The term "radical stability" seems to be meaningless thermodynamically. A radical can isomerize, can react with some molecules in solution to produce another radicals,  or react with a radical to produce non-radical species. These reactions control the life-time of a radical, which can be called a "radical stability." In this case, the "stability" is a kinetic term and depends on numerous factors. If you know the reaction rate constants, you can predict the life-time of a radical. The reaction rate constants are the key parameters for radicals

Hi Yurii，

thank you for your answer. I think that besides the kinetic stability, there is a thermodynamic stability of a radical.

My purpose is to study some relationships between O-H bond dissociation energy (BDE)and structure. Some scientist devide these effects into the effects that "stabilize/destabilize the radical", or effects that mainly "stabilize/destabilize the molecule". which means, the BDE is an indicator of not only the stability of the radical, but also of the molecule. for example, polar effect might have more influence to the energy of radical than to the precursor, and steric effect might by only significant in the precursor. And they defined the "radical stabilization energy" and "molecualr stabilization energy" separately.  But I don't know its theoretical basis and whether it is solid. 

The thermodynamic stability of a radical can be used only for the isomerization. What are asking about is commonly called the reactivity of radicals. There are tons of papers studying the relationship between radical reactivity and structure. The main factor controlling the reactivity of radicals is the difference between BDE. Evgeny T. Denisov has developed the intersecting parabolas model to calculate the reactivity of radicals. He has published numerous papers. 

New empirical models of free radical abstraction reactions

Et Denisov

USPEKHI KHIMII , 1997, Vol.66(10), p.953-971

thanks a lot！I have searched the scientist and had a glance of his paper that you recommend. I think that he agrees with you about the equivalence of the stability (reactivity) of the radicals and BDE of the precursors. 

I might be still wanting to discover how the BDEs are affected by moleular structure. For example, if the A-H BDE of COOH-A-H is 5kcal/mol higher than the A-H. Is it possible that, the caroxyl group have stabilized the A-H by 2kal/mol, and destabilized the radical by 3kcal/mol, or just say that the COOH-A· is less stable than A·by5kcal/mol? is there a method of calculation? 

Basic but interesting, Yes the functional groups affect the bond energy of molecules some stabilize and some destabilize the reactive bond, Just like Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption, in which each and every bond and functional groups affect the stability and hence its absorption maximum. 

Similarly, radical reactivity and a chance of formation from parent molecules are also controlled by these functional groups or structure of molecules.

I kind of agree with Naddem. But is there a method to quantify the amount of stabilization energy of a molecule by a functional group?

You have to define all terms using in the discussion. What is "stabilization energy of a molecule by a functional group?" 

George Leroy unsuccessfully attempted to introduce this concept in his paper 

The Theoretical Approach to Some Chemical Problems 

Pages 1-95

Georges Leroy

published in 

Advances in Quantum Chemistry

Volume 17, Pages ii-x, 1-338 (1985)

Edited by Per-Olov Löwdin

ISBN: 978-0-12-034817-6

Hi, Yurii ! By "stabilization energy of a molecule by a functional group" , I mean the relative contributions of the molecule and corresponding radical in the bond dissociation energy. As is depicted in the scheme, NH2 decreases the benzyl C-H BDE, while CHO group increase it. I think that both functional groups make the toluene molecule and the benzyl radial more stable than the unsubstituted ones. But NH2 stabilize the radical more than it does to the molecule, and things are opposite for the CHO, thus making the different BDE.

I have read the part of the book in which Georges Leroy defined the stability of a chemical species. The stabilization energy was calculated on the basis of bond contribution:

SE=ΔHa-ΣE(A-B)

To my knowledge, I don't find a bug in this definition. So, could you inform me about why you think the author "unsuccessfully attempted to introduce this concept "?