iminio)meth­yl](di­amino­methyl­idene)ammonium dibromide]. Metformin, Mf, is the first-line oral medication used to lower blood sugar in patients diagnosed with type-2 diabetes, and is sold in form of chlorhydrate, HMf+·Cl. On the other hand, the monocation HMf+ and dication H2Mf2+ have been used as counter-ions for vanadium clusters, which are also probed as medication against diabetes (e.g. Polito-Lucas et al., 2021View full citation; Chatkon et al., 2022View full citation).

The here reported crystal structure for H2Mf2+·2Br is not isostructural to H2Mf2+·2Cl (Xia, 2023View full citation; Hitchings et al., 2025View full citation). The dichloride salt crystallizes in space group P21, with Z = 2, while the dibromide salt gives crystals in space group P21/c, with Z = 4 (Fig. 1[link]). Metrics for the dication H2Mf2+ are however similar in both salts, and its twisted conformation is maintained, regardless of the counter-ion (Table 1[link]). An overlay between both dications gives an rms deviation of 0.06 Å. The introduction of a c glide plane in the case of the dibromide salt should thus result from different positions of the halide ions in the asymmetric units. In turn, these positions should determine different networks of hydrogen bonds. This is indeed the case, as shown in Fig. 2[link]: the halide ions inter­act directly with the guanidine moiety of H2Mf2+, through charge-assisted (Cl/Br)⋯(H2N)+ contacts. Cl1/Br1 ions have the same position in the asymmetric units, and behave as acceptors with H2E as donor (Table 2[link], entry 1). The key difference relates for Cl2/Br2 position: in the dichloride salt, Cl2 gives a double-acceptor hydrogen bond, with H4A and H5A as donors (Fig. 2[link], top). In the case of the dibromide salt, only one hydrogen bond is formed, N4—H4A⋯Br2 (Fig. 2[link], bottom; Table 2[link], entry 2).

Table 1
Bond lengths (Å) and valence angles (°) observed in dication H2Mf2+ for the dichloride (Xia, 2023View full citation) and dibromide salts

Parameter H2Mf2+·2Cla H2Mf2+·2Br/SHELXLb H2Mf2+·2Br/NoSpherA2 c
Bonds      
N1—C1 1.473 (4) 1.463 (3) 1.455 (3)
N1—C2 1.469 (4) 1.462 (4) 1.459 (4)
N1—C3 1.335 (4) 1.304 (3) 1.309 (3)
N2—C3 1.321 (4) 1.315 (3) 1.315 (3)
N3—C3 1.386 (3) 1.392 (3) 1.392 (3)
N3—C4 1.378 (3) 1.362 (3) 1.362 (3)
N4—C4 1.325 (4) 1.306 (4) 1.309 (4)
N5—C4 1.310 (4) 1.304 (4) 1.311 (3)
Angles      
C1—N1—C2 115.7 (3) 115.1 (3) 115.2 (3)
C1—N1—C3 122.9 (2) 123.2 (2) 123.3 (3)
C2—N1—C3 120.0 (3) 120.9 (2) 120.7 (2)
N1—C3—N2 123.3 (2) 123.6 (2) 123.5 (2)
N1—C3—N3 118.2 (2) 119.5 (2) 119.2 (2)
N2—C3—N3 118.3 (3) 116.8 (2) 117.3 (2)
C3—N3—C4 125.0 (2) 124.8 (2) 124.4 (2)
N3—C4—N4 118.1 (3) 118.0 (3) 117.9 (3)
N3—C4—N5 120.4 (3) 119.5 (2) 119.6 (2)
N4—C4—N5 121.6 (3) 122.5 (3) 122.4 (3)
Torsion angles      
N1—C3—N3—C4 −139.2 (3) −133.1 (3) −133.4 (2)
N2—C3—N3—C4 45.6 (4) 49.7 (4) 49.6 (3)
Notes: (a) Xia (2023View full citation); (b) SHELXL refinement: isotropic H atoms; free coordinates and displacement parameters for all atoms (152 parameters, R1 = 3.14% for observed reflections, wR2 = 7.84% for all reflections); (c) refinement details in Table 3[link].

