Pericyclic chemistry orbital mechanisms and stereochemistry

For example, a combination of 2s and three 2p orbitalscan be used to generate four equivalent hybrid orbitals called sp3hybrids.Each sp3 hybrid orbital has two lobes with opposite signs,

PERICYCLIC CHEMISTRY

The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom

50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States

© 2018 Elsevier Inc All rights reserved.

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright

by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing As new research and experience broaden our understanding, changes in research methods, professional practices,

or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge

in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

Library of Congress Cataloging-in-Publication Data

A catalog record for this book is available from the Library of Congress

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library

ISBN: 978-0-12-814958-4

For information on all Elsevier publications

visit our website at https://www.elsevier.com/books-and-journals

Publisher: John Fedor

Acquisition Editor: Emily McCloskey

Editorial Project Manager: Billie Jean Fernandez

Production Project Manager: Paul Prasad Chandramohan

Cover Designer: Mark Rogers

Typeset by SPi Global, India

It is about 50 years since the appearance of the pioneering work of

R B Woodward and R Hoffmann on the theory of conservation of orbitalsymmetry in concerted reactions The word pericyclic was introduced in 1969and the application of the concept of orbital symmetry to pericyclic reactionsproved to be a major turning point in understanding organic reaction mech-anisms The 1981 Nobel Prize in Chemistry was awarded to K Fukui and

R Hoffmann for developing theories of pericyclic reactions (Woodward died

in 1979 at the age of 62 and could not share this prize; however, he won theNobel Prize in 1965 for his work on organic synthesis) Pericyclic reactionshave a remarkable quality of being manifold, extremely elegant, and highlyuseful; they reveal stereochemical intricacies and idiosyncrasies and remain

as an integral part of chemistry teaching and research

Pericyclic chemistry is covered in every graduate course and in advancedundergraduate courses in organic chemistry Ergo, this book is addressedprincipally to an audience of graduate and advanced undergraduate students.The purpose of writing this book is entirely pedagogic, keeping in viewthat our students crave understanding, not factual knowledge alone Thebook evolves from a series of lecture notes and students’ feedback during

my teaching this course to graduate students for more than 20 years Themechanistic descriptions and the stereochemistry resulting from orbitalmechanisms are at the heart of this book; the synthesis of specific targetmolecules has been generally given short shrift

The book contains eleven chapters An introduction to molecular orbitaltheory (Chapter 1) and relevant stereochemical concepts (Chapter 2) havebeen provided as a background aid to follow the chapters on pericyclicchemistry In the introductory chapter (Chapter 3), I have introduced allfour classes of pericyclic reactions involving three mechanistic approacheslinked through orbital picture representation This unifying and integratedstyle would help enhance the pedagogy of this text The qualitative pertur-bation molecular orbital theory has been incorporated as the most accessibleand useful approach to understanding many aspects of reactivity and selec-tivity Three chapters (Chapters 4–6) have been devoted to cycloadditions,the most versatile class, one to electrocyclic reactions (Chapter 7), two tosigmatropic rearrangements (Chapters 8 and 9), and one to group transferreactions (Chapter 10) A separate chapter (Chapter 11) is included to

xv

illustrate the construction of correlation diagrams in a practical,

‘how-to-do-it’ manner

Besides the unifying approach of mechanistic discussion, the mostimportant difference between this book and others is the emphasis on ste-reochemistry, specifically how to delineate the stereochemistry of products

I have found that students are not often quite comfortable to work chemistry for themselves After all, reaction stereochemistry is not easy!Students need some more help To address their concerns, I have alwaysbeen looking for innovative approaches to stereochemical issues My effortshave resulted in formulating simple stereochemical rules/guidelines, some ofwhich have been published in the Journal of Chemical Education These pub-lished (also some unpublished) rules/mnemonics have been used extensively

stereo-in the relevant chapters as an aid to write quickly and correctly the productstereochemistry in pericyclic reactions

