Diels Alder Cyclo-addition

Here were will attempt to model the TS and the reactions energies of a massively important reaction in the world of chemistry.

Starting Simple

Here we are going to take on molecule of ethene and one of cis-butydiene, and using a semi-emperical method with the AM! basis set, we shall model the molecular orbitals of the two in the hopes of better understanding the HOMO/LUMO orbitals and how they might interact.

First using the same method and basis set, we must optimise the molecule.

Diene Optimisation
File Name	PG_DiENE_HE_AM1_OP
File Type	.log
Calculation Type	FOPT
Calculation Method	RAM1
Basis Set	ZDO
Charge	0
Spin	Singlet
E(RAM1)	0.04879717 a.u.
RMS Gradient Norm	0.00000068 a.u.
Imaginary Freq
Dipole Moment	0.0415 Debye
Point Group	C2V
Job cpu time:	0 days 0 hours 0 minutes 18.0 seconds.
File:	File:PG DiENE HE AM1 OP.log
Item Value Threshold Converged? Maximum Force 0.000001 0.000015 YES RMS Force 0.000000 0.000010 YES Maximum Displacement 0.000010 0.000060 YES RMS Displacement 0.000004 0.000040 YES Predicted change in Energy=-1.294434D-11 Optimization completed. -- Stationary point found.

Energy Calculation. File:PG DiENE HE AM1 EN2.log

caption
Orbital	Ethene	Butadiene
HOMO
LUMO

From the diagrams We should expect the LUMO of the Diene to interact with the HOMO of the Ethene (both of which are symmetric in respect to the plane perpendicular to their central bond) , and the HOMO with the LUMO therefor both can be allowed transitions (antisymmetric with respect to plane).

Transition state, Method 1

A guess was made of the Transition state by taking the gaussian template structure of bicyclo-2,2,2-octane, removing one of the -CH₂-CH₂- units,

Optimisation of Ene- Diene- reaction (AM1)
File Name	PG_RXN_T3_AM1_OP_TSb4
File Type	.log
Calculation Type	FREQ
Calculation Method	RAM1
Basis Set	ZDO
Charge	0
Spin	Singlet
E(RAM1)	0.11165465
RMS Gradient Norm	0.00000111
Imaginary Freq	1
Dipole Moment	0.5605
Point Group	C1
Job cpu time:	0 days 0 hours 0 minutes 54.1 seconds.
File:	File:PG RXN T3 AM1 OP TSb4.log
Item Value Threshold Converged? Maximum Force 0.000003 0.000450 YES RMS Force 0.000001 0.000300 YES Maximum Displacement 0.000144 0.001800 YES RMS Displacement 0.000038 0.001200 YES Predicted change in Energy=-4.160235D-10 Optimization completed. -- Stationary point found.

In the Orbital Diagram of the transition state we see that the interaction seems to be for the LUMO of Ethene and the HOMO of the Diene, this makes sense when remembering that stability increases as conjugation increases, therefor the HOMO of Diene will have a lower energy the the HOMO of Ethene.

Calculating with a higher basis set

Issues arose when trying to run the above using DFT/6-31Gd, as what would often happen is that either only a single bond would form between the two molecules, or the Ethene would completely reorientate to form some bizzar interaction with just one of the double bonds of the Diene-

The Decision was made to run the calculation using QTS2 as it allows us to define the product, therefore forcing the two desired bonds to be formed, in a concerted manner in the transition state.

Reoptimisation of Transition state (**DTF/6-31Gd**)
File Name	PG_RXN_T2_OP_qts_log_87530
File Type	.log
Calculation Type	FREQ
Calculation Method	RB3LYP
Basis Set	6-31G(d)
Charge	0
Spin	Singlet
E(RB3LYP)	-234.54389656 a.u.
RMS Gradient Norm	0.00000068 a.u.
Imaginary Freq	1
Dipole Moment	0.3943 Debye
Point Group	C1
Job cpu time:	0 days 0 hours 4 minutes 55.2 seconds.
File:	File:PG RXN T2 OP qts.log
Item Value Threshold Converged? Maximum Force 0.000001 0.000450 YES RMS Force 0.000000 0.000300 YES Maximum Displacement 0.000032 0.001800 YES RMS Displacement 0.000008 0.001200 YES Predicted change in Energy=-3.907341D-11 Optimization completed. -- Stationary point found.
Energy File:	File:PG RXN T2 OP qts EN.log File:PG RXN T2 OP qts EN.fchk
Frequency at 0K	File:PG RXN T2 OP qts FR0k.log
Frequency at 298K	File:PG RXN T2 OP qts FR298k.log