Table 2
Hydrogen-bond geometry (Å, °)

D—H⋯A D—H H⋯A DA D—H⋯A
N2—H2E⋯Br1 0.89 (5) 2.46 (4) 3.343 (3) 168 (3)
N4—H4A⋯Br2 0.91 (5) 2.48 (4) 3.355 (3) 163 (3)
N2—H2D⋯Br1i 0.99 (4) 2.45 (4) 3.341 (3) 149 (3)
N3—H3⋯Br1ii 0.94 (4) 2.42 (4) 3.321 (2) 160 (4)
N4—H4B⋯Br1iii 1.01 (5) 2.48 (5) 3.350 (3) 144 (4)
N5—H5A⋯Br2iv 0.90 (5) 2.49 (5) 3.346 (3) 157 (5)
N5—H5B⋯Br2v 0.99 (4) 2.34 (4) 3.322 (3) 172 (3)
Symmetry codes: (i) Mathematical equation; (ii) Mathematical equation; (iii) Mathematical equation; (iv) Mathematical equation; (v) Mathematical equation.
[Figure 1]
Figure 1
Mol­ecular structure of the title compound, with displacement ellipsoids at 30% probability level. The asymmetric unit and the labelling scheme are those adopted by Xia (2023View full citation) in the dichloride analogue. The inset shows a representative crystal with a maximum dimension of ca. 4 mm, obtained by evaporation of an aqueous solution.
[Figure 2]
Figure 2
Comparison of the asymmetric units for H2Mf2+·2Cl (Xia, 2023View full citation; space group P21; top) and H2Mf2+·2Br (this work; space group P21/c; bottom). The guanidine moiety in the cation and halides ions are shown using a spacefill representation (Macrae et al., 2020View full citation).

This difference for the position of one anion is reflected in different supra­molecular features. The smallest ring motifs found in H2Mf2+·2Br have graph set R42(8) and are centrosymmetric. Cations are connected through these rings, forming a one-dimensional network oriented along [100]. The remaining amine groups, N3 and N5, give other efficient N—H⋯Br inter­actions, to build a complex three-dimensional framework (Fig. 3[link]). A different image is obtained in the case of the dichloride salt: the bifurcated hydrogen bond including Cl2 affords an R21(6) ring motif, which is not present in the dibromide salt. The complete crystal structure is essentially diperiodic, and expands to a three-dimensional framework, documented in the supplementary information file available from the CrystEngComm article (Hitchings et al., 2025View full citation; see Table S5 and Figure S3).

[Figure 3]
Figure 3
Part of the crystal structure of the title compound, emphasizing R42(8) rings building the one-dimensional framework (yellow areas). Br atom inter­actions with N3 and N5 afford a three-dimensional supra­molecular structure.

Synthesis and crystallization

The title compound was synthesized by reacting at room temperature 3.4 g (20.5 mmol) of metforminium chloride dissolved in 15 ml of distilled water, with 6 ml of 48% HBr (53.0 mmol). After 15 min. of magnetic stirring, the solvent was evaporated at ambient conditions for about three weeks, to yield large polyhedric colourless single crystals (Fig. 1[link], inset).

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 3[link]. The structure was first refined with SHELXL (Sheldrick, 2015bView full citation) and then with OLEX2.refine using the GUI OLEX2 (Bourhis et al., 2015View full citation; Dolomanov et al., 2009View full citation). Further refinements were carried out using NoSpherA2 in the same GUI (Kleemiss et al., 2021View full citation) and ORCA for DFT computations (Neese, 2022View full citation). The last cycles for refining non-spherical scattering factors were based on a tetra­meric model, [C4H13N5Br2]4, in order to take in account non-covalent bonds, using the PBE0 functional in conjunction with the def2-TZVPD basis set, including the DKH2 correction for relativistic effects. Coordinates and anisotropic displacement parameters were refined for all atoms, without restraints nor constraints. A batch of 12 cycles of refinement for this 96-atom model including 568 electrons is completed in a few hours on an unsophisticated desktop PC (i7–6700 CPU @3.40 GHz, 8 threads, 8 Gb RAM).

Table 3
Experimental details

Crystal data
Chemical formula C4H13N52+·2Br
Mr 290.99
Crystal system, space group Monoclinic, P21/c
Temperature (K) 295
a, b, c (Å) 10.3335 (3), 15.0443 (4), 6.4977 (2)
β (°) 95.427 (2)
V3) 1005.61 (5)
Z 4
Radiation type Ag Kα, λ = 0.56083 Å
μ (mm−1) 4.29
Crystal size (mm) 0.29 × 0.20 × 0.07
 