Usually, the problem sets are given at the end of chapters without or withanswer keys One pedagogical decision I have made with respect to problemsets is that more than 130 problems are inserted within the chapters withdetailed worked solutions, reinforcing the main themes in the text It ishoped that students could test their learning immediately while readingthrough the chapters These problem sets should be considered an integralpart of the course A list of selective references to primary and review liter-ature is included at the end of each chapter These references (about 550)would enable the students at the advanced levels to supplement the materialscovered in the chapters

The approach presented in this book is distinct and class-tested I hopethis book will be of value and interest to the students, teachers, andresearchers of organic chemistry I encourage the readers to contact me(dm.pcchem@gmail.com) with comments, corrections, and with sugges-tions that might be appropriate for future editions

I would like to thank the reviewers for helpful suggestions Special thanksare due to my undergraduate, graduate, and research students for their lovinginsistence, help, and encouragement in writing this book I am grateful to theeditorial members Emily M McCloskey and Billie Jean Fernandez, produc-tion manager, and other people at Elsevier for their excellent support andcooperation Finally, I thank my family, in particular my daughter Sudipta,for her continuous support and my son Tirtha for his active help in referencing

Dipak K MandalKolkata, India

Molecular Orbitals

A basic and pictorial knowledge of molecular orbitals (MOs) is essential for amechanistic description of pericyclic reactions In this context, a simplifiedand nonmathematical description of MO theory1–4is presented in this chap-ter We shall deal with three kinds of MOs—σ, π and ω with major emphasis

onπ MOs, and discuss their properties with reference to orbital symmetry,energy and coefficient

1.1 ATOMIC ORBITALS

An atomic orbital (AO) is described by a wave functionϕ, where ϕ2

denotesthe probability of finding an electron at any point in a three-dimensionalspace The algebraic sign ofϕ may be positive or negative, which indicatesthe phase of the orbital (cf the peaks and troughs of a transverse wave) Anorbital can have nodes where ϕ¼0 On opposite sides of a node, ϕ hasopposite signs An AO as a graphical description of ϕ shows lobes with

a + or a sign (the opposite signs of two lobes are also indicated by unshadedand shaded lobes) On the other hand, ϕ2

is always positive whether ϕ ispositive or negative As such, the representation of AO in terms of ϕ2

ismade by drawing lobes without a phase sign This drawing refers to theprobability distribution of AOs, and is indicated in this text as simply orbitalpicture

1.1.1 s, p and Hybrid Orbitals

1s orbital is spherically symmetrical about the nucleus and has a single sign of

ϕ It is represented as a circle, being one cross-section of the spherical tour The 2s orbital is also spherically symmetrical but possesses a sphericalnode The node is close to the nucleus and hence the inner sphere is notimportant for bonding overlap The 2s orbital is usually drawn as a singlecircle with a single sign omitting the inner sphere

con-Unlike an s orbital, the p orbitals are directional, and oriented along thex-, y- and z-axis Each p orbital has two lobes with opposite signs and onenode (nodal plane)

1

https://doi.org/10.1016/B978-0-12-814958-4.00001-5 All rights reserved.

Carbon has four AOs (2s, 2px, 2pyand 2pz) that are available for bonding.Though this model of one s and three p orbitals is very useful, there is analternative model of four AOs of carbon, based on Pauling’s idea of hybrid-ization The hybridization involves mixing of 2s and 2p orbitals in variousproportions to produce a new set of AOs Mathematically, the mixing istaken to be the linear combination of atomic orbitals (LCAOs) SuchLCAOs on the same atom are called hybrid orbitals The combination of2s with one, two or three p orbitals can be used in different ways to producedifferent sets of hybrid orbitals, designated as spn where n may be a wholenumber or a fraction For example, a combination of 2s and three 2p orbitalscan be used to generate four equivalent hybrid orbitals called sp3hybrids.Each sp3 hybrid orbital has two lobes with opposite signs, but unlike a porbital, the two lobes of a hybrid orbital have different sizes.

