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Rep:Kh1015TS

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1. Abstract.

This paper studied eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. In Exercise 1-3, the MO calculation was used to identify the interacting frontier orbitals and possible secondary-orbital interactions. In Exercise 1, the C-C bond length of molecules optimized using PM6 level showed good agreement with literature with less than 1% percentage difference. IRC analysis at PM6 level in all exercises showed that the TS has been optimized. In Exercise 2 and Exercise 3, thermodynamic values (activation Gibbs-Free energy and Δ Gibbs-Free energy) were extracted from the log file output and rate constant was calculated using the activation Gibbs-Free energy based on method by D. A. McQuarrie (1997) [1].

2. Aim.

The aim of this study is to locate and characterize the transition states of several Diels-Alder reactions.

3. Introduction.

Chemical behaviour of a molecule is controlled by the electrons that participate in the chemical process [2]. In particular, the electronic structure and properties in its stationary state could be described by the time-independent solution of Schrödinger’s equation:

H^ψA=EAψA

, where A labels the state of interest [2].

The above equation forms the foundation for quantum chemistry and modern computational methods.

For a given reaction where there is ambiguity in structure or mechanism, computational chemistry is useful in predicting the likeliest structure or mechanism. For example, in 1986, computational calculation correctly predicted and later experimentally confirmed a bent structure for methylene, which challenged the linear experimental value by Hertzberg thought to be true at the time [3].

A. Standard Computational Methods.

The recurring challenge in computational method is that the Schrodinger equation can be solved exactly only for one-electron systems, while most molecules have much more than one electron in the system. To address this challenges, multiple methods have been developed to find increasingly accurate approximations to the Schrodinger equation for many-electron systems [2]. Each of the methods has its own trade-off between accuracy and computational cost. With that in mind, two such methods had been selected in this study: semi-quantitative Parameterization Method 6 (PM6); and Density Functional Theory (DFT), Becke, 3-parameter, Lee-Yang-Parr (B3LYP).

1) Semi Quantitative PM6 (Parameterization Method 6).

PM6 is a modified semi-empirical method categorized under Neglect of Diatomic Differential Overlap (NDDO) [4].The main advantage of modified version of NDDO (MNDO) over its predecessors lies in the optimization of parameters to simulate molecular properties which is more accurate than calculations based on atomic properties [4]. The inability of earlier MNDO to simulate hydrogen bond has been addressed in PM6 method, where the percentage difference of the average unsigned error (AUE) of a water dimer model (1.35 kcal mol-1) is 27% relative to that obtained by exhaustive analysis by Tschumper, et al. using CCSD(T) and a large basis set (5.00 kcal mol-1) [4].

Nf710 (talk) 09:37, 22 March 2018 (UTC) This is really good , you have clearly read beyond the script. However it would have been nice ot have some equations explaining these terms. eg what they represent in the hamiltonian.

2) DFT, B3LYP (Density Functional Theory, Becke, 3-parameter, Lee-Yang-Parr).

In general, DFT uses variational principle and one-electron density for the calculation and therefore bypasses the consideration of the many-electron wavefunction [2]. From the Hohenberg-Kohn Theorems, it has been established that the ground state energy and all of its properties can be extracted from one-electron density alone [2][5]. DFT includes exchange-correlation functionals and self-consistent field type formalism [2]. The basic form of DFT uses exchange and correlation terms of uniform electron gas, which is not a good approximation to the actual electron distribution in chemical systems. This error is most pronounced in two bonded atoms that have very high electronegativity difference (O-H for example), where there is a non-uniform distribution of electron density which is skewed towards the more electronegative atom. Hence, empirical inputs - such as atomic correlation energies or thermochemical databases - have been used to refine the DFT method [2]. B3LYP is a hybrid DFT functional method whose energy term includes Slater exchange, the Hartree–Fock exchange, Becke’s exchange functional correction, the gradient-corrected correlation functional of Lee, Yang and Parr, and the local correlation functional of Vosko, Wilk and Nusair [6][7].

