ChemWiki - User contributions [en]

Rep:Mod:ts Zh3615

2017-11-22T10:49:10Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] Detailed variation of bond lengths with time is shown in the table 1.1. As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 Bond lengths variations
|colspan="2" align="center"|[[File:Bondlengthlabelzh3615.png|300px]]
|-
|[[File:Bondlenvar1zh3615.png|300px]]||[[File:Bondlenvar2zh3615.png|300px]]
|}

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.2 and 1.3. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.4, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.4 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|200px]]||[[File:exolumo-1momozh3615.png|210px]]||[[File:Endo lumo+12 zh3615.png|200px]]||[[File:Endolumo-1momozh3615.png|240px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|200px]]||[[File:exolumomomozh3615.png|210px]]||[[File:Endo lumo2 zh3615.png|200px]]||[[File:Endolumomomozh3615.png|240px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|200px]]||[[File:exohomomomozh3615.png|210px]]||[[File:Endo homo2 zh3615.png|200px]]||[[File:Endohomomomozh3615.png|240px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|200px]]||[[File:Exohomo-1momozh3615.png|210px]]||[[File:Endo homo-12 zh3615.png|200px]]||[[File:Endohomo-1momozh3615.png|240px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.log]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive and relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.20-22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:47:12Z

Zh3615: /* Extension */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 Bond lengths variations
|colspan="2" align="center"|[[File:Bondlengthlabelzh3615.png|300px]]
|-
|[[File:Bondlenvar1zh3615.png|300px]]||[[File:Bondlenvar1zh3615.png|300px]]
|}

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.2 and 1.3. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.4, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.4 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|200px]]||[[File:exolumo-1momozh3615.png|210px]]||[[File:Endo lumo+12 zh3615.png|200px]]||[[File:Endolumo-1momozh3615.png|240px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|200px]]||[[File:exolumomomozh3615.png|210px]]||[[File:Endo lumo2 zh3615.png|200px]]||[[File:Endolumomomozh3615.png|240px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|200px]]||[[File:exohomomomozh3615.png|210px]]||[[File:Endo homo2 zh3615.png|200px]]||[[File:Endohomomomozh3615.png|240px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|200px]]||[[File:Exohomo-1momozh3615.png|210px]]||[[File:Endo homo-12 zh3615.png|200px]]||[[File:Endohomo-1momozh3615.png|240px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.log]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive and relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.20-22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:45:45Z

Zh3615: /* Cyclohexadiene and 1,3-Dioxole */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 Bond lengths variations
|colspan="2" align="center"|[[File:Bondlengthlabelzh3615.png|300px]]
|-
|[[File:Bondlenvar1zh3615.png|300px]]||[[File:Bondlenvar1zh3615.png|300px]]
|}

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.2 and 1.3. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.4, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.4 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|200px]]||[[File:exolumo-1momozh3615.png|210px]]||[[File:Endo lumo+12 zh3615.png|200px]]||[[File:Endolumo-1momozh3615.png|240px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|200px]]||[[File:exolumomomozh3615.png|210px]]||[[File:Endo lumo2 zh3615.png|200px]]||[[File:Endolumomomozh3615.png|240px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|200px]]||[[File:exohomomomozh3615.png|210px]]||[[File:Endo homo2 zh3615.png|200px]]||[[File:Endohomomomozh3615.png|240px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|200px]]||[[File:Exohomo-1momozh3615.png|210px]]||[[File:Endo homo-12 zh3615.png|200px]]||[[File:Endohomo-1momozh3615.png|240px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.log]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.20-22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:42:20Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 Bond lengths variations
|colspan="2" align="center"|[[File:Bondlengthlabelzh3615.png|300px]]
|-
|[[File:Bondlenvar1zh3615.png|300px]]||[[File:Bondlenvar1zh3615.png|300px]]
|}

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.2 and 1.3. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.4, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.4 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.log]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.20-22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:Bondlenvar2zh3615.png

2017-11-22T10:40:00Z

Zh3615:

File:Bondlenvar1zh3615.png

2017-11-22T10:39:50Z

Zh3615:

File:Bondlengthlabelzh3615.png

2017-11-22T10:34:26Z

Zh3615:

File:Daendoirc zh3615.log

2017-11-22T10:34:07Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T10:28:45Z

Zh3615: /* O-Xylene-So2 Cycloaddition */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.log]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.20-22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:26:47Z

Zh3615: /* Reference */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.20-22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:26:35Z

Zh3615: /* Reference */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22

[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:23:52Z

Zh3615: /* Extension */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies of the below reaction as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T10:23:01Z

