Torsional potential functions

Torsional barriers are referred to as n-fold barriers, where the torsional potential function repeats every 2n/n radians. As in the case of inversion vibrations (Section 6.2.5.4a) quantum mechanical tunnelling through an n-fold torsional barrier may occur, splitting a vibrational level into n components. The splitting into two components near the top of a twofold barrier is shown in Figure 6.45. When the barrier is surmounted free internal rotation takes place, the energy levels then resembling those for rotation rather than vibration. 

The most useful general form of the torsional potential function V(4>) is... 

Figure 6.45 Torsional potential function, V(4>), showing a two-fold barrier...

The factors influencing the conformational stability in open chain molecules have previously been treated extensively in review articles (see for example Ref.6 and 107 ). The aim of the present section is to study torsional potential functions of a series of molecules of principal importance, in particular related to the results of electron-diffraction investigations. The bulk contents of information obtainable from an electron-diffraction intensity curve of a molecule carrying out torsional motion, are not concerned with the torsional motion at all. The part of the intensity curve giving information about the torsion, is distributed over the same range of the intensity curve as where the torsional independent information may be obtained. In the RD-curve the contribution from the torsional dependent part is more clearly separated. To illustrate this and the general influence of torsional motion, three simple molecules with three-fold torsional barriers have been selected (Figs. 3-5)... 

Torsional potential function. The torsional parameters were adjusted to give the best representation of the methyl and nitro group rotation in DMNA. 

Torsional potential functions for rotation in side-chain ester groups have been suggested by Yan et al. (1968). A twofold potential function of the form (I/y/2)(l — cosy), with a barrier height of 8-75 kcal mole-1, was assigned to the (C = 0)—00 bond. The value of f7(y) for rotation about the (COO)—C bond was taken as zero for all values ofy. 

Figure 9.49 shows the SVLF spectrum of styrene (C6H5CH=CH2), in a supersonic jet, with excitation in the ()[j band of the A1 A — X] A (6) — S0) band system. There is a prominent progression in the vibration v42 which is a torsional motion of the vinyl group about the C(l)-C(a) bond. The vibronic selection rules allow only transitions with Av42 even. Those with V42 = 0, 2, 4, 6 and 10 are observed. More vibrational levels, with V42 even and odd, have been identified and fitted to a torsional potential function of the type in Equation (6.96) giving... 

Allinger, N. L., Profeta, S. (1980). The torsional potential function for n-butane. Journal of Computational Chemistry,... 

Far-infrared spectrum, ab initio, and DFT calculations and two-dimensional torsional potential function of dimethylallene (3-methyl-l,2-butadiene) ... 

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