Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.
Nf710 (talk) 23:41, 16 November 2017 (UTC) It seems like you have some confusion. There are 3N-6 degrees of freedom which can change the energy in some way. only 1 linear combination of these ar the reaction coord that goes over a saddle point from react to products. a TS has only 1 dimension of the 3N-6 with a negative force constant the rest are positive hence it is called a saddle point.
Exercise 1: Reaction of Butadiene with Ethylene
Reaction
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.
Figure 1 Mechanism for the reaction between butadiene and ethylene
Molecular Orbital Diagram
Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene
(Fv611 (talk) MO diagram is good but you could have indicated the newly formed TS HOMO and LUMO. Additionally it would have been good to number the TS MOs to be able to compare them with the calculated MOs in the Table below.)
Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.
The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.
(Fv611 (talk) The orbital overlaps dictate the symmetry rather than viceversa. AS/S interactions are forbidden because their orbital integral would be zero.)
HOMO of Butadiene
LUMO of Butadiene
HOMO of Ethylene
LUMO of Ethylene
Asymmetric Bonding MO
Symmetric Bonding MO
Symmetric Anti-Bonding MO
Antisymmetric Anti-Bonding MO
Bond Distances
C-C Bond Distances in Butadiene
C-C Bond Distance in Ethylene
C-C Bond Lengths in Transition State
C-C Bond Lengths in Cyclohexene
Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp2 C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp3 C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.
Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is an intermediate length between the van der Waals diameter and the typical sp3 C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.
Vibrations in the Transition State
Figure 3 Vibration of the Transition State corresponding to Reaction Pathway
The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.
Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole
Reaction
Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole
Molecular Orbital Diagram
Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State
(The MOs are slightly messy for the TS. You can space them out a bit as long as you show where the interactions are Tam10 (talk) 14:09, 10 November 2017 (UTC))
Endo Asymmetrical Bonding MO
Endo Symmetrical Bonding MO
Endo Symmetrical Anti Bonding MO
Endo Asymmetrical Anti Bonding MO
Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State
Exo Asymmetric Bonding MO
Exo Symmetric Bonding MO
Exo Symmetric Anti Bonding MO
Exo Asymmetric Anti Bonding MO
In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.
In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol-1 lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol-1 lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol-1 and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol-1. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.
Nf710 (talk) 23:45, 16 November 2017 (UTC) This is correct but where are your references for these values?
Thermochemistry
Sum of Electronic and Thermal Free Energies/KJmol-1
PM6 Optimisation
B3LYP/6-31G(d) Optimisation
1,3-Dioxole
-137.2505776
-701188.4294
Cyclohexadiene
306.857803
-612592.877
Endo Transition State
362.1665616
-1313621.479
Endo Product
99.26223482
-1313848.695
Exo Transition State
364.6870405
-1313613.642
Exo Product
99.7085693
-1313815.098
Endo Reaction Barrier
192.56
159.83
Endo Reaction Energy
-70.34
-67.39
Exo Reaction Barrier
195.08
167.66
Exo Reaction Energy
-69.90
-63.79
The endo reaction barrier is 2.52 KJmol-1 lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol-1 lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-Ea)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.
The endo product is 0.45 KJmol-1 lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol-1 lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.
Figure 7 Secondary Interactions in the HOMO of Endo TS
Figure 8 Secondary Interactions in the HOMO of Exo TS
NIce good understanding, anf you came to the correct conclusions. I would have been nice of you could have shown some understanding of the Quantum methods.
Exercise 3: Diels-Alder vs Cheletropic
Reaction
Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO2
IRC
Figure 10 IRC for the formation of the Endo ProductFigure 11 IRC for the formation of the Exo ProductFigure 12 IRC for the formation of the Cheletropic Product
In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.
Thermochemistry
Sum of Electronic and Thermal Free Energies/KJmol-1
Xylylene
467.56455873
SO2
-313.1406217
Diels Alder Endo TS
237.7651754
Diels Alder Endo Product
56.98645242
Diels Alder Exo TS
241.7428061
Diels Alder Exo Product
56.33007771
Cheletropic TS
260.0661626
Cheletropic Product
0.0131274942
Endo Reaction Barrier
83.34
Endo Reaction Energy
-97.44
Exo Reaction Barrier
87.32
Exo Reaction Energy
-98.19
Cheletropic Reaction Barrier
105.64
Cheletropic Reaction Energy
-154.41
The Diels Alder endo reaction barrier is 3.89 KJmol-1 lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol-1 lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO2 and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.
(Be careful that "product" really shouldn't be used to refer to the TS. The barrier is related to the TS Tam10 (talk) 14:12, 10 November 2017 (UTC))
The free energy of the cheletropic product is 56.97 KJmol-1 lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol-1 lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favoured product which is formed under equilibrating conditions.
Reaction Profile
Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO2
Conclusion
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/6-31G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.
In the reaction between butadiene and ethylene, the MO diagram shows that only MOs with the same symmetry interact and the vibration corresponding to the reaction pathway shows that the two new σ bonds are formed synchronously. The MO diagram for the reaction between cyclohexadiene and 1,3-dioxole shows that the reaction is an inverse demand Diels Alder and the thermochemistry results show that the endo product is both the kinetically and thermodynamically favoured product. The IRC calculations for the reaction between xylylene and SO2 show that the six membered ring is aromatised in all three reactions and the thermochemistry results show that the Diels Alder endo product is the kinetic product and the cheletropic product is the thermodynamic product.
Bibliography
1. Wales DJ. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses. Cambridge: Cambridge University Press;2003. p 1-5.
2. Clayden J, Greeves N, Warren S. Organic Chemistry.2nd Edition. Oxford: Oxford University Press; 2001. p.141-148.
