ChemWiki - User contributions [en]

Rep:Mod:giggidy

2010-03-29T14:52:27Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-31G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-31G* level, and so the QST2 calculation was also carried out at the B3LYP/6-31G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

===Determination of Activation Energies===

When calculating the activation energies, the most stable conformer ''gauche-3'' will be used as a reference.

{| class="wikitable" border="1"
|+ caption
! Molecule !! Energy/ a.u. !! Activation Energy/ kcalmol-1
|-
| '''''gauche-3''''' || -234.61133 || -
|-
| '''Chair''' || -234.55698 || 34.10
|-
| '''Boat''' || -232.87648 || 1088.63
|}

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T14:51:57Z

Dsb07: /* Determination of Activation Energies */

Rep:Mod:giggidy

2010-03-29T14:44:11Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-31G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-31G* level, and so the QST2 calculation was also carried out at the B3LYP/6-31G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

===Determination of Activation Energies===

{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| cell || cell
|-
| cell || cell
|}

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T13:42:17Z

Dsb07: /* Optimizing the Boat Transition Structure */

Rep:Mod:giggidy

2010-03-29T13:41:40Z

Dsb07: /* Optimization of ''Anti-2'' at a Higher Level */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-31G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-31G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T13:41:10Z

Dsb07: /* Vibrational Analysis of ''Anti-2'' */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-31G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-31G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T13:40:34Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-31G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:59:37Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:59:06Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state. The two images nearly match eachother - if conformer image matches the mirror-image of the transition state image. This suggests that they are describing the breaking/formation of opposite bonds i.e. whilst one breaks/forms, the other forms/breaks.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:55:43Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:55:17Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]
The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:54:34Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:53:47Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]

IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:53:05Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]
The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.

[[image:Chair_ts_irc_picture.gif|250px|left]][[image:Gauche_2_irc_picture.gif|250px|right]]
IRC (left) was used to confirm that the correct conformer had been assigned to the chair transition state.

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]

==References and Citations==

<references />

File:Gauche 2 irc picture.gif

2010-03-29T12:50:37Z

Dsb07:

File:Chair ts irc picture.gif

2010-03-29T12:48:56Z

Dsb07:

Rep:Mod:giggidy

2010-03-29T12:27:43Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:27:20Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|250px|left]][[Image:Gauche1_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:26:54Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|200px|left]][[Image:Gauche1_picture.gif|200px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T12:26:31Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

The boat transition state (left) corresponds to the ''gauche-1'' conformer (right) from earlier.

[[Image:Boat_ts_picture.gif|left]][[Image:Gauche1_picture.gif|right]]

==References and Citations==

<references />

File:Gauche1 picture.gif

2010-03-29T12:25:57Z

Dsb07:

File:Boat ts picture.gif

2010-03-29T12:25:06Z

Dsb07:

Rep:Mod:giggidy

2010-03-29T12:01:50Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The <jmol>
<jmolAppletButton>
<title>Boat</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Boat_qst2_b3lyp631g1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

File:Boat qst2 b3lyp631g1.txt

2010-03-29T12:01:33Z

Dsb07:

Rep:Mod:giggidy

2010-03-29T11:52:11Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer. The ''anti-2'' conformer was initially optimized at the B3LYP/6-21G* level, and so the QST2 calculation was also carried out at the B3LYP/6-21G* level.

The Boat transition structure has one imaginary frequency at 531 cm-1, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:13:01Z

Dsb07: /* Optimizing the Boat Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

The boat transition structure was optimized using the QST2 method using the Ci ''anti-2'' conformer.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:10:33Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

===Optimizing the Boat Transition Structure===

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:08:54Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:08:34Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:08:06Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:07:52Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:07:27Z

Dsb07: /* The Transition State */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:07:03Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer (on the right) from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T11:06:08Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

The Chair transition state (on the left) clearly corresponds to the ''gauche2'' conformer from earlier.
[[Image:Chair_ts_picture.gif|250px|left]][[Image:Gauche2_picture.gif|250px|right]]

