Investigation of Diels-Alder Reaction Transition States, Chemistry Lab

This computational lab report investigates the transition states of three Diels-Alder (DA) reactions using Gaussian and GaussView software. The study models transition states and reaction pathways to understand reaction mechanisms, as it's impossible to capture the transition state species. The report details the application of PM6 and B3LYP/6-31G(d) computational methods, analyzing the energy profiles, IRC paths, MOs diagrams, and bond lengths of reactants, products, and transition states. The first exercise focuses on the reaction of butadiene with ethylene, and the second examines the reaction of cyclohexadiene and 1,3-dioxole, comparing endo and exo transition states. The analysis includes the determination of reaction barriers, reaction energies, and the influence of secondary orbital interactions, providing insights into the energetics and mechanisms of these cycloaddition reactions, and the role of the Woodward-Hoffmann rule.

Investigation of the Transition States of Diels-Alder Reactions
Name: Lei Yao Date: 24/11/2019-29/11/2019
Introduction
This computational lab looked at investigating the transition states of 3 Diels-Alder (DA) reactions by
modelling the transition state and the reaction pathway using Gaussian and GaussView. Though it’s
impossible to capture the transition state species, it is possible to model the structure of the
transition state, which gives a lot of information about the reaction mechanism. The calculation of
the transition state can be applied to the calculation of the IRC subsequently for the energy profile of
the reaction.
Potential energy surface (PES) is a conceptual description of the energies for a whole reaction
system, it is usually two-dimensional, in terms of energy against some parameters (such as bond
lengths). PES is a landscape of the molecular geometries and molecular reaction dynamics. There
could be many energetic pathways between the reactant and the product (which both are minima).
What was obtained with GaussView in this lab was a simplification of the full PES, it is a one-
dimensional energy profile of energy against reaction coordination that represents a single reaction
progress. Transition states is the highest point on this energy-coordination curve.
The evaluation of some certain points, such as maxima, minima and saddle points, is crucial for
obtaining information of the reaction. Minima and maxima both belong to stationary points, which
mathematically are the points with the first derivatives of two variables, fx and fy , being equal to
zero, which means the surface is flat at that point. Viewed from the molecular geometry point, local
minimum is the lowest point in local area and is in a well, while maxima are at the top of a
mountain. The saddle point is a minimum on one direction while being a maximum in other
direction.
Satisfying the condition of fx =0 and fy = 0, if at that point (fxx fyy – f2xy ) > 0 and fxx > 0, then this point is
a minimum. Chemically, the reactants and the products of a reaction are both local minima hence sit
in a well. Oppositely, if at that point (fxx fyy – f2xy ) > 0 but fxx < 0, then this point is a maximum. When fx
=0 and fy = 0, if at that point (fxx fyy – f2xy ) < 0, then there’s a saddle at that point. Transition state in a
PES is the saddle point since it has the highest energy in a relatively low-energy reaction pathway, it
is a maximum in the degree of reaction coordination
In the process of modelling reaction and calculating the transition state, two computational methods
(PM6 and B3LYP/6-31G(d)) were used. PM6 is semi-empirical, it is a simplification of Hartree-Fock
theory with empirical correction. It obtains experimental data and made additional approximation to
help quicken up calculation, this operation mode makes it faster to calculate but less accurate. [1] As
a result, a further method of B3LYP/6-31G(d) was used to reoptimised the output of the previous
PM6 calculation. B3LYP/6-31G(d) is a hybrid exchange-correlation functional method with properties
from both density functional theory (DFT) and the Hartree-Fock theory. It uses 3 empirical
parameters, hence it should give more accurate results than the semi-empirical method PM6 does
although it takes a longer time to do the calculation.[2]
Using these computational methods, it is capable to calculate the energetic states of reactants,
products and the transition states, and subsequently the active barrier energy for a chemical
reaction, which will be useful to study the mechanism.

Exercise 1: Reaction of Butadiene with Ethylene [ Method: Semi-empirical PM6]
Figure 1. The scheme of reaction of butadiene and ethylene.
This reaction is a pericyclic [4+2] cycloaddition, also called Diels-Alder (DA) reaction, in which two
new C-C bonds are formed and a 6-membered ring is produced. The reactants are trans-butadiene
and ethylene as the dienophile.
Figure 2. The mechanism of reaction of butadiene and ethylene.
1.Energy
The correct structure and energy of the reactants, product and transition state were all confirmed
(paragraph in log file seen in appendix) since the threshold are converged and the right number of
imaginary frequencies were obtained (1 for transition state and 0 for the rest).
Table 1. The energies of the molecule species and the reaction.
2.IRC
The reaction is an exothermic reaction.
The reactants, TS and product all have 0
gradient, indicating that they are all
stationary points mathematically, hence
further confirms that the correct
structures of these species are obtained.
Figure 3. The IRC path and the RMS
gradient graph of the reaction.
Energy/Hartree Reaction
barrier/ kJ mol-1
Reaction energy
(ΔG)/ kJ mol-1
Butadiene 0.097764
170.0 -132.9
Ethene 0.050102
Transition State 0.212626
Cyclohexene (product) 0.100648
Product
Reactants

