Rep:Kh1015TSEx1RD

Exercise 1 Results and Discussion.

(Fv611 (talk) Wonderful section. Well written and a lot of extra effort put into it. Well done!)

Note to Reader/Marker:
The compartmentalization of the Results and Discussion into 3 parts was based on relevant discussion idea and for convenient navigation during the write-up.

Part 1: Symmetry Discussion.

Figure 4.1 under Methodology section shows the reaction scheme for Exercise 1.

Figure 5.1.5 shows the graphical representation of MO interactions between s-cis butadiene and ethene during the formation of the TS. Figures 5.1.1-5.1.4 and 5.1.6-5.1.9 show the visualized MO output from GaussView (isovalue=0.02 and medium cube grid). Table 5.1.1 summarizes the MO interactions to form the TS in terms of the label of the constituent MOs in Gaussview outputs.

It can be concluded that the symmetry requirement of an allowed reaction is strictly when the constituent MOs have the same symmetry. Consequently, symmetrical-symmetrical or antisymmetrical-antisymmetrical interaction has a non-zero orbital overlap integral. Meanwhile, non-symmetrical interactions of the constituent MOs are symmetry-forbidden. Conversely, symmetrical-antisymmetrical or antisymmetrical-symmetrical interaction has a zero orbital overlap integral.

Table 5.1.1: Summary of MO Interactions To Form the TS.

TS Symmetry Label (in Increasing Energy Level)	Constituent Fragment Orbital Interactions (S-Cis Butadiene - Ethene)
Anti-Symmetrical	MO12-MO6 (Bonding)
Symmetrical	MO11-MO7 (Bonding)
Symmetrical*	MO12-MO6 (Anti-Bonding)
Anti-Symmetrical*	MO11-MO7 (Anti-Bonding)

Figure 5.1.1: HOMO of S-Cis Butadiene (MO 11, PM6 Method). Click for *.log output and for *.chk output.	Figure 5.1.2: LUMO of S-Cis Butadiene (MO 12, PM6 Method). Click for *.log output and for *.chk output.	Figure 5.1.3: HOMO of Ethene (MO 6, PM6 Method). Click for *.log output and for *.chk output.	Figure 5.1.4: LUMO of Ethene (MO 7, PM6 Method). Click for *.log output and for *.chk output.
Figure 5.1.5: Frontier MO diagram for the formation of the TS. The numbers on the TS structure (bottom) are atom labels.
Figure 5.1.6: HOMO-1 of TS (MO 16, PM6 Method). Click for *.log output and for *.chk output.	Figure 5.1.7: HOMO of TS (MO 17, PM6 Method). Click for *.log output and for *.chk output.	Figure 5.1.8: LUMO of TS (MO 18, PM6 Method). Click for *.log output and for *.chk output.	Figure 5.1.9: LUMO-1 of TS (MO 19, PM6 Method). Click for *.log output and for *.chk output.

Part 2: C-C Bond Length Evolution.

Note: The carbon labels are based on the TS labels in Figure 5.1.5.

Referring to table 5.1.2, as the reaction progressed from reactants to product at rtp, {C₁-C₂, C₃-C₄, C₅-C₆} bond lengths (in Å) increased from {1.33343, 1.33343, 1.32726} to {1.37977, 1.37979, 1.38177} to {1.50084, 1.50083, 1.53457}. At the same time, the {C₂-C₃, C₄-C₅, C₁-C₆} bond lengths (in Å) decreased from {1.47078, NA, NA} to {1.41110, 2.11469, 2.11479} to {1.33704, 1.53714, 1.53721}. The change in bond lengths were due to change in hybridization or change in bond order or both.

Table 5.1.2: Summary of Evolution of Calculated C-C Bond Length (in Å) through the Reaction at 298.15 K and 1 atm (PM6 Method).

State	C-C Bond Length (Å)
	C1-C2	C2-C3	C3-C4	C4-C5	C5-C6	C1-C6
S-Cis Butadiene	1.33343	1.47078	1.33343	NA	NA	NA
Hybridization	sp2-sp2 Double Bond	sp2-sp2 Single Bond	sp2-sp2 Double Bond	NA	NA	NA
Ethene	NA	NA	NA	NA	1.32726	NA
Hybridization	NA	NA	NA	NA	sp2-sp2 Double Bond	NA
TS	1.37977	1.41110	1.37979	2.11469	1.38177	2.11479
Hybridization	Not clear	Not clear	Not clear	Not clear	Not clear	Not clear
Product	1.50084	1.33704	1.50083	1.53714	1.53457	1.53721
Hybridization	sp3-sp2 Single Bond	sp2-sp2 Double Bond	sp2-sp3 Single Bond	sp3-sp3 Single Bond	sp3-sp3 Single Bond	sp3-sp3 Single Bond

Table 5.1.3 shows typical sp³ and sp² C-C bond lengths in organic compounds at rtp. The calculated values at PM6 level show good agreement with literature values at rtp in table 5.1.3 with less than 1% difference for any given C-C bond length .

The average value of Van der Waals radius of C atom in literature is 1.88 . The calculated distance between the centres of two C atoms of the two fragments in the TS (about 2.115 Å) is less than the sum of their Van der Waals radii (3.76 Å). This suggests presence of partly-formed C-C bond in the TS.

Table 5.1.3: Literature Value for Average C-C Bond Length (Experimentally Measured in Å) in Organic Compounds at 298.15 K and 1 atm .

Hybridization	sp3-sp3 Single Bond	sp3-sp2 Single Bond	sp2-sp2 Double Bond
C-C Bond Length (in Å)	1.54	1.50	1.47

Part 3: IRC and Animated Vibrations.

Referring to Figure 5.1.10, the IRC calculation at PM6 level showed that the two C-C sigma bonds were formed in a synchronous fashion in a concerted mechanism and that the TS had been optimized.

The calculated reaction profile at PM6 suggested that the reaction was spontaneous at 298.15 K and 1 atm. The activation energy was calculated to be 171 kJ mol^-1 and Δ Gibbs-Free Energy was calculated to be -122 kJ mol^-1 at 298.15 K and 1 atm, which means that there is a very high reaction barrier to be overcome before the reaction could proceed.

Figure 5.1.10: IRC for Formation of Cyclohexene (PM6 Method).

Figure 5.1.11: IRC Graph of Energy against Reaction Coordinate for the formation of Cyclohexene at 298.15 K and 1 atm (PM6 Method). Click here for the concurrent RMS Gradient Norm analysis.

Figure 5.1.12 shows the HOMO of the TS system by default (MO 17). It is possible to right-click on the Jmol and choose any MO of interest.

Figure 5.1.13 shows non-covalent interactions at the TS (Red being non-favourable interaction and Blue being favourable interaction). There was no significant non-favourable steric clash in the reaction, which meant that steric clash was not a factor contributing to the high activation barrier.

Figure 5.1.12: HOMO of the TS (Default view is MO 17, PM6 Method).

Figure 5.1.13: Non Covalent Interactions in the Transition State of Cyclohexene Formation (PM6 Method).

Figure 5.1.14 shows an interactive vibration animation of the TS (calculation at PM6 level).

Figure 5.1.14: Interactive Vibration Animation of the TS (PM6 Method).