**Lectures
on Electronic Structure Theory**

Jack Simons, Henry Eyring Scientist and Professor

These lectures 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 ACS-PRF funded theoretical chemistry Summer School http://simons.hec.utah.edu/school
where lectures on electronic structure theory, dynamics, and statistical
mechanics appear.

Finally, I also urge you to look into the Telluride
Schools on Theoretical Chemistry where you will find much material on this
subject.

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 within YouTube[1].

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.

If you cannot view these lectures, here is a link you can go to and download them in .ppt format one at a time.

If you would like to download an updated version of the material I talked about in these lectures (just the slides, no new lectures), go to this link where you will find .ppt and .pdf versions.

[1] 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.