Handbook of Solvents - George Wypych - ChemTech - Ventech!

574 S. Bistac, M. Brogly
10.2.1.2 Quantitative determination of acid-base interaction strength
10.2.1.2.1 Perturbation theory
Hudson and Klopman 8 proposed an equation to describe the effect of orbital perturbation of
two molecules on chemical reactivity. Their hypothesis is that the initial perturbation determines
the course of a reaction or an interaction. They applied quantum-mechanical method 9
to treat the encounter of two interacting systems as reactivity. Their equation for interaction
energy can be simplified by including only two terms [10.2.2]: the Coulombic interaction
and the frontier orbital interaction between HOMO and LUMO.
ΔE
int
( C C β)
Q Q 2
N E N E
=− +
εR
E −E
2
HOMO LUMO
[10.2.2]
where:
QN total charges of nucleophile N
QE total charges of electrophile E
CN coefficient of the atomic orbital N
CE coefficient of the atomic orbital E
β resonance integral
ε permittivity
R interatomic distance
EHOMO energy level of the HOMO orbital
ELUMO energy level of the LUMO orbital
The relative magnitudes of the numerator and denominator of the second term determine
the extent of perturbation and the type of reactivity. For electrostatic interactions, the
first term dominates: this is the case of highly polar acceptors of low electron affinity and
donors highly electronegative, while for electron donor - electron acceptor interaction, the
second term dominates. Thus, a molecular interaction encompasses chiefly both acid-base
and donor-acceptor interactions. On the other hand if the second frontier orbital term dominates,
the extent of perturbation is large and the charge transfer is large, leading to a large
gain in stability. The frontier orbital controlled processes are favored by the presence of
weakly polar species lacking high charge density but possessing reactive atoms with large
orbital radii. This second term is also benefitted by bases of low electronegativity and acids
of high electron affinity.
10.2.1.2.2 Hard-Soft Acid-Base (HSAB) principle
The energy gap between HOMO and LUMO has been equated to the absolute hardness of
the HSAB principle. This principle 10 describes some basic rules about kinetics and equilibrium
of the acid-base interactions in solutions. The HSAB principle will be described as it
has evolved in recent years on the basis of the density-functional theory. 11 For organic interactions,
the following statements were proposed:
• A hard acceptor has a high energy LUMO and usually a positive charge
• A soft acceptor has a low energy LUMO but does not necessarily have a positive
charge
• A hard donor has a low energy HOMO and usually a negative charge
• A soft donor has a high energy HOMO but does not necessarily have a negative
charge