Teaching Reciprocal Space to Undergraduates via Theory and Code Components of an IPython Notebook

Abstract

In this technology report, a tool is provided for teaching reciprocal space to undergraduates in physical chemistry and materials science courses. Reciprocal space plays a vital role in understanding a material's electronic structure and physical properties. Here, we provide an example based on previous work in the Journal of Chemical Education literature, carry out a calculation of reciprocal space vectors by hand, and present a computational tool for applying this mathematical process to other systems. Along with this paper, we have provided the stand-alone Python program that converts real space vectors to reciprocal space vectors and have also provided an IPython notebook that combines theory with components of the full Python code so that instructors can use this tool in their physical chemistry or materials science lectures.

A Creative Commons Textbook for Teaching Scientific Computing to Chemistry Students with Python and Jupyter Notebooks

“…Finally, Jupyter notebooks utilize the IPython environment which allows for images and plots to be displayed directly inside the notebook. These notebooks are well-suited for lectures, homework sets, and projects; Jupyter notebooks have demonstrated their utility by being employed in other science courses and chemical research …”

Exploring the Benefits and Barriers of Using Computational Notebooks for Collaborative Programming Assignments

“…O'Hara et al exploited Jupyter to teach artificial intelligence in "easy-to-use interfaces" [17]. Srnec et al [22] explained reciprocal space to undergraduates by providing a notebook that converts real space vectors into reciprocal space vectors. Both valued the possibility to combine theory and materials from a lecture with code and executable equations.…”

Implementation of a Python Program to Simulate Sampling

“…Google Colab is a hosted Jupyter notebook service that allows for easy sharing and storing of programs in the Google Drive . Several activities and simulations illustrating chemical concepts using the Python programming language have been published, including a program to solve the Schrodinger equation, a simulation of NMR concepts, an example exploring reciprocal space, a simulation of a Boltzman distribution, a program for analyzing data from GC experiments, an online HPLC simulator, and a series of several Jupyter notebooks with applications in analytical chemistry . Although simulations have been used to support diverse learning objectives in a variety of educational settings, to our knowledge the topic of sampling suitable for use in a chemistry course has not been published.…”