Exploring the Variational Principle

Kristina Danielle Closser
California State University-Fresno
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The purpose of this assignment is to explore the variational principle as it is applied in quantum chemistry to compute the energies of multi-electron atoms. Specifically we explore the helium-like atoms (e.g. H{ , He, Li+, Be+2, etc.) containing 2 electrons. These 2-electron systems cannot be solved analytically, and must be approximated using other means.

Learning Goals

Students should learn how to apply the variational principle to simple wavefunctions to determine optimal parameters. MATLAB is used for generating the data and students need to make some minimal modifications to the script. This activity requires students to think about trends in the data and describe the main points of the method.

Context for Use

This activity was designed for an introduction to computational chemistry course taught at the graduate level. It is designed as a lab to be started during class and completed as homework. The required MATLAB knowledge is minimal but students should be comfortable with opening and running scripts. Students should have taken physical chemistry and already be familiar with the variational theorem and properties of wavefunctions.

Description and Teaching Materials

This assignment explores the variational method which results from the variational principle for computing the energy of two-electron atoms.
Student Handout for Variational Principle Lab (Acrobat (PDF) 96kB Oct15 17)
MATLAB notebook for Variational Principle Lab (Matlab File 3kB Oct15 17)

Teaching Notes and Tips

Students who are more comfortable with MATLAB should be encouraged to modify the plots. For the two parameter functions, when optimizing the results graphically, it must be done iteratively or using 3D plots.


Students hand in a written summary of their results and answers to some questions

References and Resources