First, you have to define what does antioxidant mean in  your case? What reactions are you studying? The antioxidant activity is a kinetic parameter, which is in a complex relationship with thermodynamics. Why do you ignore the reaction  entropy? Is your solvent protic (water)?

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Yuri please be kind with young researchers... although several times I asked more details and clearer explanations about the question to be answered.

In this case I limit my answer to the thermodynamic parameter in question (and do not address the kinetics): in fact it's better defined as a spectroscopic parameter, the ionization energy IE (not "potential" please). 

* First, I am not sure that the enthalpy  (at what temperature?) is the right parameter to be used. Energy (electronic energy) may be more relevant.

* Many gas-phase IE values are available in the literature.

* What is meant by "I have obtained the enthalpy values from the frequency calculations."? It is a correction (ZPVE or other) ? because enthalpy is first defined from energy, with additional corrections.

* I am not sure what will be the meaning of a IE in solution. The enthalpy of the electron is a difficult problem, as well as its solvation.

* The radical ion (ROH+.) is probably highly reactive in solution, and here, as Yuri states, kinetics come into play.

To answer just the computational part of your question, unless you want to invest in an extremely complex/difficult calculation (in which the labor would far exceed the computational accuracy), the molecular portion of the enthalpy is accounted in exactly the same way as for the gas phase (it is altered by the "reaction field" imposed by the solvation simulation, hopefully in a way which simulates actual solvation changes).  Presumably you have specified the temperature of interest; in the non-interacting particle model that is the only physical parameter that matters.

There are, however, two other important considerations in solvent.  One is the change in etnhalpy due to the portion of the solvation process which could be described as "making a hole in the solvent and moving a molecule of solute from the gas phase into the solvent".  This portion is expressed in Gaussian (the only software with which I am familiar doing solvation) as the Dis, Rep, and Cav terms, which are reported together as the "non-electrostatic terms"; they stand for solute-solvent dispersion energy, solute-solvent repulsion energy, and solvent cavitation energy and are generally formulated as described in Tomasi and Persico's Chem. Rev. article (Chem. Rev., 1994, 94, 2027ff).  Be aware that these components are not theoretically or practically well-defined as enthalpies or entropies, only as free energies, and the solvation energy is always given as a free energy even if you have not done the frequency calculation necessary to get the molecular free energy.  For this reason, if you want enthalpies and entropies, you really need to do gas-phase and solvated frequency calculations (and the latter should arguably be reoptimized first), find the solvation free energy and derive the solvation enthalpy (and solvation entropy) from it.  The free energy given in Gaussian will include the Dis/Rep/Cav terms if you have requested them (they are not computed by default).

The second important consideration is the fundamental difference in standard state between the gas phase and solution; the construction of PCM theory presumes a transfer of solute from the gas phase to the solution phase at a constant number density (generally 1M gas phase to 1M  solution); however, the computational standard state for the gas phase is not 1M but rather 1 atm (or 1 bar).  This introduces a small, constant, but significant correction factor to the free energy of solvation.

This latter issue, along with many considerations pertinent to computing entropies in solution, is taken up in Cramer and Truhlar's article (dx.doi.org/10.1021/jp205508z  J. Phys. Chem. B 2011, 115, 14556–14562), which I would recommend reading.

The researchers who answered above have pointed out many important considerations for whether what you are attempting is an appropriate approach, but hopefully this answer is useful if you decide the approach has some merit.  Like most computations, it will tend to be more reliable if you only look at relative effects; you might want to compute the IE of some simple molecule for which the solution IE is known (from electrochemistry or gamma radiolysis studies, for example).  They are quite right to point out that "antioxidant strength" can only be approximated by IE, since the same antioxidant will have differing "strengths" vs. different oxidizers and since thermodynamic "strength" only tells part of the story: a compound which is easy to oxidize but reacts slowly with a given free radical will not be a good antioxidant vs. that radical.

Try using the method as given in below mentioned paper:

www.bc.edu/schools/cas/chemistry/academics/undergrad/gen/fall/Enthalpy.pdf