14-01-2013, 04:15 PM
Physical Chemistry
[attachment=46856]
INTRODUCTION
Welcome to Chem 160, Physical Chemistry, affectionately referred to as p-chem.
You have probably heard a lot about this class. You have scrutinized the CUE guide,
you have talked to your friends. It seems that every time you have mentioned p-chem,
you were either countered with pity or the question “are you insane?” Most likely, you
have been told that “it’s just a lot of really abstract math that has next to nothing in
common with reality.” Chem 160 is designed to contradict these uninitiated infidels. The
key thing to note is that it is called Chem 160, not Physics 143a. This means that we will
develop topics in a fashion suitable to the chemist and with chemical applications in
mind. Presumably, this is why you are taking this class.
What is Chem 160?
We will begin in the familiar territory of Newtonian mechanics and Newton’s
equations of motion. These concepts will serve as the basis for delving into Hamilton’s
equations of motion and such concepts as generalized coordinates and phase space. We
will proceed to develop a classical description for particle collisions (which then lead to
chemical reactions), as well as analyze the classical behavior of the harmonic oscillator.
Our ultimate goal will be to describe how atoms bond. As you are probably
aware, bonding interactions are dominated by electrons, which are too small to be
described classically. We will, therefore, develop a quantum mechanical approach. First,
we will develop some quantum tools and vocabulary. The first will be the famous
Schrödinger wave equation. The other concepts will range from the familiar “wavelength”
and the ominous-sounding “eigenfunction” to the exotic “expectation value.”
Armed with these, we will attempt the first quantum problem – the particle in a onedimensional
box. With the solutions in hand, we will then test this model on conjugated
linear polyenes. While still in one-dimension, we will recall the harmonic oscillator
problem and solve it using quantum mechanics. We will also briefly discuss the idea of
tunneling.
How to Use These Lecture Notes
The lecture notes have been completely reworked this year. Instead of being just a series of cryptic derivations and
mathematical expressions, they feature more detailed explanations. The lectures will follow the sourcebook very closely,
both in the order and the depth of presentation. To take full advantage of the lectures, you should skim through the
appropriate section of the notes prior to the lecture. This way, even though you may not gain a complete understanding
of the material after the first reading, you will at least be able to know what to expect.
Units and Conventions
Physical chemists have refused to adopt SI units with as much fervor as the United States has clung to the English system.
Even journal publications continue to use cgs or atomic units. It turns out that for the quantities we will be measuring,
they are simply more convenient. If you are not familiar with either, take a quick look at Appendix II, where you will find
a summary of units and conversion factors. Throughout these notes, assume cgs values for constants, unless specified
otherwise.
[attachment=46856]
INTRODUCTION
Welcome to Chem 160, Physical Chemistry, affectionately referred to as p-chem.
You have probably heard a lot about this class. You have scrutinized the CUE guide,
you have talked to your friends. It seems that every time you have mentioned p-chem,
you were either countered with pity or the question “are you insane?” Most likely, you
have been told that “it’s just a lot of really abstract math that has next to nothing in
common with reality.” Chem 160 is designed to contradict these uninitiated infidels. The
key thing to note is that it is called Chem 160, not Physics 143a. This means that we will
develop topics in a fashion suitable to the chemist and with chemical applications in
mind. Presumably, this is why you are taking this class.
What is Chem 160?
We will begin in the familiar territory of Newtonian mechanics and Newton’s
equations of motion. These concepts will serve as the basis for delving into Hamilton’s
equations of motion and such concepts as generalized coordinates and phase space. We
will proceed to develop a classical description for particle collisions (which then lead to
chemical reactions), as well as analyze the classical behavior of the harmonic oscillator.
Our ultimate goal will be to describe how atoms bond. As you are probably
aware, bonding interactions are dominated by electrons, which are too small to be
described classically. We will, therefore, develop a quantum mechanical approach. First,
we will develop some quantum tools and vocabulary. The first will be the famous
Schrödinger wave equation. The other concepts will range from the familiar “wavelength”
and the ominous-sounding “eigenfunction” to the exotic “expectation value.”
Armed with these, we will attempt the first quantum problem – the particle in a onedimensional
box. With the solutions in hand, we will then test this model on conjugated
linear polyenes. While still in one-dimension, we will recall the harmonic oscillator
problem and solve it using quantum mechanics. We will also briefly discuss the idea of
tunneling.
How to Use These Lecture Notes
The lecture notes have been completely reworked this year. Instead of being just a series of cryptic derivations and
mathematical expressions, they feature more detailed explanations. The lectures will follow the sourcebook very closely,
both in the order and the depth of presentation. To take full advantage of the lectures, you should skim through the
appropriate section of the notes prior to the lecture. This way, even though you may not gain a complete understanding
of the material after the first reading, you will at least be able to know what to expect.
Units and Conventions
Physical chemists have refused to adopt SI units with as much fervor as the United States has clung to the English system.
Even journal publications continue to use cgs or atomic units. It turns out that for the quantities we will be measuring,
they are simply more convenient. If you are not familiar with either, take a quick look at Appendix II, where you will find
a summary of units and conversion factors. Throughout these notes, assume cgs values for constants, unless specified
otherwise.