Torsional potential, ethylene

In order to understand the origin of the breakdown of the SR methods away from equilibrium, consider the torsional potential in ethylene (Figure 2). While at its equilibrium geometry ethylene is a well-behaved closed-shell molecule whose ground and n-valence excited states can be described accurately by SR models (except for the doubly excited Z-state), it becomes a diradical at the barrier, when the Jt-bond is completely broken (13). Thus, at the twisted geometry all of ethylene s Jt-valence states (N, T, V, and Z) are two-configurational, except for the high-spin components of the triplet. 

The Spin-flip Method for Bond-breaking the Ethylene Torsional Potential... 

R. E. Ghosh, T.C. Waddington C.J. Wright (1973). J. Chem. Soc. Faraday Trans. II, 69, 275-281. Characterisation of the torsion potential for ethylene ligands using inelastic neutron scattering. 

A test case showing spectacular failure of MCPT is provided by the torsional potential curve of the ethylene molecule. In equilibrium the system possesses >2a symmetry. Upon rotating the CH2 groups with respect to each other, the symmetry reduces to 2. At the top of the barrier (at 90° dihedral angle) the point group becomes D2d,... 

In addition, a four body torsional potential is essential when studying many organic molecules particularly planar adsorbate molecules such as ethylene and benzene. The analytical form of the potential is given as ... 

Denny, M. and Liu, R.S.H., Photosensitized isomerization of previtamin Dj and tachysterol and the related l,2-bis-(l-cyclopentenyl) ethylene torsional potential curves of triene triplets. Now. J. Chim., 2, 637-641, 1978. 

It is customary to shift the zero point of the potential by adding a factor of 1 to each term. Most rotational profiles resemble either the ethane or ethylene examples above, and a popular expression for the torsional energy is... 

The change in potential energy accompanying torsion about die C,=C2 bond in a push-pull ethylene has an important component which depends on the overlap between the p2 orbitals on C] and C2, and which we may call E , which has maxima at torsion angles of 90° and 270°. In many of the molecules discussed... 

The value of 0 in a particular radical can be estimated by comparison of the experimental half-wave potential and HFSC with the results obtained from a series of HMO calculations using different assumed values of 0. A large number of phenyl-substituted aromatic compounds [62] and ethylenes [63] have been treated in this fashion. Similar evidence for the twisting of the nitro group in nitroaromatic anion radicals is summarized in Reference 1. Restricted rotation of alkyl substituents is also discussed in Reference 1, but this torsion does not significantly affect the electrochemical behavior. 

One example of non-IRC trajectory was reported for the photoisomerization of cA-stilbene.36,37 In this study trajectory calculations were started at stilbene in its first excited state. The initial stilbene structure was obtained at CIS/6-31G, and 2744 argon atoms were used as a model solvent with periodic boundary conditions. In order to save computational time, finite element interpolation method was used, in which all degrees of freedom were frozen except the central ethylenic torsional angle and the two adjacent phenyl torsional angles. The solvent was equilibrated around a fully rigid m-stilbene for 20 ps, and initial configurations were taken every 1 ps intervals from subsequent equilibration. The results of 800 trajectories revealed that, because of the excessive internal potential energy, the trajectories did not cross the barrier at the saddle point. Thus, the prerequisites for common concepts of reaction dynamics such TST or RRKM theory were not satisfied. 

Figure 2.2. Potential energy curves of the ground state and some excited states of ethylene as a function of the torsional angle (by permission from Michl and Bona(ii( -Kouteck, 1990).

Buenker, R. J., Bonacic Koutecky, V., Pogliani, L., Potential energy and Dipole moment Surfaces for Simultaneous Torsion and Pyramidalization of Ethylene in Its Lowest lying Singlet Excited States A Cl Study of the Sudden Polarization Effect, J. Chem. Phys. 1980,73, 1836 1849. 

Researches of Eucken and his co-workers on ethylene have in fact afforded very striking confirmation of this concept. They deduce from the effect of temperature on specific heat a torsional or turning oscillation of fairly high frequency (750 cm - 10 per sec.) so that the molecule represents a highly impeded one dimensional oscillator whose properties have been studied by Teller and Weigert. Comparison of measurement and theory shows that the barrier of potential which has to be scaled in the transition from cis- to trans-form, lies far above kT] on this depends the stability of the two isomers and the possibility of isolating them by the methods of synthetic organic chemistry. 

Two recent studies indicate the influence of strong specific interactions on the effective intramolecular potential. Depner et al. used both LD and MD to investigate the dynamics of polyethylene oxide (PEO) in water [50]. They found that the equilibrium distribution of torsional angles observed in the MD simulations differed from that predicted by the LD simulations. Widmalm and Pastor performol LD and MD simulations on one ethylene glycol molecule in water [51]. They found that the effective barrier for isomerization observed in the MD simulations was lower than that expected on the t is of intramolecular potentials alone. 

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