Electrophilic attachment of Chlorine to Ethylene

An illustrative example is the electrophilic attachment of chlorine to the carbon-carbon double bond of ethylene. 

After the CASSCF calculation with the above choice of orbitals, in order to perform an efficient VB analysis, it is better in this case to resort to an overcomplete non-orthogonal hybrid set. The five active orbitals, in fact, can be split into ten hybrids, in term of which the VB transcription of the wavefunction turns out to be the simplest and the most compact. Such kinds of overcomplete basis sets are commonly used in constructing the so called non-paired spatial orbital structures (NPSO, see for example [35]), but it should be remarked that their use is restricted to gradient methods of wavefunction optimization, such as steepest descent, because other methods, which need to invert the hessian matrix (like Newton--Raphson) clearly have problems with singularities. 

Turning to the electrophilic attachment of chlorine to ethylene, Amovilli et al in [34] recovered between 93 and 99 % of the CAS (6,5) correlation energy using four structures and ten hybrids with the following classical coupling scheme 

The localization of such hybrids comes from the combination of the CASSCF orbitals minimizing the energy for a wavefunction written in terms of structures 1-4 the degree of polarization can thus be easily studied for all geometries through these kinds of plots. 

In Ref. [34], this attachment is discussed in detail along an optimized path obtained for reaction in aqueous solution here, instead, a comparison with the reaction in gas phase will be presented. It is useful to recall that the ring structure has a maximum weight at a geometry close to that of the transition state, while Er3 4 increase monotonically, starting from zero at the T-shaped complex and arriving at a maximum when the chloronium ion intermediate is formed. The wavefunction of the intermediate is very well represented by the resonance of structures I 2, 3 and F4 with the 

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Figure 11. Contour map of hybrids 4>i-5 used for the VB structure Iq obtained by analyzing the CASSCF wavefunction at the transition state geometry for the electrophilic attachment of chlorine to ethylene in aqueous solution.

Figure 13. Adiabatic ([a]) and diabatic ([b]) energy curves (hartree versus A) for the electrophilic attachment of chlorine to ethylene in vacuo (solid line) and in aqueous solution (dashed line). Curves 1-4 correspond to VB structures...

Finally for the electrophilic attachment of chlorine to ethylene we have studied the free energy and the form of the wavefunction along the reaction coordinate maintaining the geometry at a Civ symmetry. From the stationary points we have found the geometries and the free energies of the transition state and of the chloronium intermediate. 

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