==References and Citations==

<references />

File:Gauche2 picture.gif

2010-03-29T11:04:18Z

Dsb07:

File:Chair ts picture.gif

2010-03-29T11:03:34Z

Dsb07:

Rep:Mod:giggidy

2010-03-29T10:50:59Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol> calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:49:50Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The calculation yields one imaginary frequency at <jmol>
<jmolAppletButton>
<title>818 cm-1</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:44:38Z

Dsb07: /* Vibrational Analysis of ''Anti-2'' */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ ''Table 6 - Energies''
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The Berny calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:44:29Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ ''Table 7 - Optimization of the Chair TS, at the HF/3-21G level, using two different methods''
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The Berny calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:43:44Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the following two methods:

{| class="wikitable" border="1"
|+ Optimization of the Chair TS, at the HF/3-21G level, using two different methods
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

The Berny calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:38:19Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

{| class="wikitable" border="1"
|+ Optimization of the Chair TS, at the HF/3-21G level, using two different methods
! Method !! Bond-forming~bond-breaking lengths/ ''Å''
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24
|}

====Optimization to a Transition State (Berny)====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The Berny calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

Bond forming/bond breaking lengths: 2.02 Å, 2.02 Å.

====Frozen Coordinate Method====

Bond forming/bond breaking lengths = 2.23 Å, 2.24 Å.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:32:28Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

{| class="wikitable" border="1"
|+ Optimization of the Chair TS, at the HF/3-21G level, using two different methods
! Method !! Bond-forming~bond-breaking lengths/ ''Å'' !! CPU Time
|-
| <jmol>
<jmolAppletButton>
<title>Berny</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.02, 2.02 || cell
|-
| <jmol>
<jmolAppletButton>
<title>Frozen Coordinate</title><color>black</color><size>200</size>
<uploadedFileContents>Chair_ts_guess_calc_frozen.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || 2.23, 2.24 || cell
|}

====Optimization to a Transition State (Berny)====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

Bond forming/bond breaking lengths: 2.02 Å, 2.02 Å.

====Frozen Coordinate Method====

Bond forming/bond breaking lengths = 2.23 Å, 2.24 Å.

==References and Citations==

<references />

File:Chair ts guess calc frozen.mol

2010-03-29T10:32:12Z

Dsb07:

File:Chair ts guess calc.mol

2010-03-29T10:30:16Z

Dsb07:

Rep:Mod:giggidy

2010-03-29T10:17:16Z

Dsb07: /* Optimization to a Transition State (Berny) */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

====Optimization to a Transition State (Berny)====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

Bond forming/bond breaking lengths: 2.02 Å, 2.02 Å.

====Frozen Coordinate Method====

Bond forming/bond breaking lengths = 2.23 Å, 2.24 Å.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:16:09Z

Dsb07: /* Frozen Coordinate Method */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

====Optimization to a Transition State (Berny)====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Frozen Coordinate Method====

Bond forming/bond breaking lengths = 2.23 Å, 2.24 Å.

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-29T10:12:42Z

Dsb07: /* 1 */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

====Optimization to a Transition State (Berny)====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Frozen Coordinate Method====

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-28T21:07:45Z

Dsb07: /* Optimizing the Chair Transition Structure */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

====1====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

====Frozen Coordinate Method====

==References and Citations==

<references />

Rep:Mod:giggidy

2010-03-28T20:46:44Z

Dsb07: /* 1 */

=The Transition State=

A [http://en.wikipedia.org/wiki/Transition_state transition state]

==The Cope Rearrangement==

[[Image:Reaction_mechanism.gif|left]]
The mechanism of the Cope rearrangement, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene, is believed to involve a chairlike transition state of C2h symmetry<ref>Viktor N. Staroverov; Ernest R. Davidson ''J. Am. Chem. Soc.'' '''2000''', ''122'', 186-187</ref>.
The mechanisms of the Cope and Claisen reactions remain a source of controversy in spite of having being probed repeatedly by experimental<ref>Cope, A. C.; Hardy, E. M. ''J. Am. Chem. Soc.'', '''1940''', ''62'', 441</ref> and theoretical<ref>Borden, W. T.; Loncharich, R. J.; Houk, K. N. ''Annu. Rev. Phys. Chem.'' '''1988''', ''39'', 213</ref> inquiry.