Data collection
Diffractometer Stoe Stadivari
Absorption correction Multi-scan (LANA; Folkers-Karlsson et al., 2026View full citation)
Tmin, Tmax 0.288, 0.741
No. of measured, independent and observed [I > 2σ(I)] reflections 31050, 3212, 2465
Rint 0.031
(sin θ/λ)max−1) 0.725
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.030, 0.070, 1.04
No. of reflections 3212
No. of parameters 217
H-atom treatment All H-atom parameters refined
Δρmax, Δρmin (e Å−3) 0.85, −0.57
Computer programs: X-AREA Pilatus3SV (Stoe, 2025View full citation), X-AREA Recipe (Folkers-Karlsson et al., 2026View full citation), X-AREA Integrate3D and LANA (Folkers-Karlsson et al., 2026View full citation), SHELXT2018/2 (Sheldrick, 2015aView full citation), OLEX2.refine (Bourhis et al., 2015View full citation), XP in SHELXTL-Plus (Sheldrick, 2008View full citation), Mercury (Macrae et al., 2020View full citation) and publCIF (Westrip, 2010View full citation).

Structural data


Computing details top

[Amino(dimethyliminio)methyl](diaminomethylidene)ammonium dibromide top
Crystal data top
C4H13N52+·2BrF(000) = 569.890
Mr = 290.99Dx = 1.922 Mg m3
Monoclinic, P21/cAg Kα radiation, λ = 0.56083 Å
a = 10.3335 (3) ÅCell parameters from 22061 reflections
b = 15.0443 (4) Åθ = 2.7–29.9°
c = 6.4977 (2) ŵ = 4.29 mm1
β = 95.427 (2)°T = 295 K
V = 1005.61 (5) Å3Plate, colourless
Z = 40.29 × 0.2 × 0.07 mm
Data collection top
Stoe Stadivari
diffractometer
3212 independent reflections
Radiation source: Sealed X-ray tube, Axo Astix-f Microfocus source2465 reflections with I > 2σ(I)
Graded multilayer mirror monochromatorRint = 0.031
Detector resolution: 5.81 pixels mm-1θmax = 24.0°, θmin = 2.7°
ω scansh = 1414
Absorption correction: multi-scan
(LANA;Folkers-Karlsson et al., 2026)
k = 2121
Tmin = 0.288, Tmax = 0.741l = 99
31050 measured reflections
Refinement top
Refinement on F20 constraints
Least-squares matrix: fullPrimary atom site location: dual
R[F2 > 2σ(F2)] = 0.030Secondary atom site location: difference Fourier map
wR(F2) = 0.070All H-atom parameters refined
S = 1.04 w = 1/[σ2(Fo2) + (0.0267P)2 + 1.1908P]
where P = (Fo2 + 2Fc2)/3
3212 reflections(Δ/σ)max = 0.001
217 parametersΔρmax = 0.85 e Å3
0 restraintsΔρmin = 0.57 e Å3
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Br10.90769 (3)0.642983 (18)0.06038 (4)0.03418 (8)
Br20.44558 (3)0.85428 (2)0.28006 (5)0.04693 (9)
N10.81449 (19)0.41933 (14)0.5843 (3)0.0288 (4)
N20.8743 (3)0.48014 (19)0.2806 (4)0.0341 (5)
H2D0.916 (4)0.426 (3)0.231 (5)0.048 (10)
H2E0.881 (4)0.529 (3)0.205 (6)0.061 (12)
N30.7614 (2)0.56611 (16)0.4982 (3)0.0307 (5)
H30.783 (4)0.585 (3)0.635 (7)0.065 (12)
N40.6770 (3)0.70012 (18)0.3858 (5)0.0377 (5)
