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Results and Discussion

The reactivity in the alkene homologous series, as has been pointed out, correlates strongly with the ionization potential of the alkene [4]. Thus, it is generally found that the overall rate constant, k, at room temperature, for the addition reaction of the electrophile to the alkene, increases as the I.P. of the alkene decreases. However, in the present study an opposite reactivity trend was found thus the reaction rate constants increase as the I.P. of the corresponding chloroethenes increases [5] (Figure 1).

In the molecular-orbital approach, frontier-orbital interactions generally determine the barrier heights and reaction rates in radical or atom-molecule reactions [6]. A frontier orbital treatment is based upon the interaction of the frontier molecular orbital of the molecule (HOMO) with the frontier molecular orbital of the radical or atom (SOMO or LUMO). The higher the energy of the HOMO (low I.P) or the lower the energy of the LUMO (High electron affinity), the greater the propensity for reaction, as represented by the following equation:

k (cm³ molecule^-1 s^-1) ª 1 / (E_SOMO ­ E_HOMO) ª deltaE
It can be observed in Figure 2 that for the reactions with the chloroethenes in this series this correlation is not obeyed. In fact, the reacting trend shows just the opposite, i.e., for a higher value of deltaE, a lower rate constant is observed.

However, considering the different interaction probabilities of the electrophiles with the chloroethenes, which are represented according to the Frontier Orbital Theory by the HOMO coefficients or more exactly in this kind of reactions, by the second order perturbation (e") [6], a good correlation is found between the experimental k values and the corresponding reactivities. The following equation relates the perturbation with the energies of the HOMO and LUMO frontier orbitals.

e" = (c_Hi c_Sj b_ij )2 / (E_S-E_H)
where c_Hi is the atomic orbital coefficient of atom i in the HOMO of the chloroalkene, cSj is the coefficient of the atomic orbital of the electrophile in the SOMO, bij is the resonance integral between atoms i and j.

Furthermore, the trend for the chloroethenes is similar with the different electrophiles (Figure 3), as the rate constants increase with the increasing perturbation.








Figure 4: Reaction Coordinate for the reaction of OH + CH₂=CCl₂ as an example, calculated by PM3 method, where I-1 is a long-range complex, T.S. is the corresponding Transition State and I-2 is the stable covalent adduct or Intermediate.

From the computational analysis of the reaction pathways, we have estimated the activation energies (Ea) and the total energies (DHr) of the proposed reactions (Figure 4). It was not our aim, however, to determine accurate activation energies for each reaction.
The reaction pathways were studied using semiempirical, PM3, and ab-initio calculations (at UHF and B3LYP level of theory, with 6-31G** basis set). With these semiempirical calculations it is possible to observe, with Br, Cl and OH but not with O and NO3, the presence of a long-range complex (I-1) prior to it been collisionally quenched to form a stable covalent adduct (I-2). A similar trend for the Ea and DHr was observed between the semiempirical and ab-initio calculations

Table 1: Activation Energies (Ea) (kcal mol-1) and Heat Contents (DHr) (kcal mol-1) calculated by
PM3 method for the addition reaction of different electrophiles to chloroethenes.

	C2H3Cl		C2H2Cl2		Z-C2H2Cl2		E-C2H2Cl2		C2HCl2		C2Cl2
	Ea	deltaHr	Ea	deltaHr	Ea	deltaHr	Ea	deltaHr	Ea	deltaHr	Ea	deltaHr
O(3P)	3.68	-62.07	3.59	-64.48	4.49	-66.39	4.56	-65.96	4.31	-52.07	5.29	-56.61
OH	3.76	-47.84	3.07	-50.20	4.74	-49.69	4.71	-49.25	4.21	-50.63	4.31	-50.52
Cl	0.10	-37.15	0.03	-39.05	0.50	-34.05	0.94	-34.44	0.81	-36.74	1.10	-35.12
Br	0.05	-25.25	0.37	-27.70	0.49	-23.29	0.18	-23.23	0.47	-24.52	1.45	-23.82
NO3	3.16	-43.98	3.37	-43.19	2.86	-39.29	2.73	-38.60	0.22	-40.83	1.53	-38.41

In Table 1 the activation energies for the addition reactions of the different electrophiles to the chlorinated ethenes are shown. The Ea, in general, increase with the increasing chlorine substitution, although for 1,1 dichloroethene, which is the most reactive chloroethene, the addition reaction has the lowest Ea value.
Calculated heats of reaction DHr are also presented. All the addition reactions studied are exothermic, with DHr generally decreasing with increasing chlorine substitution.