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ERIC Number: EJ1114019
Record Type: Journal
Publication Date: 2016-Sep
Pages: 8
Abstractor: As Provided
ISSN: ISSN-0021-9584
Interactively Applying the Variational Method to the Dihydrogen Molecule: Exploring Bonding and Antibonding
Cruzeiro, Vinícius Wilian D.; Roitberg, Adrian; Polfer, Nicolas C.
Journal of Chemical Education, v93 n9 p1578-1585 Sep 2016
In this work we are going to present how an interactive platform can be used as a powerful tool to allow students to better explore a foundational problem in quantum chemistry: the application of the variational method to the dihydrogen molecule using simple Gaussian trial functions. The theoretical approach for the hydrogen atom is quite straightforward, however, the level of complexity increases considerably for the dihydrogen molecule. Although, as shown in this work, it is possible to obtain an analytical expression for the dihydrogen molecule variational integral by "pen-and-paper", this expression cannot be completely appreciated without the proper tools. In this work the "dry" analytical equations were implemented into an interactive platform that allows the students to visualize results (like probability densities and meaningful graphs), play with parameters, and thus gain a deeper understanding of the problem itself. Having an interactive environment is also important as a way of minimizing complex equations, testing analytical results with numerical calculations, among other things, that otherwise would be unachievable by "pen and paper" only. Additionally, in this work the bonding and antibonding behaviors of the dihydrogen molecule were investigated and evaluated in detail. As a final outcome, this article shows that important properties regarding the dihydrogen molecule (like equilibrium bond length and favorability of formation) can be explained and approximated with the variational method.
Division of Chemical Education, Inc and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF)
Authoring Institution: N/A
Grant or Contract Numbers: CHE1403262