Investigation of the Transition States of Diels-Alder Reactions (Doc)
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Investigation of the Transition States of Diels-Alder ReactionsName: Lei Yao Date: 24/11/2019-29/11/2019IntroductionThis computational lab looked at investigating the transition states of 3 Diels-Alder (DA) reactions bymodelling the transition state and the reaction pathway using Gaussian and GaussView. Though it’simpossible to capture the transition state species, it is possible to model the structure of thetransition state, which gives a lot of information about the reaction mechanism. The calculation ofthe transition state can be applied to the calculation of the IRC subsequently for the energy profile ofthe reaction.Potential energy surface (PES) is a conceptual description of the energies for a whole reactionsystem, it is usually two-dimensional, in terms of energy against some parameters (such as bondlengths). PES is a landscape of the molecular geometries and molecular reaction dynamics. Therecould be many energetic pathways between the reactant and the product (which both are minima).What was obtained with GaussView in this lab was a simplification of the full PES, it is a one-dimensional energy profile of energy against reaction coordination that represents a single reactionprogress. Transition states is the highest point on this energy-coordination curve.The evaluation of some certain points, such as maxima, minima and saddle points, is crucial forobtaining information of the reaction. Minima and maxima both belong to stationary points, whichmathematically are the points with the first derivatives of two variables, fxand fy, being equal tozero, which means the surface is flat at that point. Viewed from the molecular geometry point, localminimum is the lowest point in local area and is in a well, while maxima are at the top of amountain. The saddle point is a minimum on one direction while being a maximum in otherdirection.Satisfying the condition of fx=0 and fy= 0, if at that point (fxxfyy–f2xy) > 0 and fxx> 0, then this point isa minimum. Chemically, the reactants and the products of a reaction are both local minima hence sitin a well. Oppositely, if at that point (fxxfyy–f2xy) > 0 but fxx< 0, then this point is a maximum. When fx=0 and fy= 0, if at that point (fxxfyy–f2xy) < 0, then there’s a saddle at that point. Transition state in aPES is the saddle point since it has the highest energy in a relatively low-energy reaction pathway, itis a maximum in the degree of reaction coordinationIn the process of modelling reaction and calculating the transition state, two computational methods(PM6 and B3LYP/6-31G(d)) were used. PM6 is semi-empirical, it is a simplification of Hartree-Focktheory with empirical correction. It obtains experimental data and made additional approximation tohelp quicken up calculation, this operation mode makes it faster to calculate but less accurate.Asa result, a further method of B3LYP/6-31G(d) was used to reoptimised the output of the previousPM6 calculation. B3LYP/6-31G(d) is a hybrid exchange-correlation functional method with propertiesfrom both density functional theory (DFT) and the Hartree-Fock theory. It uses 3 empiricalparameters, hence it should give more accurate results than the semi-empirical method PM6 doesalthough it takes a longer time to do the calculation.Using these computational methods, it is capable to calculate the energetic states of reactants,products and the transition states, and subsequently the active barrier energy for a chemicalreaction, which will be useful to study the mechanism.
Exercise 1: Reaction of Butadiene with Ethylene [Method: Semi-empiricalPM6]Figure 1. The scheme of reaction of butadiene and ethylene.This reaction is a pericyclic [4+2] cycloaddition, also called Diels-Alder (DA) reaction, in which twonew C-C bonds are formed and a 6-membered ring is produced. The reactants are trans-butadieneand ethylene as the dienophile.Figure 2. The mechanism of reaction of butadiene and ethylene.1.EnergyThe correct structure and energy of the reactants, product and transition state were all confirmed(paragraph in log file seen in appendix) since the threshold are converged and the right number ofimaginary frequencies were obtained (1 for transition state and 0 for the rest).Table 1. The energies of the molecule species and the reaction.2.IRCThe reaction is an exothermic reaction.The reactants, TS and product all have 0gradient, indicating that they are allstationary points mathematically, hencefurther confirms that the correctstructures of these species are obtained.Figure 3. The IRC path and the RMSgradient graph of the reaction.Energy/HartreeReactionbarrier/ kJ mol-1Reaction energy(ΔG)/ kJ mol-1Butadiene0.097764170.0-132.9Ethene0.050102Transition State0.212626Cyclohexene (product)0.100648ProductReactants
3.MOs DiagramFigure 4. The MOs diagram for the formation of butadiene/ethene transition state.As it could be seen in the MOs diagram, the HOMO and LUMO of both butadiene and ethene areused to construct four MOs of the transition state. The HOMO of butadiene can only interact withthe LUMO of ethene and vice versa, since the occupied orbital (HOMO) with high electron densitycan donate electron density into the empty orbital (LUMO).The orbitals are only allowed to interact with orbitals with the same symmetry (symmetric-symmetric and asymmetric-asymmetric), which is decided by the phase of lobes in one particularMO.Butadiene isπ4component while ethene is π2, the new bonds are formed on the same side(suprafacial) of each of the components hence π4s and π2s. According to the Woodward-Hoffmannrule, there’s one (4q+2)s, where q = 1, and no (4r)a. This makes the sum of (4q+2)s+ (4r)aan oddnumber, hence the reaction is allowed. If the sum is an even number the reaction will not beallowed, and the rules apply to any thermal pericyclic reaction.The overlap integral of symmetry-symmetry and asymmetry-asymmetry is 1 (non-zero), and forsymmetry-asymmetry the integral would be zero since the it cancels out.
4.Bond LengthsFigure 5. Cyclohexenewith labelled carbonatoms. Table 2. The bond lengths of the bonds involved in the reaction.Figure 6. The plot of the internuclear distances (bond lengths) against the reaction coordination.The sp2C=C bonds, C3-C1 and C6-C8, in butadiene and the C11-C14 in ethene become sp3C-C bonds,as a result the bonds weaken and are longer, changing from 1.333Å to 1.501 Å. While the C-C singlebond (C1-C6) becomes double bond after the reaction, hence the bond shortens from 1.471 Å to1.337 Å. The newly formed sp3C-C bonds (C8-C11 and C14-C3) experience a significant distancechange since the reactants are far from each other before the reaction, and the distance shortens to1.501 Å which is the length of a sp3C-C bond.Bond typeBond Length/ ÅBond Energy/kJ mol-1sp3C-C single bond1.54348Sp2C=C double bond1.33614Table 3. The typical bond lengths and bond energies of C-C single bond and C=C double bond. The Van der Waals radius of the carbon atom is 1.7 Å, which is half of the distance between twounbonded atoms (that are attracted to each other by the Van der Waal’s Force). For all types ofbonds mentioned preciously, the internuclear distances in transition states (1.38 Å, 1.411 Å, 2.11 Åand 1.38 Å) are shorter than twice of the Van der Waals radius (3.4 Å) which means there areattracting interaction existing between each pair of carbons. In the meantime, the distances arelonger than the particular bond length of the later formed bonds, indicating the bonding situation intransition states is actually partially bonded.The formation of the new bonds C3-C14 and C6-C8 are synchronous, which means the bonds areformed at the same time and the reaction is a one-step reaction.AtomsBond Lengthof ReactantsTS atomicdistancesBond Length ofProductC3-C1 & C6-C81.3331.3801.501C1-C61.4711.4111.337C14-C3 & C8-C11N/A2.1141.537C11-C141.3271.3821.536