Nf710 (talk) 09:40, 22 March 2018 (UTC) Again good extra reading. DFT is exact if we dont accoutn for 2 electron terms. These get put into the XC correlation term and then different functionals account for this in different ways.

B. Finding a Stable or Transition structure in a PES.

From the computational output, it is possible to model a potential energy surface (PES), that is dependent on one variable or more. In any given PES, there are 4 simple conditions which allow a user to find a stable structure or a transition structure [2]:

1) Determining Stationary Point via Gradient.


dE(R)dRi=0,i=1,2,...3Natoms−6

, where E(R) refers to the total energy of the system, R in E(R) refers to the set of all nuclear coordinates and Ri refers to a specific member of the set.

2) Characterizing Minimum Point via Curvature (Positive Force Constants).


d2E(R)dqi2>0,i=1,2,...3Natoms−6

, where E(R) refers to the total energy of the system, R in E(R) refers to the set of all nuclear coordinates and qi refers to a specific combination of R and bond angle (θ).

3) Characterizing Transition Point via Curvature (One Unique Negative Force Constant corresponding to First Order Saddle Point in Reaction Coordinate (RC)).


d2E(R)dqRC2<0

, where E(R) refers to the total energy of the system, R in E(R) refers to the set of all nuclear coordinates and qRC refers to a specific combination of R and bond angle (θ) at the lowest-possible transition state in the PES.

4) Characterizing Transition Point via Curvature (Positive Force Constants For The Remaining Ones).


d2E(R)dqi2>0,i=1,2,...3Natoms−7

, where E(R) refers to the total energy of the system, R in E(R) refers to the set of all nuclear coordinates and qi refers to a specific combination of R and bond angle (θ).

While useful, it should be noted that the 4 conditions above could not differentiate between global and local stationary points, which could impact the accuracy of geometry optimization if the geometry is trapped in a local minimum rather than global minimum.

Nf710 (talk) 09:52, 22 March 2018 (UTC) This is really nicely explained. What is actually happening is you put the derivative wrt to the degrees of freedom into the hessian matrix, then diagonalise it. this give you your eigenvectords as the normal modes and your eigenvalue is the force constant for that normal mode. This normal mode is a linear combination of the degrees of freedom. hence why when you move back and forth along it it looks like a vibration.

C.Intrinsic Reaction Coordinate (IRC).

In 1970, Fukui proposed the concept of IRC, which is defined as the mass-weighted, vibrationless, motionless and steepest descent path on the PES from the TS or the first-order saddle point to two minima on either side of the TS [8]. The descent from higher-order saddle point is called meta-IRC [8]. In mathematical form, IRC is obtained by solving the following differential equation [8]:


dq(s)ds=v(s)

, where q is the mass-weighted Cartesian coordinates, s is the coordinate along the IRC and v is a normalized tangent vector to the IRC corresponding to the normal coordinate eigenvector with a negative eigenvalue at the TS with s=0.

At the other points, v is the unit vector parallel to the mass-weighted gradient vector g with the following relationship [8]:


v=−g|g| for s > 0


and


v=g|g| for s < 0

IRC calculation has been used extensively to confirm the connection between a given TS and two minima (reactant(s) and product(s)) for a given reaction [8]. In this study, IRC calculation had been done for all the reactions such that it can be used to independently confirm that the TS geometry for the given reaction had truly been optimized.

From a successful IRC calculation (Minimum-TS-Minimum), it is possible to extract the calculated activation energy (linked to a given computational method) and therefore, the calculated rate constant for a reaction via transition state theory [8].

D. Predicting Rate of Reaction from Calculated Thermodynamic Values.

Once the activation free-energy of a reaction is calculated, it is possible to calculate the predicted rate of reaction via the equation below [1]:


k(T)=kBThcoe−Δ‡GoRT

, where k(T) is rate constant at a specified temperature, kB is Boltzmann constant (1.3807 x 10-23 J K-1), T is temperature (in K), h is Planck's constant (6.626176 x 10-34 J s), co is concentration (taken to be 1, unitless), Δ‡Go is the activation Gibbs-Free Energy (J mol-1) and R is gas constant (8.314 J mol-1 K-1).

