Rep:Mod3:em207

2009-12-16T09:31:20Z

Em207: /* Deils Alder reaction between Cis Butadiene and Ethene */

Edward Moore Module 3
=Part 1 Cope rearangement=
The cope rearangement is a very interesting reaction in which a [3,3] spectroscopic shif occours. In this section the reacactants will first be investigated followed by the transition structures.

==Optimising Reactants and Products==
The calculation was set up with the input file coded as
<pre>%mem=500MB
%chk=C:\Documents and Settings\em207\My Documents\Computing labs\Module 3\Cope Rearangement\Input\1_5_hexadiene_opt_1_anit.chk
# opt hf/3-21g geom=connectivity

1,5-hexadiene opt 1 anti

0 1</pre>

This gave the following output [https://www.ch.ic.ac.uk/wiki/images/3/34/1%2C5-HEXADIENE_OPT_1_ANIT.LOG log file] and [https://www.ch.imperial.ac.uk/wiki/images/7/74/1_5_HEXADIENE_ANTI_OPT.mol structure]. From which it was noted that the energy of the conformation was -231.69260236au amd the point group was C<sub>2</sub>.

The same process was repeated for the Gauch conformer and this gave the followoing [https://www.ch.ic.ac.uk/wiki/images/a/a7/1%2C5-HEXADIENE_OPT_1_GAUCH.LOG log output file] and [https://www.ch.imperial.ac.uk/wiki/images/2/23/1_5_HEXADIENE_GAUCH.mol structure] from which the energy was said to be -231.69166702au and the point group was C<sub>2</sub>. From the two calculation it can be seen that the gauch form is more stable than the anti periplanar forn, and from the literature it can be seen that this is, indead the most stable form, as this will minimise the steric interactions between the sp<sup>3</sup> carbon and sp<sup>2</sup> carbon centers. The gauch form was further manipulated to minimise the strucutres energy further giving the following [https://www.ch.ic.ac.uk/wiki/images/f/f9/1%2C5-HEXADIENE_OPT_1_GAUCH_2.LOG output log file] and [https://www.ch.imperial.ac.uk/wiki/images/b/bc/1_5_HEXADIENE_GAUCH_2.mol structure] that the ouput-energy and point group of -231.68771614au and C<sub>2</sub> respectively which was predicted to be the lowest energy conformation of the 1,5- hexadiene. This was confirmed to be the lowest energy confomer as wehen compared to [http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Apendix1] the energy obtained was verry simiar.

Next the anti2 form was drawn and the resultant [https://www.ch.ic.ac.uk/wiki/images/9/96/Anti_2_intial.log log file examined]. The energy output from this section was -231.69253529 and the point group was odemtofoed as C<sub>i</sub>. The resulting structure from this was then reoptimised using the higher basis set of B3LYP/6-31G(d) giving the following [https://www.ch.ic.ac.uk/wiki/images/e/e8/Anti_2_second_opt.log output file]. The geometries of the structures were compared, see table bellow:

{| class="wikitable" border="1"
|+ B3LYP/6-31G(d) vs HF/3-21G
! Perameter !! B3LYP/6-31G(d)!!HF/3-21G
|-
| Picture||[[Image:Anti_2_final.jpg|thumb|]]||[[Image:Anti_2_inital.jpg|thumb|]]
|-
| C1-C2-C3 and C4-c5-c6/<sup>o</sup>||125.287 ||124.808
|-
| C2-C3-C4 and C3-C4-C5/<sup>o</sup>||112.672||111.358
|-
| C1=C2 and C5=C6/angstroms||1.3352||1.131615
|-
| C2-C3 and C4-C5/angstroms||1.50419||1.50886
|-
| C3-C4/angstroms||1.54814||1.55273
|-
|}

It can be said therefore that there is a significant change in the both the bond angles and bond lengths when the caluation is shifted from the HF/3-21G to the B3LYP/6-31G* level. However it can be said that the time taken for the calcualtion must be considerd as with the increase in accuracy in the basis set (here there is an increase from 47 seconds to 6 minutes 8.0 seconds). It can be said therefore for larger moelcules there will have to be a trade off between accuracy and computation time.

