This web page is the summary of a computational laboratory experience performed during the 1999-2000 school year in CHEM 381L (Quantum Chemistry Lab) at Augustana college.

The show that is going to be viewed today is called the Sn² show.  This is a strange show, though.  Mysterious things such as F^- being a better nucleophile than Cl^-, negative imaginary frequencies, and activated complexes will be explored.

The opening scene begins with the reaction below:
 

To provide a little more insight into what was done in this lab we are going to talk a little computational chemistry (as if the above reaction wasn't mysterious enough).  The program Gaussian 98W¹ was used in this reaction calculation to provide insight into the transition state of this reaction.  The study was done on the Hartree-Fock level, using the 6-31+G(d) basis set.  The energies, as well as structure of the transition state for the reaction above were calculated.  This study required the optimization of the transition structure (which required the keyword TS for all you Guassheads), a frequency and IRC calculation for the transition structure(which required the keyword IRC=(RCFC, StepSize=20), and two geometry optimizations and frequency calculations for the intermediate minima.
 

The transition state (activated complex) for the reaction looks like this.  We all know from Chem 201 that this is called the activated complex and that this displacement reaction proceeds via a Walden inversion.
 
 

The transition state can be defined as the highest energy point along the lowest energy pathway from
reactants to products.  The IRC, or Intrinsic Reaction Coordinate, is this pathway.  A good analogy would be that of a highway running across a mountain.  The highway is most likely going to go through the lowest possible pass rather than over the top of the mountain.  This mountain pass is analogous to the IRC.

If you look below at the vibration below, the flourine, chlorine, and hydrogens are vibrating in the same direction, opposite to the carbon. So as the F^- is attacking, the Cl^- is leaving and the H's are inverting via a Walden inversion.
 
 

Below is the actual animation and climax of the Sn² show. If it looks as if you are looking at a single brown ball click in the picture and move the mouse to orient the reaction. If you fail to do this you will be missing out on some real amusing graphics.

[click right button in window for option]

The vibrational spectrum for the transition state is listed below. Notice that the normal mode of vibration that is selected (the one highlighted purple) is a negative value of -441.14 cm^-1. 

A negative wavenumber, how can this be (this just keeps getting weirder and weirder)?  This is referred to as the imaginary frequency. The imaginary frequency is the vibration along the reaction coordinate that leads to the decomposition of the activated complex.  As can be seen on the qualitatively sketched energy diagram below, the transition state (activated complex) ends up at the top.  The one vibration (imaginary
frequency) pushes it to decompose to one side or the other, usually to the side of products.

The Relative Energy Diagram² is plotted below. Notice that the products are lower in energy than the reactants. As was stated above, this goes against everything that is taught in organic chemistry about the trend in the strength of nucleophiles. This can be explained by the fact that Gaussian does its calculations in the gas phase, and the trends that we learn about are, for the most part, applicable to compounds in solution.

1. See the HTQC Guide for a general reference to Gaussian 98W.

2. Foresman, J. B.; and Frisch, A. Exploring Chemistry with Electronic Structure Methods. 2nd ed. 1996. Gaussian, Pittsuburgh, PA. 208-210.