Rotational energy profile

Using the data incorporated in Fig. 3.3 and assuming the additivity of gauche and eclipsing interactions of similar type, sketch the rotational energy profile you would expect for 2,3-dimethylbutane. 

FIGURE 3. Rotational energy profile around the methine carbon-nitrogen bond of isopropyldimethylamine (IDMA) as calculated by MM2-87. Reprinted with permission from Reference 72. Copyright (1992) American Chemical Society... 

FIGURE 5. Rotational energy profile about the N-ethyl bond for iV-ethyl-iV-t-butylneopentylamine (ETNA, 40) as calculated by MM2-85. Reproduced with permission from Reference 74... 

Maxwell, D. S., Tirado-Rives, J., and Jorgensen, W. L. (1995) A comprehensive study of the rotational energy profiles of organic systems by ab initio MO theory, forming a basis for peptide torsional parameters. J. Comput. Chem. 16, 984-1010. 

A Fourier series is an example of an orthogonal polynomial, meaning that the individual terms which it comprises are independent of each other. It should be possible, therefore, to dissect a complex rotational energy profile into a series of N-fold components, and interpret each of these components independent of all others. For example, the onefold term (the difference between syn and anti conformers) in /7-butane probably reflects the crowding of methyl groups. 

Fig. 7.5 Rotational energy profiles of ethane according to different ways of analysing the wave function (energies not drawn to scale, exaggerated for clarity).

Templeton has carried out extensive studies of rotational barriers of alkynes and has calcnlated a nnmber of rotational energy profiles his papers provide leading references to earlier work. Pyrazolylborate analogues also show similar behavior and this work as well as earlier reviews provides leading references. 

The rotational profile of n-butane can be understood as a superimposition of van der Waals repulsion on the ethane rotational energy profile. The two gauche conformations are raised in energy relative to the anti by an energy increment resulting from the van der Waals repulsion between the two methyl groups of 0.6 kcal/mol. The... 

Fig. 12.13. DFT computation of the rotational energy profile of stilbene, beginning at the trans (180°) and cis (0°) geometries. Both neutral (n) and zwitterionic (z) versions of 2 were computed. Reproduced from Chem. Phys. Chem, 3, 167 (2002), by permission of the Royal Society of Chemistry.

Figure 4 Rotational energy profile computed for 1,2-dimethoxyethane. The C-O-C-C torsional angles of the methoxyl groups were constrained to 180°.

The Vi parameters may also be negative, which corresponds to changing the minima on the rotational energy profile to maxima, and vice versa. Most commonly... 

The second route to missing parameters is to use external information, experimental data or electronic structure calculations. If the missing parameters are bond length and force constant for a specific bond type, it is possible that an experimental bond distance may be obtained from an X-ray structure and the force constant estimated from measured vibrational frequencies, or missing torsional parameters may be obtained from a rotational energy profile calculated by electronic structure calculations. If many parameters are missing, this approach rapidly becomes very time-... 

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