The schematic representations of s, p and sp3hybrid orbitals are shown inFig 1.1 InFig 1.1A, the orbitals are drawn as graphical description of wavefunction (ϕ) showing a phase sign whileFig 1.1B shows the orbital picture

in terms ofϕ2with no phase sign

The unequal size of two lobes of a hybrid orbital, say sp, arises fromthe mixing of s orbital with a p orbital on the same atom (Fig 1.2) Thetwo lobes of p orbital have the same size, but opposite signs (unshadedand shaded), and the s orbital has a single sign (unshaded) The combi-nation gives in-phase (same sign) mixing on one side of the nucleusand out-of-phase (different signs) mixing on the other side, leading to

a large lobe on the left side and a small lobe on the right side of the hybridorbital

Fig 1.1 (A) Sketch of atomic orbitals in terms of ϕ with a phase sign; (B) orbital picture in terms of ϕ2without a phase sign.

Fig 1.2 Unequal size of two lobes of a hybrid orbital.

1.1.2 Atomic Orbitals of Nitrogen and Oxygen

Nitrogen and oxygen have similar sets of s, p and hybrid orbitals as for bon However, the energies are different The relative energies of an AO ondifferent atoms follow their pattern of electronegativity An orbital on amore electronegative atom will have lower energy (Table 1.1).5

car-1.2 MOLECULAR ORBITALS

An MO is also described by a wave functionψ which can be expressed as anLCAOs The set of AOs chosen for the linear combination is called the basisset The total number of MOs will be equal to the total number of AOs com-bined The calculation of MOs using all AOs of a molecule presents massivecomputational problems However, the essential qualitative features ofbonding can be understood if the basis set is restricted just to those AOs thatare involved in a particular type of bonding MOs are designated by the sym-bolsσ, π and ω reflecting the type of bonding that occurs

Now consider the linear combination of two AOsϕ1andϕ2on atoms 1and 2 (Note that the linear combination uses only the first power of wavefunction; cf equation of a straight line.) Two MOsψ1andψ2are producedwhich are expressed as

ψ1¼ c1ϕ1+ c2ϕ2

ψ2¼ c1ϕ1 c2ϕ2

where c1and c2are the mixing coefficients which denote the relative tributions of the AOsϕ1andϕ2to an MO The coefficients may be positive,negative or even zero

con-The geometry of approach of the two AOs leads to different types ofMOs This is illustrated below taking, for example, the overlap of two pAOs centred on two identical atoms (homonuclear), when c1¼c2

End-on approach: End-on overlap of two p orbitals gives two MOs (ψ1and

ψ ) that are cylindrically symmetrical about the internuclear axis (Fig 1.3)

Table 1.1 Energies of s and p atomic orbitals

These are called σ MOs Here, ‘+’ combination signifies in-phase (samesign) overlap whenψ1has no node In contrast, ‘’ combination denotesout-of-phase (opposite sign) overlap leading to a node (nodal plane) inψ2.The MOψ1has lower energy than p AO and is called bonding σ orbital(symbolizedσ), while ψ2has higher energy and is called an antibondingσorbital (σ*).

Side-on approach: Side-on (lateral) overlap of two p orbitals produces twoMOs (ψ1andψ2) that are not cylindrically symmetrical about the internuc-lear axis, and are calledπ MOs (Fig 1.4).ψ1has lower energy with no nodeand is a bonding MO (π), while ψ2with one node (nodal plane) is of higherenergy and is an antibonding MO (π*)

Orthogonal approach: For orthogonal (perpendicular) approach of two porbitals, bonding overlap of the same sign is cancelled by an antibondingoverlap of the opposite sign (Fig 1.5) The net interaction is therefore non-bonding.ψ1andψ2have the same energy and are equivalent to individual porbitals These nonbonding MOs are calledω MOs

It may be mentioned here that besides nonbondingω MOs, there are alsononbondingπ MOs that can arise in conjugated π systems (see later)

Fig 1.3 End-on overlap of two p orbitals to produce σ MOs.

Fig 1.4 Side-on (lateral) overlap of two p orbitals to produce π MOs.

Fig 1.5 Orthogonal approach of two p orbitals to produce ω MOs.