Zh3615: /* Extension */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|268.0||align="center"|275.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|95.7||align="center"|99.1
|-
|Reaction energy||align="center"|16.5||align="center"|20.9
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:EXOTSTOTS444zh3615.LOG]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:ENDOTSTOTS444ZH3615.LOG]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:ENDOTSTOTS444ZH3615.LOG

2017-11-22T10:20:48Z

Zh3615:

File:EXOTSTOTS444zh3615.LOG

2017-11-22T10:10:27Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T10:05:12Z

Zh3615: /* Extension */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:EXOPRODUCTMIN444zh3615.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:ENDOPRODUCTMIN444zh3615.LOG]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:EXOPRODUCTMIN444zh3615.LOG

2017-11-22T09:57:06Z

Zh3615:

File:ENDOPRODUCTMIN444zh3615.LOG

2017-11-22T09:56:34Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T09:54:53Z

Zh3615: /* Extension */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|467.2
|-
|Sulphur dioxide||colspan=2 align="center"|-311.4
|-
|Reactant sum||colspan=2 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8
|-
|Reaction product||align="center"|172.3||align="center"|176.7
|-
|Activation energy||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T09:44:28Z

Zh3615: /* O-Xylene-So2 Cycloaddition */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|467.2
|-
|Sulphur dioxide||colspan=3 align="center"|-311.4
|-
|Reactant sum||colspan=3 align="center"|155.8
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|260.1
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|82.0||align="center"|86.0||align="center"|104.3
|-
|Reaction energy||align="center"|-98.8||align="center"|-83.7||align="center"|-155.8
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|469.3
|-
|Sulphur dioxide||colspan=2 align="center"|-297.7
|-
|Reactant sum||colspan=2 align="center"|171.6
|-
|Transition state||align="center"|237.8||align="center"|241.8
|-
|Reaction product||align="center"|57.0||align="center"|72.1
|-
|Activation energy||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:Oxypm6zh3615.LOG

2017-11-22T09:38:07Z

Zh3615: Zh3615 uploaded a new version of File:Oxypm6zh3615.LOG

File:So2pm6zh3615.LOG

2017-11-22T09:36:45Z

Zh3615: Zh3615 uploaded a new version of File:So2pm6zh3615.LOG

File:Endoproductpm6 zh3615.LOG

2017-11-22T09:34:50Z

Zh3615:

File:Exoproductpm6 zh3615.LOG

2017-11-22T09:34:36Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T07:33:20Z

Zh3615:

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7
|-
|Reactant sum||colspan=3 align="center"|171.6
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|xxx
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx||align="center"|xx
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Extension==

The Diels-Alder reaction between o-xylylene and SO2 is possible but unfavourable in theory. The protocol in the section 3 was followed to calculate the reaction barriers and reaction energies as shown in the table 4.1.

<center>[[File:Exrsrszh3615.png|250px]]</center>
<center>Fig. 4.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4.1 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|O-xylylene||colspan=2 align="center"|469.3
|-
|Sulphur dioxide||colspan=2 align="center"|-297.7
|-
|Reactant sum||colspan=2 align="center"|171.6
|-
|Transition state||align="center"|237.8||align="center"|241.8
|-
|Reaction product||align="center"|57.0||align="center"|72.1
|-
|Activation energy||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx
|}

The reaction barrier and reaction energy is both positive relatively large compared to the reaction at the other diene fragment in section 4, which indicates that this reaction are not spontaneous and are not likely to occur under normal conditions.

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:Exrsrszh3615.png

2017-11-22T07:23:22Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T07:17:30Z

Zh3615: /* O-Xylene-So2 Cycloaddition */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

Procedure:The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7
|-
|Reactant sum||colspan=3 align="center"|171.6
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|xxx
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx||align="center"|xx
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T07:16:43Z

Zh3615: /* O-Xylene-So2 Cycloaddition */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated as shown in the table 1.7, and energy profiles are shown in figure 3.2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7
|-
|Reactant sum||colspan=3 align="center"|171.6
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|xxx
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx||align="center"|xx
|}

Among three reaction pathway, the most kinetically stable product is endo-Diels-Alder product (due to secondary orbital interactions) and the most thermodynamically stable product is cheletropic product (less steric hindrance between the 6-membered ring and sulphone oxygen compared to both Diels-Alder products), the ring strain is also not significant due to the size of sulphur atom.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.2 Energy profile of three reaction pathways]]

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T07:00:37Z

Zh3615: /* O-Xylene-So2 Cycloaddition */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

<center>[[File:Rs3zh3615xx.png|350px]]</center>
<center>Fig 3.1 Reaction scheme</center>