The following data was abstracted from the [https://www.ch.ic.ac.uk/wiki/images/5/57/ANTI_2_FREQUENCY.LOG log file] of the vibration analysis at the basis set,nb no impaginary frequencies were detected and therefore this is a correct optimisation:

{| class="wikitable" border="1"
|+
! Energy contribution!!Energy Value
|-
| Sum of electronic and zero-point Energies (E=Eelec + ZPE at 0K)||-234.469212
|-
| Sum of electronic and thermal Energiese (E=E+Evib+Erot+Etrans 298.15 K and 1 atm)||-234.461856
|-
| Sum of electronic and thermal Enthalpies (H=E+RT)||-234.460912
|-
| Sum of electronic and thermal Free Energies(G=H-TS)||-234.500821
|}

The table above gives the values for the thermochemistry for the anti-2 confomer of the 1,5 hexadiene at the B3LYP/6-31G(*) basis set. These values were caluclated at 298.15K. It is predicted that at 0K the energy would be higher, ie less negative than at 298K, ie the confomer is less stable at the higher temperature as more energy is required to overcome the higher vibrational, rotational and translational energies for the anti-2 conformation at 0K.

==Optimizing the "Chair" and "Boat" Transition Structures==
In this section the chair and boat transition strucutres were modeled by several differnt methods

===Chair===
In this section the chair transition strucutre was modeled by 3 seperatre methods, the TS (Berny, the redundant cordinate method and then using the resultant geometry the reaction pathway was mapped using the IRC method. This gave the results bellow whilst using the Hartree Fock method and the 3-21G basis set. This gave the results bellow from the output files for the [https://www.ch.ic.ac.uk/wiki/images/f/f5/Em207_TS_OPT_AND_FREQUENCY.LOG TS (Berny)] and [https://www.ch.ic.ac.uk/wiki/images/a/a4/Em207_TS_CHAIR_FROZON_CORDINATE.LOG Frozon Cordinate method].

{| class="wikitable" border="1"
|+
! Perameter!! Optimistion to TS (Berny)!!Frozon Cordinate method
|-
| Bond forming bond length/Å||2.02052||2.02012
|-
| Bond breaking bond length/Å||2.02053||2.02092
|-
| Deils Alder reaction frequency/cm<sup>-1</sup>||-817.91||-817.91
|-
| Electronic Energies/au||-231.61932247||-231.61932247
|-
| Structures||
<jmol><jmolApplet><title>TsBerny</title><color>white</color>
<size>200</size><script>zoom 100; cpk -20;</script>
<uploadedFileContents>Em207_Chair_ts_Berny.mol</uploadedFileContents>
</jmolApplet></jmol>

||
<jmol><jmolApplet><title>Frozon Cordinate</title><color>white</color>
<size>200</size><script>zoom 100; cpk -20;</script>
<uploadedFileContents>Em207_Chair_ts_frozon_corodinate.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

It can be seen from the above results that the TS Berny is more accurate than the frozon cordinate method as the bond lengths of the forming and breaking bonds are of a more simialr value in the TS Berny than the frozon coridinate method. It can therefore be sugested that the TS Berny method be used for smaller moleucles or for where a higher degree of accuracy is required, the oppisit may therefore be said of the forzon cordinate method.

====IRC====
In this section the previously optimised geometry was taken and submitted to an IRC calculation in the forwards direction for the chair confomer to predict the reaction pathway. This gave the following [https://www.ch.ic.ac.uk/wiki/images/7/75/EM207_CHAIR_IRC_2.LOG log file] for a 50 point IRC plot with the force constants calculated for every point. Which gave the cordinate bellow from which it can be seen that the inital gemotry, in the forward sense, has reacted to go to a minimum and therefore the products. However it can be seen that the product is acutally the gauch 2 and not the formally lowest energy confomer gauch 3, this could be due to the fact that the gauce 2 is the first local minimum allong the reaction cordinate.