1.2.1 Energy Diagram

In general, the interaction of two AOs leads to a pair of bonding and bonding MOs Consider the formation ofσ and σ* MOs for hydrogen mol-ecule From quantum mechanical calculation, the energy (E) of an electron

anti-inσ and σ* orbital is expressed in terms of three integrals (α, β and S) as

Eð Þ ¼σ α + β

Eð Þ ¼σ∗ α  β

whereα is the Coulomb integral which denotes the energy of an electron in

an isolated AO;β is the resonance integral which represents the energy ofinteraction between two AOs; and S is the overlap integral which indicatesthe extent of overlap of the AOs

Now we focus on the numerator and denominator terms in Eqs (1.1),(1.2).α and β are negative quantities Therefore, (α+β) < α (indicating low-ering of energy ofσ) and (αβ)>α (raising of energy of σ*) The overlapintegral S is a function of internuclear distance and the value of S ranges from

0 to 1 For two interacting orbitals, S>0 Hence, the denominator (1 +S)>(1 S) Thus, the energy increase associated with antibonding σ* orbital isslightly greater than the energy decrease for bondingσ orbital These resultsare presented qualitatively in the MO energy diagram (Fig 1.6)

Forπ and π* orbitals, a similar pattern follows; however, the value of Sfor π overlap is much smaller If we assume S¼0, we obtain

Eð Þ ¼ α + β; E ππ ð Þ ¼ α  β∗

Fig 1.6 MO energy diagram for a two-orbital interaction x and y indicate, respectively, the energy decrease for the bonding orbital and energy increase for the antibonding orbital.

whereα is the energy of an electron in an isolated p orbital and β representsthe energy of interaction between two adjacent p orbitals.

1.2.1.1 Remarks

The above MO energy diagram serves qualitatively a general pattern for atwo-orbital interaction that may involve any AOs or MOs It can be seenfromFig 1.6that if each interacting orbital is completely filled providing

a total of four electrons, both bonding and antibonding orbitals would becompletely filled The net interaction would thus be repulsive becausethe increase in energy in the antibonding combination is greater than thedecrease in energy in a bonding combination This repulsive filledorbital/filled orbital interaction is the underlying reason for the steric strain(repulsion between closed-shell molecules or groups), and is included in thefirst term of the Salem–Klopman equation (seeSection 4.1)

1.2.2 CdH and CdC σ Bonds

A CdH bond is formed by the interaction of a hybrid orbital (say, sp3) ofcarbon with the 1s orbital of hydrogen This two-orbital interaction leads tobondingσCHand antibondingσ*CHas shown inFig 1.7A Note that theenergy of sp3C(16.1 eV) is somewhat lower than that of 1sH(13.6 eV)

A CdC σ bond is formed by the end-on overlap of two hybrid orbitals, onefrom each carbon.Fig 1.7B shows the formation of a bondingσCCand anantibonding σ*CC from two sp3 hybrid orbitals (Note the conventional

MO sketches with the AOs instead of the delocalized sketches of MOs.)The bondingσ MO has no node between lobes of the same sign, but anti-bondingσ* MO has one node between lobes of opposite sign (shaded andunshaded)

Fig 1.7 Bonding and antibonding MOs for (A) CdH bond and (B) CdC bond.

We shall see later that the more important orbitals in connection withreactivity are the highest occupied molecular orbital (HOMO) and the low-est unoccupied molecular orbital (LUMO) These are called the frontierMOs Thus, for the σ component (CdH or CdC), the HOMO is σand the LUMO is σ*.

Besides MOs, orbital picture representation (without phase sign) of aσ-component is used in the mechanistic analysis of pericyclic reactions.Fig 1.8 shows the orbital pictures of CdH and CdC σ components.The σ component is labelled as σ2 (2 is the number of electrons in thecomponent)

1.3 H€UCKEL MOLECULAR ORBITAL (HMO) THEORY

FOR ACYCLIC CONJUGATED π SYSTEMS

H€uckel theory1,6

treats aπ system independently of the σ framework (the πandσ orbitals being orthogonal to each other) The HMO theory assumesthe following:

(1) Each Coulomb integral (α) has the same value

(2) The resonance integral (β) is same for any two adjacent atoms but zerofor two atoms not directly bonded

(3) The overlap integral (S) is zero for the interaction between two

p orbitals

It might be surprising that S is assumed to be zero, while the whole concept

of chemical bonding is based on the overlap of orbitals (!) In fact, overlap isnot really neglected because it is implicitly included in other parameters such

asβ which is roughly proportional to S The assumption that S¼0 greatlysimplifies the calculation

Theπ MO wavefunction (ψj) is described by a linear combination of pAOs (ϕr) as

ψj¼Xnr¼1cjrϕr (1.3)where n is the total number of p orbitals involved and j¼1, 2, 3,…,n

Fig 1.8 Orbital pictures of CdH and CdC σ components.

