Computational Methods in Chemistry

Exploring Potential Energy Surface of NH₃ and PH₃, Part 2. Minimum Energy Path.

In this excercise, we are going to learn how to follow minimum energy path of ammonia inversion motion. The minimum energy path following subroutines in GAMESS are invoked by the keyword, RUNTYP=IRC, in the $CONTRL group. You need the optimized geometry at the transition state in order to start the IRC run. In addition to the geometry, you also need the Hessian at the transition state. The hessian matrix can be obtained from the xxx.dat file of your Hessian run at the transition state. The following input deck shows you the important modification that you have to make for your IRC calculations.

(1) $CONTRL group

Change RUNTYP to RUNTYP=IRC.

(2) Add $IRC group

Add $IRC as shown. Npoint is the number of IRC points to be located. Saddle=.t. means that you have to give $HESS group in your input file.

(3) Add $HESS group

Edit the xxx.dat file of your Hessian calculation at the transition state, and extract the $HESS. Put $HESS into your input deck.

RUNS.

You need to run similar calculations with two different levels of theory, RHF/6-31G(d,p) and MP2/6-31G(d,p) for each NH₃ and PH₃. Remember that you need to have the geometry and Hessian with the same levels of theory.

OUTPUT.

After the IRC run is finished, you can look at the output (xx.log file) to confirm you have started with the transition state then ended up as a minimum. More concise information can be found in the xx.irc file. It contains the arc distance of a point on the minimum energy path from the transition state, its energy, and geometry. You can collect the arc distance and energy in a file to plot the energy profile of the minimum energy path in your favorite plotting program. You can make, in principle, a movie of the motion along the minimum energy path.

RESULTS.

The results of the MEP calculations should look like the following:

Report

From this exercise, you can make several plots that are similar to the one shown above. Only four points are calculated to elucidate the minimum energy path of the inversion of ammonia. The energy at the transition state is not included, so you have to get the energy from your optimization or your Hessian run. What you should do is to construct the double-well potential energy curve by inverting the data points.

How does the geometry change from the transition state to the minimum? You can get these information by examining the bond length, bond angle, and dihedral angles of the molecule at each IRC point. You should prepare the table showing these quatities at each IRC point.

By plotting the results obtained with the RHF/6-31G(d,p) and MP2/6-31G(d,p), you should be able to tell the difference with the different methods. What is the difference or similarity? Plot both the NH₃ and PH₃ IRC with respect to the S_total, the arc length from the transition state. What are the difference and similarity of the IRC in NH₃ and PH₃? What can you say about vibrational frequencies when you compare NH₃ and PH₃ in this coordinate?

If you need a molecular visualization software for this report. Please let me know. I have one on my Mac.