Program for prediction dihedral angle from vicinal coupling constant with 3-sphere approach

BARTHA, Emerich; Mitan, Carmen-Irena; Drăghici, Constantin; Cãproiu, Miron Teodor; Filip, Petru; Tarko, Laszlo; Moriarty, Robert M.

doi:10.33224/rrch.2021.66.2.08

Cited by 4 publications

(23 citation statements)

References 8 publications

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“…A method easy to calculate dihedral angles by hand or with Java Script [3] in three steps: 1. Prediction of the dihedral angle only from the vicinal coupling constant, a step which gives the sign without any ambiguity [5]. 2.…”

Section: Iii)mentioning

confidence: 99%

“…15 (-167.12[deg]), but with a difference of 0.02[Hz], 0.313[deg], since from eq. 17 result trans-aa 5,2 stereochemistry (-135.69[deg]).…”

Section: Algebraic Equationsmentioning

confidence: 99%

“…where: ϕ = f(ϕ 1 /2, ϕ 2 ) -the vicinal angle. Dihedral angles are predicted [5] only from vicinal coupling constants with eq. 21, 22: the eq.…”

Section: Prediction Of the Vicinal Anglementioning

confidence: 99%

“…In step 1 are predicted [5] only from vicinal coupling constants the vicinal angles with cis-and transstereochemistry (eq. 21, 22), then the dihedral angles.…”

Section: Prediction Of the Dihedral Anglementioning

confidence: 99%

“…Dihedral angle is in close relationship with the vicinal angle [3], angle results from the vicinal coupling constant 3 J HH [Hz] (Figure 1): I. cis-ae, cis-ea, trans-ee 3,2 : θ An + θ Bn = 90, II. trans-ee 4,1 , trans-aa 6,1 , trans-aa 5,2 : θ An -θ Bn = 90. The trigonometric equations and algebraic equation [4], under 3sphere and Lie group theories ensure a great correlation between the vicinal coupling constant and the dihedral angle with its corresponding sign and stereochemistry, using one set angles (dihedral angle -θ An , vicinal angle -ϕ = f(ϕ 1A /2, ϕ 2A ), or two set angles (dihedral angle -θ An , vicinal angleθ Bn , n = 1-6) under +/-60[deg] rule.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Hopf Fibration on Relationship Between Dihedral Angle θ<sub>HnHn+1</sub>[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Mitan¹,

Bartha²,

Drăghici³

et al. 2022

SJC

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3-Sphere theory, a hypersphere in four dimensions, is applied for calculation dihedral angles with the right stereochemistry and sign in D, -L ribitol series from proton and carbon chemical shift (∆δ XnXn+1 [ppm], X = H, C) and vicinal coupling constant ( 3 J HnHn+1 [Hz]) with Java Script. A method in three steps, easy to calculate by hand or with Java Script program: 1. prediction of the dihedral angle only from 3 J HnHn+1 [Hz], 2. calculation the angle of set A with manifold equation (conic section, Villarceau circles) from chemical shift, 3. building of the seven sets unit or six sets units, from which is chose an angle almost equal with the predicted one having its stereochemistry and sign. Angles of set A and set B, relationships between vicinal angle and dihedral angle (X 0 -X 15 ) are introduced instead of polar angle and azimuthal angle in spherical coordinates (eq. 1 versus eq. 3). Hopf coordinates, trigonometric equations, confirmed by algebraic equations are disclosed for all cis-ae/ea, trans-ee, trans-aa stereochemistry. Octonionic fibration S 7 →S 15 →S 8 in R 16 , with real fibration S 0 →S 1 →S 1 as unit, reassembles all possible stereochemistry gives by the HCCH fragment on two congruent disks, each centered on the perimeter of the other with equilateral triangles as vertices. Complex Hopf fibration in R 4 ensuring the calculation of the dihedral angle from vicinal angle and vice versa, demonstrating the relationships between sets A, B, C.

show abstract

Section: Iii)mentioning

confidence: 99%

“…15 (-167.12[deg]), but with a difference of 0.02[Hz], 0.313[deg], since from eq. 17 result trans-aa 5,2 stereochemistry (-135.69[deg]).…”