Lengths
Parameter	Distance
Van der waals radius of Carbon	1.7 Å
C--C Bond length	1.54 Å
C==C Bond Length	1.34 Å
TS C C distance	2.27 Å

What we can see with the above information is that the partially formed bond is much to long to be considered a formal bond (comparing it to the C--C and C==C bond lengths) but the fact that the distance is less then twice the van der waals radius of carbon we can conclude that there is some kind of interaction taking place between the fragments.

Here we see that for the Imaginary frequency, that corresponds to the vibration associated to the formation of the bonds in the reaction, both of the bonds are being formed at the same time. This agrees with the accepted idea that the reaction is a pericyclic process.

The lowest positive frequency is just a vibration of the structure and not in itself associated with bond forming, if anything the motion would act to disrupt the bond formation as the twisting motion would break the symmetry of the process.

Cyclohexa-1,3-diene reacting with maleic anhydride

Seen above is the reaction between Cyclohexadiene and maleic anhydride. By using computation methods we hope to be able to compare the relitive stabilities between the endo and exo conformers of the reaction product.

All the calculations have first been run at HF/3-21G and then reoptimised at DTF/6-31G* all properties disscussed, unless otherwise stated, will be from the final optimisation (6-31G*)

Transition states

Due to issues encountered in earlier sections, It was decided to use the QTS2 method to calculate the TS.

Optimisation of reaction Transition states.
	Exo	Endo

File Name	PG_ExoRxn_FROP_DFT631GdT3_log_87649	PG_EndoRxn_FROP_DFT631Gd_log_87564
File Type	.log	.log
Calculation Type	FREQ	FREQ
Calculation Method	RB3LYP	RB3LYP
Basis Set	6-31G(d)	6-31G(d)
Charge	0	0
Spin	Singlet	Singlet
E(RB3LYP)	-612.67931096 a.u.	-612.68339677 a.u.
RMS Gradient Norm	0.00000166 a.u.	0.00000435 a.u.
Imaginary Freq	1	1
Dipole Moment	5.5502 Debye	6.1143 Debye
Point Group	C1	C1
Job cpu time:	0 hours 25 minutes 37.5 seconds.	0 hours 26 minutes 2.5 seconds.
File:	File:PG ExoRxn FROP 631GdT3.log	File:PG EndoRxn FROP 631Gd.log

caption
	Exo	Endo
Reactant
TS
Prod

Possible strain seen in the endo product

Table of lengths and distances
perameter	Length ( Å)
Van der waals radius of Hydrogen	1.2
Van der waals radius of Carbon	1.7
Distance between H C	2.63

What we see when looking at the distance between the Hydrogen and Carbon (indicated in the picture to the right) is that distance between the two atoms is less than the sum of their van der waals radii. While the degree to which they interact would be hard to determine as, especially for a carbonyl carbon, there will be effects on the van der waals radius by neighboring atoms.

caption
	B3LYP/6-31G*
	Electronic energy	Sum of electronic and zero-point energies	Sum of electronic and thermal energies
		at 0 K	at 298.15 K
Maleic anhydride	-379.28954470	-379.233657	-231.445306
Cyclohexadiene	-233.41893632	-233.296105	-379.228473
ExoTS	-612.67931096	-612.498013	-612.487662
EndoTS	-612.68339677	-612.502141	-612.491787
EndoProd	-612.75578550	-231.539540	-231.532566
EndoProd	-612.75829021	-231.539540	-231.532566