H4A0.612 (4)0.736 (3)0.330 (7)0.058 (12)
H4B0.749 (4)0.735 (3)0.465 (8)0.079 (15)
N50.6060 (3)0.5722 (2)0.2185 (4)0.0354 (5)
H5A0.568 (3)0.608 (4)0.118 (8)0.078 (15)
H5B0.600 (4)0.506 (3)0.215 (5)0.046 (10)
C10.7302 (4)0.4179 (3)0.7514 (6)0.0441 (7)
H1A0.671 (5)0.360 (3)0.730 (7)0.080 (15)
H1B0.675 (5)0.468 (3)0.748 (7)0.102 (18)
H1C0.780 (5)0.402 (4)0.878 (6)0.12 (2)
C20.8806 (4)0.3358 (2)0.5493 (6)0.0424 (7)
H2A0.910 (6)0.306 (4)0.683 (8)0.13 (2)
H2B0.964 (7)0.343 (3)0.475 (12)0.14 (3)
H2C0.824 (5)0.295 (4)0.451 (12)0.15 (3)
C30.8168 (2)0.48498 (16)0.4524 (3)0.0241 (4)
C40.6799 (2)0.61371 (16)0.3628 (4)0.0257 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Br10.03867 (13)0.03190 (14)0.03194 (12)0.00332 (10)0.00313 (9)0.00091 (10)
Br20.05447 (18)0.04031 (17)0.04234 (15)0.01947 (13)0.01468 (12)0.00801 (12)
N10.0322 (10)0.0297 (11)0.0238 (9)0.0024 (8)0.0007 (7)0.0022 (8)
N20.0430 (13)0.0310 (13)0.0294 (11)0.0084 (11)0.0104 (10)0.0042 (10)
H2D0.06 (3)0.05 (3)0.04 (2)0.03 (2)0.017 (19)0.01 (2)
H2E0.06 (3)0.08 (3)0.05 (3)0.02 (2)0.01 (2)0.00 (2)
N30.0358 (11)0.0285 (11)0.0262 (10)0.0087 (9)0.0055 (8)0.0039 (9)
H30.08 (3)0.03 (2)0.09 (3)0.01 (2)0.01 (3)0.01 (2)
N40.0376 (13)0.0237 (12)0.0518 (16)0.0065 (10)0.0042 (11)0.0007 (11)
H4A0.08 (3)0.02 (2)0.08 (3)0.01 (2)0.03 (2)0.01 (2)
H4B0.06 (3)0.06 (3)0.11 (4)0.03 (3)0.03 (3)0.00 (3)
N50.0348 (12)0.0298 (13)0.0391 (13)0.0012 (10)0.0091 (10)0.0038 (11)
H5A0.02 (2)0.11 (4)0.11 (4)0.00 (2)0.02 (2)0.01 (3)
H5B0.07 (3)0.04 (2)0.019 (18)0.00 (2)0.016 (17)0.007 (17)
C10.0488 (18)0.052 (2)0.0331 (15)0.0020 (16)0.0106 (13)0.0068 (15)
H1A0.09 (3)0.07 (3)0.08 (3)0.05 (3)0.02 (3)0.00 (2)
H1B0.16 (4)0.07 (3)0.09 (3)0.05 (3)0.08 (3)0.05 (3)
H1C0.15 (5)0.18 (6)0.04 (2)0.03 (4)0.06 (3)0.03 (3)
C20.057 (2)0.0293 (15)0.0398 (16)0.0100 (14)0.0006 (14)0.0062 (12)
H2A0.17 (6)0.12 (5)0.09 (4)0.04 (4)0.04 (4)0.03 (4)
H2B0.17 (6)0.07 (4)0.18 (6)0.06 (4)0.07 (6)0.05 (4)
H2C0.06 (3)0.12 (5)0.25 (7)0.01 (3)0.04 (4)0.09 (5)
C30.0247 (10)0.0249 (11)0.0219 (9)0.0021 (8)0.0015 (8)0.0024 (8)
C40.0262 (10)0.0215 (10)0.0293 (10)0.0036 (9)0.0020 (8)0.0008 (9)
Geometric parameters (Å, º) top
N1—C11.455 (3)N4—C41.309 (4)
N1—C21.459 (4)N5—H5A0.90 (5)
N1—C31.309 (3)N5—H5B0.99 (4)
N2—H2D0.99 (4)N5—C41.311 (3)
N2—H2E0.89 (5)C1—H1A1.06 (4)
N2—C31.315 (3)C1—H1B0.95 (4)
N3—H30.94 (4)C1—H1C0.96 (5)
N3—C31.392 (3)C2—H2A1.00 (5)
N3—C41.362 (3)C2—H2B1.04 (6)
N4—H4A0.91 (5)C2—H2C1.02 (5)
N4—H4B1.01 (5)
C2—N1—C1115.2 (3)H1B—C1—H1A108 (4)
C3—N1—C1123.3 (3)H1C—C1—N1109 (3)
C3—N1—C2120.7 (2)H1C—C1—H1A99 (4)
H2E—N2—H2D116 (3)H1C—C1—H1B120 (4)
C3—N2—H2D125 (2)H2A—C2—N1111 (3)
C3—N2—H2E119 (3)H2B—C2—N1114 (3)
C3—N3—H3114 (2)H2B—C2—H2A105 (5)
C4—N3—H3122 (2)H2C—C2—N1111 (3)