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

All carbons in o-xylylene is sp2 hybridised, which makes o-xylylene a planar molecule that can be attacked at the cis diene easily from both sides. During the approaching of SO2 molecule, the 6-membered ring quickly becomes 6 pi aromatic system by resonance with the two double bonds adjacent to the 6-membered ring. The structure of o-xylylene is changed due to the stabilization from aromatic system.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7
|-
|Reactant sum||colspan=3 align="center"|171.6
|-
|Transition state||align="center"|237.8||align="center"|241.8||align="center"|xxx
|-
|Reaction product||align="center"|57.0||align="center"|72.1||align="center"|-0.00525
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|xxx||align="center"|xxx||align="center"|xx
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!O-Xylene(minimum,PM6)!!SO2(minimum,PM6)
|-
|[[File:oxypm6zh3615.LOG]]||[[File:so2pm6zh3615.LOG]]
|-
!Exo-D-A-T.S.(T.S. Berny,PM6)!!Exo-D-A-T.S.(IRC analysis)!!Exo-D-A-product(minimum,PM6)
|-
|[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:Daexoproductminpm6.LOG]]
|-
!Endo-D-A-T.S.(T.S. Berny,PM6)!!Endo-D-A-T.S.(IRC analysis)!!Endo-D-A-product(minimum,PM6)
|-
|[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:Daendoproductminpm6.log]]
|-
!Cheletropic-T.S.(T.S. Berny,PM6)!!Cheletropic-T.S.(IRC analysis)!!Cheletropic-product(minimum,PM6)
|-
|[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:Rs3zh3615xx.png

2017-11-22T06:38:08Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T06:11:53Z

Zh3615: /* Cyclohexadiene and 1,3-Dioxole */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.</center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T06:11:13Z

Zh3615: /* Cyclohexadiene and 1,3-Dioxole */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3. The energy gap between the LUMO of diene and the HOMO of alkene was calculated to be smaller than the energy gap between the HOMO of diene and LUMO of alkene. It suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in an inverse demand D-A reaction. In both reactions, the HOMO of alkene react with the LUMO of diene,

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for view of overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

<center>NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.<center>

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product. It is because of the favourable secondary orbital interactions during the formation of endo-product (lower the activation energy) and steric clashes in the exo-product (make the exo-product less thermodynamically stable), both effects are observable by comparing the HOMOs of transition states.

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T05:48:57Z

Zh3615: /* Cyclohexadiene and 1,3-Dioxole */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

Procedure:The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature. Obtained transition states were confirmed with frequency calculation (only 1 imaginary frequency).

<center>[[File:Ex2_rs_copyZh3615.png|350px]]</center>
<center>Fig 2.1 Reaction scheme</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Cyclohexadiene (minimum,PM6)!!Cyclohexadiene (minimum,B3LYP)!!1,3-dioxole (minimum,PM6)!!1,3-dioxole (minimum,B3LYP)
|-
|[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
!Exo-T.S. (T.S. Berny,PM6)!!Exo-T.S. (T.S. Berny,B3LYP)!!Exo-T.S. IRC!!Exo-T.S. energy analysis
|-
|[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
!Endo-T.S. (T.S. Berny,PM6)!!Endo-T.S. (T.S. Berny,B3LYP)!!Endo-T.S. IRC!!Endo-T.S. energy analysis
|-
|[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2ENDOtoENERGY zh3615.LOG]]
|-
!Exo-reaction product (minimum,PM6)||Exo-reaction product (minimum,B3LYP)||Endo-reaction product (minimum,PM6)||Endo-reaction product (minimum,B3LYP)
|-
|[[File:exoproductpm6 zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]||[[File:endoproductpm6 zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.3, which suggested that both reactions are reverse demand Diels-Alder reactions. In a normal demand D-A reaction the HOMO of diene reacts with the LUMO of the alkene while the HOMO of the alkene reacts with the LUMO of diene in inverse demand D-A reactions.

The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in two different angle (for overlap and symmetry respectively) in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

File:Ex2 rs copyZh3615.png

2017-11-22T05:17:03Z

Zh3615:

Rep:Mod:ts Zh3615

2017-11-22T05:04:24Z

Zh3615: /* Cyclohexadiene and 1,3-Dioxole */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state (side view) !! Exo- transition state (top view) !! Endo- transition state (side view) !! Endo- transition state (top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T05:01:34Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the vibration that passes through the transition state is -949 cm-1, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T04:58:17Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å. [2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the relatively heights of MOs calculated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. *NB height of each T.S. MO is the height of corresponding product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The energy gap between HOMO and LUMO is smaller for butadiene due to its stronger conjugation system. The HOMO and LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are symmetric, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. It can be mathematically demonstrated by observing the equation of wavefunction overlap integral (S) (eq. 4) below:

Equation 4:
<center><math>S=\int {\psi_a\psi^*_b d\tau}</math></center>

Where ψa and ψb are the wavefunctions of reactant MOs, for these MOs to react, they must have non-zero wavefunction overlaps. S is non-zero for S-S, AS-AS interactions and is zero for S-AS and AS-S interactions. Hence Diels-Alder reaction is allowed for MOs of the same symmetry and forbidden for the MOs of different symmetries.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T04:17:08Z

Zh3615: /* Reference */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å.[2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the MO relatively heights generated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22
[2] A. Bondi, The Journal of Physical Chemistry, 1964, 68, 441-451.

