Simplified Pseudopotential Problems for the Classroom

Ab initio methods have been used for many decades to accurately predict properties of solids such as the physical, electronic, optical, magnetic, and elastic. A generation ago, many research groups developed their own in-house codes to perform ab initio calculations. In doing so, research students were intimately involved in many aspects of the coding, such as developing the theoretical framework, and algorithmic and programming details. Over time, however, collaborations between various research groups within academia and in industry have resulted in the creation of more than 50 large, open source, and commercial electronic structure packages. These software packages are widely used today for condensed matter research by students who, unfortunately, often have little understanding of the fundamental aspects of these codes. To address this shortcoming, a program at the University of Pretoria aims to devise a range of simplified, easily programmable computational problems appropriate for the classroom, which can be used to teach advanced undergraduate students about particular theoretical and computational aspects of the electronic structure method. This article focuses on the pseudopotential, which is a centrally important concept in many modern ab initio methods. Whereas the full implementation of the pseudopotential construct in a real electronic structure code requires complex numerical methods--for example, accelerated convergence to self-consistency including the interactions between all the electrons in the system--the essential principles of the pseudopotential can, nevertheless, be presented in a simpler class of problems, which students can readily code.