solute bases such as fluoride and oxide anions. On the other hand, dipolar aprotic solvents such as dimethyl sulfoxide and acetone are soft solvents with a preference for solvating large anions and soft bases. In coordination chemistry soft–soft and hard–hard interactions exist between ligands and metal centers. Chemical hardness 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: . The factor of one-half is arbitrary and often dropped as Pearson has noted. An operational definition for the chemical hardness is obtained by applying a three-point finite difference approximation to the second derivative: where I is the ionization potential and A the electron affinity. This expression implies that the chemical hardness is proportional to the band gap of a chemical system, when a gap exists. 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. The hardness and Mulliken electronegativity are related as , and in this sense hardness is a measure for resistance to deformation or change. Likewise a value of zero denotes maximum softness, where softness is defined as the reciprocal of hardness. In a compilation of hardness values only that of the hydride anion deviates. Another discrepancy noted in the original 1983 article are the apparent higher hardness of Tl3+ compared to Tl+. Modifications If the interaction between acid and base in solution results in an equilibrium mixture the strength of the interaction can be quantified in terms of an equilibrium constant. An alternative quantitative measure is the heat (enthalpy) of formation of the Lewis acid-base adduct in a non-coordinating solvent. The ECW model is quantitative model that describes and predicts the strength of Lewis acid base interactions, -ΔH . The model assigned E and C parameters to many Lewis acids and bases. Each acid is characterized by an EA and a CA. Each base is likewise characterized by its own EB and