E. Diels-Alder Reaction as a Study Topic.

Diels-Alder reaction is a concerted [π4s + π2s] cycloaddition between an s-cis conjugated diene and a dienophile to form a cyclohexene [9]. In the reaction, 3 π bonds are broken and 2 sigma bonds and 1 new π bond is formed. In a normal Diels-Alder reaction, the interaction happens between an electron-rich s-cis dienophile and an electron poor diene. In an inverse-electron-demand Diels-Alder reaction, the interaction happens between an electron-poor s-cis dienophile and an electron rich diene.

There is a strong research interest in this reaction due to its importance in biosynthetic processes, use as a protecting group and recent discovery of enzyme Diels-Alderase in nature (for example, spirotetronate cyclase AbyU), which could unlock new and efficient Diels-Alder reactions [9][10][11][12][13][14][15][16][17][18]. In the area of computational chemistry, there are many researches about the geometry of the transition states involved in Diels-Alder reactions and the overall reaction profiles [9][19][10][20].

Nf710 (talk) 09:56, 22 March 2018 (UTC) This is an extremely good intro, you have clearly done lots of extra reading and you have backed up a lot of your discussion with equations to make it more clear.

4. Methodology.

The calculation results assumed two reacting molecules in gaseous phase (in absence of solvation and other interactions with non-reacting, neighbouring molecules). The temperature and pressure settings in the calculations were 298.15 K and 1 atm (default settings). The symmetry and molecular geometries of the products and reactants were not restricted in the optimization process. All of the calculations were performed in GaussView 5.0 and the calculation grid was set to ultrafine (integral=grid=ultrafine). For TS calculations, additional keyword (opt=noeigen) was used in response to possible error in link 9999.

The non-covalent interaction plots were generated using a script by Henry Rzepa and Bob Hanson [21] using default parameters for intermolecular reaction (minimum rho cutoff set to 0.3, covalent density cutoff set to 0.07, fraction of total rho that defined intramolecular interaction set to 0.95, data scaling set to 1).

Unless stated otherwise, all of the optimization jobs were followed by frequency analysis.

Exercise 1: Reaction of Butadiene with Ethylene.

(Fv611 (talk) Good, in depth discussion, but keep in mind that Berny is the name of the algorithm used for our transition state optimisations rather than the name of a type of transition structure (more information here).)

Cyclohexene (product) was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Butadiene and Ethylene.

Figure 4.1 shows the reaction scheme for Exercise 1.

Figure 4.1: Exercise 1 Reaction Scheme.

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.

The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.2 Å at the reacting C-C termini. While freezing the coordinates of the reacting C-C termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of Cyclohexadiene and 1,3-Dioxole.

The optimized structure at PM6 level was reoptimized at B3LYP/6-31G(d) level for the endo product, TS and the reactants.

The above procedures were repeated for the exo-product, with the exception of the reactants.

Figure 4.2 shows the reaction scheme for Exercise 2.

Figure 4.2: Exercise 2 Reaction Scheme.

Exercise 3: Reaction of 5,6-dimethylenecyclohexa-1,3-diene and Sulfur Dioxide.

The endo product was drawn and its geometry optimized to a minimum at PM6 level. Subsequently, the two sigma bonds that were formed due to the Diels-Alder reaction was broken such that two isolated fragments were generated. The two fragments were then manually separated by approximately 2.0 Å at the reacting C-O termini and 2.4 Å at the reacting C-S termini. While freezing the coordinates of the reacting termini, the geometry of the system was optimized to a minimum at PM6 level. Afterwards, the system was optimized to a transition state (Berry) and the force constant calculation was set to once. The output is then used as an input for the IRC calculation at PM6 level, where the force constant calculation was set to "calculate always" and the textbox for compute more points was set to 400.

The two isolated fragments generated during the fragmentation process were individually optimized to a minimum at PM6 level to generate the stable structure of 5,6-dimethylenecyclohexa-1,3-diene and sulfur dioxide.

The above procedures were repeated for the exo-product, cheletropic-product and two minor Diels Alder regio-isomers, with the exception of reactants.

