ChemWiki - User contributions [en]

Rep:Mod:Quantopia

2013-03-15T15:13:08Z

Alf10: /* Molecular Orbitals */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

==Geometry==

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

This shows that the LUMO of the butadiene and the HOMO of the ethene have reacted to form a symmetric orbital...obeying the rule that two orbitals of the same symmetry react to give two orbitals of the same symmetry.

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==
The HOMOs of the Endo and Exo structures are shown below.

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''ENDO''' || '''EXO'''
|-
| '''[[File:Maleic_TS_ALF_HOMO.png|250px]]''' ||'''[[File:Maleic_TS_ALF_EXO_HOMO.png|250px]]'''
|-
| '''Four nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Antisymmetric with respect to phase.'''
|}

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>. The exo is more strained than the endo form, because the oxygen atoms are forced up against the hydrogens of the ch2 groups. This leads to more steric strain than is present in the endo form.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T15:04:52Z

Alf10: /* Geometry */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

==Geometry==

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==
The HOMOs of the Endo and Exo structures are shown below.

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''ENDO''' || '''EXO'''
|-
| '''[[File:Maleic_TS_ALF_HOMO.png|250px]]''' ||'''[[File:Maleic_TS_ALF_EXO_HOMO.png|250px]]'''
|-
| '''Four nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Antisymmetric with respect to phase.'''
|}

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>. The exo is more strained than the endo form, because the oxygen atoms are forced up against the hydrogens of the ch2 groups. This leads to more steric strain than is present in the endo form.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T15:04:14Z

Alf10: /* Conclusion */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==
The HOMOs of the Endo and Exo structures are shown below.

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''ENDO''' || '''EXO'''
|-
| '''[[File:Maleic_TS_ALF_HOMO.png|250px]]''' ||'''[[File:Maleic_TS_ALF_EXO_HOMO.png|250px]]'''
|-
| '''Four nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Antisymmetric with respect to phase.'''
|}

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>. The exo is more strained than the endo form, because the oxygen atoms are forced up against the hydrogens of the ch2 groups. This leads to more steric strain than is present in the endo form.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T15:01:25Z

Alf10: /* MO analysis */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==
The HOMOs of the Endo and Exo structures are shown below.

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''ENDO''' || '''EXO'''
|-
| '''[[File:Maleic_TS_ALF_HOMO.png|250px]]''' ||'''[[File:Maleic_TS_ALF_EXO_HOMO.png|250px]]'''
|-
| '''Four nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Antisymmetric with respect to phase.'''
|}

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:56:43Z

Alf10: /* MO analysis */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==
The HOMOs of the Endo and Exo structures are shown below.

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''ENDO''' || '''EXO'''
|-
| '''[[File:Maleic_TS_ALF_HOMO.png|250px]]''' ||'''[[File:Maleic_TS_ALF_EXO_HOMO.png|250px]]'''
|-
| '''Five nodes in orbital. Symmetric with respect to phase||'''Six nodes in orbital. Symmetric with respect to phase.'''
|}

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:55:08Z

Alf10: /* MO analysis */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''ENDO''' || '''EXO'''
|-
| '''[[File:Maleic_TS_ALF_HOMO.png|250px]]''' ||'''[[File:Maleic_TS_ALF_EXO_HOMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:53:49Z

Alf10: /* MO analysis */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==

Maleic_TS_ALF_HOMO.png

Maleic_TS_ALF_EXO_HOMO.png

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>.

=References=
<references> </references>

File:Maleic TS ALF EXO HOMO.png

2013-03-15T14:52:25Z

Alf10:

File:Maleic TS ALF HOMO.png

2013-03-15T14:52:24Z

Alf10: uploaded a new version of "File:Maleic TS ALF HOMO.png"

Rep:Mod:Quantopia

2013-03-15T14:30:09Z

Alf10: /* Conclusion */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions<ref> J.Garcia, J. Mayoral, L. Salvatella, Acc. Chem. Res. , 2000, 33, 658-664 </ref>.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:28:15Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

==MO analysis==

==Conclusion==

From the visualised HOMO we can see that there is a nodal plane running between the -(C=O)-O-(C=O)- fragment and the rest of the system. This leads me to believe that the stereospecificity is not a result of the Secondary Orbital Interactions (SOI). This is backed up in papers that suggest that the endo is favoured, not because of orbital interactions, but because of solvent effects or hydrogen bonding, amongst other more common interactions.

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:23:07Z

Alf10: /* Exo */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

The log file for the optimisation doubles as the log file for frequency analysis as an opt+freq was run.

