INSTRUCTOR: Frank Rioux
TEXTBOOK: Quantum Chemistry and Spectroscopy by Thomas Engel
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Course Description: This course deals with the fundamental principles of
quantum theory and their application to the atomic and molecular systems of
interest to chemists. A major goal of CHEM 334 is to illustrate how theory and
experiment work together in the development of a viable model for the nano-world of atoms and molecules. However, while the
primary concern of this course is an operational mastery of fundamental
principles, the rich historical and philosophical background of quantum theory
will not be neglected.
There are a number of interesting
quantum sites on the World Wide Web that can serve as resources for this
course. They are listed below. To visit just point and click.
· Chemistry Resources
Home Page
· A
Brief Review of Quantum Chemistry
· Quantum
Chemistry in Molecular Modeling
· Computational
Chemistry and Organic Synthesis
· University of Georgia's Center for
Computational Quantum Chemistry
· Computational Chemistry
Resources
· NIST Physical
Reference Data
· Dan Thomas'
Quantum Chemistry Course
· Jack Simons'
Theoretical Chemistry Page
· Introduction to Quantum
Computing
Many of the scientific achievements that we study
in this course have earned their discoverers the Nobel Prize. There are two web
sites that have extensive treatments of the contributions of the Nobel
Laureates.
· The Nobel Prize Internet Archive
The following journals frequently publish quantum
mechanical articles and also contain daily updates on current advances in
science. CSB|SJU has online subscriptions to both journals.
Lecture: In
lecture we will cover the following chapters in McQuarry
and Simon. We will spend between three and four days on each chapter.
In a mathematically oriented course such as this it
is extremely important that you work at it on a daily basis. This means regular
attendance in class, asking lots of questions, working recommended problems at
the end of the chapter, and faithfully completing the computer and spectroscopy
exercises.
Your grade in CHEM 334 will be based on your performance
on exams, quizzes and a cumulative final (May 7, 2008, 1:00 – 3:00 pm,
ASC 135). There will be three exams and as many as five quizzes during the
semester. You will be given a week's notice on exams and at least a day's
notice on quizzes.
Laboratory: The laboratory work in this course falls
into two major classifications: theoretical computer exercises and analysis of
spectroscopic data. The purpose of the computer exercises is to illustrate
important theoretical principles and computational techniques. The emphasis in
the spectroscopy labs is on the various ways that theoretical models are used
to interpret the interaction of electromagnetic radiation with matter. Material
covered in lab will also appear on exams and quizzes.
Lab will consist of twelve computer/spectroscopy
exercises chosen from the following lists.
Computer Exercises
Spectroscopy
Exercises
Naturally, you will be expected to be present for
all exams, quizzes and laboratory sessions. Only under unusual circumstances
will make-up exams, quizzes or labs be permitted.
Students who register CHEM 334 are charged a $90
laboratory fee. This fee is assessed to cover part of the cost of maintaining
the computer laboratories, the equipment in them and the course manual you have
been provided with.
Miscellaneous: The Calculus I and II prerequisites are very important for CHEM 334
because of its mathematical orientation. If you do not feel that your
background in differential and integral calculus is adequate it would be
advisable to spend some time reviewing these subjects early in the semester.
Our textbook has a number of mini-chapters that provide mathematical support. MathChapters A, C, F, G, and H are particularly important.
They deal with complex numbers, vectors, spherical coordinates, determinants,
matrices, and partial differentiation.
Computer Hardware and Software: All computer labs and much of the day-to-day calculations
will be done on the PCs located in Room 135 of the Ardolf
Science Center. Two major software packages will be used in this course: Mathcad and Spartan. Mathcad is a
high level programming environment for doing essentially all the mathematics
(numerical and analytical) we will encounter in our study of quantum chemistry.