Figure 4.3 shows the reaction scheme for Exercise 3.

Figure 4.3: Exercise 3 Reaction Scheme.

5. Results and Discussion.

Exercise 1: Reaction of Butadiene with Ethylene.

Exercise 1 Results and Discussion.

Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole.

Exercise 2 Results and Discussion.

Exercise 3: Diels-Alder vs Cheletropic.

Exercise 3 Results and Discussion.

6. Conclusion.

In conclusion, this paper had successfully carried out computational calculations to study eight Diels-Alder reactions and one Cheletropic reaction using two popular computational methods: PM6 and B3LYP (6-31 G(d) basis set) in GaussView 5.0. For future work, the calculated results could be shared with other teams who could carry out the experiments in the lab to verify the results.

7. References.

  1. ↑ 1.0 1.1 D. A. McQuarrie, in Physical Chemistry : A Molecular Approach, University Science Books, 1997.
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 J. J. W. McDouall, in Computational Quantum Chemistry: Molecular Structure and Properties in Silico, Royal Society of Chemistry, 2013, ch. 1, pp. 1-62.
  3. ↑ H. F. SCHAEFER III, Science, 1986, 231, 1100-1107.
  4. ↑ 4.0 4.1 4.2 J. J. P. Stewart, J Mol Model, 2007, 13, 1173-1213.
  5. ↑ P. Hohenberg, W. Kohn, Phys. Rev., 1964, 136(3B), B864–B871.
  6. ↑ D. Avci, A. Başoğlu, Y. Atalay, Z. Naturforsch., 2008, 63a, 712-720.
  7. ↑ S.H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys, 1980, 58, 1200.
  8. ↑ 8.0 8.1 8.2 8.3 8.4 8.5 S. Maeda, Y. Harabuchi, Y. Ono, T. Taketsugu, K. Morokuma, International Journal of Quantum Chemistry, 2015, 115, 258-269.
  9. ↑ 9.0 9.1 9.2 T. J. Brocksom, J. Nakamura, M. L. Ferreira and U. Brocksom, J. Braz. Chem. Soc., 2001, 12, 597-622.
  10. ↑ 10.0 10.1 J. Chen, Q. Deng, R. Wang, K. N. Houk, D. Hilvert, ChemBioChem, 2000, 1, 255-261.
  11. ↑ K. N. Houk, J. Gonzalez, Y. Li, Acc. Chem. Res., 1995, 28, 81-90.
  12. ↑ W. M. Bandaranayake, J. E. Banfield, D. St. C. Black, J. Chem. Soc., Chem. Commun., 1980, 902-903.
  13. ↑ K. C. Nicolaou, N. A. Petasis, in Strategies and Tactics in Organic Synthesis, ed. T. Lindberg, Academic Press, 1984, ch. 6, pp. 153-170.
  14. ↑ W. R. Roush, K. Koyama, M. L. Curtin, K. J. Moriarty, J. Am. Chem. Soc., 1996, 118, 7502-7512.
  15. ↑ H. Oikawa, T. Kobayashi, K. Katayama, Y. Suzuki, A. Ichihara, J. Org. Chem., 1998, 63, 8748-8756.
  16. ↑ E. M. Stocking, J. F. Sanz-Cervera, R. M. Williams, J. Am. Chem. Soc., 2000, 122, 1675-1683.
  17. ↑ G. A. Wallace, C. H. Heathcock, J. Org. Chem., 2001, 66, 450-454.
  18. ↑ K. Auclair, A. Sutherland, J. Kennedy, D. J. Witter, J. P. Van den Heever, C. R. Hutchinson, J. C. Vederas, J. Am. Chem. Soc., 2000, 122, 11519-11520.
  19. ↑ K. N. Houk, J. Gonzalez, Y. Li, Acc. Chem. Res., 1995, 28, 81-90.
  20. ↑ D. J. Tantillo, K. N. Houk, M. E. J. Jung, Org. Chem., 2001, 66, 1938-1940.
  21. ↑ Mod:NCI, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:NCI, (accessed March 2018).
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