Rep:Mod:Mrh214

Diels Alder Cycloaddition

Butadiene and Ethene optimization to Cyclohexene via PM6

Method

1) Butadiene and ethene were optimized to a minimum seperately. Once optimized, they were placed in a similar geometry closely resembling that of the transition state (TS) required for the Diels Alder reaction; with the 4 carbon atoms in the reaction centre being frozen approximately 2.2 angstroms from eachother. This geometry was optimized to a minimum. The optimized geometry was then re-optimized to a TS (Berny), and this was confirmed by the presence of 1 negative frequency in the vibrations. An IRC was run on this TS in both directions with N=100. This geometry was manually displaced and optimized further to a minimum and product confirmation was given by all positive frequencies.

Butadiene

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Ethene

The C=C bonds in butadiene are 1.33531 Å; the C-C is 1.46835 Å. The C=C in ethene is 1.32731 Å.

TS

This is the imaginary vibration at -949.3 icm^-1, which corresponds to the TS.

And this shows the first positive vibration at 144.91 icm^-1. The motions are synchronous, therefore implying that the bond formations are also, synchronous.

In the TS the 2 C=C bonds of butadiene are now 1.37978 and 1.37974 Å. The previous C-C in butadiene is now 1.41114 Å; this has compressed as in the products, it will become a double bond. Similarly, the C=C bonds are now elongated slightly, due to becoming single bonds in the product.

The C=C in ethene for the TS has elongated to 1.38173, as this will be a single bond in the product.

The C atoms involved in the reaction centre for the Diels-Alder mechanism, from butadiene to the ethene carbons are at length 2.11423 and 2.11494 Å.

Frontier Orbitals of Reactants

FMO	Butadiene	Ethene
HOMO
LUMO

(FMO = Frontier Molecular Orbitals)

TS MO's

Cyclohexene

Bond Distance Variation Over Course of Reaction

Bond lengths in reactants

	Bond lengths Å
Bond Type	Butadiene	Ethene
C-C	1.46835	-
C=C	1.33531	1.32731

Bond lengths in TS

	Bond lengths Å
Bond Type	Butadiene fragment	Ethene fragment
C-C	1.41114	-
C=C	1.37978 / 1.37974	1.38173

2 C-C lengths in reaction centre

Reaction centre	Carbon atom distances Å
C-C	2.11423 / 2.11494

Bond lengths in Cyclohexene product

	Cyclohexene
Bond type	Bond lengths Å
C-C	1.50085 / 1.50087
C-C	1.53714 / 1.53704
C-C (opposite C=C)	1.53453
C=C	1.33698

In the final product, the C=C is 1.33698 Å, the neighboring C-C on either side to the double bond are 1.50085 and 1.50087 Å. The adjacent C-C to these bonds are 1.53714 and 1.53704 Å. And the C-C directly opposite the C=C is 1.53453 Å.

Typical C-C sp³ length is 1.54 Å and the corresponding sp² length is 1.34 Å. The Van der Waals radius of carbon is 1.70 Å. The sum of Van der Waals radii for 2 carbon atoms is 3.4 Å. The bond distances displayed in the above tables, are all less than this, and so there is bonding interaction. The key aspect here is for the 4 C atoms in the reaction centre, with both being approximately 2.114 Å distance between each C-C pair, this shows progressive bonding interaction, as these distances are far less than the Van der Waals radius for 2 C atoms.^[1][2]

The Diels-Alder MO Diagram^[3]

The MO diagram shows that the HOMO for the diene is closer in energy to the LUMO of the dienophile, hence will allow more efficient/constructive overlap (and lower energy antibonding MO) than the opposite case; which would be the LUMO of the diene with the HOMO of the dienophile.

The Symmetry Conditions^[5]

Let g = gerade (symmetric) and u = ungerade (antisymmetric).

Orbitals of the same symmetry may combine, ie. g-g, u-u, which is an allowed reaction. However, orbitals of mis-matched symmetry may not, ie. g-u / u-g, and so is a forbidden reaction.

