PES: Exercise 5

Locating a 1st Order Saddle Point on a Potential Energy Surface

Transition state theory can be used to explain reaction rates by locating saddle points on a potential energy surface (PES). By locating the saddle point on the PES using quantum chemistry and calculating the energy difference between saddle point and reactant one gets the activation energy, which is related to the reaction rate by the Eyring equation. While optimizing to minima on a potential energy surface (such as the reactant or product of a reaction) is relatively straightforward, locating a saddle point requires more work and care must be taken to ensure that a proper saddle point is found.

Locating a saddle point requires a very good guess starting structure as guess, which can be obtained through a relaxed surface scan by selecting an appropriate reaction coordinate (usually an internal coordinate such as bond length or angle). In a relaxed scan, the reaction coordinate is held fixed at a value while all other geometric coordinates are optimized; the reaction coordinate is next changed to a new value and the structure again relaxed. Plotting the optimized energy for each value of the reaction coordinate results in a reaction profile, hopefully smoothly connecting the two minima.

Computing the Hessian (the 2^nd derivative of the energy w.r.t. nuclear coordinates) allows one to predict harmonic vibrational frequencies from first principles. The Hessian is also often used to aid geometry optimizations and is crucial to reliably locating saddle points.

In this exercise, you will locate the saddlepoint (that can though of as an approximation to a transition state) of the S_N2 reaction of CH₃Cl + F^- → Cl^- + CH₃F using relaxed surface scans and Hessian calculations.

1. Create starting geometries for the left hand side and right hand side of the reaction, using a molecular builder (Chemcraft) or use coordinates you have been given. Start with the free halogen ion in ~3-5 Å distance from the carbon and appropriately aligned. Remember to set the correct charge of the system.

In the next steps you can choose any level of theory you prefer. An inexpensive option is using a semiempirical method such as AM1 or PM3. A slightly more reliable (and more expensive) level would be a DFT method such as:

! PBE COSMO D3BJ def2-SVP def2-SVP/J

(Recently discovered that HF-3c was giving a rather pad potential energy surface so it's not recommended in this exercise anymore)

2. Optimize the [CH₃Cl···F]^- and [CH₃F···Cl]^- structures you created in step 1 using your selected level of theory.

3. Using either the optimized geometry of [CH₃Cl···F]^- or [CH₃F···Cl]^-, run a relaxed surface scan, tracing the path from either [CH₃Cl···F]^- to [CH₃F···Cl]^- or the other way around. For the relaxed surface scan use 'Opt' keyword and the %geom scan feature. The appropriate reaction coordinate for our example will be a bond distance. Enter the parameters to change the %geom block of the input file provided.

Refer to the ORCA manual and ORCA input library (https://sites.google.com/site/orcainputlibrary/geometry-optimizations) for a description of how to generate relaxed surface scan and TS optimization inputs for the ORCA program.

4. When the relaxed surface scan is done, the output file will reveal a table of optimized energies for each value of the reaction coordinate. The same table is also found in the file "jobname.relaxscanact.dat". To visualize the surface scan, the optimized geometries for each reaction coordinate are found in files jobname.0XX.xyz (where XX=number of point), which can be opened with ChemCraft for example. Make a plot of energies vs. reaction coordinate of the surface scan using e.g. Excel.

5. A relaxed surface scan can only reveal an approximate minimum energy path and an approximate guess for the energy of the saddle point. The highest energy point on the calculated profile should be a reasonable guess for a saddlepoint optimization (eigenvector-following algorithm). Locate the saddle point using the highest energy structure as starting point with the "OptTS" keyword (include also the "NumFreq" keyword), make sure you calculate the exact Hessian before the first optimization step.

6. Make sure you have located the correct saddle point by checking the following.

a. The final geometry of the saddle point has a gradient close to zero (should be the case if the job finished without errors).

b. The saddle point geometry looks appropriate.

c. The "NumFreq" output gives 1 and only 1 imaginary vibrational mode of a reasonable size (usually larger than 200 cm-1).

d. Visualizing the imaginary mode reveals a mode connecting the two minima.

Chemcraft can open the ORCA outputfile directly and visualize the calculated vibrational frequencies.

What is the activation energy of the reaction (for both left and right side) according to your calculations?

7. Is the energy of the saddle point higher or lower than saddlepoint estimate from the relaxed surface scan? Why?

8. Think about ways to improve the theoretical prediction of the activation energy. Oh, and also write those thoughts down in your report.