Achieving understanding of complicated molecular phenomena from two-dimensional drawings can be a challenge. Three examples are the C₂ and C₃ symmetry operations in chiral tris chelates, the assignment of absolute configurations in these molecules, and the non-dissociative mechanisms (Bailar Twist and Rây-Dutt) that interchange Λ and Δ enantiomers. Combining three-dimensional representations of the molecules from the Cambridge Structural Data Base, computational output examining the imaginary frequencies of transition states, and the powerful molecular visualization program Jmol, we present here a Web site to aid in teaching these concepts.

Population versus Sampling Statistics

When scientists draw random samples to be measured they expect their results will be accurate, assuming all systematic errors have been removed from the experiment. Unlike systematic errors, random errors cannot be removed from the experiment—only reduced. If several replicates are measured for each sample, random errors are mathematically minimized and are relegated to affecting precision, not accuracy. For some students, the difference between accuracy and precision is not clear enough for this to make sense. The solution is for students to interact with the statistics, which requires the laborious generation of multiple sets of random numbers, numerical comparisons, and graphical presentations of the data. The purpose of the spreadsheet exercise presented here is to remove the hurdle of constructing and generating such an interaction. The spreadsheet provides students with a self-led exercise that reinforces the statistics of sample and population distributions.

Courses in computational chemistry are increasingly common at the undergraduate level. Excellent user-friendly programs, which make the execution of ab initio calculations quite simple, are available. However, there is a danger that the underlying SCF procedure (usually coupled with contracted Gaussian atomic orbital basis sets) can become a ‘black box’ for the student. This Microsoft Excel spreadsheet contains all the essential elements of far more complicated ab initio calculations, but on the simplest possible molecular system.

In typical physical chemistry courses the student is told how the van der Waals equation works. The mathematics needed for making a Maxwell construction is difficult for the average chemistry student (what is needed are the roots of a cubic polynomial). This makes it difficult to show how the liquid–gas phase diagram is obtained from the equation of state. Here a spreadsheet experiment is presented that can be used to illustrate various aspects of the van der Waals equation of state.

SymmetryApp is a new visualization program characterized by a high level of user interactivity. Specifically, it is able to define a symmetry element anywhere in the molecule and determine the effect of the corresponding symmetry operation. This allows students to capitalize on the most important aspect of interactive learning—to make mistakes and to learn from them.