Before anything, the following points should carefully be considered: ... As can be seen, if the formation of pre-complex is not considered, activation total ...
Before anything, the following points should carefully be considered: -
Structures of reactant(s) and corresponding transition state, TS, must be optimized using same method and basis set.
-
Validity of your optimizations should be verified using a frequency calculation for both reactant(s) and TS; that is, there must be no any imaginary frequency for the optimized reactant(s) and there must be one and only one imaginary frequency for the corresponding optimized TS. Additionally, the unique imaginary frequency found for TS should properly be associated with the breaking the bond(s) you are looking for. An IRC calculation is recommended to be performed in order to ensure that your located TS correctly connects to the two associated minima (reactants and products) along PES (potential energy surface).
Now, we can return to your problem. Let us to consider a bimolecular reaction as follows:
The activation energy or, in the more appropriate word, the activation total electronic energy (
)
is defined as the difference between total electronic energy of TS and the sum of total electronic energy of separate reactants. Total electronic energy which is reported at the end of any optimization calculation is usually not an appropriate quantity in kinetic studies because, as you know, this energy does not include ZPVE (zero point vibrational energy,
) and, consequently,
due to the lack of such consideration, your results may noticeably be affected. What is the meaning of “negative activation energy” and can such negativity be resulted in some calculations? It means that TS is located below the separated reactants on the PES of the reaction under study. In other word, TS is energetically more stable than the separated reactants. SN2 reactions in the gas phase are one of the well-known examples providing negative activation total electronic energy. Indeed, as two separated reactants are approached, a pre-complex which is energetically more stable than the separated reactants is initially formed between them in an appropriate distance and, then, TS is formed from this pre-complex instead of separated reactants. Assume that aforementioned reaction is a nonspontaneous SN2 reaction:
As can be seen, if the formation of pre-complex is not considered, activation total electronic energy becomes negative (follow the path shown in black) while corresponding activation total electronic energy becomes positive by considering of a stabilizing pre-complexation (follow the path shown in red). While negative activation total electronic energy is usually reported in some publications (I refer you to study of some publications of Professor Luis Ramon Domigo who is much expert in theoretical chemistry field), in order to overcome this problem you also have to consider a precomplexation for your study similar to the SN2 reaction if you would not like to report negative activation energy. It should be noted that locating a pre-complex on the PES of a given reaction can sometime be a difficult try. Instead, you can compute activation enthalpy and, then, calculate activation energy considering transition state theory (TST) as follows: E a= Δ
+
(1)
Where n denotes the molecularity of the reaction. Note that enthalpy, H, includes both total electronic energy and ZPVE. Sometimes, activation energy (Ea) calculated using equation (1) provides a negative value as well. It is worth to note that in the calculation of Ea based on equation (1) energetic effects are the unique effects which are just considered. I, personally, believe that activation Gibbs free energy (Δ
) in which both energetic and entropic terms are included is
the best parameter for any kinetics consideration. Consequently, calculation of activation
Gibbs free energy followed by the calculation of the corresponding rate constant (k) for the investigated reaction can clearly provide all necessary information about what really happens during a kinetics study without worrying about negativity or no negativity of activation energy.
