Molecular orbitals soft acid-base theory

One possible set of guidelines for acid-base interactions follows concepts from hard and soft acid-base theory to identify the hardness of the metal center as an acid and the hardness of the ligands, including important functional groups in the polymer, as bases. Frontier orbital energy differences between the highest occupied and lowest imoccupied molecular orbitals are small and perturbations in the electronic distribution occur rather easily, yielding covalent bonds for soft acid-base pairs. In... 

Further examination of the results indicated that by invocation of Pearson s Hard-Soft Acid-Base (HSAB) theory (57), the results are consistent with experimental observation. According to Pearson s theory, which has been generalized to include nucleophiles (bases) and electrophiles (acids), interactions between hard reactants are proposed to be dependent on coulombic attraction. The combination of soft reactants, however, is thought to be due to overlap of the lowest unoccupied molecular orbital (LUMO) of the electrophile and the highest occupied molecular orbital (HOMO) of the nucleophile, the so-called frontier molecular orbitals. It was found that, compared to all other positions in the quinone methide, the alpha carbon had the greatest LUMO electron density. It appears, therefore, that the frontier molecular orbital interactions are overriding the unfavorable coulombic conditions. This interpretation also supports the preferential reaction of the sulfhydryl ion over the hydroxide ion in kraft pulping. In comparison to the hydroxide ion, the sulfhydryl is relatively soft, and in Pearson s theory, soft reactants will bond preferentially to soft reactants, while hard acids will favorably combine with hard bases. Since the alpha position is the softest in the entire molecule, as evidenced by the LUMO density, the softer sulfhydryl ion would be more likely to attack this position than the hydroxide. 

A quantitative scale of reactivity for aromatic substrates (fused, heterocyclic, and substituted rings) has been devised, based on the hard-soft acid-base concept (p. 375). From molecular-orbital theory, a quantity called activation hardness can be calculated for each position of an aromatic ring. The smaller the activation hardness, the faster the attachment at that position hence the treatment predicts the most likely orientations for incoming groups. 

Li, Y, Evans, J. N. S. (1995). The fukui function a key concept linking frontier molecular orbital theory and the hard-soft-acid-base principle. J. Am. Chem. Soc. 117, 7756-7759. 

To go into this idea quantitatively, we need definitions of hardness and softness, and a rank order for acids and bases on a scale of hardness. This has been done in two ways one based on molecular orbital theory, and the other on density functional theory. 

Here the term orbital may refer to a discrete molecular orbital or a band (or an atomic orbital in the case of atomic species). The donor orbital on the base is usually the highest occupied MO (or HOMO), and the acceptor orbital on the acid is usually the lowest unoccupied MO (or LUMO). Simple perturbational MO theory predicts that for two interacting orbitals of suitable symmetry and overlap, the smaller the difference in the orbital energies, the greater the mutual perturbation or interaction. The terms soft and hard relate to a range of properties, but essentially soft acids are... 

Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons AN transferred is given by Equation 3.14. 

Why is such a trend observed Actually, the reason that hard acids and bases prefer to interact with each other is different than the reason that soft acids and bases prefer to interact. To see this, let s examine some mathematics that is meant to model the interaction between Lewis acids and bases in an early stage of their interaction. The analysis derives from pertur-bational molecular orbital theory (PMOT), which was briefly introduced in Chapter 1, and is explored in more depth in Chapter 14. In essence, three forces are considered to mediate the energy of interaction (Ej) between the acid and base as they approach each other in space (Eq. 5.28). One is the electrostatic repulsion between the electron clouds of the two entities, referred to as Ecore/ a positive destabilizing term. The second and third factors are both attractive and stabilizing. An electrostatic attraction between an acid and base occurs due to opposite charges on the acid and base this is called E s- Lastly, a term called Eoveriap/ which is related to the net overlap of the nucleophilic and electrophilic orbitals, is found to lower the energy of the system as the nucleophilic electrons delocalize into the empty electrophilic orbital. 

The chemical potential, chemical hardness and sofmess, and reactivity indices have been nsed by a number of workers to assess a priori the reactivity of chemical species from their intrinsic electronic properties. Perhaps one of the most successful and best known methods is the frontier orbital theory of Fukui [1,2]. Developed further by Parr and Yang [3], the method relates the reactivity of a molecule with respect to electrophilic or nucleophilic attack to the charge density arising from the highest occupied molecular orbital or lowest unoccupied molecular orbital, respectively. Parr and coworkers [4,5] were able to use these Fukui indices to deduce the hard and soft (Lewis) acids and bases principle from theoretical principles, providing one of the first applications of electronic structure theory to explain chemical reactivity. In essentially the same form, the Fukui functions (FFs) were used to predict the molecular chemical reactivity of a number of systems including Diels-Alder condensations [6,7], monosubstituted benzenes [8], as well as a number of model compounds [9,10]. Recent applications are too numerous to catalog here but include silylenes [11], pyridinium ions [12], and indoles [13]. 

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