We will use it on a daily basis for routine problem solving and also to do the
computer labs. The first two computer labs will be devoted to an introduction
to Mathcad. Approximately 75% of exam and quiz
questions will be answered using Mathcad. Reference
manuals for this program will be available in the Ardolf
135. Spartan is an advanced software package for doing molecular mechanics,
semi-empirical and ab initio quantum mechanics on
molecules of intermediate complexity. It has a powerful graphical user
interface and is very easy to use. Your previous experience with Spartan in
organic chemistry (and perhaps general chemistry) will be helpful.
This introductory chapter provides historical
background on the failures of classical physics and the need for a new
mechanics. Among the phenomena that could not be explained classically were:
black body radiation, the photo- electric effect, Compton scattering, low
temperature heat capacities, atomic line spectra, and atomic and molecular
stability.
Assigned problems: 1 2 3 9 11 13 14 16 17 18 19 21
22 24 25 27 29 33 35
There are two great
traditions in quantum theory: Heisenberg's matrix mechanics and
Schrödinger's wave mechanics. They are formally equivalent, but each has
particular strengths in certain applications. Schrödinger's wave mechanics
might be considered the default for chemists, but the basic concepts of quantum
theory are probably most easily introduced via matrix mechanics.
In the early days of quantum theory Dirac
introduced an elegant and powerful notation that is useful in setting up
quantum mechanical calculations. After using Dirac's notation to set a
calculation up, one then generally chooses either matrix or wave mechanics to
complete the calculation, using that method which is most computationally
friendly.
There is no Chapter 1.5 in our text. The instructor
will provide several handouts which cover these areas.
The Schrödinger equation is the key equation
of non-relativistic quantum mechanics. It is a mathematical generalization of
de Broglie's wave hypothesis for matter. De Broglie's conjecture that matter
has wave-like properties and that its wavelength is inversely proportional to
its momentum is the foundation of quantum mechanics. In this chapter we see
that the Schrödinger equation can be derived by substituting the de
Broglie wave equation into the classical wave equation.
While de Broglie's wave equation can be used
directly to solve a number of simple problems, the Schrödinger equation is
more general and is the basis of all computational quantum mechanics at the
atomic and molecular level. In this chapter we learn how to solve
Schrödinger's equation for the celebrated particle-in- the-box problem. In
lab we will explore numerical solutions for Schrödinger's equation for a
number of simple models.
Assigned problems: 1-6 11-14 22 24 25 27 28 33 34
This chapter presents the basic postulates and
computational procedures of quantum mechanics. Among the key postulates of
quantum theory are the assertions that the wavefunction
contains all the physically meaningful information about a system and that
there is an operator associated with every observable property. The postulates
tell us how to obtain values for observable properties of a system from its wavefunction.
Assigned problems: 1 2 3ab 5 6-10 14 25 and
additional exercises provided by instructor.
Schrödinger's equation is solved for the
simple harmonic oscillator and the rigid rotor. Chemists use these simple
concepts to model molecular vibrations and rotations in the infrared and microwave
regions of the electromagnetic spectrum.
Assigned problems: 1 7-10 13-16 20 21 23 33 34 35
and additional exercises provided by instructor.
Schrödinger's equation can be solved exactly
for only a small number of problems. Fortunately, the hydrogen atom is among
the list of exactly soluble problems. The reason this is important is that the
exact solution of the hydrogen atom problem, suitably parameterized, can serve
as a starting point in obtaining approximate solutions for more complicated
atomic and molecular systems.
When Schrödinger's equation is solved for the
hydrogen atom one obtains a set of eigenfunctions (orbitals) and associated eigenvalues
(allowed energies) for the electron. This solution is in excellent agreement
with the atomic line spectrum for hydrogen. Futhermore,
the solutions for this one-electron problem form a basis for interpreting and
understanding the chemist's periodic table.
Assigned problems: 1 5 9 11 17 18 20 21 23 24 26 27
33 39 40 41.
