Dear Tian,
Too many thanks for your highly kind attention to guide me with your much informative comments.
Indeed, if we take the below reaction in vacuum:

A+B--->TS        Delta_E_act(vacuum)= E(TS, fully optimized in vacuum)-E(A, fully optimized in vacuum)-E(B, fully optimized in vacuum)= XX kcal/mol

Then, this reaction follows in the presence of a solvent:

A+B--->TS        Delta_E_act(solvent)=E(TS, fully optimized in solvent)-E(A, fully optimized in solvent)-E(B, fully optimized in solvent)= YY kcal/mol

Based on your highly valuable recommendation, a direct comparison between "XX" and "YY" values may lead to erroneous conclusions, particularly, when the difference between dipole moments of TS, A, and B to be very small or, one of the reactants has a dipole moment of zero (for such a species and due to dipole moment=0, one may expect solvent does not stabilize this species while due to solvent-solute interactions, a given species would ALWAYS be stabilized in a solvent even if its dipole moment in gas to be zero). Consequently, to have a quite reasonable comparison between "XX" and "YY" values, one should write:

Delta_E_act(solvent)=Delta_E_act(vacuum)+Delta_Delta_E(solvation) --->
                                               Delta_E_act(solvent)-Delta_E_act(vacuum)=Delta_Delta_E(solvation)  (1)                       

in which Delta_Delta_E(solvation)=Delta_E(solvation TS)-Delta_E(solvation A)-Delta_E(solvation B)         

Evidently, due to involvement of difference in solvation energies, equation (1) gives us a correct and reasonable comparison between values of Delta_E_act and, correctly clarifies impact of solvent on a given gas phase reaction. Indeed, when solvation energy is considered, both electrostatic and non-electrostatic solute-solvent interactions are taken into account:

Delta_E(solvation)=Delta_E(els)+Delta_E(non-els)

and some times non-electrostatic interactions are as important as electrostatic ones. If our judgment on the effect of given solvent on the gas phase reaction to be based only value of gas phase dipole moments, we only take electrostatic solute-solvent interactions which, as mentioned, is a quite raw approximation of solvent effects.

Please let me know if you completely agree with my point of view and interpretations.

Sincerely,
Saeed

Dear Saeed,

I suggest to calculate solvation free energy for each reactant and TS, so that you can make clear about the role of solvation energy in E_act.

Best,

Tian

Dear Tian,

Please suppose a simple reaction as: A+B--->TS

This reaction was studied in vacuum, Benzene, Dichloromethane and Formamide using implicit solvation model (only SCRF keyword was employed).

Activation energy E_act for any medium was calculated as E(TS, fully optimized)-E(A, fully optimized)- E(B,fully optimized).
E_act is increased from vacuum to benzene to dichloromethane. But, in the formamide and compared with vacuum (as reference), E_act is surprisingly slightly decreased.

The polarity of these media is as:
Formamide>>Dichloromethane>Benzene>Vacuum

The value of E_act is as follows in vacuum, benzene, dichloromethane, and formamide, respectively:

5.09, 5.31, 6.52, 4.73

It is expected that E_act continuously increases as the polarity of medium increases. But, suddenly, and in formamide, E_act shows a decrease with respect to vacuum! Please let me know why such a strong result is obtained for formamide. Once again, please note that I did compute activation total electronic energy. Hence, there is no thermal as well as entropic contribution.

Sincerely,
Saeed