Section: Algebraic Equationsmentioning

confidence: 99%

“…where: ϕ = f(ϕ 1 /2, ϕ 2 ) -the vicinal angle. Dihedral angles are predicted [5] only from vicinal coupling constants with eq. 21, 22: the eq.…”

Section: Prediction Of the Vicinal Anglementioning

confidence: 99%

“…In step 1 are predicted [5] only from vicinal coupling constants the vicinal angles with cis-and transstereochemistry (eq. 21, 22), then the dihedral angles.…”

Section: Prediction Of the Dihedral Anglementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hopf Fibration on Relationship Between Dihedral Angle θ<sub>HnHn+1</sub>[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Mitan¹,

Bartha²,

Drăghici³

et al. 2022

SJC

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Manifold inversion on prediction dihedral angle from vicinal coupling constant with 3-sphere approach

MITAN,

BARTHA,

FILIP

et al. 2024

Rev.Roum.Chim.

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Dihedral angles are predicted from vicinal coupling constant 3JHH[Hz] with 3-sphere approach, sphere or torus trigonometric equations of circle 1, 2 and circle inversion 3-5 for all cis-, trans-ee, trans-aa stereochemistry. The existence of circle inversion was demonstrated with conformational analysis on five and six membered rings. The sign and the stereochemistry result from vicinal coupling constant under trigonometric equations confirmed by algebraic equations, Hopf and Lie algebra theory. 3-Sphere, a hypersphere in 4D enable for all stereochemistry calculation dihedral angles under magnetic wave (NMR data -3JHH[Hz]), and all isomers from only one vicinal coupling constant.

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Relationship between tetrahedral and dihedral on hypersphere coordinates

MITAN,

BARTHA,

FILIP

2023

Rev.Roum.Chim.

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The wave character of the NMR data (chemical shift ΔδCn[ppm] – vicinal coupling constant 3JHH[Hz]) enable calculation the tandem dihedral-vicinal or tetrahedral-internal angles with 3-sphere approach. Golden ratio, invers of Fibonacci number, and manifold inversion torus to Dupin cyclide under 3-sphere units ensure the calculation of the tetrahedral angles of five membered ring in opposite with dihedral angles sin versus tan functions. The transformation from space/time to space under electric and magnetic rule gives dodecahedron and icosahedron values for calculation tetrahedral angles from polyhedron and hypersphere equations. Tetrahedral angles of five membered ring can be calculated from carbon chemical shift ΔδCn[ppm] with Java Script program and hypersphere equations.

show abstract

Program for prediction dihedral angle from vicinal coupling constant with 3-sphere approach

Cited by 4 publications

References 8 publications

Hopf Fibration on Relationship Between Dihedral Angle θ<sub>HnHn+1</sub>[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Hopf Fibration on Relationship Between Dihedral Angle θ<sub>HnHn+1</sub>[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Manifold inversion on prediction dihedral angle from vicinal coupling constant with 3-sphere approach

Relationship between tetrahedral and dihedral on hypersphere coordinates

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Program for prediction dihedral angle from vicinal coupling constant with 3-sphere approach

Cited by 4 publications

References 8 publications

Hopf Fibration on Relationship Between Dihedral Angle θ&lt;sub&gt;HnHn+1&lt;/sub&gt;[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Hopf Fibration on Relationship Between Dihedral Angle θ&lt;sub&gt;HnHn+1&lt;/sub&gt;[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Manifold inversion on prediction dihedral angle from vicinal coupling constant with 3-sphere approach

Relationship between tetrahedral and dihedral on hypersphere coordinates

Contact Info

Product

Resources

About

Hopf Fibration on Relationship Between Dihedral Angle θ<sub>HnHn+1</sub>[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script

Hopf Fibration on Relationship Between Dihedral Angle θ<sub>HnHn+1</sub>[deg] and Vicinal Angle ϕ[deg], Angles Calculated from NMR Data with 3-Shere Approach and Java Script