For most problems of interest to a chemist
Schrödinger's equation does not have an exact solution. However,
approximate methods are available which, under ideal circumstances, provide
solutions to an arbitrary degree of accuracy. Two approximate techniques for
solving Schrödinger's equation will be emphasized in this chapter and used
throughout the remainder of the course - the variation method and perturbations
theory.
Assigned problems: 1 2 4 5 7 8 9 10 12-15 20 21 22
25 26.
The Schrödinger's equation for the helium atom
cannot be solved exactly, but the variational method
(previous chapter) yields results in agreement with experiment. Simple variational calculations will be performed on atoms
containing two, three, and four electrons. The multitude of electronic states
that arise for multi-electron atoms will be analyzed by deriving atomic term
symbols and comparing the theoretical results with atomic line spectra.
Assigned problems: 1-6 12 13 19 20 26-30 32 33 37
47 and additional exercises provided by instructor.
The prototype in explaining atomic structure and
stability was the simplest atom, the one-electron hydrogen atom. It is not surprising,
therefore, that the one- electron hydrogen molecule ion, H2+,
will be exploited to explain molecular stability and the physical nature of the
chemical bond. In particular, the contributions of John C. Slater and Klaus Ruedenberg to our understanding of the chemical bond will
be studied.
In addition to this simple molecule, the molecular
orbital theory of the homonuclear diatomics
from H2 to F2 and several heteronuclear
diatomics will be studied.
Assigned problems: 1 9 12-19 22-28 31 38 39 41.
The use of hydrid orbitals in interpreting the bonding in polyatomic
molecules is introduced. The Huckel molecular orbital
approximation is used to model the pi-electrons of conjugated organic molecules.
Molecular orbital theory is used to interpret the photoelectron spectroscopy of
di- and tri-atomic molecules.
Assigned problems: 1 5 7 19 27-38 and additional
exercises provided by instructor.
John Pople (see page 410
of our text for a biographical sketch and picture) shared the 1998 Nobel Prize
in Chemistry for his enormous contributions to the development of the field of
computational quantum chemistry. While the basic principles of quantum theory have
been known for 75 years it is only recently through the efforts of Pople and others that calculations on large molecules have
become feasible. This has enhanced the stature of theory and made it an equal
partner with experiment in contemporary chemical research. This chapter
provides a concise outline of computational quantum chemistry that will provide
the background necessary to appreciate the capabilities of the electronic
structure program, Spartan, that we will use in lab.
Assigned problems: 2 3 4 5 8 10 11 20 24 28 and
additional exercises provided by instructor.
Most molecules don't have any symmetry, but for
those that do group theory is a powerful analytic tool. In this chapter we
learn how to classify molecules into symmetry groups. Then we will use this
information plus the principles of group theory to construct molecular orbitals and to interpret the vibrational
and electronic spectra of molecules. The power of group theory will be demonstrated
by its application to a detailed study of the water molecule and the recently
discovered new allotropic form of carbon, C60.
Assigned problems: 3-6 19 22 40-43 and additional excercises provided by instructor.
The pure rotational and vibrational-rotational
spectra of simple di- and tri- atomic molecules will
be studied. The rigid rotor, non-rigid rotor, harmonic oscillator, and anharmonic oscillator models will be used to interpret
spectra.
Assigned problems: 1-5 7-9 14 15 18 20 22 27 30
44-48 and additional exercises provided by instructor.
The quantum mechanical basis of nuclear magnetic
resonance will be clarified by the analysis of the nmr spectra of two ABC spin systems: acrylonitrile and vinyl acetate (the vinyl protons do not
interact appreciably with the methyl protons). The high field and low field nmr spectra of both molecules will
be analyzed using a variational calculation on the
nuclear spin states.
Assigned problems: Will be provided by instructor.
Following a basic introduction statistical
mechanics (Bolztmann, Fermi-Dirac, and Bose-Einstein)
quantum mechanical principles will be used to understand the structure and
operation of a laser and its spectroscopic applications.
Assigned problems: Will be provided by instructor.
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