Introductory quantum chemistry courses usually illustrate fundamental quantum concepts by discussing the solution of the Schrödinger equation as applied to simple models such as the particle in the box, the potential step, or the harmonic oscillator (1, 2). The use of more realistic potentials is in general postponed to advanced courses in quantum chemistry, since they only admit numerical solutions for the corresponding Schrödinger equation, which involve the manipulation of state-of-the-art mathematical techniques. Sidestepping this difficulty, the present Internet toolkit allows undergraduate students to obtain numerical solutions to the one-dimensional Schrödinger equation as applied for bound-state problems involving realistic potentials. It uses a "black box" Fortran code, which implements the popular discrete-variable representation (DVR) method (3), and a graphical user interface developed in Hypertext Preprocessor (PHP) (4) and JavaScript programming languages.
Description of the Toolkit
The Internet toolkit, formed by the DVR Fortran program and the graphical front end, allows the calculation of bound states for a specified potential function in real time by remote access through a HTML Web page. Several one-dimensional potential models are provided, including the simple particle in a box (for various types of boxes), harmonic oscillator, double-well potentials, Morse (5) and Lennard-Jones (6) potentials, and the more realistic extended-Rydberg function (7)
Wave functions calculated for an asymmetric double-well potential. Two different values of the reduced mass have been used: (A) 1 au; (B) 2 au. The charts were created with Gnuplot (8) using files generated by the toolkit.
After accessing the Web page, the student has to fill in a set of self-explanatory boxes with input data for the calculation; although all fields are already provided with default values, students should be encouraged to input their own data (e.g., reduced mass of the system and all parameters associated with the model potential). Once all values are established, the data file may be created through the "submit data" button. Then, the calculation is started by clicking on the "calculate energies and wave functions" button. Finally, the output files may be used to make charts with Gnuplot and Excel. Additionally, the toolkit allows for the joint representation of the potential and corresponding bound states.
Literature Cited
Atkins, P. W.; de Paula, J. Atkins' Physical Chemistry, 8th ed.; W. H. Freeman: New York, 2006.
Levine, I. N. Quantum Chemistry, 5th ed.; Prentice Hall: New Jersey, 2000.
Bacic, Z.; Light, J. C. J. Chem. Phys.1986,85, 4594.
Our Secondary School editors work hard to distill all the JCE materials to produce a fraction of particular interest to high school teachers. We call it CLIC.
In recent years we have worked hard to better match our advertisers with our readers. When shopping for chemistry education materials, visit our advertisers' WWW sites first.
Take JCE along on your outreach missions. Copies of the Journal, guest access to JCE Online, our publications catalog, and more are available for your participants.