[[File:Maleic_ALF_EXO.gif]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:22:29Z

Alf10: /* Exo */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

[[File:Maleic_ALF_EXO.gif]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:21:48Z

Alf10: /* Frequency Analysis */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

===Exo===

[[File:Maleic_ALF_Exo.gif]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:20:48Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
[[File:Last_Ditch_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || LAST_DITCH_ALF
|-
| File Type || .log
|-
| Calculation Type || FREQ
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.60359125
|-
| Gradient || 0.00000720
|-
| Dipole Moment || 5.9365
|-
| Point Group || C1
|-
| Duration of Calculation || 36 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000475 0.001800 YES
RMS Displacement 0.000099 0.001200 YES
Predicted change in Energy=-4.942929D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:17:52Z

Alf10: /* Exo */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===
Last_Ditch_ALF.LOG

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

=References=
<references> </references>

File:Last Ditch ALF.LOG

2013-03-15T14:17:35Z

Alf10:

File:EXO TS HF 3 21G OPT FREQ.LOG

2013-03-15T14:15:40Z

Alf10: uploaded a new version of "File:EXO TS HF 3 21G OPT FREQ.LOG": Reverted to version as of 06:11, 15 March 2013

File:EXO TS HF 3 21G OPT FREQ.LOG

2013-03-15T14:15:08Z

Alf10: uploaded a new version of "File:EXO TS HF 3 21G OPT FREQ.LOG"

Rep:Mod:Quantopia

2013-03-15T14:14:43Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

===Exo===

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

[[File:Maleic_ALF_Endo.gif]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:13:30Z

Alf10: /* Endo */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:13:19Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system with either the endo isomer or the exo.

==Optimisation of transition state==
===Endo===
[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

====Results table====

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:11:39Z

Alf10: /* Results table */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system.

==Optimisation of transition state==

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

===Results table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000338 0.001800 YES
RMS Displacement 0.000052 0.001200 YES
Predicted change in Energy=-3.129281D-09
Optimization completed.
-- Stationary point found.
</pre>

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:10:15Z

Alf10: /* Optimisation of transition state */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system.

==Optimisation of transition state==

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

===Results table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || MALEIC_ANHYDRIDE_TS_ALF
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -605.61036823
|-
| Gradient || 0.00000579
|-
| Dipole Moment || 6.7141
|-
| Point Group || C1
|-
| Duration of Calculation || 13 minutes 24 seconds
|}

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:07:28Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cyclohexadiene to give a bicyclic system.

==Optimisation of transition state==

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

===Results table===

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:06:58Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cylohexadiene to give a bicyclic system.

==Optimisation of transition state==

[[File:MALEIC_ANHYDRIDE_TS_ALF.LOG]]

===Results table===

==Frequency Analysis==

[[File:MALEIC_ANHYDRIDE_TS_ALF_FREQ.LOG ]]

=References=
<references> </references>

File:Maleic ALF EXO.gif

2013-03-15T14:05:23Z

Alf10:

File:Maleic ALF Endo.gif

2013-03-15T14:05:22Z

Alf10: uploaded a new version of "File:Maleic ALF Endo.gif"

File:MALEIC ANHYDRIDE TS ALF.LOG

2013-03-15T14:05:22Z

Alf10:

File:MALEIC ANHYDRIDE TS ALF FREQ.LOG

2013-03-15T14:05:20Z

Alf10:

Rep:Mod:Quantopia

2013-03-15T14:03:43Z

Alf10: /* Maleic Anhydride and Cyclohexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

Maleic anhydride reacts with cylohexadiene to give a bicyclic system.

==Optimisation of transition state==

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:02:37Z

Alf10: /* Molecular Orbitals */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=Maleic Anhydride and Cyclohexadiene=

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T14:02:17Z

Alf10:

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}
=Maleic Anhydride and Cyclohexadiene=

=References=
<references> </references>

File:Maleic TS ALF HOMO.png

2013-03-15T14:00:50Z

Alf10:

Rep:Mod:Quantopia

2013-03-15T13:34:59Z

Alf10: /* MO's */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''Two nodal planes in orbital. Antisymmetric with respect to phase||'''Three nodal planes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T13:33:07Z

Alf10: /* APP Ci Reopt */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

A selection of structures were optimised and compared to the structures found in the appendix in the manual.[[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3#Appendix_1]].
===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This molecule matches the energy and symmetry of anti 1 in the manual.

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The energy and symmetry match the gauche 1 structure in the manual.

