Torsional energy surface

Werpetinski, K. S., Cook, M., 1997, A New Grid-Free Density Functional Technique Application to hie Torsional Energy Surfaces of Ethane, Hydrazine, and Hydrogen Peroxide , J. Chem. Phys., 106, 7124. 

C. Jaime and E. Osawa, Tetrahedron, 17,2769 (1983). A Repatameterization of Empirical Hydrocarbon Force Field MM2 for Improved Performance in Torsional Energy Surface Calculations. 

To calculate N (E-Eq), the non-torsional transitional modes have been treated as vibrations as well as rotations [26]. The fomier approach is invalid when the transitional mode s barrier for rotation is low, while the latter is inappropriate when the transitional mode is a vibration. Hamionic frequencies for the transitional modes may be obtained from a semi-empirical model [23] or by perfomiing an appropriate nomial mode analysis as a fiinction of the reaction path for the reaction s potential energy surface [26]. Semiclassical quantization may be used to detemiine anliamionic energy levels for die transitional modes [27]. 

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

Figure 4. Anion (lower) and neutral (upper) potential energy surfaces illustrative of enolate cases where the surface spacing varies strongly along the H2C-C torsion angle 6 and becomes very small near 6 = 90°.

The calculations were performed into two basis sets, with full geometiy optimization except for the torsional angles a and 6. Two non planar conformations were considered, which correspond to minima on the potential energy surface into the GVB approximation [21]. In these conformations, the molecule adopts a pyramidal conformation, as in methanal. In addition, the hydroxilic group is rotated up or down the OCO plane. 

As an example, this approach was applied to the calculation of the PMF for alanine dipeptide as a function of the two torsion angles

resulting free energy surface is shown in Fig. 4.5. Bilinear Qi elements were used to approximate the free energy. Control points were chosen such that there are four of them around each data point. This was done in order to increase the smoothness and quality of the reconstructed free energy. The position of the Q i nodes and control points is shown in Fig. 4.6. 

Figure 9. Schematic reprsentation of a classical trajectory moving on the Si and So energy surfaces of the H2—(CH) -NHt trans cis photoisomerization, starting near the planar Franck-Condon geometry. The geometric coordinates are (a) torsion of the C2—C3 and C3 C4 bonds and (b) asymmetric stretching coupled with pyramidalization. Both Si and So intersect at a conical intersection (Si/S0 Cl) located near the minimum of the Si surface (Min-C ) where the C2C3C4N5 torsion angle is 104°. [Reproduced with permission from [87], Copyright 2000 Amercian Chemical Society],...

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