Rep:Mod:ts Zh3615

2017-11-22T04:16:41Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1 and the literature bond lengths are shown in the figure 1.2, all obtained values are in literature range. The Van Der Waals radius of carbon atoms is 1.7 Å.[2] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than two times of Van der Waals radius of carbon (3.4 Å).

MO diagram (fig 1.3) was constructed with symmetry labels in normal demand DA according to the MO relatively heights generated. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22

Rep:Mod:ts Zh3615

2017-11-22T04:09:56Z

Zh3615:

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1.Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

==Reference==
[1] E. V. Anslyn and D. A. Dougherty, Modern physical organic chemistry, Univ. Science Books, Sausalito, CA, 2008, pp.22

Rep:Mod:ts Zh3615

2017-11-22T04:09:15Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing to PM6 level. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was confirmed with frequency calculation (only 1 imaginary frequency) and IRC(correct shape).

<center>[[File:Ms zh3615.png|540px]]</center>
<center>Fig 1.1 Reaction scheme and bond lengths (unit: Å)</center>

<center>[[File:Bondlength_copy_zh3615.png|320px]]</center>
<center>Fig 1.2 literature bond lengths(unit: Å)[1]</center>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Log file download
!Butadiene (minimum)!!Ethylene (minimum)!!Transition state (T.S. Berny)!!IRC analysis!!Cyclohexene (minimum)
|-
|align="center"|[[File:Butadiene zh3615.LOG]]||align="center"|[[File:Ethylene_zh3615.LOG]]||align="center"|[[File:1tstots_zh3615.LOG]]||align="center"|[[File:1tstoirc_zh3615.LOG]]||align="center"|[[File:1ptomin zh3615.LOG]]
|}

The carbon-carbon bonds lengths and their variation during the reaction are shown in the figure 1.1.Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

<center>[[File:Mo zh3615.png|350px]]</center>
<center>Fig 1.3 MO diagram of the Diels-Alder reaction</center>

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

File:Bondlength copy zh3615.png

2017-11-22T04:06:08Z

Zh3615:

File:Ms zh3615.png

2017-11-22T03:48:01Z

Zh3615: Zh3615 uploaded a new version of File:Ms zh3615.png

Rep:Mod:ts Zh3615

2017-11-22T03:21:50Z

Zh3615: /* Result and Discussion */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Butadiene and Ethylene==

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

==Cyclohexadiene and 1,3-Dioxole==

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

==O-Xylene-So2 Cycloaddition==

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

Rep:Mod:ts Zh3615

2017-11-22T03:21:03Z

Zh3615: /* Butadiene and Ethylene */

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Result and Discussion==

===Butadiene and Ethylene===

Procedure: The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

===Cyclohexadiene and 1,3-Dioxole===

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

===O-Xylene-So2 Cycloaddition===

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

Rep:Mod:ts Zh3615

2017-11-22T03:15:54Z

Zh3615:

This page was created by Zehua Hu, for third year computational laboratory Transition States and Reactivity.

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Result and Discussion==

===Butadiene and Ethylene===

The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

===Cyclohexadiene and 1,3-Dioxole===

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

===O-Xylene-So2 Cycloaddition===

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

Rep:Mod:ts Zh3615

2017-11-22T03:12:52Z

Zh3615:

==Transition states and reactivity of Diels-Alder reactions==
Zehua Hu, Department of Chemistry, Imperial College London, SW7 2AZ, United Kingdom

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Result and Discussion==

===Butadiene and Ethylene===

The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

===Cyclohexadiene and 1,3-Dioxole===

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

===O-Xylene-So2 Cycloaddition===

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

Rep:Mod:ts Zh3615

2017-11-22T03:11:47Z

Zh3615: /* Introduction */

==Transition states and reactivity of Diels-Alder reactions==
Zehua Hu, Department of Chemistry, Imperial College London, SW7 2AZ, United Kingdom

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BY3LYP/6-31(d) was used to obtain refined data e.g. for energy calculations.

