Finding Transition States and Barrier Heights: First Order Saddle Points

8. Finding Transition States and Barrier Heights: First Order Saddle Points#

So far, you have already considered several systems that did not reside in a minimum of the potential energy surface. Both the bond breaking in the dissociation of H\(_2\) as well as the internal rotation of butane were examples of off-equilibrium processes, where the system moves from one equilibrium conformer, i.e. from one minimum, to another. It is intuitively clear that the likelihood of two equilibrium conformers to be transformed into each other by moving along some random path is negligible, and different methods have been established to find reasonable paths for such transitions. A frequently used approach is transition state theory, which is concerned with finding a realistic path between potential energy minima. In this set of exercises, you will search for the transition state for a the cyclisation of a deprotonated chloropropanol to propylene oxide, and you will find the minimum energy path that connects reactants to products via this transition state.

https://badgen.net/static/Report%20Template/Google%20Docs/yellow

https://badgen.net/static/Report%20Template/Overleaf/green

🎯 Learning goals

  • Understand how to navigate the PES to transition states

  • Visualize chemical reactions

📖 Chapter in script

Not in script but of practical relevance

📚 Resources

Frank Jensen - Computational Chemistry Ch12.8 p.416ff

Questions for the Interview

  1. What kind of reaction mechanism would you expect for Ex8 Q1? Would you expect the stereochemistry at the chiral carbon to be preserved?

The reaction mechanism is a intramolecular S 2 reaction (nucleophilic substitution), where the stereochemistry is inverted: the nucleophile attacks the electrophilic center on the side that is opposite to the leaving group, and during a backside attack, the stereochemistry at the carbon atom changes.

Chirality centre = carbon has 4 individual (different) substituents ; show them on the molecule.

  1. How to obtain the barrier height of reaction from found transition state? How to verify whether you have found a meaningful transition state?

Forward Barrier Height: Compute the electronic energy (or Gibbs free energy if considering temperature effects) of the transition state (TS) and the reactants.

From the TS it is necessary to find a minimum energy reaction path on the PES joining the reactants with the TS and the TS with the products. TS corresponds to a saddle point of the PES, this can be verified through the eigenvalues of the Hessian matrix. The TS found should be a maximum of the PES over the reaction coordinate.

Verify the Found Transition State:

  • Frequency Analysis: Perform a vibrational frequency analysis on the TS structure. A true transition state will have exactly one imaginary frequency (negative eigenvalue of the Hessian matrix). This frequency corresponds to the reaction coordinate.

  • Mode Visualization: Visualize the vibrational mode corresponding to the imaginary frequency. Ensure that this mode represents the movement along the expected reaction coordinate (e.g., bond-breaking or bond-forming).

  • Intrinsic Reaction Coordinate (IRC) Calculation: Perform an IRC calculation starting from the TS. Following the negative Hessian eigenvalues from the transition state to the next local minimum, the IRC should connect the TS to the correct reactants and products, confirming it is on the reaction pathway.

  1. In Exercise 7, why is the barrier for the epoxide formation so low?

  • The barrier is low because with the IRC profile we are joining the intermediate state of the epoxide formation (where the H in the OH group is already removed) with the final state.

  • Moreover, we are calculating the potential energy, and not the free energy. This also influence the result since the proper PES (using the free energy) is smoother than the one that would be obtained with the energy alone. Thermal energy might help the reaction overcome the barrier easily.

  1. In the course, we have seen many methods to calculate the electronic structures. Can you list them all ?

HF, MPn, Truncated CI and Full CI, CASSCF, CC, Exact DFT, Orbital-free DFT, KS-DFT.

  1. Which ones include (some, exact) electron correlation ?

Some: all of them except HF / Exact: exact DFT.

If there is time

  1. What is size-consistency? Which methods are size-consistent?

  • Size-consistency = can break up the Hamiltonian per system part E(AB) = E(A) + E(B)

  • HF, MPn, CC, Full CI, all DFT methods