Research Article
3-Spherical Conformational Insights into Iminocyclitols with 1-α-D-Ribose and 1-β-L-Ribose Stereochemistry Under Homotopic Behaviour of Nuclear Magnetic Resonance Data
Issue:
Volume 14, Issue 1, February 2026
Pages:
1-11
Received:
22 December 2025
Accepted:
6 January 2026
Published:
2 February 2026
Abstract: 3-Sphere, a hypersphere in 4 dimensions approach, applied for calculating stereochemical parameters of iminocyclitol 1 – 5 with Hopf fibration and Lie algebra is described. Three angles have been considered, i.e. dihedral θHnHn+1 [deg] – tetrahedral φCn [deg] – phase angle of the pseudorotation P [deg] calculated from NMR data, vicinal coupling constant 3JHH [Hz] and carbon chemical shift δC [ppm]. This approach gave for 1-α-methyl-1,4-imino-1,4-dideoxy-D-ribitol 2 two conformers E3 and 3T2 having different dihedral θHnHn+1 [deg] and tetrahedral φCn [deg] angles with same vicinal angles ϕ [deg]. Notably, phase angle of pseudorotation P [deg] placed the conformations on the south side for D-ribitols 1 - 3 and on the north side for L-ribitol 4, excepting trifluoroacetate salt of L-ribitol 5. The wave character of NMR data introduced few homotopic switches, the transformation from torus to inverse of torus, the relationship between angles of set A and set B, the transformation from Planck constants h to h-bar, along with the transformation from Joule to Calorie (J 4.1868 ⇆ J-1 0.238). Two methods for calculation of tetrahedral angles φCn [deg], energy-graph and Euler conic with two ways for representing the angles, polyhedron and unit models are analyzed. The conformational parameters, phase angle of the pseudorotation P [deg] established with VISION molecular model and exocyclic 3-Sphere dihedral angles θHnHn+1 [deg] relative to endocyclic torsional angles θn,n+1 [deg] from Altona-Sundaralingan model have been evaluated. In addition, the corresponding angle of deviation from planarity θm [deg] has been determined.
Abstract: 3-Sphere, a hypersphere in 4 dimensions approach, applied for calculating stereochemical parameters of iminocyclitol 1 – 5 with Hopf fibration and Lie algebra is described. Three angles have been considered, i.e. dihedral θHnHn+1 [deg] – tetrahedral φCn [deg] – phase angle of the pseudorotation P [deg] calculated from NMR data, vicinal coupling con...
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Research Article
Conic Projection as Manifold and 3-Sphere Dihedral Angles θHnHn+1[Deg] Under Homotopy
Issue:
Volume 14, Issue 1, February 2026
Pages:
12-24
Received:
20 January 2026
Accepted:
30 January 2026
Published:
26 February 2026
DOI:
10.11648/j.sjc.20261401.12
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Abstract: Conic projection as manifold enable calculation dihedral θHnHn+1[deg] angles from differences between two atoms of carbon ΔδCnCn+1[ppm] in three steps or from only one atom of carbon δCn[ppm] in close relationships with tetrahedral φCn[deg] angles under 3-Sphere approach. Hopf fibration and Lie algebra ensuring calculation dihedral θHnHn+1[deg] angles from vicinal ϕ[deg] angle, angle results from vicinal coupling constant 3JHH[Hz]. Real Hopf fibration for calculation dihedral θHnHn+1[deg] angle in real space, and R16 octonionic Hopf fibration, double of quaternionic R7, for all cis, trans-ee, trans-aa stereochemistry, unreal space relative to calculated dihedral θHnHn+1[deg] angle. Continue “deformation”, homotopic behaviour h ⇆ h-1 characteristic for wave NMR data, probably a point of swich on Möbius band, in case of radius r of the cone inscribes on sphere at tangent point, calculated from height of cone h or inverse of height h-1, the tan function of h is equal with sin function of h-1. Dihedral θHnHn+1[deg] and tetrahedral φCn[deg] angles are from the trigonometric point of view under sin and tan function, or viceversa, homotopic behavior of NMR data under conic projection demonstrating that. Because the dihedral θHnHn+1[deg] angles are not found in first unit, for few vicinal coupling constants 3JHH[Hz], the rule accepted until now are explored taking in consideration other sets for building unit along the set C, respectively D, E and F, G, or vicinal angle ϕ[deg] with its three possible dihedral θHnHn+1[deg] angles in close relationships with tetrahedral φCn[deg] angles under seven sets unit. Building units through sets U or S calculated from sin or tan functions until calculated angles are almost equals with angles of unit U1 or S1, required long time for calculation.
Abstract: Conic projection as manifold enable calculation dihedral θHnHn+1[deg] angles from differences between two atoms of carbon ΔδCnCn+1[ppm] in three steps or from only one atom of carbon δCn[ppm] in close relationships with tetrahedral φCn[deg] angles under 3-Sphere approach. Hopf fibration and Lie algebra ensuring calculation dihedral θHnHn+1[deg] ang...
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Research Article
Synthesis and Spectrometric Study of New Iron Phthalocyanine Polymers: Influence of Peripheral COOH and CN Groups on Vibrational and Electronic Properties
Lassane Tarpaga*,
Wend-Kuny Guy Aristide Nitiema,
Seydou Ouedraogo,
Bertrand Ouemega,
Bintou Sessouma,
Mabinty Bayo-Bangoura,
Karifa Bayo
Issue:
Volume 14, Issue 1, February 2026
Pages:
25-37
Received:
4 February 2026
Accepted:
14 February 2026
Published:
27 February 2026
DOI:
10.11648/j.sjc.20261401.13
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Abstract: We have prepared and isolated in solid form two types of polymers formed between iron (II) complexes ([FePc(COOH)8] and [FePc(CN)8]) and two bidentate ligands [trans-1,2-bis (4-pyridyl) ethylene (bpe); trans-1,2-bis (4-pyridyl) ethane (bpa)]. The electronic and vibrational absorption spectra of these complexes are discussed in comparison with those of previous work on [FePcL2]n polymers with the same ligands. Infrared spectrometry shows a modulation in the intensities of certain characteristic bands of the complexes, reflecting a reorganization of the structure of these compounds through the formation of polymers and, above all, the emergence of new vibration bands attributable to the ligands. In electron absorption spectrometry, our results confirm those already available in the literature with the [FePcL2]n series. The presence of the bpa ligand causes each macrocycle of the polymer to behave independently. In contrast, the bpe ligand induces a perfect linear connection between the macrocycles due to its alkene function, which allows electrons to move easily along the polymer chain. The presence of peripheral groups (COOH and CN) provides a novel result because they strongly influence not only the energy of the π→π* band, but especially that of the central metal-axial ligand charge transfer band (CT Fe→L). These charge transfers are responsible for the conductive properties of these compounds.
Abstract: We have prepared and isolated in solid form two types of polymers formed between iron (II) complexes ([FePc(COOH)8] and [FePc(CN)8]) and two bidentate ligands [trans-1,2-bis (4-pyridyl) ethylene (bpe); trans-1,2-bis (4-pyridyl) ethane (bpa)]. The electronic and vibrational absorption spectra of these complexes are discussed in comparison with those...
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,
Emerich Bartha,
Petru Filip
