Wolfram Computation Meets Knowledge

Wolfram Summer School


Carlos Arango

Science and Technology

Class of 2017


Carlos Arango received his bachelor’s in chemistry from Universidad del Valle, Cali, Colombia, in 1997. In 2000, he obtained a master’s in chemistry under the direction of professor Julio C. Arce from Universidad del Valle. He worked on spin-boson models to study intramolecular energy transfer. From 2000 to 2005, Carlos was a graduate student at Cornell University; working under the direction of Greg Ezra, he obtained his PhD in the summer of 2005. Carlos’s dissertation was on the use of classical and semiclassical mechanics to study molecular rotors in tilted fields. In the summer of 2005, Carlos began work as a postdoctoral fellow in the Chemical Physics Theory Group at the University of Toronto under the direction of Paul Brumer. As a postdoctoral researcher, Carlos worked in coherent control of Penning and associative ionization and the phase control of retinal photoisomerization. In the summer of 2008, he returned to Colombia to join the chemistry faculty of Universidad Icesi in Cali, Colombia. Carlos is part of an active research group working on the application of coherent control to molecular processes of importance in chemical physics.

Computational Essay

Rotational Dynamics of a Free Triatomic Molecule »

Project: Quantum States for 1-Electron Systems Using NDEigensystem

Goal of the project:

Develop an interactive notebook to be used in quantum chemistry undergraduate courses.

Summary of work:

Although the hydrogen atom and molecule ion are the simplest cases to study in quantum chemistry, finding their analytical solutions is not trivial, even in one dimension. This notebook allows chemistry students to solve Schrödinger’s equation numerically and obtain eigenvalues and eigenvectors for one-electron systems. For the systems of interest, H and H+2, electronic states are calculated numerically using NDEigensystem. The electronic wavefunctions are visualized as functions of numerical parameters and physical constraints by using the interactive interface of Manipulate.

Results and future work:

Through this notebook, students can calculate electronic states of H and H+2 by varying numerical and physical parameters such as the discretization interval or the bond length. The exercises and investigations allow students to explore the validity of numerical solutions. For H+2 in one dimension, the student is guided to the calculation of nuclear energy curves within the Born–Oppenheimer approximation. The definitions of the Hamiltonian and functions—based on NDEigensystem—allow an easy and systematic extension to larger systems in three dimensions, or with two electrons.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022