==Experimental==

===Butadiene and Ethylene===

The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

===Cyclohexadiene and 1,3-Dioxole===

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

===O-Xylene-So2 Cycloaddition===

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

==Result and Discussion==

===Butadiene and Ethylene===

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

===Cyclohexadiene and 1,3-Dioxole===

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

===O-Xylene-So2 Cycloaddition===

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

Rep:Mod:ts Zh3615

2017-11-22T03:11:22Z

Zh3615: /* Experimental */

==Transition states and reactivity of Diels-Alder reactions==
Zehua Hu, Department of Chemistry, Imperial College London, SW7 2AZ, United Kingdom

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BYELYP-6-31(d) was used to obtain refined data e.g. for energy calculations.

==Experimental==

===Butadiene and Ethylene===

The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

===Cyclohexadiene and 1,3-Dioxole===

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constants for once) allowing Opt=NoEigen after freezing the bond lengths between two reaction sites of two alkenes to lengths of corresponding literature range, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Orders of MOs via each reaction pathway were generated from the single point energy calculation. Each calculation was then further optimized to B3LYP/6-31G(d) level for the calculation of the reaction barriers and reaction energies at room temperature.

===O-Xylene-So2 Cycloaddition===

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. The optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constants for once), allowing Opt=NoEigen after freezing the bond lengths to lengths of corresponding literature range between two reaction sites of two alkenes followed by IRC analysis (PM6).

==Result and Discussion==

===Butadiene and Ethylene===

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

===Cyclohexadiene and 1,3-Dioxole===

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

===O-Xylene-So2 Cycloaddition===

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.

Rep:Mod:ts Zh3615

2017-11-22T02:49:12Z

Zh3615: /* Introduction */

==Transition states and reactivity of Diels-Alder reactions==
Zehua Hu, Department of Chemistry, Imperial College London, SW7 2AZ, United Kingdom

==Introduction==

Computational Chemistry is a commonly adopted method to optimize and calculate molecular structures and variations of their properties during a reaction because of its theoretical accuracy and cost-efficiency. Commonly the optimization are achieved by calculating the first and second derivative of the potential energy surface (PES). The PES is obtained by plotting the potential energy V(q1, q2, ..., qn) against order parameters q1, q2, ..., qn (where n=3N-6, N=number of atoms) for each reaction. The reactant(s) and product(s) of each reaction are the minimums of the PES respectively and the transition state(s) is the saddle point(s) of the PES between the reactant(s) and product(s). Knowing the whole PES is concave, the reactant(s) and product(s) hence have zero first derivative dV/dqi and positive second derivative dV2/dqi2 while the transition state(s) has zero first derivative dV/dqi and negative derivative dV2/dqi2.

In 1-dimension, with approximating the chemical bonds between atoms to harmonic oscillators, the vibration modes of chemical bonds then obey the Hooke's Law (eq.1), and the vibrational frequencies (ω) of harmonic oscillators obey the (eq.2):

Equation 1:<center><math> V = \frac{1}{2} kx^2 </math></center>

Equation 2:<center><math> \omega = {\frac{1}{2\pi}}\sqrt {\frac{k}{m}} </math></center>

Where V is the elastic potential energy, k is the characteristic constant, x is the relative displacement of one atom to its connected atoms, m is the mass(for spring-mass model) or reduced mass (for atom-atom model). d2V/dx2=k can be obtained by differentiating the equation 1 twice, since the dV2/dqi2 is positive for reactant(s) and product(s) and negative for transition state(s) as suggested above, all vibrational frequencies are positive for reactant(s) and product(s) while a order parameter q that passes through the transition state produces one imaginary vibrational frequency. The only one imaginary vibrational frequency hence can be considered as the criteria for a successfully optimized transition state for multiple-transition-state reactions (e.g. exo- and endo-transition states).

In this computational laboratory, Gaussian worked similarly but in multiple dimensions to optimize and calculate reactant/product structures (min) and transition state structures (saddle point), relevant data was also obtained from the results of calculation and optimization e.g. bond lengths, MOs and energies. The less accurate semi-empirical method PM6 was applied for quick calculation and the DFT method BYELYP-6-31(d) was used to obtain refined data e.g. for energy calculations.

==Experimental==

===Butadiene and Ethylene===

The structures of butadiene and ethylene were drawn in Gaussview. Optimized structures, MOs and corresponding bond lengths of reactants were obtained from optimizing with semi-empirical PM6 method. The optimized structure of transition state was obtained by drawing guessed structures, optimizing to minimum (PM6), then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond length between two reaction sites of two alkenes to 2.2 Å, followed by IRC analysis (PM6). IRC analyzed structure i.e. the product cyclohexene was then optimized (PM6) to minimum to obtained optimized reaction product structure. Transition state was checked with frequency calculation and IRC.

