Electrostatic potential mathematical methods

Lewis [5] was the first to describe acids and bases in terms of their electron accepting and electron donating properties. Mulliken [6] further refined the understanding of the acid base interactions for which he was awarded the Nobel Prize for Chemistry. His quantum mechanical approach introduced the concept of two contributions, an electrostatic and a covalent, to the total acid-base interaction. Pearson [7] introduced the concept of hard and soft acids and bases, the HSAB principle, based on the relative contributions from the covalent (soft) interaction and the electrostatic (hard) interaction. In his mathematical treatment he defined the absolute hardness of any acid or base in terms of its ionisation potential and electron affinity. Pearson s is probably the most robust approach, but the approaches in most common use are those developed by Gutmann [8] and Drago [9], who separately developed equations and methods to quantify the acid or basic strength of compounds, from which their heats of interaction could be calculated. 

We shall follow the practice of denoting all standard potentials in the reduction direction, called the lUPAC, or Stockholm convention. This has the advantage, over the oxidation potential method, of giving the potentials the electrostatic sign of the electrode when connected to standard hydrogen, and also the mathematical sign indicating spontaneity (-I-) or nonspontaneity ( —) in the Nernst equation. The methods are evaluated in detail by Bockris and Reddy. ... 

Solutions to the Poisson—Boltzmann equation in which the exponential charge distribution around a solute ion is not linearized [15] have shown additional terms, some of which are positive in value, not present in the linear Poisson—Boltzmann equation [28, 29]. From the form of Eq. (62) one can see that whenever the work, q yfy - yfy), of creating the electrostatic screening potential around an ion becomes positive, values in excess of unity are possible for the activity coefficient. Other methods that have been developed to extend the applicable concentration range of the Debye—Hiickel theory include mathematical modifications of the Debye—Hiickel equation [15, 26, 28, 29] and treating solution complexities such as (1) ionic association as proposed by Bjerrum [15,25], and(2) quadrupole and second-order dipole effects estimated by Onsager and Samaras [30], etc. 

---