Exercise 7: Reaction Mechanisms In this exercise, a simple S N 2 reaction is studied using quantum chemical methods: F C Cl F C Cl F C Cl + Reactant Transition State Product The goal is to determine the geometry of the transition state and to determine the barrier and the reaction energy. Geometry optimization of transition states is somewhat more difficult than optimization of a minimum. The geometries of the reactant and product can be found by simple minimizing techniques leading to a minimum. The transition state on the other hand is a saddle point on the potential energy surface. At the saddle point all coordinates not involved in the reaction will have their minimum energy. Only the atoms involved in the reaction will be in a geometric arrangement that is at its maximum energy. The geometric changes involving the reacting atoms is referred to as the reaction coordinate. In the above reaction, an approximate reaction coordinate is the distance between F -, C, and Cl -. When F - is stepped towards C, the C-Cl bond gets longer. At the transition state, both F - and Cl - interact with carbon, but none of them form a full bond. This interaction between F -, C and Cl - is energetically unfavourable for the system (the reaction coordinate is at a maximum energy). When the C-F bonds start to form and the Cl - ion is kicked out, the energy starts to go down again, until we reach a minimum (the product state). ere we will optimize the transition state for the above reaction and find the reaction barrier and reaction energy.
Exercise 7, KJE-3102 2 Calculations to be performed in this exercise: B3LYP/6-31+G(d,p) freq on TS guess B3LYP/6-31+G(d,p) opt=(ts,readfc,noeigentest) on TS guess B3LYP/6-31+G(d,p) freq on TS B3LYP/6-31+G(d,p) freq on Reactant B3LYP/6-31+G(d,p) freq on Product Transition State Optimization Take the geometry of the reactant (given on the last page). Copy it into a file and open it in Molden. During the reaction, the F - atom will attack the carbon center and Cl - will be released. If you want to optimize the transition state (TS) for this reaction, it helps if you have an idea how the geometry will look. For example, it is known that for an S N 2 reaction, the F-C-Cl angle at the TS should be ca 180, the C 3 unit should be almost planar and the Cl-C and F-Cl distances should be longer than normal bond lengths. Change the geometry (using the Zmat window) so that the F-C distance is 2.0 Å and the C-Cl distance 2.1 Å. Make the C 3 unit planar (try to change the angles in the Zmat to 90 ). The result should look something like this: Save the geometry. Run a Gaussian B3LYP/6-31+G(d,p) frequency calculation (freq) (notice the + in the basis set this is a diffuse function. Diffuse functions are especially important for calculations on anionic systems). Make sure the input has the same name as the checkpoint (you need the.chk file later). Submit the calculation on 1 processor, 1 node, 2 h. Open the resulting output in Molden. Press Norm. Mode. A list of frequencies appears, with the top one having a negative value. This is the imaginary frequency of the reaction coordinate. If you animate it, you will see how the carbon atom changes
Exercise 7, KJE-3102 3 from being bound to F to being bound to Cl, and back again (if the atoms move too fast, try to display them as Solid Ball and Stick). Your geometry is almost at the correct TS, but it needs to be optimized to obtain the correct geometry. Copy the checkpoint file from the frequency calculation into TS_SN2.chk. Make a new Gaussian input (TS_SN2.inp) : ----------------- %chk=ts_sn2 %mem=500mb #p b3lyp/6-31+g(d,p) opt=(ts,readfc,noeigentest) geom=check Comments -1 1 ---------------- opt=ts will result in a transition state optimization. Both the geometry (geom) and the force constants (readfc) will be read from.chk file. Submit the calculation as above. Visualize the output with Molden (press movie). If everything worked, you should have gotten your first transition state! Take your new optimized TS and run a frequency calculation (same basis set as above) on the optimized geometry. Visualize the freq output. In your report, give the final imaginary frequency you got. Thermochemistry To obtain the reaction barrier, the Gibbs free energy is computed for all structures by performing frequency calculations. The freq calculation on the TS has already been done, so only do freq calculations for the geometry of the reactant and the product using B3LYP/6-31+G(d,p) (see coordinates at the end). Submit as above. Try this command on the frequency output of the product: $ grep -A 50 Thermochemistry Myproduct_freq.out You will get 50 lines of text, where the important part is this: ---------------------- Zero-point correction= 0.039550 (artree/particle) Thermal correction to Energy= 0.044765 Thermal correction to Enthalpy= 0.045709 Thermal correction to Gibbs Free Energy= 0.010483 Sum of electronic and zero-point Energies= -600.003953 Sum of electronic and thermal Energies= -599.998738 Sum of electronic and thermal Enthalpies= -599.997794 Sum of electronic and thermal Free Energies= -600.033020
Exercise 7, KJE-3102 4 E (Thermal) CV S KCal/Mol Cal/Mol-Kelvin Cal/Mol-Kelvin Total 28.090 13.054 74.140 Electronic 0.000 0.000 0.000 --------------------- The enthalpy () is: -599.997794 artree. The Gibbs free energy (G) is: -600.033020 artree. The entropy (S) is: 74.140 cal mol -1 K -1. Do the following: Extract the same values for the transition state and the reactant. Compute: the activation energy ( G ) and the reaction energy ( G r ). G = G(TS)-G(reactant) G r = G(product)-G(reactant) Convert artree energies into kj/mol by multiplying with 2625.5. Compute and r in kj/mol and S and S (convert the entropy units to J mol -1 K -1 by multiplying with 4.184.). Extract the Zero-point vibrational energy (ZPVE) using this command: $ grep -A 1 " Zero-point vibrational energy" MYOUTPUT.out Do this for all geometries. Note how big the ZPVE is. Determine the relative ( ZPVE and ZPVE r ) in kj/mol. In your report: Show the geometry of the transition state, give angles and distances. Give the final imaginary frequency of the TS. Report G, G r,, r (kj/mol) and S, S (J mol -1 K -1 ). Report the ZPVE (kj/mol) for all geometries and determine ZPVE and ZPVE r Discuss if this reaction could occur spontaneously.
Exercise 7, KJE-3102 5 Coordinates Reactant (In Molden format, copy into file and visualize in Molden. For calculations, remove first two lines, use only coordinates) 6 C -0.293181 0.002306-0.006286 F -2.710355-0.001074 0.002951 Cl 1.641830-0.000723 0.002013-0.582982 1.001737-0.297284-0.583681-0.747840-0.727660-0.592164-0.245769 1.001887 Coordinates Product 6 C -1.253968 0.006125-0.000172 F -2.686565-0.004995 0.000139 Cl 2.025094-0.001077 0.000030-0.903426-0.497067 0.899405-0.916639 1.041336-0.012166-0.903637-0.517747-0.887975