===Cyclohexadiene and 1,3-Dioxole===

The structures of cyclohexa-1,3-diene, 1,3-dioxole and their corresponding Diels-Alder products via exo- and endo- transition states were drawn in Gaussview. Optimized structure were obtained by optimizing to PM6 level. The optimized transition states were obtained by breaking the formed bond in the D-A reaction, then optimizing to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond length between two reaction sites of two alkenes to 2.2 Å, followed by IRC analysis (PM6), where MOs of transition states were also obtained. MOs generated from the single point energy calculation were further analyzed. Each calculation was then further optimized to B3LYP/6-31G(d) level to obtain the reaction barriers and reaction energies at room temperature.

===O-Xylene-So2 Cycloaddition===

The structure of 5,6-dimethylenecyclohexa-1,3-diene, sulphur dioxide and their corresponding products via exo-Diels-Alder, endo-Diels-Alder and cheletropic transition states were drawn in Gaussview. Optimized structures were obtained by optimizing to PM6. The optimized transition states were obtained by breaking the formed bond in each reaction, then optimized to transition state (PM6, Berny, calculating force constancts for once) allowing Opt=NoEigen after freezing the bond length between two reaction sites of two alkenes to 2.2 Å, followed by IRC analysis (PM6), where MOs of transition states were also obtained. Each calculation was then further optimized to B3LYP/6-31G(d) level to obtain the reaction barriers and reaction energies at room temperature.

==Result and Discussion==

===Butadiene and Ethylene===

Following the procedure in experimental, optimized structures of reactant were obtained and all carbon-carbon bond lengths were shown in fig 1.1. In order to understand the MO interactions during this reaction, MO diagram (fig 1.2) was constructed with symmetry labels in normal demand DA. HOMOs-LUMO region orbitals were visualized in table 1.1 and 1.2. IRC analysis result were included in the table 1.3. *NB height of each T.S. MO is the height of corresponding product, transition state have higher energy than both reactants and product.

[[File:Ms zh3615.png|thumb|center|450px|Fig 1.1 Reaction scheme and bond lengths (unit: Å)]]

[[File:Mo zh3615.png|thumb|center|350px|Fig 1.2 MO diagram of the Diels-Alder reaction]]

The in-phase HOMO and out-of-phase LUMO of the transition state is formed by the interaction between the HOMO of ethylene and LUMO of butadiene. Both the reacting orbitals and formed orbitals are gerade, which indicates that the reacting orbitals in the allowed Diels-Alder reaction for 6-pi-electron system should have the same symmetry. The orbital overlaps integral is zero (no wavefunction overlap) for gerade-ungerade interaction and non-zero gerade-gerade/ungerade-ungerade interaction.

Given that (1) a typical sp3 carbon-carbon bond has a bond length of 1.54 Å, (2) a typical sp2 carbon-carbon bond has a bond length of 1.34 Å and (3) the Van der Waals radius of carbon atom is 1.7 Å.[1] As the reaction proceeds,the bond lengths of double bonds in both alkenes increases as they are gradually transformed to single carbon-carbon bonds, the bond length of the only single bond in the butadiene decreases as it was transformed to a double carbon-carbon bond gradually. The forming single carbon-carbon bonds of transition state between two alkenes have a bond length of 2.115 Å, which are shorter than double Van der Waals radius (3.4 Å).

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.1 MOs and corresponding visualizations of reactants
! !!LUMO!!HOMO
|-
|Butadiene MO||[[File:butalumozh3615.png|120px]]||[[File:butahomozh3615.png|120px]]
|-
|Butadiene MO Visualization||align="center"|[[File:butalumomozh3615.png|80px]]||align="center"|[[File:butahomomozh3615.png|80px]]
|-
|Ethylene MO||[[File:ethlumozh3615.png|120px]]||[[File:ethhomozh3615.png|120px]]
|-
|Ethylene MO Visualization||align="center"|[[File:ethlumomozh3615.png|80px]]||align="center"|[[File:ethhomomozh3615.png|80px]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.2 MOs and corresponding visualizations of transition states
! !!LUMO+1!!LUMO!!HOMO!!HOMO-1
|-
|T.S. MO||[[File:cyclumo+1zh3615.png|120px]]||[[File:cyclumozh3615.png|120px]]||[[File:cychomozh3615.png|120px]]||[[File:cychomo-1zh3615.png|120px]]
|-
|T.S. MO Visualization||align="center"|[[File:lumo+1mozh3615.png|80px]]||align="center"|[[File:lumomozh3615.png|80px]]||align="center"|[[File:homomozh3615.png|80px]]||align="center"|[[File:homo-1mozh3615.png|80px]]
|}

