# Radical addition to the vinyl C=C bond: Quantum chemistry model of the reaction

## Comparison of Direct TS Calculations with Indices of Reactivity

Let us return to our consideration of radical addition. Earlier, we suggested that the activation energy of this reaction is a total of two effects: deformation and polar interaction. The first can be evaluated by standard deformation energy, *E _{0}^{def}* (see above), and the second by CT energy of the PMO method. To try the possibility of a general scheme of radical activity, all previously obtained results of direct TS calculations were considered within the following equation:

(3)

*E*

_{a}= a_{0}+ a_{1}E_{0}^{def}+ a_{2}E^{CT}To use the advantages of the *N/G* method of calculation of *E ^{CT}* we used the formula (2')

Parameters *N* and *G* calculated relatively `HOO`

were used for the standard set of monomers' parameters. Parameters of radicals could be easily derived from linear dependencies shown in Figure 5. So, we just needed to obtain parameters ^{•}*a _{0}*,

*a*,

_{1}*a*of reactions. That was done by the usual optimization procedure. But, it was found that parameters of radicals obtained from π-approximation poorly correspond to the true picture of reactivity (and, really, they have considerable σ-character in TS). So, we decided to adjust parameters of radicals within the same optimization process. Final optimized values are collected in Tables VII and VIII. Figure 6 shows the quality of usage of Eq. (3) for evaluation of activation energies.

_{2}β-addition | α-addition | |||||
---|---|---|---|---|---|---|

E^{def} | N | G | E^{def} | N | G | |

E, kcal/mol; ^{def}N, G, eV | ||||||

Eth | 6.83 | 1.30 | 14.1 | |||

Prop | 6.51 | 1.15 | 13.7 | 7.45 | 1.46 | 14.2 |

AN | 6.57 | −1.74 | 14.1 | 7.19 | 0.28 | 14.8 |

MA | 7.01 | −2.19 | 14.4 | 7.65 | 0.73 | 14.8 |

VA | 5.64 | 2.01 | 13.3 | 6.10 | 0.74 | 14.4 |

VCl | 6.56 | −0.36 | 14.1 | 7.08 | 0.23 | 14.7 |

VCl2 | 6.07 | −1.63 | 14.0 | 6.96 | −0.46 | 15.1 |

St | 4.82 | 1.37 | 13.0 | 7.88 | 1.40 | 14.3 |

Bu2 | 4.786 | 1.39 | 13.1 | |||

Hex3 | 4.438 | 1.40 | 12.9 | |||

ViNaph | 4.890 | 1.38 | 12.9 | |||

2ViPy | 5.204 | 0.79 | 13.3 | |||

4ViPy | 5.113 | 0.12 | 13.4 | |||

4ViPm | 5.611 | −0.42 | 13.6 | |||

2ViPm | 5.783 | −0.32 | 13.4 |

N | G | β-addition | α-addition | |||
---|---|---|---|---|---|---|

a_{0} | a_{1} | a_{0} | a_{1} | |||

^{*} `HOO` is chosen to be the reper reactant, so relative parameters of other radicals are presented here (N < 0 means a more electronegative and G < 0 a more “sensitive” radical). | ||||||

`HOO` | 0 | 0 | 28.0 | 1.46 | 20.8 | 2.85 |

`CH` | 1.60 | −1.00 | 21.0 | 0.75 | 23.8 | 0.75 |

`CH` | −0.55 | −0.65 | 26.2 | 0.92 | 14.0 | 3.05 |

`CCl` | −1.75 | −1.30 | 28.6 | 0.80 | 24.3 | 2.00 |

`CF` | −3.50 | −0.23 | 23.8 | 0.60 | 16.0 | 2.30 |

**Figure 6**. Relationship between directly calculated activation energies and those evaluated by Eq. (3) values, kcal/M (β-addition indicated by □, α-addition by +).

The main significance of that correlation is that regulations of radical addition to the `C=C`

bond (how they are seen by semiempirical methods of quantum chemistry) could be explained by the electronic structure of reagents using two indices of reactivity: ability of reaction center to deform and change its hybridization and the energy of interaction of π-MOs of reagents. It is a justification of our next step: to explain experimental regulations by these same characteristics of reagents and try the mathematical form of Eq. (3) for a correlation analysis of experimental data.