Here, we shall consider the linear conjugated systems and obtain theirπMOs and energies using Coulson equations7as follows:

cjr¼

ffiffiffiffiffiffiffiffiffiffi2

The wavefunctions (π MOs) can now be sketched as

The relative magnitudes of the coefficients are usually indicated by the ative sizes of the lobes Here the two coefficients have the same size for both

rel-ψ1and ψ2 Forψ1, the coefficients have the same sign indicating in-phase(bonding) overlap For ψ2, the coefficients have opposite signs indicatingout-of-phase (antibonding) overlap which creates a node (nodal plane)

The energies of theπ MOs are estimated using Eq.(1.5)as

E1¼ α + 2βcosπ

3¼ α + β

E2¼ α + 2βcos2π

3 ¼ α  β:

Fig 1.9shows the MO energy diagram whereψ1is a bonding MO (π) as

it has lower energy than the energy of p orbital (α) and ψ2is an antibonding

MO (π*) having an energy higher than α

The ground stateπ electron configuration of ethylene is π2π*0 fore, π is HOMO and π* is LUMO A thermal pericyclic reaction is aground state process whereas a photochemical reaction is a first excited stateprocess On photochemical excitation by absorption of light, one electron ispromoted fromπ (HOMO) to π* (LUMO) with the conservation of spin,and the resulting excited state is a singlet with singly occupiedπ (formerlyHOMO) and singly occupiedπ* (formerly LUMO) (Fig 1.10)

There-Fig 1.9 MO energy diagram of ethylene.

Fig 1.10 Frontier orbitals in the ground state and in the excited state of ethylene.

A useful convention8 is to designate the singly occupied excited stateorbitals of a molecule by its former ground state HOMO/LUMO labels Thisexcited state frontier orbital convention as shown inFig 1.10will be usedwhile dealing with the frontier orbital analysis of photochemical reactions.(An alternative excited state nomenclature that specifiesπ* as HOMO and

π as NHOMO, next lower HOMO, will not be used in this text.)

At the instant of excitation, the nuclei retain the planar ground stategeometry (Frank–Condon principle) The π bond order [½ (no of bondingelectrons no of antibonding electrons)] in the excited state is zero Theinitial planar excited state then quickly relaxes to the minimum energygeometry in which the two sp2 carbons are twisted by about 90 degreeswhen there is noπ overlap (Fig 1.11) This twisted, excited state, sometimescalled the p state, permits the possibility of returning to either E or Z con-figuration of the ground state alkene

We shall see later that the phase relationship of terminal p orbitals inHOMO/LUMO is important in the mechanistic analysis of pericyclic reac-tions This phase relationship is characterized by orbital symmetry.Fig 1.12shows the orbital symmetries of HOMO and LUMO of ethylene TheHOMO (π) has the same phase at the two ends and possesses a plane of sym-metry (symbolized by m) since a lobe (labelled*) reflects to a lobe of the samesign Note that the mirror plane (m) bisects the CdC bond and is perpen-dicular to the plane of the molecule On the other hand, the LUMO (π*) hasopposite phases at the two ends and is characterized by C2symmetry as the

C2operation brings a lobe (labelled*) to a position of a lobe with the samesign Note that the C2axis bisects the CdC bond and is lying in the plane ofthe molecule

Fig 1.11 Orbital pictures of the ground state and excited state of ethylene.