3.MOs Diagram
Figure 4. The MOs diagram for the formation of butadiene/ethene transition state.
As it could be seen in the MOs diagram, the HOMO and LUMO of both butadiene and ethene are
used to construct four MOs of the transition state. The HOMO of butadiene can only interact with
the LUMO of ethene and vice versa, since the occupied orbital (HOMO) with high electron density
can donate electron density into the empty orbital (LUMO).
The orbitals are only allowed to interact with orbitals with the same symmetry (symmetric-
symmetric and asymmetric-asymmetric), which is decided by the phase of lobes in one particular
MO.
Butadiene is π4 component while ethene is π2 , the new bonds are formed on the same side
(suprafacial) of each of the components hence π4 s and π2 s. According to the Woodward-Hoffmann
rule, there’s one (4q+2)s , where q = 1, and no (4r)a . This makes the sum of (4q+2) s + (4r)a an odd
number, hence the reaction is allowed. If the sum is an even number the reaction will not be
allowed, and the rules apply to any thermal pericyclic reaction.
The overlap integral of symmetry-symmetry and asymmetry-asymmetry is 1 (non-zero), and for
symmetry-asymmetry the integral would be zero since the it cancels out.

4.Bond Lengths
Figure 5. Cyclohexene
with labelled carbon
atoms. Table 2. The bond lengths of the bonds involved in the reaction.
Figure 6. The plot of the internuclear distances (bond lengths) against the reaction coordination.
The sp2 C=C bonds, C3-C1 and C6-C8, in butadiene and the C11-C14 in ethene become sp3 C-C bonds,
as a result the bonds weaken and are longer, changing from 1.333 Å to 1.501 Å. While the C-C single
bond (C1-C6) becomes double bond after the reaction, hence the bond shortens from 1.471 Å to
1.337 Å. The newly formed sp3 C-C bonds (C8-C11 and C14-C3) experience a significant distance
change since the reactants are far from each other before the reaction, and the distance shortens to
1.501 Å which is the length of a sp3 C-C bond.
Bond type Bond Length/ Å Bond Energy/kJ mol-1
sp3 C-C single bond 1.54 348
Sp2 C=C double bond 1.33 614
Table 3. The typical bond lengths and bond energies of C-C single bond and C=C double bond. [3] [4]
The Van der Waals radius of the carbon atom is 1.7 Å, which is half of the distance between two
unbonded atoms (that are attracted to each other by the Van der Waal’s Force). For all types of
bonds mentioned preciously, the internuclear distances in transition states (1.38 Å, 1.411 Å, 2.11 Å
and 1.38 Å) are shorter than twice of the Van der Waals radius (3.4 Å) which means there are
attracting interaction existing between each pair of carbons. In the meantime, the distances are
longer than the particular bond length of the later formed bonds, indicating the bonding situation in
transition states is actually partially bonded.
The formation of the new bonds C3-C14 and C6-C8 are synchronous, which means the bonds are
formed at the same time and the reaction is a one-step reaction.
Atoms Bond Length
of Reactants
TS atomic
distances
Bond Length of
Product
C3-C1 & C6-C8 1.333 1.380 1.501
C1-C6 1.471 1.411 1.337
C14-C3 & C8-C11 N/A 2.114 1.537
C11-C14 1.327 1.382 1.536

Showing in Figure 7, the vibration vector of C3 and C8, C11 and C14 is
pointed to the other carbon in their pairs at the same time in a single
vibration movement, showing that these four carbons are approaching
each other at the same time, hence the formation of the new sp 3 C-C
bonds is synchronous. Also, there is only one TS and zero intermediate
in this reaction according to Figure 3.
Figure 7. The vibration mode and the vibration vector of the imaginary
frequency of the TS.
Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole [ Method: B3LYP/6-31G(d)]
Figure 8. The scheme of reaction of cyclohexadiene and 1,3-dioxole.
The reaction is a pericyclic [4+2] cycloaddition (Diels-Alder reaction), in which two new C-C bonds
are formed between the diene and dienophile, and a new 6-membered ring will be produced. The
reactants are cyclohexadiene and 1,3-dioxole as the dienophile.
Figure 9. The mechanism of reaction of cyclohexadiene and 1,3-dioxole.
1.Energy
The correct structure and energy of the reactants, product and transition state can be confirmed by
the converged threshold (paragraph in log file and the pictures see in appendix) and the right
number of imaginary frequencies (1 for transition state and 0 for the rest).
Energy/Hartree Reaction barrier
/kJ mol-1
Reaction energy
(ΔG)/ kJ mol-1
Cyclohexadiene -233.324376
/1,3-Dioxole -267.068643
Reactants -500.393019
Endo TS -500.350532 111.5 -67.4