{| class="wikitable" border="1"
|+
! IRC reaction curve !!Intermediate!!Product
|-
| [[Image:EM207_IRC_curves_chair.jpg|thumb]]||[[Image:Em207_IRC_intermediate.jpg|thumb]]||[[Image:Em207_IRC_product.jpg|thumb]]
|}

===Boat===
In this section the transition structure was modeled in two seperate ways using TS(QST2).

====TS(QST2)====
In this section TS(QTS2) was used to obtain the itermediate. It should be noted that the calulation required the starting materials and poducts, in which the atoms had to be labeled initially in the reactants and then in their correct positions after the reaction had occoured, in order to do this the following method was emploied number the atoms, the cyclic sceltal structure was numbered first followed by the substituent atoms ie the carbons were numbered first and then the hydrogens. It should be noted that if the atoms are not labled correctly, ie that the atoms as numbered in their starting positions should be given the same number in the starting product. This gave the resulting structure and the infomation as extracted from the [https://www.ch.ic.ac.uk/wiki/images/c/cb/EM207_CHAIR_OPT_QST2.LOG log file].

{| class="wikitable" border="1"
|+
! Perameter!! Value
|-
| Vibration frequency/cm<sup>-1</sup>||-840.21
|-
| Forming bond/Å||2.12840
|-
| Breaking Bond/Å||2.14068
|-
| Electronic energy/au||-231.60280319
|-
| Immage||[[Image:Em207_TS_(QST2).JPG|thumb|]]
|}

It can be seen from the above results that the chair structure is at a higher energy than the boat intermediate ie is more positive. It can also be seen that there is a significant difference between the forming and breaking bond, 0.03Å. It can also be seen that the imaginary frequency does represent the reaction and therefore represents the rearangement occouring.

==Activation Energy Calculations==
In this section the activation energies of the chair and boat confomers for the cope rearangement were calulated at the B3LYP/6-31G* level of theory. This gave the following output files for the chair and boat confomers. This was done by taking the sum of electronic and thermal free energies and multiplying this by 627.509 to get the energy of intermediate geometry in kcal mol<sup>-1</sup>, which was then subtracted from the starting materials energy to give the acitavation energy in kcal mol<sup>-1</sup>.

{| class="wikitable" border="1"
|+ Activation energy calculations at 298.15K and 1 atm
! Properites!!Chair!!Boat
|-
| Sum of electronic and thermal free energies/hartrees||-234.443813||-234.431768
|-
| Acitvation Energy,ΔE/kcal mol<sup>-1</sup>||35.77||43.33
|-
| Acitvation Energy,ΔE/kcal mol<sup>-1</sup> literature values|| 33.17 || 41.32
|}

From the above table it can be seen that the acitavtion energy for the boat is lower than the chair as would be expected, due to the difference in the steric repulsion forces in the transition states. However it may be said in comparison to the literature values from [http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Results_Table Appendix 2], that there is a small error for both the chair and the boat confomers in comparison to the experimental values. This may be due to the transition sturctures not being optimised to the absolute energy of the transition structure. However when the time availabe was considered against the accuracy it may be said that this result is an acceptable one.

=Part 2 Deils Alder Reactions=
In this section the selectivity and reaction mechanism of the deils alder reaction was studdied.

==Cis Butadiene==
In this section a semi-imperical AM1 calulation was carried out and the HOMO and LUMO of Cis butadiene studdied. This gave the following [https://www.ch.ic.ac.uk/wiki/images/7/77/EM207_CIS_BUTADIENE_OPT_1.LOG log file] and resulted in the HOMO and LUMO as picuted bellow.

{| class="wikitable"
|+
! Optimised Structure||HOMO!!LUMO
|-
| [[Image:EM207_Cis_butadiene.jpg|thumb]]||[[Image:EM207_Cis_butadiene_homo.jpg|thumb]]||[[Image:EM207_Cis_butadiene_lumo.jpg|thumb]]
|}

It can be seen from the above pictures that the HOMO is asymetric and the LUMO is symetric with regard to the plane as defined in the scirpt (perpendicular to the C2-C3 bond.

