ChemWiki - User contributions [en]

Rep:Module3:Dima1407

2010-12-19T13:16:13Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. HOMO is formed from The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{Doi|10.1088/0022-3719/19/24/006}}</ref>. The Carbon van der Waals radius is 0.17nm<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{Doi|10.1021/j100785a001}} </ref>. So the TS distance is smmaller than 2 van der Waals radius and bigger than proper C-C bond.

The vibration that corresponds to the reaction path at the transition state is imagine with the magnitude of 956cm<sup>-1</sup> The formation of the two bonds is synchronous.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>rExo_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>rEndo_ts.mol</uploadedFileContents> </jmolApplet></jmol>

=Reference=
<references />

File:REndo ts.mol

2010-12-19T13:13:44Z

Dr708:

Rep:Module3:Dima1407

2010-12-18T16:49:11Z

Dr708: /* The Diels Alder Cycloaddition */

Rep:Module3:Dima1407

2010-12-18T16:33:48Z

Dr708: /* The Diels Alder Cycloaddition */

Rep:Module3:Dima1407

2010-12-18T16:31:23Z

Dr708: /* The Diels Alder Cycloaddition */

Rep:Module3:Dima1407

2010-12-18T16:29:35Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. HOMO is formed from The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{Doi| 10.1088/0022-3719/19/24/006}}</ref>. The Carbon van der Waals radius is 0.17nm<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{doi|10.1021/j100785a001}}</ref>. So the TS distance is smmaller than 2 van der Waals radius and bigger than proper C-C bond.

=Reference=
<references />

Rep:Module3:Dima1407

2010-12-18T16:28:16Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. HOMO is formed from The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{Doi= 10.1088/0022-3719/19/24/006}}</ref>. The Carbon van der Waals radius is 0.17nm<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. {{doi:10.1021/j100785a001}}</ref>. So the TS distance is smmaller than 2 van der Waals radius and bigger than proper C-C bond.

=Reference=
<references />

Rep:Module3:Dima1407

2010-12-18T16:25:12Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. HOMO is formed from The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{Doi= 10.1088/0022-3719/19/24/006}}</ref>. The Carbon van der Waals radius is 0.17nm<ref name="Bondi1964">{{cite journal | first = A. | last = Bondi | year =1964 | url = http://pubs.acs.org/doi/pdf/10.1021/j100785a001 | title = Van der Waals Volumes and Radii | journal = [[Journal of Physical Chemistry|J. Phys. Chem.]] | volume = 68 | issue = 3 | pages = 441–51 | doi= 10.1021/j100785a001}}</ref>. So the TS distance is smmaller than 2 van der Waals radius and bigger than proper C-C bond.

=Reference=
<references />

Rep:Module3:Dima1407

2010-12-18T16:17:40Z

Dr708: /* Reference */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{doi: 10.1088/0022-3719/19/24/006}}</ref>

=Reference=
<references />

Rep:Module3:Dima1407

2010-12-18T16:16:28Z

Dr708: /* Reference */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{doi: 10.1088/0022-3719/19/24/006}}</ref>

=Reference=
<reference/>

Rep:Module3:Dima1407

2010-12-18T16:14:48Z

Dr708: /* Reference */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{doi: 10.1088/0022-3719/19/24/006}}</ref>

=Reference=
{{reference}}

Rep:Module3:Dima1407

2010-12-18T16:13:32Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{doi: 10.1088/0022-3719/19/24/006}}</ref>

=Reference=

Rep:Module3:Dima1407

2010-12-18T16:12:41Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO(-0.344) and LUMO(0.017) orbitals of butadiene:

[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:

[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

Butadiene's HOMO is anti-symmetric, LUMO is symmetric.

