Torsion angle deformation

Torsional rotations about single bonds and multiple bonds are different processes. In a multiple bond a torsional rotation results in the transformation of one configurational isomer into another. In contrast, the rotation about single bonds leads to interconversion of conformational isomers (Fig. 3.9). 

In both cases, repulsion of the substituents is modeled by van der Waals interactions (see below) and the torsional potential describes the additional electronic component, including distortion of the molecular orbitals and repulsion by the electron clouds. 

It is common practice to describe torsional rotations about single bonds and those about multiple bonds with the same type of potential function but with very different force constants. The function must be able to describe multiple minima. Generally, a Fourier expansion of the torsional angle f with only cosine terms is used (Eq. 3.23), 

7 More details and examples of this approach are discussed in Chapter 11. 

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The units for the force constants are usually given in mdyn A-1 (bond length), mdyn A rad"2 (valence angle bending and out-of-plane distortion) and mdyn A (torsion angle deformation). 

Yy = angle between two planes, ky = force constant, and y = ideal twist angle. Torsion angle deformation ... 

The five terms in Eq. 26.1 compute the energies of bond stretching, angle bending, torsion angles deformation, and non-bonded van der Waals (vdW) and electrostatic interactions, respectively. Detailed explanation of the parameters in the above equation can be found elsewhere [42]. In this study, we derive all parameters for the ether group (except for vdW, adopted directly from AMBER). 

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