Torsional energy butane

Figure 2.4 Fourier decomposition of the torsional energy for rotation about the C-C bond of n-butane (bold black curve, energetics approximate). The Fourier sum (A) has a close overlap, and is composed of the onefold (o), twofold (o), and threefold ( ) periodic terms, respectively...

Torsional energy of butane. The anti conformation is lowest in energy, and the totally eclipsed conformation is highest in energy. 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

Figure 2-102. Dependence of the potential energy ctirve of n-butane on the torsion angle r between carbon atoins C2 and C3.

The trans conformation corresponds to a torsion angle of 180°, the gauche(+) conformation to oni + 60° and the gauche -) conformation to -60°. These approximately correspond to the torsion anj of the three minimum energy conformations of butane. 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

Somewhat more complicated but also familiar is a plot of energy vs. the torsion angle involving the central carbon-carbon bond in -butane. 

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