The transition structure maximizes the overlap between the ethylene π orbitals and the π system of butadiene:

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 100</script> <uploadedFileContents>Guess_ts_ii.mol</uploadedFileContents> </jmolApplet></jmol>

TS HOMO and LUMO:

[[Image:Hex_TS_HOMO.png|300px| ]] [[Image:Hex_TS_LUMO.png|300px| ]]

The TS HOMO is anti-symmetric, LUMO - symmetric. The bond length of the partly formed σ C-C bond is 0.212nm, while typical sp3 and sp2 C-C bond lengths are 0.154nm and 0.148nm<ref>J M Baranowski 1986 J. Phys. C: Solid State Phys. 19 4613 {{doi: 10.1088/0022-3719/19/24/006}}</ref>

File:Hex TS HOMO.png

2010-12-18T15:41:16Z

Dr708:

File:Hex TS LUMO.png

2010-12-18T15:40:17Z

Dr708:

Rep:Module3:Dima1407

2010-12-18T15:39:19Z

Dr708: /* The Diels Alder Cycloaddition */

File:Guess ts ii.mol

2010-12-18T15:34:20Z

Dr708:

Rep:Module3:Dima1407

2010-12-18T15:27:55Z

Dr708: /* The Diels Alder Cycloaddition */

Rep:Module3:Dima1407

2010-12-18T14:51:45Z

Dr708: /* The Diels Alder Cycloaddition */

Rep:Module3:Dima1407

2010-12-18T14:49:06Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and Gauche3 isomer formation from Boat TS {{DOI|10042/to-6345}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

HOMO and LUMO orbitals of butadiene:
[[Image:But_HOMO.png|300px| ]] [[Image:But_LUMO.png|300px| ]]

HOMO(-0.387) and LUMO(0.052) orbitals of ethylene:
[[Image:Et_HOMO.png|300px| ]] [[Image:Et_LUMO.png|300px| ]]

File:Et LUMO.png

2010-12-18T14:48:54Z

Dr708:

File:Et HOMO.png

2010-12-18T14:47:28Z

Dr708:

File:But LUMO.png

2010-12-18T14:39:55Z

Dr708:

File:But HOMO.png

2010-12-18T14:37:11Z

Dr708:

Rep:Module3:Dima1407

2010-12-17T17:05:16Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T16:45:46Z

Dr708: /* The Diels Alder Cycloaddition */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and isomer formation from Boat TS {{DOI|10042/to-xyz}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

Rep:Module3:Dima1407

2010-12-17T16:13:14Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and isomer formation from Boat TS {{DOI|10042/to-xyz}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies (Hartree)!! Sum of electronic and thermal energies (Hartree)!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960
|}

=The Diels Alder Cycloaddition=

Rep:Module3:Dima1407

2010-12-17T16:10:21Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and isomer formation from Boat TS {{DOI|10042/to-xyz}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies!! Sum of electronic and thermal energies!! ΔE at 0 K (kcal/mol)!! ΔE at 298.15 K (kcal/mol)!! Expt.at 0 K (kcal/mol)
|-
| Chair TS|| -234.505467|| -234.362663|| -234.356753|| 33.62|| 32.76|| 33.5 ± 0.5
|-
| Boat TS || -234.492915|| -234.351359|| -234.345054|| 40.71|| 40.10|| 44.7 ± 2.0
|-
| Reactant (Anti2)|| -234.559715|| -234.416239|| -234.408960||
|}

Rep:Module3:Dima1407

2010-12-17T15:40:49Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.68772|| 12.97
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69167|| 2.60
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69266|| 0.0
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69153|| 2.97
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2</sub>|| -231.69260|| 0.16
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>i</sub>|| -231.69254|| 0.31
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>2h</sub>|| -231.68907|| 9.43
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| C<sub>1</sub>|| -231.69097|| 4.44
|}

We have obtained the same results optimizing our structures as in the table in Appendix1.

The energy obtained in optimization at the higher level of theory is -234.55972 Hartrees. The energy difference is very big. But geometry obtained in both cases are very similar - maximum angle difference is 1 degree between carbon atoms and less than 0.2 degrees between Hydrogen-Carbon-Hydrogen atoms.

Angles at high theory level:

C1-C2-C3 =125,23

C2-C3-C4 = 112.65

Angles at low theory level:

C1-C2-C3 =124.81

C2-C3-C4 = 111.35

We have done a vibrational analysis and have not found any imaginary (negative) frequencies - the structure is energy minimum.

