Rotational barriers of ethane

The four-electron destabilization rationale The rotation barrier of ethane is sometimes explained in terms of the mnemonic energy-level-splitting diagram shown in Fig. 3.58. The figure purports to depict how two filled MOs of ethane ( and 4>+) evolve perturbatively from two... 

We conclude that the four-electron stabilization rationalization lacks both physical and numerical relevance to barrier problems and should not be taken as evidence in support of a picture of the rotation barrier of ethane based on steric repulsions. 

Simple yet important mechanistic cases concern the computation of rotational barriers around single bonds. A timely case in point is the rotational barrier of ethane, an old yet much debated subject [27, 28]. While the notion of hindered rotation in ethane is often... 

Table 1. Contribution of various excitation types to the rotation barrier of ethane in kcal/mol)...

There is a class of reactions whose correlation energy is commonly assumed to remain constant as function of the nuclear coordinates. Examples are the rotational barrier of ethane the interaction of two water molecules 5) or the reaction... 

The reader who is familiar with qualitative MO theory will have no difficulty recognizing the ominous forebodings of the analysis presented above for we have hardly ever incorporated nonbonded interaction effects in qualitative MO models except when discussing problems such as the rotational barrier of ethane, where consideration of nonbonded interaction is actually inevitable since the staggered and eclipsed conformers are differentiable only if vicinal nonbonded interaction is assumed to be nonzero. 

In electron-precise systems, processes which do not change the nature of the bonding along the reaction path can often be computed with reasonable accuracy even at low levels of theory. For example, the rotational barrier of ethane, which... 

Table 1 Bond-Antibond Interaction Contributions to the Internal Rotation Barrier of Ethane (kcal mor ), Level HF/6-31 G(d)...

Fig. 15.21. The electronic rotation barrier of ethane (kJ/mol) calculated at the Hartree-Fock level (thick grey line), the valence-electron MP2 level (dotted line), the valence-electron CCSD level (dashed line) and the valence-electron CCSD(T) level (full line).

The haloethanes all have similar rotational barriers of 3.2-3.7 kcal/mol. The increase in the barrier height relative to ethane is probably due to a van der Waals rqjulsive efiect. The heavier halogens have larger van der Waals radii, but this is ofiset by the longer bond lengths, so that the net efiect is a relatively constant rotational barrier for each of the ethyl halides. 

The nature of the rotational barrier in ethane is not easily explained. It is too high to be due to van der Waal s forces. It is considered to arise by interactions among the electron clouds of C—H bonds and quantum mechanical calculations show that the barrier should exist. 

Semi-empirical models are markedly inferior to all other models dealt with (except the SYBYL molecular mechanics model) for barrier calculations. Major trends in rotation barriers are often not reproduced, for example, the nearly uniform decrement in rotation barrier from ethane to methylamine to methanol. None of the semi-empirical models is better than the others in this regard. One the other hand, AMI is clearly superior to MNDO and PM3 in accounting for nitrogen inversion barriers. All in all, semi-empirical models are not recommended for barrier calculations. 

Determination of the Rotational Barrier in Ethane by Vibrational Spectroscopy and Statistical Thermodynamics 166... 

Estimate the cost of nonbonded HH repulsion as a function of distance by plotting energy (vertical axis) vs. HH separation (horizontal axis) for methane+melham (two methanes approaching each other with CH bonds head on ). Next, measure the distance between the nearest hydrogens in eclipsed ethane. What is the HH repulsion energy in the methane dimer at this distance Multiplied by three, does this approximate the rotation barrier in ethane ... 

When rotation occurs about a bond there are two sources of strain energy. The first arises from the nonbonded interactions between the atoms attached to the two atoms of the bond (1,4-interactions) and these interactions are automatically included in most molecular mechanics models. The second source arises from reorganization of the electron density about the bonded atoms, which alters the degree of orbital overlap. The values for the force constants can be determined if a frequency for rotation about a bond in a model compound can be determined. For instance, the bond rotation frequencies of ethane and ethylamine have been determined by microwave spectroscopy. From the temperature dependence of the frequencies, the barriers to rotation have been determined as 12.1 and 8.28 kJ mol-1, respectively1243. The contribution to this barrier that arises from the nonbonded 1,4-interactions is then calculated using the potential functions to be employed in the force field. 

The results of a valence bond treatment of the rotational barrier in ethane lie between the extremes of the NBO and EDA analyses and seem to reconcile this dispute by suggesting that both Pauli repulsion and hyperconjugation are important. This is probably closest to the truth (remember that Pauli repulsion dominates in the higher alkanes) but the VB approach is still imperfect and also is mostly a very powerful expert method [43]. VB methods construct the total wave function from linear combinations of covalent resonance and an array of ionic structures as the covalent structure is typically much lower in energy, the ionic contributions are included by using highly delocalised (and polarisable) so-called Coulson-Fischer orbitals. Needless to say, this is not error free and the brief description of this rather old but valuable approach indicates the expert nature of this type of analysis. 

Now, there is no satisfactory theory of steric effects, although attempts to rationalize the barrier of ethane by quantum-mechanical calculations are appearing more frequently (dementi and Davis, 1966). Furthermore, simple group-additivity schemes of various kinds have had limited success, at best, e.g. for estimating rotational barriers in ethanes (Tang and Chen, 1962), correlating relative reactivities with Taft EB values (Wells, 1963), or evaluating asymmetric induction (Ugi, 1965 Ruch and Ugi, 1966). Semi-empirical calculations by equation (197) have... 

Peter R. Schreiner Teaching the Right Reasons Lessons from the Mistaken Origin of the Rotational Barrier in Ethane, Angew. Chem. 114(19), 3729-3731 (2002), Angew. Chem. Int. Ed. 41(19), 3579-3581 (2002)... 

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