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Pyramidal Inversion in Ammonia

Ammonia presents the simplest example of a transition state. This demonstration is a lecture in itself!

In the "expert" builder of Spartan, select Nitrogen, trigonal planar, and then click anywhere on the the screen. Optimize the structure in the builder by clicking on the minimize button from the builder menu to obtain D3h symmetry. Setup and submit a job for geometry optimization and frequency calculation at the HF/3-21G(*) level. When the calculation has finished select Vibrations.. from the Display menu. Locate the "imaginary" vibrational mode at the top of the vibrations list at approximately ~i615cm-1. This "imaginary" mode corresponds to the reaction coordinate for a pyramidal inversion and the structure you have optimized is the transition state.

In Spartan'02 for Windows, create a sequence for this vibration with at least 11 steps by clicking on Make List. The program extrapolates in either direction along this vibrational mode and generates "snapshots" of the structures. Save the sequence under a new name using Save As... from the File menu. Close the original file and Open the spreadsheet from the File menu to verify that each of the frames are present in the spreasheet.

In Spartan'02 for Linux/Unix, select Follow Vibration from the Build menu, change the Frame setting from 7 to 11 and click on Generate. The program extrapolates in either direction along this vibrational mode and generates "snapshots" of the structures. Save the sequence under a new name using Save As... from the File menu. Now, select return to main from the File menu and select Spreadsheet from the Display menu to verify that each of the frames are present in the spreadsheet.

Next, setup a single point energy calculation using Semi-empirical PM3. Also, specify the generation of an electrostatic potential surface by opening surfaces from the Setup menu, selecting Add.., density from Surfaces:, potential from Properties:, and then Save. In Spartan'02 for Linux/Unix click Add after selecting the surface and property values. This sets up a "global" job in which the energy is calculated at each point. Submit the Job by selecting submit from te setup menu.

After the job (actually multiple jobs) has finished, use the spreadsheet menu to add the relative energy (kcal/mol) and Dipole moment(debye) to separate columns. Create plots for these values.

 For a spectacular demonstration, animate your sequence by selecting the arrow at the bottom left corner. You should see that the energy passes through a maximum at the planar structure, while the dipole goes to zero at this point. Animating the electrostatic potential or HOMO shows what happens to the lone pair electrons as the structure changes hybridization. Finally, you can display the dipole moment of the vector to show that it changes direction during the process, passing through the zero at the center.

Remember that the extrapolated structures are approximate so that the barrier and dipole moment won't be accurate. Optimize the planar and pyramidal structures at the higher levels of theory for improved quantitative results.

The experimental inversion barrier for Ammonia is 5.8 kcal/mol, while the dipole moment is 1.47 Debye.

 

 


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