==Deils Alder reaction between Cis Butadiene and Ethene==
In this section the transition state geometry was isolated using TS (Berny) at the HF 3-21G level and then submiting this to IRC calualtion in both the forwards and reverse direction allong with a frequency analysis to proove that the transition state geometry obtained was indead the transition state. This optimisation and frequency analysis resulted in the follwoing [https://www.ch.ic.ac.uk/wiki/images/5/5e/EM207_DA_TS_OPT.LOG log file] and the transition state strucutre and HOMO and LUMO as shown bellow. It can be said in this case the vibration analysis resulted in one imagionary frequency output again as shown bellow which was characteristic of the concerted deils alder reaction that was occouring here. The IRC calculation resulted in the following [https://www.ch.ic.ac.uk/wiki/index.php/Image:EM207_IRC_DA_1.out output file] with the IRC plot shown bellow

{| class="wikitable" border="1"
|+
! Property !! TS Geometry!!TS HOMO!!TS LUMO!!Imagionary Vibration!!IRC Plot
|-
| Immage||
<jmol><jmolApplet><title>Part_2_intermediate</title><color>white</color>
<size>150</size><script>zoom 100; cpk -20;</script>
<uploadedFileContents>Em207_Part_2_TS.mol</uploadedFileContents>
</jmolApplet></jmol>
||[[Image:EM207_DA_intermediate_part_2_homo.JPG|thumb|widthpx| ]]||[[Image:EM207_DA_intermediate_part_2_lumo.JPG|thumb|widthpx| ]]||[[Image:EM207_DA_intermediate_part_2.JPG|thumb|widthpx| ]]||[[Image:EM207_IRC_Graph_part_2.jpg|thumb|widthpx| ]]
|}

From the above diagrams several conclusions can be made, firstly that the following geometries apply:

{| class="wikitable" border="1"
|+
! Gemetry variable !! heading
|-
| Partly formed σ distances||2.12
|-
| All c=c bond lengths|| 1.38
|}
From the above table it can be seen that the partly formed σ bonds not of typical C<sub>sp<sup>3</sup></sub>-C<sub>sp<sup>3</sup></sub> bond lengths (1.54Å<ref name="S. J. Stuart, M. T. Knippenberg, O. Kum and P. S. Krstic, Phys. Scr., 2006, T124, 58 - 64">S. J. Stuart, M. T. Knippenberg, O. Kum and P. S. Krstic, Phys. Scr., 2006, T124, 58 - 64</ref>). It can also be said that the psudo σ bond is not within the range of the Van der Waals radius of a C atom (1.7Å<ref name="S. J. Stuart, M. T. Knippenberg, O. Kum and P. S. Krstic, Phys. Scr., 2006, T124, 58 - 64">S. J. Stuart, M. T. Knippenberg, O. Kum and P. S. Krstic, Phys. Scr., 2006, T124, 58 - 64</ref>). Therefore implying that this is not a fully fledged σ bonds or are there Vand der Vaal interactions occouring but instead overlap between the molecular orbitals of ethene and the cis dibutadiene respectively.

Secondly it may be said that the imagiery frequency does imply that a syncroneous process is occouring, however on studdying the vibrations more carfully the first real vibration involves a rotation of the ethene in the moeluclar plane and thus implying a degree of asyncorarity about the process, it is sujested that were calualtions run at a higher degree of accuracy that the result would be an imagery frequency at a lower level, ie more positive which would incorperate the exisitng imagionary frequency and the first real frequency.

Thirdly it can be said that the HOMO is anitsymetric and the LUMO is symetric, this is as the same with the ethene and the cis butadiene, ie emphasising the fact that for the orbitals to overlap they must have the same symetry properties and therefore the reaction is controlled by the HOMO of the Cis butadiene overlaping with the LUMO of the ethene (which also have the better match in orbital energies).

Finaly it can be seen fromm the IRC calulation that the reaction that has occoured is an exothermic one and the intermidiate identified was indead the intermediate for the given process.

Rep:Mod3:em207

2009-12-15T21:53:47Z

Em207: /* Optimizing the Chair and Boat Transition Structures */