Fig 1.12 Orbital symmetries of HOMO and LUMO of ethylene.

qsin25π¼0.600 Theother coefficients are calculated similarly We obtain

2 and 3, respectively This indicates that an orbitalψjhas ( j 1) nodes

As the number of nodes increases, the energy of the orbital increases inthe order:ψ1<ψ2<ψ3<ψ4 In another fashion, if we count the number ofbonding/antibonding interactions between the adjacent p orbitals, it is seenthatψ1with three bonding overlaps andψ2with two bonding and one anti-bonding interactions become bonding MOs whereasψ3with two antibond-ing and one bonding interactions andψ with three antibonding interactions

Fig 1.13 Sketches of π MOs of butadiene in s-trans conformation.

become antibonding MOs The MO energy therefore increases in the sameorder as shown above.

The energies of theπ MOs can however be estimated using Eq.(1.5).For example, E1¼ α + 2βcosπ

5¼ α + 1:618β The estimated energies of all

π MOs are shown in the MO energy diagram (Fig 1.14) Note that the morepositive or less negativeβ values imply a decrease in energy; less positive ormore negativeβ values indicate an increase in energy

The bonding/antibonding classification of theπ MOs is now clearly dent.ψ1andψ2have energies lower than the energy (α) of a p orbital and aretherefore bonding MOs whereasψ3 andψ4are antibonding MOs as theirenergies are higher thanα

evi-(Since the decrease or increase in energy of an MO is considered relative

to the energy of the AO,α can be arbitrarily assumed to be zero and the MOenergy can be expressed in onlyβ terms; however in this text MO energy isexpressed in bothα and β terms, as obtained from the energy expression.)The ground stateπ electron configuration of butadiene is ψ12ψ22 Thus,ψ2

is HOMO andψ3is LUMO In the first excited state, one electron is moted fromψ2(HOMO) toψ3(LUMO) As per the frontier orbital con-vention used in this text (see p 10), the singly occupied ψ2 and ψ3 alsorepresent HOMO and LUMO in the first excited state

pro-The HOMO/LUMO energies in s-trans and s-cis conformations of diene are not the same In s-cis conformation, the HOMO energy is raisedand the LUMO energy is lowered relative to those in the s-trans form(Fig 1.15) Unlike the s-trans form, the s-cis conformation has a possibleinteraction between the two terminal p orbitals An antibonding interactionraises the HOMO energy, while a bonding interaction lowers the LUMOenergy in s-cis conformation

buta-Fig 1.14 MO energy diagram of butadiene.

In frontier orbital analysis, the higher energy HOMO and lower energyLUMO would make the s-cis-butadiene more reactive than s-trans-butadiene in pericyclic reactions It may be mentioned here that the lowerHOMO/LUMO energy gap in s-cis conformation leads to UV absorption at

a longer wavelength (253 nm) for a homoannular diene locked in s-cis formation compared with aλmaxof 215 nm for an acyclic or a heteroannulardiene existing predominantly or exclusively in s-trans conformation.The orbital symmetry of frontier orbitals is important in the context ofmechanism of pericyclic reactions.Fig 1.16shows that the HOMO has theopposite phase relationship at the two termini and is characterized by C2symmetry while the LUMO with the same phase relationship at the twoends exhibits m symmetry

Note the pattern in the size (not sign) of coefficients: the first three andlast three values in each MO hold a mirror image relationship The energies

of the π MOs are estimated using Eq (1.5) For instance,

E3¼ α + 2βcos3 π

7¼ α + 0:445β The sketches of six π MOs, their nodalproperties and energies are shown inFig 1.17 It is evident that the sixπMOs constitute three bonding and three antibonding MOs

In the ground state, theπ electron configuration of hexatriene is ψ12ψ22ψ32.Thus,ψ3is HOMO andψ4is LUMO In the first excited state,ψ3andψ4

also represent HOMO and LUMO when each is half-filled (Only HOMOand LUMO are labelled with coefficient values in the figure.)

In pericyclic reactions, the two termini of the hexatriene componentought to be generally close to each other This is achieved when the middledouble bond is Z and the molecule adopts s-cis conformation The symmetry

of the frontier orbitals of hexatriene is shown inFig 1.18 The HOMO has

m symmetry while the LUMO is characterized by C2symmetry

Fig 1.17 MO energy diagram and sketches of the π MOs of 1,3,5-hexatriene.