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

This matches the energy and symmetry of the anti 2 structure.

===APP Ci Reopt===

The above anti2 structure was reoptimised further with a better basis set.

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

Using this better basis set, the energy has dropped dramatically, showing the benefits of using better basis sets in your modelling.

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-15T13:31:13Z

Alf10: /* APP Ci */

Rep:Mod:Quantopia

2013-03-15T13:30:29Z

Alf10: /* AntiPeriPlanar (APP) */

Rep:Mod:Quantopia

2013-03-15T13:30:14Z

Alf10: /* Gauche */

Rep:Mod:Quantopia

2013-03-15T13:28:29Z

Alf10: /* AntiPeriPlanar (APP) */

Rep:Mod:Quantopia

2013-03-15T13:26:21Z

Alf10: /* Optimisation of guess structures */

Rep:Mod:Quantopia

2013-03-15T13:23:09Z

Alf10: /* Hexadiene */

= Cope Rearrangement of Hexadiene=

==Optimisation of guess structures==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-14T15:14:12Z

Alf10: /* Vibrations */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to the motion the carbons undergo while forming the bonds:

[[File:Diels_Tran_ALF.gif|300px]]

Comparing this to the lowest frequency positive vibration, which is a simple rotation, with the two molecules rotating in opposition to each other:

[[File:Diels_Tran_ALF_Real.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

File:Diels Tran ALF Real.gif

2013-03-14T15:13:44Z

Alf10:

Rep:Mod:Quantopia

2013-03-14T14:59:03Z

Alf10: /* Geometry */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987,12, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å<ref> A.Bondi, The Journal of Physical Chemistry, 1964, 68 (3), 441-451 </ref>. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. , 1987,12, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to this motion:

[[File:Diels_Tran_ALF.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-14T14:55:34Z

Alf10: /* Geometry */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987, S1-S19 </ref>, and for sp2-sp2, 1.46Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987, S1-S19 </ref>. For sp3 - sp3 1.53Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987, S1-S19 </ref>. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987, S1-S19 </ref>. The van der Waals radius for carbon is 1.7Å. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987, S1-S19 </ref>
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to this motion:

[[File:Diels_Tran_ALF.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-14T14:54:53Z

Alf10: /* Geometry */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å<ref name = "F.Allen"> Frank H. Allen, Olga Kennard, David G. Watson, J. CHEM. SOC. PERKIN TRANS. ,12, 1987, S1-S19 </ref>, and for sp2-sp2, 1.46Å. For sp3 - sp3 1.53Å. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å. The van der Waals radius for carbon is 1.7Å. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to this motion:

[[File:Diels_Tran_ALF.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-14T14:45:16Z

Alf10: /* Summary Table */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

===Geometry===

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf. The typical sigma bond bond lengths for an sp2 carbon to an sp3 is 1.507Å, and for sp2-sp2, 1.46Å. For sp3 - sp3 1.53Å. The typical double bond length for an sp2 carbon to another sp2 carbon is 1.316Å. The van der Waals radius for carbon is 1.7Å. Obviously the van der Waals contact distance is twice that: 3.4Å This means that our calculated value of 2.10Å sits two thirds of the way between vdW contact and a single bond.

{| class="wikitable" border="1"
|+ Carbon Bondlengths
! Type of Carbons !! Length Å
|-
| sp3 - sp3||1.53
|-
| sp3 - sp2 || 1.507
|-
| sp2 - sp2 || 1.46
|-
| sp2 = sp2|| 1.316
|}

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to this motion:

[[File:Diels_Tran_ALF.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-14T14:28:40Z

Alf10: /* Summary Table */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf.

[[File:Transition_Structure_ALF.png|300px]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to this motion:

[[File:Diels_Tran_ALF.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>

Rep:Mod:Quantopia

2013-03-14T14:28:16Z

Alf10: /* Summary Table */

=Hexadiene=

==Optimisation==

===AntiPeriPlanar (APP)===

Energy:-231.68165912

[[File:HEXA_ALF_ANTI.LOG]]

[[File:HEXA_ALF_ANTI.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || hexa_ALF_anti
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69260236
|-
| Gradient || 0.00001296
|-
| Dipole Moment || 0.2021
|-
| Point Group || C2
|-
| Duration of Calculation || 18 seconds
|}

a jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_ANTI.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===Gauche===

Energy: -231.00983652

[[File:HEXA_ALF_GAUCHE_2.LOG]]

