Lectures on Electronic Structure Theory

 

Jack Simons, Henry Eyring Scientist and Professor

Chemistry Department

University of Utah

 

 

            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.

 

 

 

If you cannot download these lectures directly, 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] 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.