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Design for catalysis : steps leading to a solution :

Design for catalysis is primarily concerned with reacting molecular systems. Chemical reactions are investigated with kinetics experiments, where the speed of a chemical reaction under various conditions is considered. A reaction can then be modelled by means of a reaction mechanism. Basically a reaction mechanism is a conceptual model that explains various related experiments.

Such a reaction mechanism is often interpreted in terms of the Lewis acid and base concept. Do not confuse Lewis acids and bases with Bronsted acids and bases. The lewis acid and base concept is much more general then the Bronsted acid and base concept where we primarily deal with protonation and deprotonation reactions.

A Lewis acid is any species with a vacant orbital and a Lewis base is a species with an available pair of electrons.
All reactions where a covalent bond is formed and where one species contributes an electron pair and where another species contributes an empty electron pair is a lewis acid and base reaction.

The concept of Lewis acids and bases is a very powerfull logical tool because it is supported by overwelming experimental evidence and is firmly rooted into the quantum theory and the density functional theory. A Lewis acid base reaction is controlled by electrostatic factors and orbital interactions.
The orbital interaction factor is a purely non-classical factor.

From density functional theory we know that the reaction is controlled by the difference in electron affinity, the hardness, the electron density and the fukui function.

• The hardness of a molecular species is a quantity that describes the difficulty anything will experience if it wants to extract an electron from the molecular species under consideration.
• The fukui function gives us information about the position and the direction of electron exchange between two species. It is a function of the electronic matterwave of the system.

A molecule can be represented by a Lewis formula. The Lewis formula gives us information about the relative positions of the nucleï and about the electronic structure of a molecular species. We can make a link between the Lewis formula and the electronic wave function.

Example :

The H₂⁺ molecule is a molecule consisting of two hydrogen atoms and an electron. It is possible to solve the Schrödinger equation exactly for it (i.e. without making use of the variational theorem).

The exact solution for the H₂⁺ molecule shows that in the ground state the electron of this molecule spends most of its time either near one of the two nucleï or in the middle and thus forms a bonding orbital.
This means the electron tends to hold both nucleï together.
In the first excited state the electron spends least of its time in the region in between the nucleï and most of its time outside the inner region ,therefore this orbital tends to keep the nucleï seperated, it is an antibonding orbital.

For multi electron molecules we can model molecular orbitals by linear combinations of atomic orbitals. In order to obtain information about the Lewis structure of a system I use the method proposed by Mulliken (i.e. the mulliken analysis) and the natural population analysis proposed by Weinhold.

The Hellmann-Feynmann theorem :

Another important aspect of quantum mechanics that deserves consideration here is the Hellmann-Feynman theorem.

F₀ is the force acting on a system, E the energy of the system, H the quantum mechanical energy operator, q the nuclear coördinate and the matterwave function.

The Hellmann-Feynman theorem makes a statement about the change of the energy of a molecular system as a function of the nuclear coördinates of the atoms. We thus obtain an expression for the quantum mechanical forces acting on the nucleï.

If the Born-Oppenheimer energy operator (i.e. the Born-Oppenheimer Hamiltonian) is combined with the equation of Hellmann-Feynmann we obtain the following equation :

.

F_A is the force acting on nucleus A due to the other nucleï B and the electron density. R_Aand R_B are the positions of the nucleus A and the other nucleï B, Z_A and Z_B are the nuclear charges on nucleï A and B respectively and is the electron density for the molecular system.

If we know the exact electron density function ,then the quantum mechanical forces acting on the nucleï could be evaluated by taking into account only the electrostatic forces acting on the nucleï.

This statement may lead to extremely misleading reasonments. It is important to realise that a molecular transformation does not involve only a rearrangement of the nucleï.

Electronic and nuclear rearrangements may happen concurrently.
And for many processes (e.g. biomolecular processes and chemical reactions) this is important.
Moreover nuclear motion is also subject to the formalism of quantum mechanics and cannot be explained accurately by classical mechanics.