Relationship between tetrahedral and dihedral on hypersphere coordinates

,; MITAN, Carmen-Irena; BARTHA, Emerich; ,; FILIP, Petru; ,

doi:10.33224/rrch.2023.68.5-6.09

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…7 between 5.5 -13. 4[Hz] for trans-aa stereochemistry. In case of cis stereochemistry with higher values of vicinal constant coupling will be used eq.…”

Section: Resultsmentioning

confidence: 99%

“…The conformation of 6-O-(7,8-di-O-Benzyl-9,11-Obenzylidene-α-D-galactopyranosyl)-1-butyl-2,3-Oisopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1 as simulated with VISION molecular models from 3-Sphere dihedral angles calculated only from vicinal constant coupling are C 1 4 for six and C 3 (P = 18[deg]) for five membered rings (Table 1, Figure 5). The shape of the six and five membered ring in 2D with sin and tan trigonometric functions (Table 2) predicted a higher biological activity.…”

Section: Discussionmentioning

confidence: 99%

“…[2] 3-Sphere equations for calculation of the tetrahedral angles of six membered ring from carbon chemical shift. [4] 4D: sin…”

Section: Relationships Between Biological Activity and Dimension Spacementioning

confidence: 99%

“…From manifold equations result dihedral angles with values almost equals with angles calculated from vicinal coupling constant 3 J HH [Hz] recorded experimentally. The 3-Sphere approach, with its characteristic system of units, enable calculation the tetrahedral angles of five [4] and six [5] membered rings based on relationships between two pairs of angles: dihedral -vicinal and tetrahedral -internal. VISION molecular models ensuring a good simulation of the conformation, phase angle of the pseudorotation P[deg], with dihedral angles calculated with 3-sphere approach.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol

Moriarty,

Mitan,

Bartha

et al. 2024

AJQCMS

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The conformation of 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-Oisopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1, phase angles of the pseudorotation of five (C 3 ) and six (C 1 4 ) membered rings, was analyzed with dihedral angles θ HnHn+1 [deg] calculated only from vicinal coupling constants 3 J HH [Hz] with 3-Sphere approach and VISION molecular models. The dimension space around the six and five membered ring are established based on hypersphere equations results from calculation of the dihedral angles from carbon chemical shift. Higher biological activity was observed to date at iminocyclitols having dihedral or vicinal angles calculated in 2D. Tetrahedral angles in close relationships with dihedral angles are calculated from carbon and / or proton chemical shift with manifold equations, conic and rectangle geometries. Equations for calculation of the tetrahedral angles φ Cn [deg] only from vicinal coupling constant 3 J HnHn+1 [deg] or from chemical shift δ Cn [ppm] are analyzed for five and established for six membered ring, resulting general rules for calculation of tetrahedral angles. Conic as manifold in case of six membered ring enable calculation of dihedral angle θ HnHn+1 [deg] from tetrahedral angle φ Cn [deg] starting with tetrahedral angle on unit, and in case of five membered ring based on opposite relationship between dihedral and tetrahedral (sin versus tan function), unit start with dihedral angles. Rectangle as manifold enable calculation for both the tetrahedral angle from dihedral angle starting with dihedral angle on unit, for six membered ring using two or three units with three sets angles and in case of five membered ring only one unit with seven set angles. The bond distances l CnCn+1 [A 0 ] of five and six membered ring are calculated from 3-Sphere-dihedral angles θ HnHn+1 [deg].

