EPMO methods exercises.PDF

OC-IV Exercises

Exercise 23 :

The π-electron systems of butadiene, cyclobutadiene, and methylene-cyclopropene can be

obtained by formally by connecting two ethylene units according to A, B, C.

(a) Use the EPMO method to discuss the π-orbital level diagrams and the approximate shape

of the MO’s for cyclobutadiene and methylene-cyclopropene.

(b)

Compare the net π-resonance energies ΔE π (relative to two non-interacting ethylene units)

obtained for B and C to that of 1,3-butadiene (see Script). Where do the differences arise

from?

(c)

While 1,3-butadiene is non-polar, what can you say about the polarity of methylene-

cyclopropene?

(d)

Cyclobutadiene is an unstable ‘anti-aromatic’ compound. Highly substituted

cyclobutadienes have been prepared successfully, but they tend to adopt a rectangular

(B’), rather than a square (B) structure with equal π-interactions around the perimeter.

Explain in simple π-MO terms the π-electronic difference between structures B and B’.

β ‘

β ‘< β

B’

Exercise 24:

The stereoelectronic control and course of thermal electrocyclic reactions, cycloadditions, and

sigmatropic shifts have been discussed in the Script. They are manifestations of the more general

‘Woodward-Hoffmann-Rules’ which have been formulated in the most general, but somewhat

abstract form as

For a concerted, thermally allowed pericyclic reaction

the total number of (4n+2) s + (4m) a components must be odd.

Here, components is an orbital element (σ-LMO, π-LMO, n-LMO, or composite

π-orbital system) that takes part in a pericyclic reaction; the indices ‘s’ and ‘a’

stand for suprafacial and antarafacial interaction modes, respectively, indicating

orbital lobal interactions on the same or opposite side of the respective component.

β ‘

β ‘< β

B’

Examples of pericyclic reactions taken from the course and exercise work are:

π 4 s

n 0 s

. n 2 a

π 4 s

π 2 s

π 2 a

π 2 s

σ 2 s

π 2 s

σ 2 s

I II III IV V VI

The Diels-Alder cycloaddition (I; see Chapter 6 of the Script) is an example of 4 s + 2 s . Note that

4 s -components are not counted; thus, there is one countable component (2 s ) for this thermally

allowed reaction. The disrotatory ring opening of the cyclopropyl cation to an allyl cation (II;

see Chapter 5 of the Script), is an example of (2 s + 0 s ), again with an odd number of countable

components. The conrotatory ring opening of an aziridine derivative (III; Exercise 20), on the

other hand, is an example of (2 s +2 a ), the N-lonepair being involved in an antarafacial mode; thus,

the number of countable components, 2 s , is again odd. The suprafacial [1,5]-sigmatropic H-shift

(IV; see Chapter 6 of the Script) is an example of (2 s +4 s ) with an odd number of countable (2 s )

components. The cycloaddition of three acetylenic units to form a benzene ring (V; see Chapter 6

of the Script) illustrates a thermally allowed (2 s +2 s +2 s )-type reaction, with an odd number of

countable components. Finally, the conrotatory ring opening of cyclobutene to 1,3-butadiene

(VI; Chapter 5 of the Script) is a manifestation of a (2 s +2 a )-transformation, with one (odd)

countable component (2 s ).

(a)

Consider the two reaction modes (A and B) for a cycloaddition reaction of two ethylene

units depicted below. Which mode would correspond to a thermally allowed synchronous

addition according to the ‘Woodward-Hoffmann Rules’?

Mode A

π 2 s

Mode B

π 2 a

π 2 s

(b)

Discuss in simple MO-terms the interaction patterns and level splitting consequences

for concerted cycloaddition reaction modes A and B. Which reaction mode should be

electronically feasible/unfeasible according to a smooth transition of the electronic

ground state from the reactants through a concerted intermediate to the product?

n 0 s

π 4 s

. n 2 a

π 2 s

π 2 a

π 4 s

π 2 s

σ 2 s

π 2 s

σ 2 s

π 2 s

π 2 a

π 2 s

Exercise 25:

Consider again the problem of Exercise 17. Assess the orbital interaction effects semi-

quantitatively in a HMO scheme with standard parameterization for the ethylene units,

assuming the following additional parameters

β 1,3 = 0.3 β

α π -type CH2

= α + 2 β

H H

β 1,2 π -type CH2 - pAO

= β

β 1,4 ( π CH 2 … π CH 2 ) = 0

β 1,2 π -type CH2 - pAO = β

β 1,3 = 0.3 β

α π -type CH2 = α + 2 β

Use the EPMO method in conjunction with symmetry-adapted group orbitals.

Exercise 26:

The first two ionization potentials of 1,3-butadiene and cyclobutadiene are given below. They

correspond to the ionizations from the two π-type CMO’s of the two compounds. The difference

between these first two ionization potentials is conspicuously smaller in cyclopentadiene than in

1,3-butadiene. A first hypothesis might be that the fixation of the diene unit into an s-cis

arrangement with very close distance between the terminal π-centers could result in a small, but

significant (1,4)-type π-interaction, which would be absent in the s-trans butadiene.

