Applied Quantum Chemistry, NWI-MOL106

• Prospectus (September 2018)
• Schedule (September 2018)
• Book: Ian Fleming, Molecular Orbitals and Organic Chemical Reactions, Student Ed. (Wiley, 2009), ISBN: 978-0-470-74660-8
• Guest lectures week 5+6: Wednesday, 4-October-2018 and 11-October-2018, Prof. Matthias Bickelhaupt

• 1981 Nobel lecture Kenichi Fukui: The role of frontier orbitals in chemical reactions

Lectures

Week 1, Frontier orbitals and the theory of acids and bases

• week1.pdf
• Born-Oppenheimer approximation
• Slater-determinant
• Hartree-Fock/Roothaan, Fock-operator
• Semi-empirical methods, AM1, PM3, PM6, MOPAC
• Denisty functional theory (DFT)
• Acids and bases, Arrhenius, Brønsted, Lewis
• Conjugate acids and bases
• pKa and Gibbs free energy: $pK_a = \frac{\Delta G}{RT\ln(10)}$
• Solvent effects, Born continuum model
• FERMO vs HOMO

Week 2, Frontier orbital theory of reactivity

• week2.pdf
• Thermodynamics vs kinetics, Hammond postulate (Fleming 3.3)
• Perturbation approach to reactivity (Fleming 3.4)
• MO theory, Salem-Klopman equation (third term, Fleming 3.5)
• -C, -Z, -X Substituents (Fleming 2.1 and 6.5.1)
• Hückel theory with hetero atoms (Fleming 1.7.4, Table 1.2)
• Aromaticity, anti-aromaticy and isodesmic reactions

Week 3, effects of charges, reactivity indices

• week3a.pdf, week3b.pdf
• Mulliken charges
• Bond order
• Ambident electrophiles and nucleophiles (Fleming, 4.3)
• Hard and soft acids and bases (Fleming 3.2)
• Salem-Klopman equation (Fleming 3.5)
• Reactivity indices
• Fukui functions, indices
• Super-deloclizability enolate ion 4.3.2)

Warning: there are some errors in Fleming:

• Equation (4.6)[Reference edition] has an incorrect minus sign in the denominator. The correct formula is: \[ f=2\frac{c_3^2+c_2^2e^{-D\Delta\lambda}}{1+e^{-D\Delta\lambda}} \] [See Fukui et al., J. Chem. Phys. 22, 1433 (1954), doi]
• Equation (4.7), the denominator should be E_j-α (for Hückel theory): \[ s_r = \sum_{j}^{\mathrm{occ}} \frac{c_j^2}{E_j-\alpha} \] In MOPAC α can be replaced with the average of the HOMO and LUMO energies.

Week 4

• week4.pdf
• Pericyclic reactions (Fleming 6)
• Woodward-Hoffmann rules (Fleming 6.3)
• Orbital correlation diagram (Fleming 6.4.3)
• Cyclo-additions, supra-/antara-facial (Fleming Fig 6.2)
• Electrocyclic reactions, con- and dis-rotatory
• Sigmatropic shifts, retention/inversion

Week 5, lecture Matthias Bickelhaupt (I)

• Activation Strain Model (Slides-AQC-171004.pdf)

Week 6, lecture Matthias Bickelhaupt (II)

• Fragment-oriented Design(Slides-AQC-171011.pdf)

Week 7, Intermolecular interactions

• week7.pdf
• Exchange interaction
• Electrostatic interactions
• Dipole-dipole interaction
• Induction
• Dispersion Lecture notes by Prof. Ad van der Avoird (pdf) - we mainly discussed part 2 "Intermolecular forces"

Computer class

Week 1, estimating the acidity of molecules

• Use the PM6 hamiltonian (implemented in MOPAC2016)
• HOMO or LUMO of the acid
• HOMO or LUMO of the conjugate base
• Use the FERMO instead (see paper of R. da Silva below)
• Do calculations with and without solvent effects
• Try the relation pKa = delta(G)/(R*T*ln(10))
• A good start are the molecules on page 6 of the table of the Evans group (link below) and: HF, HCl, HBr, HCN (page 1)
• Compare the solvent effect on the pKa of a neutral molecule and
• MOPAC gives energy in kcal/mol, gas constant: R=1.9872 cal/K/mol on for a molecular ion
• Try calculating the pKa of water
• Try calculating the pKa of different protons in a molecule