===Optimizing the Reactants and Products===

A molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms were in an anti-linkage. The geometry was then optimized at the HF/3-21G level. This optimization initially returned the conformer labelled ''anti-3'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all four ''anti''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 1 - Stable ''Anti'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69260 || 0.04
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -231.69254 || 0.08
|-
| <jmol>
<jmolAppletButton>
<title>Anti-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2h || -231.68907 || 2.25
|-
| <jmol>
<jmolAppletButton>
<title>Anti-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69097 || 1.06
|}
<nowiki>*</nowiki>''Relative Energies are relative to most stable conformation of 1,5-hexadiene - '''Gauche-3'''''

Energies are in perfect agreement with those given in Appendix 1.

Another molecule of 1,5-hexadiene was created in GaussView 5.0. The geometry was adjusted so that the central four carbon atoms had a gauche linkage. The geometry was then optimized at the HF/3-21g. This optimization initially returned the conformer labelled ''gauche-2'' in the table below.
The geometries were then, once again, adjusted manually - this time to attain all six ''gauche''-conformers listed in [http://neon-tmp.cc.ic.ac.uk/wiki/index.php/Mod:phys3#Appendix_1 Appendix 1].

{| class="wikitable" border="1"
|+ ''Table 2 - Stable ''Gauche'' Conformations of 1,5-hexadiene, '''HF/3-21G'''''
! Conformer !! Point Group !! Energy/ ''hartree'' !! Relative Energy*/ ''kcalmol-1''
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-1</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche1.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.68772 || 3.10
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche2.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69167 || 0.62
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-3</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche3.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.69266 || 0.00
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-4</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche4.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C2 || -231.69153 || 0.71
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-5</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche5.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68962 || 1.91
|-
| <jmol>
<jmolAppletButton>
<title>Gauche-6</title><color>black</color><size>200</size>
<uploadedFileContents>React_gauche6.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || C1 || -231.68916 || 2.20
|}

Energies are in perfect agreement with those given in Appendix 1.

'''Discussion of Relative Energies''':

The stability of a given conformer of 1,5-hexadiene will be governed by [http://en.wikipedia.org/wiki/Steric_effects steric effects] and the [http://en.wikipedia.org/wiki/Gauche_effect gauche effect].

*''Anti-3'' is the least stable ''anti''-conformer. This is despite the fact that it has zero dipole moment (c.f. 0.20, 0.00, and 0.29 Debye for ''anti-1'', ''anti-2'', and ''anti-4'', respectively) and has no [http://en.wikipedia.org/wiki/Allylic_strain A-1,3] interactions (c.f. 2, 2, and 1 interaction(s) for ''anti-1'', ''anti-2'', and ''anti-4'', respectively).
The higher energy of ''anti-3'' must therefore be due to the two 1,4-interactions between a terminal hydrogen on the alkene and the two methylene hydrogens.
*''Anti-4'' has one of these 1,4-interactions (c.f. 0 interactions for both ''anti-1'' and ''anti-2'') and is therefore the second least stable ''anti''-conformer.
*''Anti-1'' is only slightly more stable (0.04 kcalmol-1) than ''anti-2'' and the reason for this phenomenon is less obvious. Thus, the following table has been created to try to quantify the various steric interactions:

{| class="wikitable" border="1"
|+ ''Table 3 - Quantification of three different types of steric interactions, using the internuclear distances between specified nuclei''
! Interaction !! Anti-1/ ''Å'' !! Anti-2/ ''Å'' !! Anti-3/ ''Å'' !! Anti-4/ ''Å''
|-
| [[Image:Steric_effect_in_anti1.gif|center]] || 2.45, 2.45 || 2.45, 2.45 || -, - || 2.44, -
|-
| [[Image:Steric_effect_in_anti3.gif|center]] || -, - || -, - || 2.41&2.41, 2.41&2.41 || -, 2.45&2.41
|-
| [[Image:Steric_effect_in_anti4.gif|center]] || 2.64, 2.64 || 2.67, 2.67 || -, - || 2.63, -
|}

