HSAB orbital theory

The principle of hard and soft acids and bases [I] (HSAB), and the principle of electronegativity equalization [2], together with frontier orbital theory [3] have been, over the years, very useful to establish the behavior of molecules under different circumstances, their reactive sites, and possible reaction mechanisms [4]. Through these principles, and through the values of the parameters associated with them hardness, softness, and electronegativity, it has been possible to correlate and to analyze experimental information that allows one to characterize the interactions involved between different chemical species in many different situations. From this exp>erience it has been possible to establish a priori the development of a wide variety of chemical reactions. 

In 1967, another major paper by Pearson and Songstad (5), applying the HSAB principle to organic chemistry, appeared. Saville published a full account of his analysis of multicenter reactions (10) based on the HSAB principle. Efforts have been made to determine quantitatively the hardness (softness) of some donors and acceptors (11). Klopman presented a perturbation treatment (12) of chemical reactivity and related HSAB to molecular orbital theory. 

Pearson has described S how the concepts of hardness and softness can be understood through application of density functional theory (DFT) to chemical systems and, further, how the results correlate with molecular orbital theory. A firm theoretical basis for the HSAB principle is evolving from these studies that links chemical hardness to absolute electronegativity which, in this sense, refers to the electronic chemical potential of a system rather than the electronegativity of a single atom within a molecule. 

Calculations at several levels of theory (AMI, 6-31G, and MP2/6-31G ) find lower activation energies for the transition state leading to the observed product. The transition-state calculations presumably reflect the same structural features as the frontier orbital approach. The greatest transition-state stabilization should arise from the most favorable orbital interactions. As discussed earlier for Diels-Alder reactions, the-HSAB theory can also be applied to interpretation of the regiochemistry of 1,3-dipolar cycloaddi-... 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

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. 

Any suspected new electron flow path should be well tested before it is accepted as a new pathway. It may be just a combination of (Section 7.3) or a variation on (Section 7.4) already known paths. Watch for AS problems of too many things happening at once. Look for steric and strain problems and check the orbital alignment with molecular models—orbitals that will become double bonds in the product must be able to get close to coplanar in the starting material. Check any intermediates for stability, especially if charged. Check that the electronics fit HOMO-LUMO and HSAB theory. Check the energetics with a Af/ calculation or the Ap Ta rule, and be skeptical anyway, it s healthy. 

Klopman attempted to quantify Pearson s HSAB principle using frontier molecular orbital (FMO) theory (Klopman 1968), with the following equation ... 

Theoretical determinations are mainly based on the assumption that the initial perturbation of the orbital of interacting species determines the course of a reaction or an interaction. In terms of equation of state, the perturbation theory was developed first. In terms of energy gap between HOMO and LUMO, acids and bases were defined by their hardness and softness. The Hard-Soft Acid-Base principle (Pearson 1963) describes some basic rules about kinetics and equilibrium of the acid-base interactions. The HSAB principle will be described as it has evolved in recent years on the basis of the density-functional theory (Parr and Yang 1989). For organic interactions, the following statements were proposed ... 

The HSAB principle was, originally, entirely empirical. Its first theoretical rationale was given by Klopman s perturbation theory [3,33]. It was proposed [2,3] to equate the strength and softness terms of Equation 1.110 to the charge-controlled and orbital-controlled terms... 

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