As shown in the IRC analysis in table 1.3, the variation of the bond lengths of forming bond is identical in shape and value, which indicates that the new c-c single bonds are made simultaneously during the approaching of alkenes. In contrast, asynchronous formation of new bonds will produce different bond length curves between two forming bonds.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1.3 IRC analysis
! Transition state vibration !! Transition state animation
|-
|align="center"|[[File:Ts ZH3615.gif]]||align="center"|[[File:Ircgifgif.gif]]
|-
| colspan="2" align="center"|[[File:Irc zh3615.png|500px]]
|-
| colspan="2" align="center"|[[File:Bondlengthzh3615.png|500px]]
|}

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to transition state(PM6)!!IRC analysis(PM6)
|-
|Butadiene||[[File:Butadiene zh3615.LOG]]
|-
|Ethylene||[[File:Ethylene_zh3615.LOG]]
|-
|Transition states||[[File:1tstomin_zh3615.LOG]]||[[File:1tstots_zh3615.LOG]]||[[File:1tstoirc_zh3615.LOG]]
|-
|Reaction product||[[File:1ptomin zh3615.LOG]]
|}

===Cyclohexadiene and 1,3-Dioxole===

The obtained transition states were ensured by observing the vibrational frequencies(only 1 negative/imaginary frequency and rest were all positive). The MO diagram of this reaction was drawn according to the MO order calculated from energy analysis in the Gaussview as shown in table 2.1 following the rule in the figure 1.2, which suggested that both reactions are reverse demand Diels-Alder reactions. The HOMO-LUMO region orbitals of the endo- and exo- transition states were visualized and shown in the table 2.2. The activation energies, reaction energies and other related data were calculated and tabulated in table 2.3.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.1 MO diagrams via two T.S.
! MO diagram via exo-T.S. !! MO diagram via endo-T.S.
|-
|[[File:Rs2exo_zh3615.png|center|400px]]||[[File:Rs2endo_zh3615.png|center|400px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.2 Visualization of Molecular orbitals
! !! Exo- transition state(side view) !! Exo- transition state(top view) !! Endo- transition state(side view) !! Endo- transition state(top view)
|-
|LUMO+1||[[File:Exo lumo+12 zh3615.png|250px]]||[[File:exolumo-1momozh3615.png|260px]]||[[File:Endo lumo+12 zh3615.png|250px]]||[[File:Endolumo-1momozh3615.png|310px]]
|-
|LUMO||[[File:Endo lumo2 zh3615.png|250px]]||[[File:exolumomomozh3615.png|260px]]||[[File:Endo lumo2 zh3615.png|250px]]||[[File:Endolumomomozh3615.png|310px]]
|-
|HOMO||[[File:Exo homo2 zh3615.png|250px]]||[[File:exohomomomozh3615.png|260px]]||[[File:Endo homo2 zh3615.png|250px]]||[[File:Endohomomomozh3615.png|310px]]
|-
|HOMO-1||[[File:Exo homo-12 zh3615.png|250px]]||[[File:Exohomo-1momozh3615.png|250px]]||[[File:Endo homo-12 zh3615.png|250px]]||[[File:Endohomo-1momozh3615.png|310px]]
|}

As shown in the table 2.2, the

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2.3 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S.
|-
|Cyclohexadiene||colspan=2 align="center"|306.9 (-612593)
|-
|1,3-dioxole||colspan=2 align="center"|-137.3 (-701187)
|-
|Reactant sum||colspan=2 align="center"|169.6 (-1313781)
|-
|Transition state||align="center"|362.2 (-1313622)||align="center"|364.7 (-1313614)
|-
|Reaction product||align="center"|99.2 (-1313849)||align="center"|99.7 (-1313846)
|-
|Activation energy||align="center"|192.6 (159.0)||align="center"|195.1 (167.0)
|-
|Reaction energy||align="center"|-70.3 (-68.0)||align="center"|-69.9 (-64.0)
|}

*NB the values in brackets were the value calculated from DFT-B3LYP-6-31G(d) method, the other values were the value calculated from PM6 method.

As shown in the table 2.3, both the activation energy and reaction energy via endo-transition state is less compared to the Diels-Alder reaction via exo-transition state, which indicates the endo-reaction product is both the kinetic and thermodynamic product.