• Evans Group, Harvard,
• R. da Silva et al., J. Phys. Chem A 110, 1031 (2006) (pKa table: pdf)
• www.ochemonline.com/PKa_data
• A. Hassanali, J. Chem. Educ, 55, 378 (1978)
• Googling "substituent effects on acidity" gives, e.g., chemwiki.ucdavis.edu

Week 2, Conjugation and substituent effects

• π-conjugated molecules and Hückel theory is described in Fleming 1.4
• Aromaticity and anti-aromaticity is discussed in Fleming 1.5-1.5.3
• Hückel theory for molecules with hetero atoms is discussed in Fleming 1.7.4
• -C, -Z, and -X type substituents are defined in the Fleming, 2.1.1, Fig 2
• The effect on orbital energies are given in 6.5.1, page 223

• Calculate energy levels and HOMO-LUMO gap for linear conjugated systems of N carbons (ethylene, allyl, butadiene, hexatriene, etc.) with Hückel and with MOPAC/PM6. Compare with equation 1.10 in the the book:
  \[ E = 2 \beta \cos \frac{k\pi}{N+1}, \;\;\; \mbox{for $k=1,2,...,N$} \]
• Test additivity of hydrogenation enthalpy for a system with two not-conjugated pi-bonds (e.g. H₂C=CH-CH₂-C=CH-CH₃ + n H₂, with n=1,2)
• Calculate the hydrogenation of a molecule with two conjugated pi-bonds (but with exact same atoms, e.g. H₃C-CH=CH₂-C=CH-CH₃ + n H₂)
• Compare hydrogenation enthalpies (PM6) with Hückel delocalization energies
• Check the theory of aromaticity/anti-aromaticity (cyclic systems with either 4n+2 or 4n π electrons) with Hückel calculations for cyclopentadienyl anion and cation. Also compare the cyclic structures with the corresponding linear structures.
• Take your favorite π conjugated molecule and check the substituent effects described in the book (Fig 2.1 and Section 6.5.1 - page 60 and 223 in the student edition). Use Hückel to investigate the π electrons and MOPAC for combined effects. Note: in the "view" panel there is an "edit" button, which pops up a new panel. Select the "labels" button to find the labels of the atoms matching the output file, click again to get the atomic charges. There is also a button for bond-orders.
• 1,3,5,7-Cyclooctatetraene should be anti-aromatic. Use PM6 to optimize the singlet and the triplet state. Look at the heat of formation - what is wrong? Find the explanation by looking at bond-distances and bond-orders, and calculate the singlet state with 1SCF for the geometry optimized at the triplet state, and vice versa.
• According to Fleming, Section 1.4.3 (page 31 in the student edition), Hückel; theory breaks down for long polyenes. This is particularly true if there are small perturbations that would not have any effect in Hückel theory: introduce some -CH3 substituents, s-cis configurations, -CH2-CH2-X substituents etc. This is a general phenomenon of waves known in condensed matter physics as Anderson localization.

Week 3, Substituent effects on the stability of carbocations

• Read Fleming 2.1.3 on the stability of carbocations
• Study Apeloig, Schleyer, and Pople et al., JACS 99, 1291 (1977) and try to verify the ideas with MOPAC/PM6
• To test the presence of a pi-bond: use "edit", rotate bond, recalculate with geometry frozen (e.g. in H2C-BH2)

Week 4

• Fleming states that 4.45b is a better representation of the dienolate ion than 4.45a. Check this statement with a Hückel calculation and with a semi-empirical calculation. Think of all possible ways to use the calculations to do the check.
• Use MOPAC to determine which is the most stable product thermodynamically, will the methyl group be on carbon number 2, 3, or 4?
• Compute the MOs and the orbital energies of the reactants to determine which orbital interaction is expected to control the reaction rates for soft electrophiles.
• What would the calculations predict for hard electrophiles?
• In sectio 4.3.3.3 Fleming claims that Hückel theory, in combination with HSAB theory, gives the wrong prediction for the reactive site for a soft electrophile reacting with a dienolate ion. Verify this claim, and check whether a MOPAC calculation gives the correct prediction (orient the molecule as explained here).

