Internal rotation definition

As a result of the small, but apparent single bond character of the triafulvene C3/C4 bond and the good stabilization of the transition state of the rotation established earlier, rotation around this bond should be lower in energy in comparison to simple ethylene derivatives183. In fact, 1H-NMR spectra of several types of asymmetrically substituted triafulvenes 219-224 proved to be temperature-dependent and showed reversible coalescence phenomena at definite temperatures diagnostic for internal rotation processes. These were characterized by the free enthalpy of activation AG at the coalescence point of appropriate substituent signals61. ... 

These results demonstrate that conformer F is definitely not involved in the course of the hydrolysis reaction. For example, if conformer F, i.e. 83 of orthoester 78 is examined on the basis of the stereoelectronic principle, it must yield a mixture of the two hydroxy-esters 81 and 82. Indeed, conformer 83 must produce first the open-chain dialkoxycarbonium ion 84 which after hydration would give the acyclic tetrahedral intermediates 85 and 86. Since internal rotation is allowed in 85 and 86, they would then give a series of different conforrners which should fragment to give a mixture of the hydroxy-esters 81 and 82. 

Let US first examine current practice in nomenclature of the phenom-menon of internal rotation. Standard textbooks on conformational analysis on the one hand and those on spectroscopy on the other hand deal differently with the basic definitions. Internal rotation is measured by one or more torsion angles (dihedral angles, azimuthal angles). In the simple cases of e.g. a 1,2-disubstituted ethane the potential energy associated with the internal rotation may be written in a formal sense as a truncated Fourier expansion ... 

Figure 4 Rigid internal rotation (torsional angle 0) involving the methyl group as a unit, and the dihedral motions (t), which describe a single H —C —C —H deformation, in ethane. Although there is a single definition of , there are 9 independent...

With such a definition, the r-NRG for the double internal rotation in dimethylamine is a group of order 18 ... 

Coordinates defined in [59], Units are mdyn/A, mdyn A/rad and mdyn/rad for stretches, stretch-bend and bends, respectively. The internal coordinates are numb ed according to the definition of BzjCr. The definition of internal rotation is different for BzjCr and BzCr(CO)3. 

The values of the force constants of BzjCr for ligand-metal-ligand bending-, ligand tilting-, and internal rotation are very close to those of ferrocene. The corresponding constants of BzCr(CO)3 are somewhat different, a feature that might also be related to (unavoidable) differences in the definitions of the internal coordinates. 

Barn, definition, 1-23 to 26 Barometer corrections, 15-30 Barriers to internal rotation, 9-59 to 63 Baryons, summary of properties, 11-1 to 55 Bases... 

Reduced Axis Method analysis, combined fit of the = 0 1 2 torsional states. All parameters in em except p which is dimensionless. For the definition of the parameters see Nr. 195, acetic acid. The internal rotation program BELGI was used see [94Hou]. ... 

These are invariant to translation and rotation of a stereomodel. Most experimental chemists are familiar with internal coordinates from crystal structure analyses and the employment of molecular modelling computer programs. With regard to fundamental concepts of stereochemistry, internal coordinates are of prime importance as they allow clear definitions of terms to be formulated. ... 

From what has been shown in the preceding sections (cf. Eqs. 61 and 73, 83), it is possible to present the molecular structure resulting from both the r -fit method and any of the r()-derived methods in a convenient and easily comparable form, as a structural description in both Cartesian and internal coordinates, and with consistent errors and correlations (for small and larger molecules). A detailed comparison would require a sufficiently large SDS to determine a complete molecular structure, but the requirements are still the least restrictive of all methods presented. The input data must include the covariance matrix of the rotational constants or moments. This matrix may have to be adequately modeled to avoid grossly different weighting of isotopomers which is usually not warranted. The definition of the input data set... 

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