Product -500.418691
Exo TS -500.347595 119.2 -63.8
Product -500.417310
Table 4. The energies of the molecules and the reactions.
2.MOs Diagram
The HOMO and LUMO of the reactants
interact to form four of the MOs in the
endo TS. In this case the HOMO of the
dienophile act as the nucleophile and the
LUMO of the diene act as the electrophile,
since they have similar energy, they interact
most strongly.
The MOs of reactants can only interact with
another MO only when they have the same
symmetry.
Two kinds of interaction are observed in the
structure of endo TS, one is the primary
bonding interaction between the π/ π *c=c
orbitals of diene and dienophile, and the
other is the secondary orbitals interaction
represented by dashed line in the MOs
diagram (Figure 10).
The MOs diagram of exo TS is similar to that
of the endo TS. Orbitals with same
symmetry interact and form the MOs of the
transition state. Due to the orientation of
the dienophile pointing to the diene, there’s
no stabilising secondary orbital interactions
in exo TS. The MOs of exo TS are all slightly
higher in energy than the same ones in
endo TS (except for LUMO+1).
The order of how the HOMOs and LUMOs
of the reactants arranged is based on the
energy calculation of the reactants taken
from the IRC.
Figure 11. The MOs diagram of the
cyclohexadiene/1,3-dioxole exo TS.
Figure 10. The MOs diagram of the
cyclohexadiene/1,3-dioxole endo TS.

3.IRC
Endo reaction:
Figure 12. The IRC path and the RMS gradient graph of the endo reaction.
Exo reaction:
Figure 13. The IRC path and the RMS gradient graph of the exo reaction.
Both the reactions have negative values of ΔG, and the reactants have lower energies than the
products, hence both the DA reactions producing the endo and exo products are exothermic, and
they release energy in the process. The right-hand side (higher in energy) of the reaction coordinate
represents the reactants and the left-hand side (lower in energy) represents the products.
In the RMS gradient graphs, it can be seen clearly that reactants (minima), TSs (maxima) and
products (minima) have the gradient of 0, indicating that they are stationary points mathematically.
The continuous IRC path (Figure 12 and Figure 13) have the correct energy levels of reactant, TS and
product. These all testify the correct energies and structures of these species.
Reactants
Reactants
Product
Product

4. Secondary Interactions
By comparing the reaction barriers of these two reactions, it takes more energy to overcome the exo
transition state barrier than that of endo, hence the endo product would form faster in the reaction.
As a result, the endo product is kinetically favourable. This is because of the secondary orbital
interactions between the nOp orbitals and the double bonds orbitals (shown in Figure 14 and Figure
15) which stabilises the endo transition state and lower the energy. It can be seen in Table 4 that the
endo product (-67.4 kJ mol-1 ) is deeper in energy than the exo product (-63.8 kJ mol-1 ), which makes
the endo product the thermal product, and this is due to the secondary orbital interactions which
stabilises the endo product as well
The oxygen in 1,3-dioxole is electron-donating, making the dienophile electron-rich. As a result, the
favourable cycloaddition between the LUMO of cyclohexadiene and the HOMO of 1,3-dioxole
undergoes since now the energy of LUMOdiene and HOMOdienophile matches and they interact most
strongly (shown in Figure 16), producing the largest splitting energy and the lowest energy of HOMO
of TS. Hence the reaction is an inverse demand DA reaction.
Exercise 3: Diels-Alder vs Cheletropic [ Method: Semi-empirical PM6]
Figure 17. The scheme of two types of reactions of ortho-xylylene and SO2 .
Figure 18. The mechanism of two reactions of ortho-xylylene and SO2 .
Figure 14. The interactions in the
HOMO of endo TS by ChemDraw.
Figure 15. The interactions in the
HOMO of endo TS by GaussView.
Figure 16. The MOs of reactants.

