[1] The theory is used in contexts where a qualitative, rather than quantitative, description would help in understanding the predominant factors which drive chemical properties and reactions.
[2] Ralph Pearson introduced the HSAB principle in the early 1960s[3][4][5] as an attempt to unify inorganic and organic reaction chemistry.
Some examples illustrating the effectiveness of the theory: In 1983 Pearson together with Robert Parr extended the qualitative HSAB theory with a quantitative definition of the chemical hardness (η) as being proportional to the second derivative of the total energy of a chemical system with respect to changes in the number of electrons at a fixed nuclear environment:[11] The factor of one-half is arbitrary and often dropped as Pearson has noted.
[12] An operational definition for the chemical hardness is obtained by applying a three-point finite difference approximation to the second derivative:[13] where I is the ionization potential and A the electron affinity.
The first derivative of the energy with respect to the number of electrons is equal to the chemical potential, μ, of the system, from which an operational definition for the chemical potential is obtained from a finite difference approximation to the first order derivative as which is equal to the negative of the electronegativity (χ) definition on the Mulliken scale: μ = −χ.
A related method adopting the E and C formalism of Drago and co-workers quantitatively predicts the formation constants for complexes of many metal ions plus the proton with a wide range of unidentate Lewis acids in aqueous solution, and also offered insights into factors governing HSAB behavior in solution.
This rule (established in 1954)[19] predates HSAB theory but in HSAB terms its explanation is that in a SN1 reaction the carbocation (a hard acid) reacts with a hard base (high electronegativity) and that in a SN2 reaction tetravalent carbon (a soft acid) reacts with soft bases.
Isocyano compounds are only formed with highly reactive electrophiles that react without an activation barrier because the diffusion limit is approached.
It is claimed that the knowledge of absolute rate constants and not of the hardness of the reaction partners is needed to predict the outcome of alkylations of the cyanide ion.