An R Shiny Application for Visualizing the Radial Distribution Functions of Hydrogen-Like Atoms

Abstract

The radial distribution functions of the hydrogen atom are discussed as an overview in General Chemistry courses and examined in detail in Physical Chemistry. While every relevant textbook has quality figures to aid students in grasping the underlying theory, gaps in understanding the connection between mathematical functions and orbital diagrams may be partially corrected by improved instructional tools. Presented here is an R Shiny application that dynamically calculates the associated Laguerre polynomial and the radial function for every orbital from 1s to 7i based on user input for the first four hydrogen-like atoms. Plots are then produced with gglot2 of the radial function, R_nl(r), the radial function squared, R_nl(r)², and the normalized radial distribution function, 4πr²× R_nl(r)², with the ability to change the range of r values of the three plots. The trapezoidal integration method within the pracma package is used to solve for the electron probability within a user-defined region of the third plot. The result of the integration is then included in the plot as a shaded area under the curve to clarify the significance of the distribution function. This technology report includes suggested problem sets to assist instructors in lower and upper division chemistry courses utilizing the application to enhance student outcomes in quantum chemistry.