I. WHY MESS WITH QUANTUM MECHANICS?

II. THE WAVE EQUATION, HY / Y = E

IF Y IS A FUNCTION, WHAT IS IT A FUNCTION OF?

H , THE HAMILTONIAN OPERATOR

III. SOLUTIONS OF THE WAVE EQUATION

IV. INTERPRETATION OF THE SOLUTION

V. ATOMIC QUANTUM MECHANICS IN PRACTICE

Table for Hydrogen-Like Wave Functions

Frequently Asked Questions

ATOMIC ORBITAL PROBLEMS

VI. SEVERAL ELECTRONS : ORBITALS AND THE TROUBLE WITH THEM

VII. HYBRID ORBITALS

VIII. MOLECULAR ORBITALS : WHAT IS A BOND?

IX. ORGANIC CHEMISTRY FROM THE HOMO-LUMO VIEW

Hybridization and Overlap
Overlap and Energy Match in an harmonic double minimum
Guidelines for Using Energy-Match and Overlap
Examples of MOs of Functional Groups
Hybridization and Structure of XH₃ Molecules Experimental Evidence

 

As we'll see in several weeks, for the past 175 years generations of organic chemists have been in the business of developing an empirical model to correlate and predict the chemical and physical properties of organic substances. It is hardly surprising that hypothesis was piled on hypothesis during this evolution and that some of these turned out to be dead ends. By now the organic chemists' model is highly developed, and it works well and conveniently for many purposes. It is completely adequate for a normal elementary course in organic chemistry, and most practicing organic chemists do most of their thinking and communicating in terms of it. But it has serious problems: there are some chemical properties that it won't handle correctly, and many physical properties that it doesn't even pretend to handle. Furthermore, fundamental physical laws play a very minor role in most aspects of the model. "Why?" can't be traced back to a few simple hypotheses. It all seems distressingly ad hoc, how can you really know when a particular resonance structure is good and when it isn't. A practical model based on fewer, and more physically significant, hypotheses would certainly be welcome.

Imagine how delighted physicists were in 1926, exactly 75 years ago, when Schrödinger proposed his quantum mechanical "wave" equation, the physical model which is supposed to answer all legitimate questions about matter. Of course the validity of the Schrödinger Equation is itself an hypothesis, but its assumptions are very few compared with those behind the organic model.

It would be intellectually satisfying if we could dispense with the organic model. Unfortunately, no one (and no machine) can exactly solve the Schrödinger Equation for a real organic molecule. Even though most of our thinking in organic chemistry will have to be in terms of the organic model, it is important for two reasons to understand how the Schrödinger Equation works:

(1) To answer that nagging question "Why" the traditional organic model works so well, e.g. What are bonds? Why don't atoms collapse? Which "resonance structures" are reasonable? What makes a "functional group" have a particular reactivity pattern? It is reassuring to know that chemical theory is not just a house of cards.

(2) To understand cases where the historical organic model doesn't work, e.g. "aromaticity", and "pericyclic reactions", which come along next semester.

Furthermore quantum mechanics is one of humankind's great intellectual achievements which educated people should know about and appreciate. This year, on its 75th birthday, all knowledgable scientists agree that, as they say of gravity, "It's not just a good idea, it's the law!"

The ideas are not really difficult, but they are not intuitively obvious. In fact they require retooling your idea of the nature of things, especially kinetic energy. If we don't spend a couple weeks on chemical quantum mechanics in this course, many of you may never have it presented to you in an accurate, but simple and non-mathematical way.