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“…7 between 5.5 -13. 4[Hz] for trans-aa stereochemistry. In case of cis stereochemistry with higher values of vicinal constant coupling will be used eq.…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…[2] 3-Sphere equations for calculation of the tetrahedral angles of six membered ring from carbon chemical shift. [4] 4D: sin…”

Section: Relationships Between Biological Activity and Dimension Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol

Moriarty,

Mitan,

Bartha

et al. 2024

AJQCMS

View full text Add to dashboard Cite

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Java Script Programs for Calculation of Dihedral Angles with Manifold Equations

Mitan,

Bartha,

Filip

et al. 2024

SJC

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Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δXn[ppm] and vicinal coupling constant 3JHnHn+1[Hz]. 3-Sphere approach for calculation of the dihedral angles from NMR data in four steps: 1. Prediction, or more exactly calculation of the dihedral angles from vicinal coupling constant with trigonometric equations, 2. Calculation of the dihedral angles from manifold equations; 3. Building units from angle calculated with one of the manifold equations; 4. Calculation the vicinal coupling constant of the manifold dihedral angle. In this paper are presented Java Script programs of step 2 and from step 3 only the Java Script program for calculation of seven sets angles. The bond distances lCnCn+1[A0] between two atoms of carbon are under different polar equations (i.e. limaçons or cardioid, rose or lemniscale), our expectation was to find different manifold equations for calculation the best angle, differences are smaller but can be find sometimes a preferred one for a vicinal coupling constant. 3-Sphere approach has the advantages of calculation from vicinal angle or/and chemical shift the dihedral angle, tetrahedral angle and the bond distance lCnCn+1[A0], with application on conformational and configurational analysis.

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3-Sphere Tetrahedral Angles and Phase Angle of the Pseudorotation P[deg] of C1-CH3-α-D Ribitol Iminocyclitol

Filip,

Mitan,

Bartha

2024

SJC

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3-Sphere dihedral angles θHnHn+1[deg] calculated from NMR data, from vicinal coupling constant 3JHnHn+1[Hz] with right sign and stereochemistry, are used for simulation of the conformation of the five membered ring with VISION molecular models and Gausian09W. For a vicinal angle ϕ[deg], angle result from vicinal coupling constant 3JHnHn+1[Hz], result three possible dihedral angles with negative and positive sign. Different phase angles of the pseudorotation results from combination of dihedral angles (exocyclic angles) with positive and negative sign in case of cis stereochemistry, and only negative sign for trans stereochemistry, in accord with D-ribitol stereochemistry. The sign of the endocyclic trans-ee torsional angle is positive, relative to trans-aa and cis stereochemistry with same sign as exocyclic angle, as visualized on VISION molecular models. Tetrahedral angles φCn[deg] in close relationship with dihedral angles θHnHn+1[deg] are calculated only from vicinal coupling constant 3JHnHn+1[Hz] in attempt to corelate the change in conformation with tetrahedral values φCn[deg] and bond lengths l[A0], once the iminocyclitol push out from planarity one or two atoms of carbon, and once again to confirm the method for calculation of tetrahedral angles of five membered ring, sin/tan versus sin/cos units.

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Relationship between tetrahedral and dihedral on hypersphere coordinates

Cited by 3 publications

References 6 publications

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-<I>N</I>-dehydro-L-ribitol

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-<I>N</I>-dehydro-L-ribitol

Java Script Programs for Calculation of Dihedral Angles with Manifold Equations

3-Sphere Tetrahedral Angles and Phase Angle of the Pseudorotation P[deg] of C<sub>1</sub>-CH<sub>3</sub>-α-D Ribitol Iminocyclitol

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Relationship between tetrahedral and dihedral on hypersphere coordinates

Cited by 3 publications

References 6 publications

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-&lt;I&gt;N&lt;/I&gt;-dehydro-L-ribitol

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-&lt;I&gt;N&lt;/I&gt;-dehydro-L-ribitol

Java Script Programs for Calculation of Dihedral Angles with Manifold Equations

3-Sphere Tetrahedral Angles and Phase Angle of the Pseudorotation P[deg] of C&lt;sub&gt;1&lt;/sub&gt;-CH&lt;sub&gt;3&lt;/sub&gt;-α-D Ribitol Iminocyclitol

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3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-<I>N</I>-dehydro-L-ribitol

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-<I>N</I>-dehydro-L-ribitol

3-Sphere Tetrahedral Angles and Phase Angle of the Pseudorotation P[deg] of C<sub>1</sub>-CH<sub>3</sub>-α-D Ribitol Iminocyclitol