The orbital overlap integral is non-zero for g-g / u-u, but zero for g-u / u-g.

Nf710 (talk) 00:12, 15 December 2016 (UTC) You have done most of the stuff asked of you, but it is written in a disjointed fashion.

A Comparison of Endo- and Exo- Products

The Reaction of Cyclohexadiene and 1,3-Dioxole by PM6

Method

Both reactants were optimized, and subsequently placed in the endo TS conformation with the 4 C atoms involved in the reaction centre being frozen from eachother at a distance of 2.2 Å. An optimization to a minimum was carried out, followed by an optimization to a TS (Berny). An IRC was done on this TS structure, which ran in both directions, at N=20. The geometry obtained at the start of the reaction profile from the IRC was optimized to a minimum and no imaginary frequencies confirmed this to be the product.

The same procedure was carried out for the exo-conformer.

B3LYP frequency pictures for exo and endo

A B3LYP/6-31G(d) calculation was run on both TS geometries and the presence of 1 imaginary frequency in both TS structures confirmed them to be the TS. These frequencies were 520.86 and 528.8icm^-1 for the endo and exo TS's respectively.

B3LYP Vibrations and TS

Endo	Exo

The releveant FMOs for Diels-Alder by symmetry

From the MO diagram for Diels-Alder, the same orbitals come into play for these reactions; combining g symmetry with g, and u with u.

endo-TS MO's

Bonding Orbitals
Antibonding Orbitals

exo-TS MO's

Bonding Orbitals
Antibonding Orbitals

(It's pretty difficult to see what's going on in the above tables. The angles chosen and opacity make it hard to see the interactions. Specify HOMO/LUMO etc Tam10 (talk) 14:41, 6 December 2016 (UTC))

Endo vs Exo TS's

	Endo	Exo
TS vibrations
TS Geometry

The presence of 1 imaginary negative frequency shows that these are the TS structures for the 2 reactions.

Endo and Exo Product Formation from IRC

	Endo	Exo
IRC
Reaction coordinate

Thermochemistry of Exo- vs Endo-

Endo

Optimizations	Hartrees	EA (kJmol-1)	∆Greaction (kJmol-1)
Reactants	0.130081	20.64	-
TS	0.137942	-	-
Product	0.244570	-	300.59

Exo

Optimizations	Hartrees	EA (kJmol-1)	∆Greaction (kJmol-1)
Reactants	0.136771	5.60	-
TS	0.138905	-	-
Product	0.037977	-	-259.38

Secondary Orbital Interactions

HOMO of exo and endo TS

TS	HOMO
endo
exo

Primary orbital interactions lead to sigma bond formation. The dienophile, in this case the 1,3 Dioxole, is pointing away from the diene which does not allow for any further orbital interactions; and so only has primary orbital interactions, and forms the exo-product.

In the endo conformation, the dienophile is positioned such that the lobes of the C-O and the back orbitals in the cyclohexadiene can form a favourable bonding interaction, which lowers the energy of the TS, and in turn, is the kinetic product. Such an interaction is a secondary orbital interaction. A point to note is that no such bonds are formed in this case.⁴

This such reaction is a normal demand Diels-Alder reaction, as the diene is electron rich whereas the dienophile, has electronegative oxygen atoms making it electron poor.⁵

Nf710 (talk) 00:23, 15 December 2016 (UTC) You havent linked this conclusion to the ordering of your MOs. you also worked out your energies at PM6 when you should have done it at B3LYP hence why your energies look so peculiar. B3LYP is ma much more powerful method and will hence give a better answer.

Diels-Alder and Chelotropic Pathways

o-Xylylene and SO₂ optimization to adducts of both reaction types

Diels-Alder

The product was drawn and optimized to a minimum using the PM6 method. The C-S and C-O bonds in the resulting structure were removed and separated by 2.4 and 2.0 Å respectively, and frozen. This was then optimized to a TS (Berny). An IRC was then run on this TS geometry, and the lowest energy conformation from the resulting reaction profile was optimized to a minimum.