The information obtained from Thermochemistry part:

Sum of electronic and zero-point Energies= -234.416239

Sum of electronic and thermal Energies= -234.408960

Sum of electronic and thermal Enthalpies= -234.408016

Sum of electronic and thermal Free Energies= -234.447788

=Optimizing the "Chair" and "Boat" Transition Structures=

From the guess transition state optimization we can see that chair TS is lover in energy than boat TS.

Chair TS = -231.61932 Hartree

Boat TS = -231.60280 Hartree

Energy difference = 0.01652 Hartree (or 43.4kJ/mol)

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rChair_ts.mol</uploadedFileContents> </jmolApplet></jmol><jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>rBoat_ts.mol</uploadedFileContents> </jmolApplet></jmol>

Boat TS has an imaginary frequency of magnitude 839 cm<sup>-1</sup>and Chair TS has an imaginary frequency of magnitude 818 cm<sup>-1</sup>

Using the frozen coordinate method the result is differed in seventh decimal place, so those methods are similar.

QST2 method is good when you can not predict the TS, but it also has disadvantages - for example it could not be used for predicting chair TS, only Boat one. The predicted Boat TS energy is the same as in guess transition state optimization. E = -231.60280 Hartree.

<jmol><jmolApplet><color>white</color> <size>250</size><script>zoom 150</script> <uploadedFileContents>Boat_ts_qst2_mod.mol</uploadedFileContents> </jmolApplet></jmol>

IRS predicts us Gauche2 isomer formation from Chair TS {{DOI|10042/to-6305}} and isomer formation from Boat TS {{DOI|10042/to-xyz}}.

{| class="wikitable" border="1"
|+ caption
! !! Electronic energy!! Sum of electronic and zero-point energies!! Sum of electronic and thermal energies!! heading!! heading!! heading
|-
| Chair TS|| cell|| cell|| cell|| cell|| cell|| cell
|-
| Boat TS || cell|| cell|| cell|| cell|| cell|| cell
|-
| Reactant (Anti2)|| cell|| cell|| cell|| cell|| cell|| cell
|}

Rep:Module3:Dima1407

2010-12-17T15:34:02Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T15:32:25Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T14:40:32Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T14:39:56Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

File:Boat ts qst2 mod.mol

2010-12-17T14:39:46Z

Dr708:

Rep:Module3:Dima1407

2010-12-17T14:14:56Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T14:07:21Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T14:06:59Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T14:06:27Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T14:05:58Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

File:RBoat ts.mol

2010-12-17T14:02:36Z

Dr708:

File:RChair ts.mol

2010-12-17T14:01:46Z

Dr708:

Rep:Module3:Dima1407

2010-12-17T13:57:04Z

Dr708: /* Optimizing the "Chair" and "Boat" Transition Structures */

Rep:Module3:Dima1407

2010-12-17T13:27:17Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T13:26:14Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T13:17:00Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T13:16:25Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T12:56:18Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T12:46:11Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T12:44:35Z

Dr708: /* Optimizing 1,5-hexadiene */

Rep:Module3:Dima1407

2010-12-17T12:36:03Z

Dr708: /* Optimizing 1,5-hexadiene */

=Optimizing 1,5-hexadiene=

{| class="wikitable" border="1"
|+ caption
! Conformer !! Structure!! Point Group!!Energy/Hartrees !!Relative Energy/kJ/mol
|-
| Gauche1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche1.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| -231.68772|| cell
|-
| Gauche2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche2.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| -231.69167|| cell
|-
| Gauche3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche3.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| -231.69266|| cell
|-
| Gauche4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rGauche4.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| -231.69153|| cell
|-
| Anti1|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| cell|| cell
|-
| Anti2|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti2.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| cell|| cell
|-
| Anti3|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti3.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| -231.68907|| cell
|-
| Anti4|| <jmol><jmolApplet><color>white</color> <size>150</size><script>zoom 125;</script> <uploadedFileContents>rAnti1.mol</uploadedFileContents> </jmolApplet></jmol>|| cell|| -231.69097|| cell
|}