# Why does strong Lewis acid-strong Lewis base interactions prevail over hard-soft acid-base interactions?

In Pearson's paper, he mentions that strong acid-strong base interactions are more favourable compared to hard-soft acid-base interactions. He cites the example of $\ce{H+ + H- -> H2}$. In this example, the hydrogen cation is a strong and hard Lewis acid while the hydride ion is a strong yet soft Lewis base. By just considering hardness and softness of the acid and base, we would not expect a particularly favourable interaction between the two species. However, Pearson says it is because of a more favourable interaction which is the strong acid-strong base interaction which is at work in this case.

Some background information:

When the HOMO of the Lewis base and the LUMO of the Lewis acid are similar in energy, the bonding molecular orbitals produced are significantly lower in energy and thus, electron occupation of these bonding MOs give rise to significant stabilisation. This occurs when hard Lewis acids and hard Lewis bases react and also when soft Lewis acids and soft Lewis bases react. This is the molecular orbital basis of Pearson's Hard Soft Acid Base Principle.

Can we explain the favourable interaction of strong Lewis acids and strong Lewis bases using molecular orbitals as well?

Reference: Pearson, R. G., & Songstad, J. (1967). Application of the Principle of Hard and Soft Acids and Bases to Organic Chemistry. Journal of the American Chemical Society, 89(8). Retrieved June 5, 2017 (link to paper)

The Klopman-Salem equation accounts for the energy gain (or loss) when the orbitals of one reactant overlap with those of another. The equation is

$$\Delta E=-\sum_{ab}(p_a+p_b)\beta_{ab}S_{ab}+\sum_{k<l}\frac{Q_kQ_l}{\varepsilon R_{kl}}+\sum_{r}^{\text{occ}}\sum_{s}^{\text{unocc}}-\sum_{s}^{\text{occ}}\sum_{r}^{\text{unocc}}\frac{2(\sum_{ab}c_{ra}c_{sb}\beta_{ab})^2}{E_r-E_s}$$ where $p_a$ and $p_b$ are the electron population in the atomic orbitals $a$ and $b$, $\beta$ and $S$ are the resonance and overlap integrals, $Q_k$ and $Q_l$ are the local charges on atoms $k$ and $l$, $c_{ra}$ is the coefficient of atomic orbital $a$ in molecular orbital $r$, where $r$ refers to the molecular orbitals on one molecule and $s$ refers to those on the other, $E_r$ is the energy of molecular orbital $r$ and $E_s$ is the energy of molecular orbital $s$.

The first term is a closed-shell repulsion term, the second term is the Coulombic repulsion or attraction, and the third term is the interaction of all the filled orbitals with all the unfilled of correct symmetry. This equation was derived using perturbation theory being the first term is a first-order perturbation term and the third the second-order perturbation term.

Now, the HSAB theory is affected by charge and orbital interactions. The h-h interactions is mainly electrostatic in nature, while in a s-s interaction the orbitals involved are close in energy. With the Klopman-Salem equation we can see that the second term is the hard contribution and the third is the soft contribution. There is a simplified form, which accounts only for frontier orbitals, that is $$\Delta E=\frac{Q_{\text{Nu}}Q_{\text{El}}}{\varepsilon R}+\frac{2(c_{\text{Nu}}c_{\text{El}}\beta)^2}{E_{\text{HOMO}(\text{Nu})}\pm E_{\text{LUMO}(\text{El})}}$$ So, back to the question, a hard molecule or ion is characterized by a large HOMO-LUMO gap (definition of hardness) and the second term, in the simplified version, is very small, so the contribution is mainly electrostatic, i.e., the more charged the sites in the molecule/ion the greater will be the stabilization (or repulsion, in case of like charges). The electric field of the two parts in the molecules/ions would diminish $R$ and the term would be very large. In the case of soft-soft interactions, the orbital term is the dominant because the HOMO-LUMO gap is smaller.

But sure, the interaction has to be between to molecules or ions, not a single specie. You can apply this to nucleophiles and electrophiles as well. A hard nucleophile (negative charge localized and low-energy HOMO) would tend to react with a hard electrophile (positive charge localized and high-energy LUMO), leading to a great stabilization by the electrostatic term. Meanwhile a soft nucleophile (high-energy HOMO) would react with a soft electrophile (low-energy LUMO), stabilized by the orbital term, because $E_{\text{HOMO}(\text{Nu})}-E_{\text{LUMO}(\text{El})}$ is small.

If it is necessary, I can edit with a MO diagram to see this more visually.

• Thanks for the insightful response. I now have a better understanding of Pearson's theory. Previously, I had the misconception that for hard acid-hard base, they would have similar high-energy HOMO and LUMO but that is not the case as you have pointed out. – Tan Yong Boon Jun 6 '17 at 6:20
• Although u have explained very in a very detailed manner of the molecular orbital basis of Pearson's theory, u still have not answered my question as to why STRONG acid- STRONG base interactions would outweigh hard and soft interaction. Note that strength and hardness/softness are different. – Tan Yong Boon Jun 6 '17 at 6:26
• Oh! you're right. Bad reading from me. For the moment I don't have the answer, but I think that this case is like comparing kinetic vs thermodynamic reactivity. The strength of an acid or base is determined by molecular structure, solvent effects, H-bonds, sterics, etc. Then, as far as I know, there is no a clear tendency based only on the electronic structure of the reactants. – Verktaj Jun 6 '17 at 8:20
• Why does high positive charge result in a high-energy LUMO? Wouldn't a high positive charge stabilise the HOMOs and LUMOs and result in them being lower in energy? – Tan Yong Boon Apr 3 '18 at 23:01
• Similarly, why does a localised, high negative charge result in a lower energy HOMO? Wouldn't the negative charge consequently destabilise the frontier MOs and raise their energies? – Tan Yong Boon Apr 3 '18 at 23:03