This gave the exo product; so the TS geometry was altered by manually displacing the O atom of the SO₂ into an approximate endo geometry for TS. This was then optimized to a TS (Berny), after which an IRC was run and a subsequent optimization to a minimum on the product to obtain the energies. Using this method, allowed for both reaction paths to be analysed.

Chelotropic

The chelotropic product was drawn and optimized to a minimum. The C-S bonds of this resulting geometry were broken and the coordinates were frozen at approximately 2.2 Å apart. This structure was then optimized to a minimum, and the subsequent geometry reoptimized to a TS (Berny). An IRC was run on this TS with N=200, forward only, to obtain a reaction path.

Diels-Alder & Chelotropic Reactions

	Endo	Exo	Chelotropic
TS
IRC
Reaction Profile

During the course of all 3 reactions, xylylene's 6 membered ring becomes aromatized, which gives it extra thermodynamic stability due to the lowering in energy. This extra energy provides the driving force(ΔG) of the reaction. The stabilization of the TS in this way allows the o-xylylene reaction to progress at a faster rate. This is very true for the Diels-Alder reaction.

Thermochemistry of o-Xylylene and SO₂

Endo

Optimizations	Hartrees	EA (kJmol-1)	∆Greaction (kJmol-1)
Reactants	0.090737	-0.47	-
TS	0.090559	-	-
Product	0.021693	-	-181.28

Exo

Optimizations	Hartrees	EA (kJmol-1)	∆Greaction (kJmol-1)
Reactants	0.092130	-0.000053	-
TS	0.092077	-	-
Product	0.021455	-	-185.56

Chelotropic

Optimizations	Hartrees	EA (kJmol-1)	∆Greaction (kJmol-1)
Reactants	0.097953	2.9	-
TS	0.099059	-	-
Product	-0.000002	-	-257.18

(You should definitely not have TS energies lower than reactants! This means your reactants energies are wrong Tam10 (talk) 14:41, 6 December 2016 (UTC))

A Comparison of Reaction Profiles

(There must be a gradient of 0 at the TS Tam10 (talk) 14:41, 6 December 2016 (UTC))

It can be seen that the chelotropic product has the lowest energy and is the most thermodynamically stable product. It also has the highest activation energy out of all 3 reactions, suggesting it may have the largest kinetic stability in comparison to the other reactions. The endo and exo products are very close in energy suggesting similar thermodynamic stability, however, the secondary orbital interactions which occur in the endo TS conformation from the lobes of the oxgeyn atom as the dienophile SO₂ approaches will allow lowering of the TS activation barrier, thus allowing the endo product to be the kinetic product and form faster than the exo product.

References

1. Allen, F.H., Kennard, O., Watson, D.G., Brammer, L., Orpen, G.A. and Taylor, R.(1987) ‘Tables of bond lengths determined by x-ray and neutron diffraction. Part 1. Bond lengths in organic compounds’, Journal of the Chemical Society, Perkin Transactions 2, (12), pp. 1–19. doi: 10.1039/P298700000S1.

2. Inorganic Materials, Vol. 37, No. 9, 2001, pp. 871–885. Translated from Neorganicheskie Materialy, Vol. 37, No. 9, 2001, pp. 1031–1046. Original Russian Text Copyright © 2001 by Batsanov.

3. Clayden, J., Greeves, N., Warren, S. and Claydon, J. (2000) Organic chemistry. New York: Oxford University Press.

4. Gheorghiu, M.D. (no date) Diels Alder Reactions. Available at: https://ocw.mit.edu/courses/chemistry/5-32-intermediate-chemical-experimentation-spring-2003/labs/Appendix_1_Diels_Alder_Reactions_03.pdf.

5. Prof Sue Gibson, Pericyclics Lecture Course 2016, Imperial College Chemistry Department.

By Riashat Hossain