''Note I: Two values (separated by a comma) are given for each interaction as there are two terminals and, hence, two possible interactions per molecule.
Note II: Each 1,4-interactions are given as ''x.xx&x.xx''. This is because the methylene group has two hydrogens involved in the interaction, therefore there are two distances.''

*The table does not reveal any significant differences between ''anti-1'' and ''anti-2'' which would explain the greater stability of ''anti-1''.

*''Gauche-1'' is the least stable ''gauche''-conformer due to the large interaction arising from forcing the two terminal =CH2 groups to share the same space.

===Optimization of ''Anti-2'' at a Higher Level===

''Anti-2'' was re-optimized at the '''B3LYP/6-31G*''' level:

{| class="wikitable" border="1"
|+ ''Table 4 - ''Anti-2'', '''B3LYP/6-31G*'''''
! Conformer !! Point Group !! Energy/ ''hartree''
|-
| <jmol>
<jmolAppletButton>
<title>Anti-2</title><color>black</color><size>200</size>
<uploadedFileContents>React_anti2_631g.mol</uploadedFileContents>
</jmolAppletButton>
</jmol> || Ci || -234.61171
|}

The following table compares the geometries of ''anti-2'' returned by HF/3-21G and B3LYP/6-31G*:

{| class="wikitable" border="1"
|+ ''Table 5 - Displaying the differences in geometry given by ''HF/3-21G'' and ''B3LYP/6-21G*''''
! Method !! C=C bond length/ ''Å'' !! C-C bond length/ ''Å'' !! H-C-H terminal alkene bond angle/ o
|-
| HF/3-21G || 1.32, 1.32 || 1.51, 1.55, 1.51 || 116.3, 116.3
|-
| B3LYP/6-31G* || 1.33, 1.33 || 1.50, 1.55, 1.50 || 116.5, 116.5
|-
| '''Percentage Change/ %''' || 0.8, 0.8 || 0.7, 0.0, 0.7 || 0.2, 0.2
|}

As shown by the above table, the re-optimization results in only very small changes in geometry.

===Vibrational Analysis of ''Anti-2''===

A frequency calculation was carried out on ''anti-2'' at the B3LYP/6-21G* level.

{| class="wikitable" border="1"
|+ Table 6 - Energies
! Energy !! Calculated/ ''Hartree'' !! Experimental
|-
| Sum of electronic and zero-point energies || -234.46920 || cell
|-
| Sum of electronic and thermal energies || -234.46186 || cell
|-
| Sum of electronic and thermal enthalpies || -234.46091 || cell
|-
| Sum of electronic and thermal free energies || -234.50078 || cell
|}

===Optimizing the Chair Transition Structure===

An allyl fragment was created in GaussView and then optimized at the HF/3-21G level. This fragment was duplicated, and a ''guess'' chair structure was created. This guess transition structure was then optimized via the floowing two methods:

====1====

*Job Type - '''Opt+Freq'''
*Optimize to a '''TS (Berny)'''
*Calculate Force Constants '''Once'''
*Additional Keywords - '''Opt=NoEigen'''

The calculation yields one imaginary frequency at 818 cm-1, which corresponds to the Cope rearrangement.

<jmol>
<jmolAppletButton>
<title>Chair TS vibration</title><color>black</color><size>200</size>
<script>color vectors green; zoom 100; frame 3; vectors 4; vectors scale 2; vibration 2; spin 30</script>
<uploadedFileContents>Chair_ts_guess_calc1.txt</uploadedFileContents>
</jmolAppletButton>
</jmol>

====2====

==References and Citations==

<references />