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to min(631G)!!Optimized to T.S.(PM6)!!Optimized to T.S.(631G)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|Cyclohexadiene||[[File:Hextominpm6 zh3615.LOG]]||[[File:Hextomin631 zh3615.LOG]]
|-
|1,3-dioxole||[[File:diotominpm6_zh3615.LOG]]||[[File:diotomin631_zh3615.LOG]]
|-
|Exo-T.S.||[[File:2EXOtominpm6 zh3615.LOG]]|| ||[[File:2EXOtoTSpm6 zh3615.LOG]]||[[File:2EXOtoTS631 zh3615.LOG]]||[[File:2EXOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Endo-T.S.||[[File:2ENDOtominpm6 zh3615.LOG]]|| ||[[File:2ENDOtoTSpm6 zh3615.LOG]]||[[File:2ENDOtoTS631 zh3615.LOG]]||[[File:2ENDOtoIRC zh3615.LOG]]||[[File:2EXOtoENERGY zh3615.LOG]]
|-
|Exo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:EXOproduct631_zh3615.log]]
|-
|Endo-reaction product||[[File:1ptomin zh3615.LOG]]||[[File:ENDOproduct631_zh3615.log]]
|}

===O-Xylene-So2 Cycloaddition===

Each reaction was visualized by carrying out IRC analysis at the PM6 level as shown in the table 1.6. Activation energies and reaction energies were calculated at DFT-B3LYP-6-31G-d level in KJ/mol as shown in the table 1.7, where corresponding energy profiles are also shown.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.1 Animation from IRC analysis for each reaction pathway
! !! Endo-Diels-Alder T.S. !! Exo-Diels-Alder T.S. !! Cheletropic T.S.
|-
|Animation||[[File:Endoendozh3615.gif|300px]]||[[File:Exoexozh3615.gif|300px]]||[[File:Chechechezh3615.gif|300px]]
|-
|Animation||[[File:Endoirc_zh3615.png|300px]]||[[File:Exoirc_zh3615.png|300px]]||[[File:Cheirc_zh3615.png|300px]]
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3.2 Energy calculations of each reaction pathway (KJ/mol)
! !! via endo-Diels-Alder T.S. !! via exo-Diels-Alder T.S. !! via cheletropic T.S.
|-
|O-xylylene||colspan=3 align="center"|469.3 (-812604)
|-
|Sulphur dioxide||colspan=3 align="center"|-297.7 (-1440092)
|-
|Reactant sum||colspan=3 align="center"|171.6 (-2252696)
|-
|Transition state||align="center"|237.8 (||align="center"|241.8 (-2253042)||align="center"|xxx
|-
|Reaction product||align="center"|57.0 (-2253040)||align="center"|72.1 (-2253042)||align="center"|-0.00525 (-2253030)
|-
|Activation energy||align="center"|xxx||align="center"|xxx||align="center"|xxx
|-
|Reaction energy||align="center"|||align="center"|xxx||align="center"|
|}

*NB the values in brackets were the value calculated from DFT-B3LYP method, the other values were the value calculated from PM6 method.

[[File:Energy_profile_zh3615.png|thumb|center|Figure 3.1 Energy profile of three reaction pathways]]

File download:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! !!Optimized to min(PM6)!!Optimized to T.S.(PM6)!!IRC analysis(PM6)!!Energy analysis(PM6)
|-
|O-Xylene||[[File:oxypm6zh3615.LOG]]
|-
|SO2||[[File:so2pm6zh3615.LOG]]
|-
|Exo-D-A-T.S.||[[File:Daexototspm6.log]]||[[File:daexototstspm6.log]]||[[File:Daexoirc_zh3615.log]]||[[File:DAEXO6energy_zh3615.LOG]]
|-
|Endo-D-A-T.S.||[[File:Daendototspm6.log]]||[[File:daendototstspm6.log]]||[[File:Daendoirc_zh3615.gjf]]||[[File:DAENDOenergy_zh3615.LOG]]
|-
|Cheletropic-T.S.||[[File:chetotspm6.log]]||[[File:chetotstspm6.log]]||[[File:CHE_IRC_zh3615.log]]||[[File:CHEenergy_zh3615.LOG]]
|-
|Exo-D-A-reaction product||[[File:Daexoproductminpm6.LOG]]
|-
|Endo-D-A-reaction product||[[File:Daendoproductminpm6.log]]
|-
|Cheletropic reaction product||[[File:Cheproductpm6_zh3615.LOG]]
|}

==Conclusion==

The structures of reactants, product and transition states of three Diels-Alder reactions were determined using GaussView 5.0.9. Semi-empirical method PM6, density functional theory method (DFT) B3LYP, IRC analysis and energy analysis were adopted in the optimization, visualisation and calculation. Theoretical values of bond lengths, MO order, sum of electronic and thermal free energies etc. were obtained and the competition between Dies-Alder reaction and Cheletropic reactions was investigated. All obtained data agreed with theory or was in literature range.