The Diels-Alder (DA) reaction involves the diene in ortho-xylylene and a S=O bond in SO2 as
dienophile, after the [4+2] cycloaddition, a new 2-ring polycyclic product is formed. Exo and endo
products are observed, with S=O bond pointing outward in the exo product and pointing towards
the phenyl ring in the endo product.
1.Energy
Energy/Hartree Reaction barrier
/kJ mol-1
Reaction energy
(ΔG)/ kJ mol-1
Ortho-xylylene 0.178083
/SO2 -0.118614
Reactants 0.059469
DA-Endo TS 0.090559 81.6 -99.1
Product 0.021700
DA-Exo TS 0.092077 85.6 -99.6
Product 0.021453
Cheletropic TS 0.099061 103.9 --156.1
Product -0.000003
Table 5. The energies of the molecules and the reactions.
The reaction barrier of the endo reaction (81.6 kJ mol-1 ) is lower than that of
the exo reaction (85.6 kJ mol-1 ). For the small difference between the endo and
the exo reaction barrier, it can be due to the weak secondary orbital
interactions between nOp and the double bonds orbitals. Cheletropic has higher
activation energy (103.1 kJ mol-1 ), making the DA product the kinetic product.
Figure 19. The secondary orbital interactions in the endo TS.
However, the cheletropic product is much deeper in energy (-0.00003 Hartree) leading to a more
negative and exothermic reaction energy, hence the cheletropic product is thermodynamically
favourable. The cheletropic is more stable because of the existence of the stable 5-membered ring
in the bicyclic system.[5] Overall, the reaction route preferred would be the cheletropic reaction since
the incapacity of SO2 towards the DA reaction would be dominated by the instability of the DA
products instead of the reaction barriers.[6]
Figure 20. The energy profile of endo and exo DA reaction as well as cheletropic reaction.

2.IRC
Endo DA reaction:
Figure 21. The IRC path and the RMS gradient graph of the endo DA reaction.
Exo DA reaction:
Figure 22. The IRC path and the RMS gradient graph of the exo DA reaction.
Reactants
Product
Reactants
Product

Cheletropic reaction:
Figure 23. The IRC path and the RMS gradient graph of the cheletropic reaction.
The 0 gradient, the continuous IRC path and the energy levels of the reactants, the TS and the
product indicate the correct structures and energies of these three species each of three reactions.
3.Bond Lengths
Figure 26. The bond lengths of the 6-ring.
Reactants
Product
O-xylylene Product
Figure 24. O-xylylene with labelled
carbons atoms in the 6-membered ring.
Figure 25. The reactants (left) and the
product (right)of the DA reactions.

There’s a significant change of the bonding in the ring of o-xylylene even though there is no bond
breaking or making during the reaction. The o-xylylene is unstable because of the electron-rich
HOMO of the double bonds which are also nucleophilic, tend to react with electrophile. And the ring
tends to obtain full aromaticity of the ring. After the reactions, the 6-membered ring becomes stable
since now it is aromatic, and all the bonds are converged (shown in the right of Figure 23).
As it can be seen in Figure 24, bond C2-C3, C4-C5, C6-C1 and C3-C4, that are sp3 single bond before,
shorten their length after the reaction from 1.46~1.49 Å to about 1.4 Å. The C1-C2 and C5-C6 sp2
double bonds slightly increase the bond length from 1.35 Å to about 1.4 Å as well. The value 1.4 Å
indicates the formation of a delocalised system in the product since it between the sp3 C-C bond’s
typical length (1.54 Å) and that of sp2 C=C bond (1.33 Å). [3] [4]
Due to the ring strain (created by the two rings in products) weakening the C3-C4 bond, the bond is
the longest one no matter in xylylene or in the product.
Conclusion
The lab investigates the transition states and the reactivity of some Diels-Alder reactions, for the
ones with several possible mechanisms, it also looks into the energy differences and the preferability
of those mechanisms. By running the optimising calculation and IRC calculation on the TS with two
computational methods B3LYP/6-31G(d) and PM6, the correct structure and energy of TS could be
confirmed by the energy levels and a continuous IRC path with correct curvature.
It is found that for the asymmetrical dienophile with electron-donating groups, the endo mechanism
of the DA reaction has lower activation energy due to the stabilising secondary orbital interactions,
hence endo mechanism will be more preferable kinetically. Reaction of o-xylylene and SO2 has
another pericyclic mechanism called cheletropic reaction besides the DA. Calculation shows that the
DA products with lower reaction barrier are the kinetic products, but cheletropic product having
lower reaction energy (ΔG) are thermodynamically favourable.
Further investigation can dig into other pericyclic reactions, such as sigmatropic rearrangement and
electrocyclic reactions, instead of only focusing on cycloaddition. Ring opening and ring closure are
involved. The breaking and the formation of bonds in these processes differ from that of
cycloaddition and it would be crucial to understand the bonds changing process when looking at the
mechanisms. Via the calculation, the ring-like transition states and the changing of bonds can be
studied.
The methods B3LYP/6-31G(d) and PM6 give difference values of energies of the molecules and of
the MOs. Since PM6 is based on both experimental data and approximation, whilst B3LYP/6-31G(d)
PM6 calculation runs much faster whilst B3LYP/6-31G(d) gives more accurate results. In future
investigation, B3LYP/6-31G(d) is preferred method if time allows.
Reference
[1] The University of Munchen, https://www.cup.uni-
muenchen.de/ch/compchem/energy/semi1.html , (accessed December 2019).
[2] A.D. Becke, J. Chem. Phys. 98 (2): 1372–1377.