scholarly journals The Chirality Chain in Valine: How the Configuration at the C α Position through the O cis C′C α N Torsional System Leads to Distortion of the Planar Group C α C′(O cis )O trans to a Flat Tetrahedron

ChemistryOpen ◽  
2018 ◽  
Vol 7 (9) ◽  
pp. 696-700 ◽  
Author(s):  
Henri Brunner ◽  
Takashi Tsuno
Keyword(s):  
Torsional System ◽  
Planar Group

The non-planar vibrations of some substituted ethylenes and related compounds

1951 ◽  
Vol 206 (1084) ◽  
pp. 17-39 ◽  
Keyword(s):  
Resonance Effect ◽  
Aromatic Substitution ◽  
Fluorine Substitution ◽  
Vinyl Halides ◽  
Group Frequency ◽  
Related Series ◽  
Planar Group ◽  
Vinyl Group ◽  
Related Compounds ◽  
Resonance Hybrid

By applying a general normal co-ordinate treatment to the non-planar group of vibrations of related series of substituted ethylenes, it has been found possible to obtain consistent sets of force constants for the non-planar bending motions, and to correlate their variation with the observed shifts in the group frequencies and with the electro-negativities and electrondonating powers of the substituents. From calculations on twelve compounds, a linear relation between the CH 2 = bending constant, (ƒ CH 2 ), and fbe corresponding group frequency (δ CH 2 ) is obtained and used to fit a further nine compounds into the series. Substitution by CH 3 —, CH 3 .CO.O—, and the halogens leads to a decrease in ƒ CH 2 compared with its ‘neutral’ value in ethylene; the increment in CH 2 = C X 2 is greater than in CH 2 =CH. X for all the examples studied, and increases with the electronegativity of the substituent X , being particularly large for fluorine. Substitution by —CN and —CO.O.CH 3 leads to positive increments. These results suggest that the main effect operative is the electromeric, (resonance) effect directing aromatic substitution, the powers of conjugation of vinyl and phenyl being known to be approximately equal. CH 3 —, CH 3 . CO . O— and the halogens lead to ortho-para- substitution, and —CN and —CO. O . CH 3 to meta- substitution. Thus, withdrawal of electrons from the terminal carbon atom of the vinyl group results in an increase in the forces opposing non-planar bending of the = CH 2 group. The results can be extended to include related u n satu rated compounds. The relatively high value of ƒ CH 2 in form aldehyde can be related to the fact that this molecule is a resonance hybrid in which the ionic structure CH 2 + — O - is of considerable im portance. The low value of ƒ CH 2 in allene suggests that this is also a resonance hybrid, with contributions from ionic structures CH - 2 — C + = CH 2 . In the allyl halides, the resonance effect is inhibited by the CH 2 group, and the order of the frequencies is the reverse of that in the vinyl halides. The chloride lies midway between propylene and ethylene, agreeing with the fact that in C 6 H 5 . CHCl 2 there is no appreciable difference in the reactivity at the ortho-, para- and meta- carbon atoms. The resonance effect cannot operate directly on the odd = C —H bond in CH 2 —CH X ; the bending constant / CH decreases as th e electronegativity of th e sub stitu en t X increases, — CN now lying between CH 3 and Cl and the effect again being particularly large for fluorine. The values of ƒ CH in acetylene and benzene (non-planar) suggest that there may be an inverse relation between the constants for C— C stretching and for bending of the adjacent C— H bonds.

An Improvement of the Holzer Method

1958 ◽  
Vol 25 (4) ◽  
pp. 618-620
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequency ◽  
Moment Of Inertia ◽  
Torsional System

Abstract This paper presents a method of obtaining the next trial frequency from the results given by the previous Holzer table. The basis of the method is the effect of a small (fictitious) change in moment of inertia on the natural frequency of the torsional system. Although basically different, the method leads to a result which is very close to that given by Crandall and Strang. The relative merits of the two methods depend on whether the trial frequency is above or below the exact one and on whether or not the next approximation will overshoot the exact value.

Non-planar Boron Lewis Acids Taking the Next Step: Development of Tunable Lewis Acids, Lewis Superacids and Bifunctional Catalysts

Synlett ◽  
2020 ◽  
Vol 31 (17) ◽  
pp. 1639-1648
Author(s):  
Guillaume Berionni ◽  
Aurélien Chardon ◽  
Arnaud Osi ◽  
Damien Mahaut ◽  
Ali Ben Saida
Keyword(s):  
Recent Work ◽  
Research Group ◽  
Lewis Acids ◽  
Experimental Studies ◽  
Planar Geometry ◽  
Bifunctional Catalysts ◽  
Group 13 ◽  
Recent Developments ◽  
Stereoelectronic Properties ◽  
Planar Group

Although boron Lewis acids commonly adopt a trigonal planar geometry, a number of compounds in which the trivalent boron atom is located in a pyramidal environment have been described. This review will highlight the recent developments of the chemistry and applications of non-planar boron Lewis acids, including a series of non-planar triarylboranes derived from the triptycene core. A thorough analysis of the properties and of the influence of the pyramidalization of boron Lewis acids on their stereoelectronic properties and reactivities is presented based on recent theoretical and experimental studies.1 Non-planar Trialkylboranes2 Non-planar Alkyl and Aryl-Boronates3 Non-planar Triarylboranes and Alkenylboranes3.1 Previous Investigations on Bora Barrelenes and Triptycenes3.2 Recent Work on Boratriptycenes from Our Research Group4 Applications of Non-planar Boranes4.1 Non-planar Alkyl Boranes and Boronates4.2 Non-planar Triarylboranes (Boratriptycenes)5 Other Non-planar Group 13 Lewis Acids6 Further Work and Perspectives

A Closed-Form Planet Load Sharing Formulation for Planetary Gear Sets Using a Translational Analogy

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
H. Ligata ◽  
A. Kahraman ◽  
A. Singh
Keyword(s):  
Closed Form ◽  
Discrete Model ◽  
Deformable Body ◽  
Planetary Gear ◽  
Load Sharing ◽  
Position Errors ◽  
Model Predictions ◽  
Planetary Gear Sets ◽  
Torsional System

A simplified discrete model to predict load sharing among the planets of a planetary gear set having carrier planet position errors is presented in this study. The model proposes a translational representation of the torsional system and includes any number of planets positioned at any spacing configuration. The discrete model predictions are validated by comparing them to (i) the predictions of a deformable-body planetary gear set model and (ii) planet load sharing measurements from planetary gear sets having three to six planets. A set of closed-form planet load sharing formulas are derived from the discrete model for gear sets having equally-spaced planets for conditions when all of the planets are loaded. These formulas allow, in an accurate and direct way, calculation of planet loads as a function of position errors associated with each planet.

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