Lectures on Electronic Structure Theory
Jack Simons, Henry Eyring Scientist and
Professor
These lectures[1]
are intended to provide graduate students in chemistry and related fields,
experimental chemists, and theoretical chemists specializing in other
sub-disciplines with an introduction to the underpinnings of electronic
structure theory. I have tried to present the material with a focus on physical
and conceptual content while keeping the mathematical level appropriate to the
broad audience just described. For those who want access to additional
information at or a bit beyond the level of these lectures, I can recommend the
following texts:
T. Helgaker, J. Olsen, and P.
Jorgensen, Molecular Electronic Structure Theory, Wiley (2000). I think this is
the best book to use as a source for further details about the methods
introduced in these lectures.
J. Simons, and J.
Nichols, Quantum Mechanics in Chemistry, Oxford University Press (1997);
J. Simons, An
Introduction to Theoretical Chemistry, Cambridge University Press (2003). These
two books are good at explaining the concepts underlying the equations, offer
good physical pictures of what the theories contain, and make connections to
experiments.
J. Simons,
Energetic Principles of Chemical Reactions, Jones and Bartlett Publishers, Inc.
(1983). This is a good source for making connections between electronic
structure theory and reaction dynamics.
Other good
sources are the web site http://simons.hec.utah.edu/TheoryPage,
as well as that of the theoretical chemistry Summer School http://simons.hec.utah.edu/school
where lectures on electronic structure theory, dynamics, and statistical
mechanics appear.
I hope you enjoy
and benefit from these lectures and I wish you the very best in your own
scholarly career.
Table of Contents for the twelve lecture sessions. Click on the Session
number to start viewing it as a streaming video[2].
Overview: This brief
video offers an overview of what I intend to cover in the subsequent twelve
lecture sessions.
Session 1: The Born-Oppenheimer approximation; non-adiabatic
couplings; the electronic and vibration-rotation Schrodigner equations; atomic
units; electronic cusps, electronic wave functions and energy surfaces;
orbitals and spin-orbitals, Slater determinants; effects of antisymmetry;
problems arising when using single determinant approximations; certain states
require more than one determinant; restricted and unrestricted wave functions.
Session 2: Slater-Condon rules; the Hartree-Fock approximation;
Coulomb and exchange interactions; Koopmans theorem, the meaning of orbital
energies; Brillouin theorem; molecular orbitals are delocalized; reminder on
the limitations of single determinant wave functions.
Session 3: Dynamical and essential electron correlation;
polarized orbital pairs; dynamical correlation; configuration interaction; how
important correlation is; reminder about cusps and introduction to explicitly
correlated wave functions.
Session 4: The Hartree-Fock molecular orbitals; LCAO-MO
expansion; Hartree-Fock equations in matrix form; one- and two-electron
integrals; the iterative SCF process; scaling with basis set size; how virtual
orbitals change with basis set; core, valence, polarization, and diffuse basis
functions; Slater-type and Gaussian-type basis functions; contracted Gaussian
functions; Rydberg and extra-diffuse basis functions.
Session 5: Basis set notations; complete-basis extrapolation of
the Hartree-Fock and correlation energies.
Session 6: Determining the CI amplitudes using Moller-Plesset
perturbation theory (MPn); Brillouin theorem; strengths and weaknesses of MPn;
non-convergence of MPn can give crazy results.
Session 7: Configuration interaction (CI) and
multi-configuration self-consistent field (MCSCF) methods; strengths and
weaknesses; two-electron integral transformation.
Session 8: Coupled-cluster (CC) theory; analogy to cluster
expansion in statistical mechanics; the CC equations are quartic.
Session 9: Special tricks for studying metastable anions;
variational collapse; virtual orbitals are difficult to identify- examples;
long-range potentials and the centrifugal potential; valence and long-range
components of the wave function; relation to electron scattering; charge
stabilization method; the stabilization method.
Session 10: Typical error magnitudes for various methods and various
basis sets.
Session 11: Density functional theory fundamentals, strengths
and weaknesses.
Session 12: Response theory; molecular deformation gradients and
Hessians; reaction paths.
[1] The lectures were recorded, edited, and produced by Jimmy Miklavcic and Sam Liston of the University of Utah Center fro High Performance Computing. They are transmitted in MP4 format at a rate of 512 Kb/s. One needs to have a QuickTime player installed to view these (you can download one for free: http://www.apple.com/quicktime/download/)
[2] I watched these videos and so I am aware that I
misspoke on some occasions, but I think the listener will be able to detect and
overlook these minor errors. Also, I noted that, in several slides, some of the
math/greek characters do not display properly; again, I think the listener can
overlook these errors for which I am sorry.