The Schrodinger Equation in Action

Pour Elise Dumont, une chimiste française, elegante comme tous les françaises

The arrogant but brilliant physicist Paul Dirac, after solving one of the foundational problems of quantum mechanics, was alleged to have said "...the rest, is chemistry." Oh what weasely words they were. True, quantum chemistry can be seen as "merely" the solution of the Schrodinger equation, but what rich solutions! Dirac would not have known the dazzling complexity that was to take place in the field that would come to be known as quantum chemistry.

There have been, at times, heroic attempts to find tractable approximations to solve the Schrodinger equation for larger and larger molecules. We've also realized that the Schrodinger equation is actually an insufficient principle to do chemistry because in the end, the Schrodinger equation is a single electron equation. Reality is made up of more than 1 electron. However, there does not exist an authoritative multi-electron theory, there are several competing multi-electron theories, from quantum field theory, fractional electron solids, Wilson effective field theories, to the Walter-Kohn approximations.

Quantum chemistry is a demandingly technical field where computers are pushed to the limit, in order to calculate the detailed properties of molecules on an electronic level. Every electron is modeled as a wave function, a kind of diffuse cloud of charge that oozes into 3-dimensional space. As a rule of thumb, there are as many electron in an atom as the number of the atom in the periodic table. The complexity quickly blows up in your face.

Nevertheless, a mind-boggling amount of chemical properties have been reproduced in calculation. The most exciting perhaps, is direct calculation of chemical reactions, how one molecule can turn into another. However, what has been missing, at least for me, is a easy lay-man way to see the results of these calculations. Chemical textbooks are filled with millions of intricate chemical equations giving reactants and products, and little arrows that kind of point to what happens. But I can't and won't ever understand them. I say to chemists, Keep It Real, Fool. What I want, is a visceral way of looking at a chemical reaction.

Well, I found one.

The reaction is kind of obscure, but Sheng-Yong Yang and Tom Ziegler have kindly provided a wonderful animation of a chemical reaction calculated using Quantum Mechanics/Molecular Mechanics.

First, I'll introduce the players in this reaction:

The reaction consists of a catalyst for a polymerization reaction, which requires an counterion.

The counterion (right) is [B(C6F6)3)]-. I don't know its name, and I don't care. It consists of three rings of C atoms (grey). The white atoms are F. The fulcrum is a B atom (green) that carries most of the charge.

The actual catalyst (left) consists of two rings of Cyclopentadienyl (CP) (grey atoms in a membered rings), bound to a Zirconium atom (Zr) (tan). Together, this forms zirconene. There are two methyl groups (CH3) bound to the Zr atom, one on the bottom, and one on the right. One of these methyls will polymerize with ethylene to form propene.

The ethylene floats in from the bottom left hand of the screen towards the Zr atom. Meanwhile the counterion steals one of the methyl groups from the Zr atom. This makes the Zr hungry to bind any available methyl group. The closest thing available is the ethylene. When the ethylene binds to the Zr atom, the ethylene is in prime position to bind to the the methyl group. Then they CHEMICALLY REACT!!!!. You have now seen a chemical reaction, complete with flickering chemical bonds.

Good luck, and good night.