Transition States of Diels-Alder Reactions - Assignment
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Added on 2021-02-24
Transition States of Diels-Alder Reactions - Assignment
Added on 2021-02-24
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Investigation of the Transition States of Diels-Alder Reactions Name: Lei Yao Date: 24/11/2019-29/11/2019 Introduction This computational lab looked at investigating the transition states of 3 Diels-Alder (DA) reactions by modelling the transition state and the reaction pathway using Gaussian and GaussView. Though it’s impossible to capture the transition state species, it is possible to model the structure of the transition state, which gives a lot of information about the reaction mechanism. The calculation of the transition state can be applied to the calculation of the IRC subsequently for the energy profile of the reaction. Potential energy surface (PES) is a conceptual description of the energies for a whole reaction system, it is usually two-dimensional, in terms of energy against some parameters (such as bond lengths). PES is a landscape of the molecular geometries and molecular reaction dynamics. There could 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 reaction progress. 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 for obtaining information of the reaction. Minima and maxima both belong to stationary points, which mathematically are the points with the first derivatives of two variables, fxand fy, being equal to zero, which means the surface is flat at that point. Viewed from the molecular geometry point, local minimum is the lowest point in local area and is in a well, while maxima are at the top of a mountain. The saddle point is a minimum on one direction while being a maximum in other direction. Satisfying the condition of fx=0 and fy= 0, if at that point (fxxfyy – f2xy) > 0 and fxx> 0, then this point is a minimum. Chemically, the reactants and the products of a reaction are both local minima hence sit in 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 a PES is the saddle point since it has the highest energy in a relatively low-energy reaction pathway, it is a maximum in the degree of reaction coordination In 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-Fock theory with empirical correction. It obtains experimental data and made additional approximation to help quicken up calculation, this operation mode makes it faster to calculate but less accurate.[1]As a result, a further method of B3LYP/6-31G(d) was used to reoptimised the output of the previous PM6 calculation. B3LYP/6-31G(d) is a hybrid exchange-correlation functional method with properties from both density functional theory (DFT) and the Hartree-Fock theory. It uses 3 empirical parameters, hence it should give more accurate results than the semi-empirical method PM6 does although it takes a longer time to do the calculation.[2]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 chemical reaction, which will be useful to study the mechanism.
Exercise 1: Reaction of Butadiene with Ethylene [Method: Semi-empirical PM6]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 two new C-C bonds are formed and a 6-membered ring is produced. The reactants are trans-butadiene and ethylene as the dienophile. Figure 2. The mechanism of reaction of butadiene and ethylene. 1.Energy The 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 of imaginary 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 0 gradient, indicating that they are all stationary points mathematically, hence further confirms that the correct structures of these species are obtained. Figure 3. The IRC path and the RMS gradient graph of the reaction. Energy/Hartree Reaction barrier/ kJ mol-1Reaction energy (ΔG)/ kJ mol-1Butadiene 0.097764 170.0 -132.9 Ethene 0.050102 Transition State 0.212626 Cyclohexene (product) 0.100648 Product Reactants
3.MOs Diagram Figure 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 are used to construct four MOs of the transition state. The HOMO of butadiene can only interact with the LUMO of ethene and vice versa, since the occupied orbital (HOMO) with high electron density can 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 particular MO. Butadiene is π4component 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-Hoffmann rule, there’s one (4q+2)s, where q = 1, and no (4r)a. This makes the sum of (4q+2)s+ (4r)aan odd number, hence the reaction is allowed. If the sum is an even number the reaction will not be allowed, and the rules apply to any thermal pericyclic reaction. The overlap integral of symmetry-symmetry and asymmetry-asymmetry is 1 (non-zero), and for symmetry-asymmetry the integral would be zero since the it cancels out.
4.Bond LengthsFigure 5. Cyclohexene with labelled carbon atoms. 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 single bond (C1-C6) becomes double bond after the reaction, hence the bond shortens from 1.471 Å to 1.337 Å. The newly formed sp3 C-C bonds (C8-C11 and C14-C3) experience a significant distance change since the reactants are far from each other before the reaction, and the distance shortens to 1.501 Å which is the length of a sp3 C-C bond. Bond type Bond Length/ Å Bond Energy/kJ mol-1sp3C-C single bond 1.54 348 Sp2C=C double bond 1.33 614 Table 3. The typical bond lengths and bond energies of C-C single bond and C=C double bond.[3] [4] The Van der Waals radius of the carbon atom is 1.7 Å, which is half of the distance between two unbonded atoms (that are attracted to each other by the Van der Waal’s Force). For all types of bonds mentioned preciously, the internuclear distances in transition states (1.38 Å, 1.411 Å, 2.11 Å and 1.38 Å) are shorter than twice of the Van der Waals radius (3.4 Å) which means there are attracting interaction existing between each pair of carbons. In the meantime, the distances are longer than the particular bond length of the later formed bonds, indicating the bonding situation in transition states is actually partially bonded. The formation of the new bonds C3-C14 and C6-C8 are synchronous, which means the bonds are formed at the same time and the reaction is a one-step reaction. Atoms Bond Length of Reactants TS atomic distances Bond Length of Product C3-C1 & C6-C8 1.333 1.380 1.501 C1-C6 1.471 1.411 1.337 C14-C3 & C8-C11 N/A 2.114 1.537 C11-C14 1.327 1.382 1.536
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