Transition state calculations:

Step 1:

Click on the angle button on the tool bar (looks like this ). Then consecutively click on the hydrogen atom, then the carbon atom, and finally the nitrogen atom. In the lower right of the teal work space you should see this:

Click in the white box where the 180 is, now you can change the angle between the three atoms. To find the transition state we will run a transition state geometry calculation using the density functional calculation method. But first we need to make a good guess as to what the transition state looks like. Remember we are studying a reaction where the hydrogen moves from the carbon atom to the nitrogen atom. So the logical way to arrive at a transition state is by changing the HCN angle from 180 to something smaller. Go ahead and change the 180° to 90° for our first guess. Then go to the calculations menu and select transition state geometry like so:

and select density functional as the calculation method, like so:

and, click the box next to Freq. and Thermodynamics so we can compare the values to the reactant values. Then click submit. This calculation should take around thirty seconds to a minute on a 2.4 GHz computer and up to five minutes on a less powerful computer. So don't change that channel, we will be right back!

OK, the calculation should be done by now, go ahead and click the OK button on the dialog box that reads that the calculation is done. You should see the HCN angle move directly after you click OK. Using the angle button again check what the HCN angle is now. It should be very close to 70.79°. This is the transition state geometry for the HCN isomerization reaction. That was very easy, because we had a good initial guess. Try doing the same calculation but with 170° and 50°, and you will get some very interesting results. Sometimes the transition state geometry is hard to find that is why one must always have a fairly good idea as to what the transition state might look like.

The output of the calculation should look something like this:


Spartan '02 Semi-Empirical Program: (PC/x86) Release 116


Optimization:
Step Energy Max Grad. Max Dist.
1 -93.3503440 0.092137 0.234107 1
2 -93.3433277 0.029136 0.129305 1
3 -93.3431328 0.010729 0.058761 1
4 -93.3428651 0.003444 0.005847 1
5 -93.3428852 0.001615 0.003840 1
6 -93.3428894 0.000132 0.000487 1

Molecule is non-linear


1 imaginary frequencies ignored in
thermodynamics calculations.

Zero-point vibrational energy is 6.665 kcal/mol

Standard Thermodynamic quantities at 298.15 K and 1.00 atm

Translational Enthalpy: 0.889 kcal/mol
Rotational Enthalpy: 0.889 kcal/mol
Vibrational Enthalpy: 6.665 kcal/mol
....Total Enthalpy: 8.443 kcal/mol

Translational Entropy: 35.816 cal/mol.K
Rotational Entropy: 16.342 cal/mol.K
Vibrational Entropy: 0.001 cal/mol.K
....Total Entropy: 52.159 cal/mol.K

Free Energy (H-TS): -7.109 kcal/mol


Take notice of the bold text in the output that indicates that the calculation has found an imaginary frequency, this as we stated before is characteristic of a transition state geometry.

Compare the ground state energies of the transition state and the reactant:

Reactant

-93.423

au

 

-58622.933

kcal/mol

Transition State

-93.342

au

 

-58572.105

kcal/mol

The ground state energy has increased by 0.081 au, that may not seam like much but an au is a vary large unit of energy, so the 0.081 au change equates to 50.828 kcal/mol which is substantial. This is the energy that is needed by a mole of HCN to reach the transition state.

Let's check out the vibrations for the transition state.

Notice the imaginary frequency that facilitates the reaction. Click on the yellow box beside the imaginary frequency and see how the vibration is directly along the path of the reaction.

Now let's move on to the products geometry calculation