• Study Fleming 7.1 and check it with Hückel and MOPAC calculations.

• J. Chem. Soc. Perkin Trans. I, 1, 21 (1989), Unsaturated Carboxylic Acid Dienolates. Reaction with Substituted Cyclohexanones and Unsubstituted Cycloalkanones. Regio- and Stereo- selectivity
• Further study: using Fukui functions to study regioselectivity
• The paper on HSAB theory by Pearson J. Chem. Educ., 45, 581 (1968)

Week 5

• Study this: paper on using Fukui functions to study regioselectivity by Nguyen et al. (J. Org. Chem. 62, 6404 (1997)), and try this approach with MOPAC
• Decide on a project for you final report

• Note: to make a radical with JSME use the +/- button, but use the default charge in MOPAC.
• To find these structures by name activate the "NIH" button in the JSME panel, then right-click and select the option "Paste any chemical text repr."
• The polymerization of dimethyl fumarate and vinyl acetate proceeds in an alternating fashion. Study the structures of both compounds and give an explanation for the observed alternating copolymerization. Test your theory with MOPAC calculations.
• Apply the same theory to the copolymerzation of maleic anhydride and styrene and butadiene and styrene with MOPAC.

More literature on reactive indices

• (Superdelocalisability): Theory of substitution in Conjugated Molecules, K. Fukui, T. Yonezawa and C. Nagata, Bull. Chem. Soc. Jpn., 27, 423 (1954).
• Application of superdelocalisability to nitration: Quantitative frontier orbital theory: Part I. Electrophilic aromatic substitution, Robert J. Elliott, Valerie Sackwild, W.Graham Richards, J. Mol. Struct, Theochem, 86, 301 (1982)

Web resources

• Virtual Textbook of Organic ChemistryWilliam Reusch (MSU)
• ChemWiki (UC Davis)
• Organic chemistry at UCLA
• pKa table (Evans group, Harvard)
• Organic chemistry FAQ (Ken Shimizu, SC)

Checklist for the report:

• A title
• Name/names + student number
• Date
• Abstract
• Introduction
• Method/results/discussion (or some combination of these)
• Conclusion
• References

• Provide details that would be needed to reproduce the results.

• Define all abbreviations the first time they are used (treat the abstract as a "separate text", so it may be published independently).
• Number your pages.
• Number equations.
• Equations are part of a sentence, and may have comma or period at the end.
• Give units - use symbol (e.g. N), or write in lower case (newton).
• Use spelling checker.
• All Tables and Figures must have captions.
• The main text should refer to all figures and tables in the order in which they appear in the report.
• Use only one type of paragraph (alinea), e.g., a new paragraph starts at a new line with indentation, or always separate paragraphs by empty line.

Extra hints for the report of the first week's assignement:

• Send the report as pdf file (not doc!) to gerritg at theochem.ru.nl
• Make sure your name, student number, and the date are in the report
• Pages must be numbered
• No abstract is required, introduction can be short, however:
• The results in your report must be well defined - which method was used, which Hamiltonian, the structure of the molecule (a figure helps!), which solvent (for calculated as well as experimental pKa), etc
• It is OK to use tables, but to show correlations always make a plot
• Make sure that the data in the plot is well defined, axes must be labeled, it must be clear which molecules the points in the plot refer to.
• If some points are clearly not in line with the others, try to identify what may be reason.
• If you test the use of, e.g., HOMO and FERMO energies, it should be easy to see whether the FERMO is equal to the HOMO or not. If not, is it the HOMO-1, HOMO-2, ...? It may help to put the experimental pKa on the x-axis, so it is easier to compare plots that contain the same molecules, but different methods to determin the pKa
• If the choice of the FERMO was not easy, show the plots of the orbitals
• Use the various orbital correlations, and also try the formula for the pKa
• Summarize the main conclusions

Previous exams

• exam28Oct2015.pdf (Answers on brightspace)