Rep:Mod:TP1414

Introduction

Gaussian and Transition State Characterization

2D energy surface showing the locations of transition state (TS), local minimum (LM) and global minimum (GM).^[1]

Gaussian is a molecular modelling software that allows researchers to carry out extensive investigation of molecules and their reactions. In these exercises, the transition states of several Diels-Alder reactions are located and characterized using Gaussian. A transition state is a first order saddle point on a potential energy surface (PES). It is the maximum along the minimum energy path (or reaction path) between two minima (the reactants and the products). Geometry optimization to find the minimum energy structure will usually lead to a stationary point that is closest to the initial geometry. The stationary point, where the first derivative of energy is zero, can be a global minimum, a local minimum or a saddle point. In a reaction path, the minima (global or local) correspond to the reactants and the products, while the saddle point corresponds to the transition state. To differentiate between a minimum and a saddle point, the second derivatives of energy will have to be analysed. For global or local minima, where energy rises in all directions, the second derivative of energy is positive. In contrast, for transition state, where the energy decreases in one direction (reaction path), the second derivative of energy along the reaction coordinate is negative. The analysis of the second derivatives of energy can be done by a frequency calculation of the optimized structure. If the structure corresponds to the reactants or products, all the vibrational frequencies (v) are real. In contrast, if the structure corresponds to a transition state, there will be one imaginary frequency. This imaginary frequency indicates that the force constant (k), which is given by the second derivative, is negative. ^[2]

v = \frac{1}{2 π} \cdot \sqrt{\frac{k}{μ}}

where

k = \frac{\partial^{2} E}{\partial q^{2}}

Following a successful frequency calculation (one imaginary frequency) of the transition state, an Intrinsic Reaction Coordinate (IRC) calculation may be set up to examine the transition state along the minimum energy path more closely. The reaction path, or minimum energy path, can be defined as the steepest descent path from the transition state to the reactions and products.

In this exercise, two calculation methods are used. The first is the semi-empirical method PM6, a fitted method used to obtain the initial geometry of the molecule or transition state so as to save time during calculations. The second is the Density Functional Theory (DFT) method B3LYP, a method that is capable of reproducing chemical data and is used to further optimise the geometry obtained from the PM6 method.

Diels-Alder Reactions

A Diels-Alder reaction is a [4+2] cycloadditon between a conjugated s-cis diene (4π-electron system) and a dienophile (2π-electron system). The reaction has a cyclic transition state with 6π-electrons, is concerted, and results in the formation of two new sigma bonds. According to the Woodward-Hoffmann Rules, the Diels-Alder reaction is thermally allowed and is an orbital-controlled reaction, in which the six electrons are interacting suprafacially. The reaction can mainly proceed in two ways:

Normal electron demand: HOMO of diene overlaps with LUMO of dienophile
Inverse electron demand: LUMO of diene overlaps with HOMO of dienophile

Several papers divide the Diels-Alder reactions into three categories instead of two ^[3] ^[4], the third being a neutral electron demand Diels-Alder, in which the energy separation between the HOMO and LUMO of both reactants is similar. ^[3] Neutral electron demand Diels-Alder reactions are seldom observed and believed to be a transition between normal electron demand and inverse electron demand Diels Alder reactions.^[4] Below is a comparison of the energy levels of the HOMO and LUMO of the reactants in each case of Diels-Alder reaction where EDG = electron donating group and EWG = electron withdrawing group.

Nf710 (talk) 10:36, 7 April 2017 (BST) This is a good intro. YOu couyld have said how the PES is N dimensional. Where N is the number of degrees of freedom.

Exercise 1: Reaction of Butadiene with Ethylene

The reaction between butadiene and ethylene presents the simplest type of Diels-Alder reaction, in which butadiene is the diene and ethylene is the dienophile. This reaction yields cyclohexene as the product, and the reaction scheme is as follow:

Molecular Orbital Diagram

MO Representation

Jmol

Symmetry

MO Representation

Jmol

Symmetry

Butadiene

LUMO

Symmetric

Transition State

MO 4

LUMO+1

Antisymmetric

HOMO

Antisymmetric

MO 3

LUMO

Symmetric

Ethylene

LUMO

Antisymmetric

MO 2

HOMO

Symmetric

HOMO

Symmetric

MO 1

HOMO-1

Antisymmetric

Only orbitals of the same symmetry can interact to form molecular orbitals. This means that only symmetric-symmetric interactions and antisymmetric-antisymmetric interactions are allowed. Symmetric-antisymmetric interactions, on the other hand, are forbidden. This is because the orbital overlap integral is non-zero for interactions between orbitals of the same symmetry and zero for interactions between orbitals of different symmetry.

As shown on the MO diagram above, both interactions (between the HOMO of butadiene and the LUMO of ethylene, and between the LUMO of butadiene and the HOMO of ethylene) occur, generating four molecular orbitals for the transition state. As the energy separation for the two interactions is similar, the reaction between butadiene and ethylene progress with aspects of both normal electron demand and inverse electron demand. This is because both butadiene and ethylene are neutral molecules without any obvious nucleophilic or electrophilic reacting centrers. Both molecules are neither electron-rich nor electron-poor. As a result, orbital overlap is possible for both HOMO-LUMO sets. Several papers classify this reaction as a neutral electron demand Diels-Alder. ^[3] ^[4] This particular Diels-Alder reaction between butadiene and ethylene is well-known for its poor yield.

Internuclear Distances

File:Internuclear distance.pdf

Internuclear Distances (Å)
	C1-C2	C2-C3	C3-C4	C4-C5	C5-C6	C6-C1
Reactants	1.34	1.47	1.34	-	1.33	-
Transition State	1.38	1.41	1.38	2.11	1.38	2.11
Product	1.50	1.34	1.50	1.54	1.54	1.54

As the reaction progresses, C1-C2, C3-C4 and C5-C6 elongate as the double bond breaks to form single carbon-carbon bonds, while C2-C3 shortens to form carbon-carbon double bond. Simultaneously, C4-C5 and C6-C1 decrease in distance and ultimately single carbon-carbon bonds are formed. A more detailed overview of how the internuclear distances change over the course of the reaction is shown on the graph on the right.

A typical carbon-carbon single bond length is 1.54 Å and a typical carbon-carbon double bond length is 1.34 Å. ^[5]

The Van der Waals radius of one carbon atom is 1.70 Å. ^[6] The length of the partly formed carbon-carbon bonds in the transition state is about 2.11 Å. This distance is shorter than twice the Van der Waals radius of carbon atom (3.40 Å), indicating bonding interactions are occuring.

Vibration and Reaction Path

The vibration that corresponds to the reaction path at the transition state is illustrated above. This vibration has an imaginary frequency that occurs at 948.97i cm^-1.

The formation of the two bonds are synchronous as shown below. This means that the two sigma bonds are formed simultaneously. hence, the reaction between butadiene and ethylene goes by a concerted synchronous mechanism.

Calculation Files

File:TP1414 Exercise 1 Ethylene.log

File:TP1414 Exercise 1 Butadiene.log

File:TP1414 Exercise 1 Product.log

File:TP1414 Exercise 1 Transition State.log

File:TP1414 Exercise 1 IRC.log