β ββ

IP 1 = 9.0 eV

IP 2 = 11.5 eV

Δ IP 12 = 2.5 eV

IP 1 = 8.6 eV

IP 2 = 10.6 eV

Δ IP 12 = 2.0 eV

0.3 β

(a) Assuming β 1,4 = 0.3 β (similar to a (1,3)-type interaction!), with all other π-interactions

remaining unchanged, estimate in qualitative terms the expected energy changes in the

π-MO levels of butadiene.

(a1) Do this by applying first-order perturbation theory to the unperturbed butadiene

CMO’s (the CMO’s are given in the Script, Chapter 5, last slide).

(a2) Do this by using symmetry-adapted group orbitals (ϕ ± in , ϕ ± out , see Chapter 5, last

slide) and calculating the orbital energy levels and splitting effects by the EPMO method.

(a3) Compare the results obtained from (a1) and (a2).

Does the additional β 1,4 interaction in the s-cis butadiene fragment serve to rationalize the

experimental observations?

(b)

What other effects would you consider to rationalize the observed changes in the π-type

ionization potentials?

α π -type CH2

= α + 2 β

β 1,3 = 0.3 β

H H

β 1,2 π -type CH2 - pAO

= β

β 1,4 ( π CH 2 … π CH 2 ) = 0

β 1,2 π -type CH2 - pAO = β

H H

α π -type CH2 = α + 2 β

β 1,3 = 0.3 β

β ββ

0.3 β

IP 1 = 9.0 eV

IP 2 = 11.5 eV

Δ IP 12 = 2.5 eV

IP 1 = 8.6 eV

IP 2 = 10.6 eV

Δ IP 12 = 2.0 eV

Exercise 27 (competition for a prize):

Secondary amides can engage in hydrogen bonding, either by accepting a hydrogen bond from an

H-bond donator group (OH or NH) to the amide carbonyl oxygen, or by donating a hydrogen

bond from the amide-NH unit to an H-bond acceptor group.

N H

If a secondary amide engages simultaneously in two hydrogen bonds, one by accepting, one

by donating a hydrogen bond, there is often a ‘cooperativity’ effect, strengthening the overall

hydrogen bonding interaction (effects ranging in the 1-2 kcal/mol and resulting in slightly shorter

non-bonded XH … Y heteroatom contact distances by 0.1-0.2Å) compared to two individual

H-bonding interactions. Such cooperative hydrogen bonding interactions are ubiquitous for

α-helices or β-sheets in proteins (see Figure right).

The cooperativity effect can be rationalized by two simultaneously operating electronic effects:

(a)

An electronic effect operating purely in the σ-system of the amide unit. Explain.

(b)

An effect that illustrates the indirect interactions between the orthogonal σ-electron

and π-electron systems of an amide unit:

Engaging the carbonyl oxygen lone pair in a hydrogen bond lowers the energy of

the p O level; this results in a stronger π-charge transfer from the p N electron pair to

the more electrophilic C=O group, reducing the net π-charge at nitrogen; the latter

increases the acidity of the N-H unit and thus renders it a stronger H-bond donor.

The π-resonance picture of an amide unit using standard HMO parameterization is

discussed in Chapter 5 of the Script. We may assume that the involvement of the

carbonyl oxygen lone pair in a hydrogen bond will induce an energy lowering of

the p O level by ca. 1/3 of the amount typically taken for the energy lowering upon

engaging the oxygen lone pair into a σ-bond (see “Basic Features of MO Theory”, p.26).

By means of the EPMO method, using otherwise standard HMO parameterization,

estimate the π-resonance effect of the N electron pair and the net π-electron transfer

from nitrogen into the more electrophilic carbonyl unit, and compare these results

to the ones obtained for an unperturbed amide unit.

Exercise 28:

Consider the isoelectronic species benzoate anion and nitrobenzene.

Using symmetry-adapted group orbitals for the carboxylate anion and the nitro group, examine

the possibility for π-conjugative interactions, in particular:

(a)

Which interactions of the NO 2 π-orbitals result in a π-charge transfer from the benzene

π-system to the NO 2 group?

(b)

Can the negative charge of the carboxylate group be delocalized into the benzene

π-system? Which orbital interactions are relevant for such a delocalization? Based on

estimates using the EPMO method, how much π-charge transfer would you expect?

Suggestion: Use standard HMO parameterization; for the symmetrical carboxylate anion, an

oxygen α-parameter between that of a carbonyl oxygen (α O = α + β) and an oxy-anion

(α O = α + 0.5β, see “Basic Features of MO Theory”, p.26) may be used; hence, α O = α + 0.75β.

For the NO 2 group, α N = α + 2β and α O = α + β may be appropriate.

Exercise 29:

The (1,3)-dipolar cycloaddition of a (1,3)-dipolar unsaturated system is a powerful method for the

generation of heterocyclic ring systems which can then be further transformed. This is illustrated

below for the (1,3)-dipolar cycloaddition of a nitrone to a simple alkene.

(a)

Considering this 1,3-dipolar cycloaddition to occur in a synchronous suprafacial fashion

(see Figure), examine the π-orbital interactions of the reactants and verify that the orbital

amplitudes of the respective highest occupied MO’s (HOMO’s) and lowest unoccupied

MO’s (LUMO’s) of the reactant systems are set in a way that they result in a significant

resonance effect for a transition state of a synchronous suprafacial cycloaddition.

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