[[File:HEXA_ALF_GAUCHE.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_GAUCHE_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.68771435
|-
| Gradient || 0.00003625
|-
| Dipole Moment || 0.4553
|-
| Point Group || C2
|-
| Duration of Calculation || 1 minute 1 second
|}

a jmol file can be found

<jmol>
<jmolAppletButton>
<uploadedFileContents> HEXA_ALF_GAUCHE.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci===

Energy: -231.68029455
Symmetry: Ci

[[File:HEXA_ALF_ANTI2.LOG]]

[[File:HEXA_ALF_ANTI2.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_2
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.69253528
|-
| Gradient || 0.00001891
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 19 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti2.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

===APP Ci Reopt===

[[File:HEXA_ALF_ANTI3.LOG]]

[[File:HEXA_ALF_ANTI3.png|300px]]

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || Hexa_ALF_Anti_3
|-
| File Type || .log
|-
| Calculation Type || FOPT
|-
| Calculation Method || RB3LYP
|-
| Basis Set || 6-31G
|-
| Final Energy (au) || -234.55971600
|-
| Gradient || 0.00001343
|-
| Dipole Moment || 0.000
|-
| Point Group || C1/Ci
|-
| Duration of Calculation || 1 minute 16 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> Hexa_ALF_anti3.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

<pre>
Sum of electronic and zero-point Energies= -234.416221
Sum of electronic and thermal Energies= -234.408945
Sum of electronic and thermal Enthalpies= -234.408001
Sum of electronic and thermal Free Energies= -234.447765
</pre>

=Butadiene =

Butadiene was optimised at the semi empirical AM1 level.

The MO's were then visualised from the checkpoint file [[File:Cis_Buta_ALF.chk]]

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> CIS_BUTA_ALF.mol </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

==MO's==

Homo

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Buta_ALF_HOMO.png|300px]]''' ||'''[[File:Buta_ALF_LUMO.png|300px]]'''
|-
| '''One node in orbital. Antisymmetric with respect to phase||'''Two nodes in orbital. Symmetric with respect to phase.'''
|}

These MO's agree with the postulate that the HOMO is of the same symmetry as the HOMO ethene, and also the LUMOs.

=Diels Alder transition state=

Using this optimised structure of butadiene, the transition state in the diels alder cyclisation reaction between butadiene and ethene was modelled.

==Optimisation==

To form the transition state guess structure, the 2,2 bicycle was formed, two CH2 fragments were removed and two bonds were changed to dashed bonds. Double bonds were added where necessary, and the calculation was run.
Logfile: [[File:BUTA_ALF_TRANS.LOG]]

===Summary Table===

{| class="wikitable" border="1"
|+ Optimisation Report
! Title !! Result
|-
| File Name || BUTA_ALF_TRANS
|-
| File Type || .log
|-
| Calculation Type || FTS
|-
| Calculation Method || RHF
|-
| Basis Set || 3-21G
|-
| Final Energy (au) || -231.60320856
|-
| Gradient || 0.00001777
|-
| Dipole Moment || 0.5753
|-
| Point Group || C1
|-
| Duration of Calculation || 1 minute 35 seconds
|}

A jmol file can be found
<jmol>
<jmolAppletButton>
<uploadedFileContents> BUTA_ALF_TRANS.mol2 </uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>

The optimisation has found a stationary point, so it has run to the stable minima.

<pre> Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000459 0.001800 YES
RMS Displacement 0.000109 0.001200 YES
Predicted change in Energy=-7.545022D-09
Optimization completed.
-- Stationary point found.
----------------------------
</pre>

The structure is shown here, the bond distances for the half formed C-C bonds are 2.10Å 3sf.

[[File:Transition_Structure_ALF.png]]

==Frequency Analysis==

A frequency analysis was run on this optimised molecule.
Logfile: [[File:BUTA_ALF_TRANS_FREQ.LOG]]

===Vibrations===

There is one imaginary vibration at -818, which corresponds to this motion:

[[File:Diels_Tran_ALF.gif|300px]]

==Molecular Orbitals==

The HOMO of the transition state is shown below:

{| border="1" cellpadding="5" cellspacing="0" align="centre"
|+ Molecular Orbitals of Butadiene .
|-
| '''HOMO''' || '''LUMO'''
|-
| '''[[File:Tran_ALF_HOMO.png|250px]]''' ||'''[[File:Tran_ALF_LUMO.png|250px]]'''
|-
| '''Three nodes in orbital. Symmetric with respect to phase||'''Four nodes in orbital. Symmetric with respect to phase.'''
|}

=References=
<references> </references>