C4—N3—C3124.4 (2)H2C—C2—H2A113 (5)
H4B—N4—H4A113 (4)H2C—C2—H2B103 (5)
C4—N4—H4A125 (3)N2—C3—N1123.5 (2)
C4—N4—H4B123 (2)N3—C3—N1119.2 (2)
H5B—N5—H5A123 (4)N3—C3—N2117.3 (2)
C4—N5—H5A115 (3)N4—C4—N3117.9 (3)
C4—N5—H5B121.7 (19)N5—C4—N3119.6 (2)
H1A—C1—N1107 (2)N5—C4—N4122.4 (3)
H1B—C1—N1112 (2)
N1—C3—N3—C4133.4 (2)N2—C3—N3—C449.6 (3)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N2—H2E···Br10.89 (5)2.46 (4)3.343 (3)168 (3)
N4—H4A···Br20.91 (5)2.48 (4)3.355 (3)163 (3)
N2—H2D···Br1i0.99 (4)2.45 (4)3.341 (3)149 (3)
N3—H3···Br1ii0.94 (4)2.42 (4)3.321 (2)160 (4)
N4—H4A···N4iii0.91 (5)3.18 (4)3.579 (2)109 (3)
N4—H4B···Br1iv1.01 (5)2.48 (5)3.350 (3)144 (4)
N4—H4B···N4iv1.01 (5)3.06 (5)3.579 (2)113 (3)
N5—H5A···Br2iii0.90 (5)2.49 (5)3.346 (3)157 (5)
N5—H5B···Br2v0.99 (4)2.34 (4)3.322 (3)172 (3)
C1—H1A···N5vi1.06 (4)3.08 (5)3.501 (5)104 (3)
C1—H1B···N30.95 (4)2.43 (4)2.808 (5)104 (3)
C1—H1B···N5vi0.95 (4)2.99 (5)3.501 (5)115 (4)
C2—H2A···Br1vii1.00 (5)3.24 (6)3.630 (3)105 (4)
Symmetry codes: (i) x+2, y+1, z; (ii) x, y, z+1; (iii) x, y+3/2, z1/2; (iv) x, y+3/2, z+1/2; (v) x+1, y1/2, z+1/2; (vi) x+1, y+1, z+1; (vii) x+2, y1/2, z+1/2.
Bond lengths (Å) and valence angles (°) observed in dication H2Mf2+ for the dichloride (Xia, 2023) and dibromide salts top
ParameterH2Mf2+·2Cl- aH2Mf2+·2Br-/SHELXLbH2Mf2+·2Br-/NoSpherA2 c
Bonds
N1—C11.473 (4)1.463 (3)1.455 (3)
N1—C21.469 (4)1.462 (4)1.459 (4)
N1—C31.335 (4)1.304 (3)1.309 (3)
N2—C31.321 (4)1.315 (3)1.315 (3)
N3—C31.386 (3)1.392 (3)1.392 (3)
N3—C41.378 (3)1.362 (3)1.362 (3)
N4—C41.325 (4)1.306 (4)1.309 (4)
N5—C41.310 (4)1.304 (4)1.311 (3)
Angles
C1—N1—C2115.7 (3)115.1 (3)115.2 (3)
C1—N1—C3122.9 (2)123.2 (2)123.3 (3)
C2—N1—C3120.0 (3)120.9 (2)120.7 (2)
N1—C3—N2123.3 (2)123.6 (2)123.5 (2)
N1—C3—N3118.2 (2)119.5 (2)119.2 (2)
N2—C3—N3118.3 (3)116.8 (2)117.3 (2)
C3—N3—C4125.0 (2)124.8 (2)124.4 (2)
N3—C4—N4118.1 (3)118.0 (3)117.9 (3)
N3—C4—N5120.4 (3)119.5 (2)119.6 (2)
N4—C4—N5121.6 (3)122.5 (3)122.4 (3)
Torsion angles
N1—C3—N3—C4-139.2 (3)-133.1 (3)-133.4 (2)
N2—C3—N3—C445.6 (4)49.7 (4)49.6 (3)
Notes: (a) Xia (2023); (b) SHELXL refinement: isotropic H atoms; free coordinates and displacement parameters for all atoms (152 parameters, R1 = 3.14 % for observed reflections, wR2 = 7.84 % for all reflections); (c) refinement details in Table 3.
 

Funding information

Funding for this research was provided by: Vicerrectoría de Investigación y Estudios de Posgrado, BUAP (grant No. 00118-PVG/2026; studentship to Luis E. Hernández-Márquez (Program Haciendo Ciencia en la BUAP Primavera 2026)); Consejo Nacional de Ciencia y Tecnología (grant No. 268178).

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