Fig 1.18 Orbital symmetries of ΗΟΜΟ and LUMO of 1,3,5-hexatriene.

1.3.2 Linear Conjugated System With Odd Number

of p Orbitals

We have seen that theπ MOs of a conjugated system (n¼ even) compriseequal number of bonding and antibonding MOs When n¼ odd, the con-jugatedπ system is a reactive intermediate (carbocation, carbanion or carbonradical) when theπ MOs will contain a nonbonding MO besides bondingand antibonding orbitals as described below

ofψ2, a node passes through the middle carbon C-2 The energy of ψ2is

α, which is same as the energy of a p orbital, and hence ψ2is a nonbonding

MO It is seen thatψ1is bonding andψ3is antibonding Thus, the threeπMOs of an allyl system comprise a bonding, a nonbonding and anantibonding MO

The frontier orbitals of an allyl system depend on whether it is a cation, aradical or an anion The number ofπ electrons in allyl cation, radical andanion is 2, 3 and 4, respectively The frontier orbitals are given below:

Allyl cation (ψ 1 ) Allyl radical (ψ 1 ψ 2 ) Allyl anion (ψ 1 ψ 2 )

The frontier orbital for an allyl radical isψ2which is a singly occupiedmolecular orbital (SOMO) The symmetry properties of the π MOs areshown inFig 1.20

Problem 1.1

Derive the π MOs of a pentadienyl system using Coulson equations Sketch the MOs in s-cis conformation of the molecule showing node(s) Indicate the frontier orbitals for cation, anion and radical species with symmetry Answer

The pentadienyl system (cation, radical or anion) is

The π MOs (ψ 1 – ψ 5) and their energies are derived as

Fig 1.20 Orbital symmetries of π MOs of an allyl system.

The energies indicate that ψ1 and ψ2 are bonding MOs; ψ3 is a nonbonding MO; and ψ4 and ψ5 are antibonding MOs.

The sketches of the π MOs are shown below It is seen that an orbital ψj has ( j – 1) nodes.

The frontier orbitals for the pentadienyl cation, radical and anion, and their symmetry are given below:

Cation (ψ1ψ2) Radical (ψ1ψ2ψ3) Anion (ψ1ψ2ψ3)

1.3.2.2 A Short-Cut Method for Sketchingπ MOs

The sketches of theπ MOs can be simplified by ignoring the difference ofcoefficients, where the coefficients are not important in a mechanisticdescription of pericyclic reactions A short-cut method to drawing such asimplified picture ofπ MOs is to use the nodal properties which indicate that

an MOψjhas (j– 1) nodes The procedure is illustrated for the drawing offrontier orbitals inFig 1.21 Note that the nodes are to be placed in the mostsymmetrical manner in the prospective MO

The symmetry properties of theπ MOs can be summarized as follows:

ψj( j¼ odd) ) m symmetry;

ψj( j¼ even) ) C2symmetry

Besides the MOs, orbital picture representation (without phase sign) oftheπ components is also used in mechanistic analysis of pericyclic reactions.The orbital pictures of the diene and triene components are sketched as

1.4 CARBONYL π SYSTEM

The symmetry properties ofπ MOs of the carbonyl system are similar tothose of alkenes; however, the energy and coefficient patterns differ Theenergy of a p orbital on oxygen (15.9 eV) is much lower than that on car-bon (10.7 eV) (seeTable 1.1) This would lead to lowering of energy ofbothπCOandπ*COcompared with those for alkene (Fig 1.22)

For the carbonyl group, the lower energy pOwould contribute more tothe lower energyπCOand the higher energy pCwould contribute more tothe higher energyπ*CO As a result, there will be a larger coefficient on oxy-gen inπCOand a larger coefficient on carbon inπ*COas shown inFig 1.22

πCO is HOMO and π*CO is LUMO, the polarization of HOMO and

Fig 1.21 Sketches of frontier orbitals from nodal properties.

Fig 1.22 Energy diagram of π MOs of carbonyl group vis-a-vis alkene π MOs.

LUMO being opposite The presence of low-lying LUMO with a largecoefficient on carbon makes the carbonyl group a particularly importantelectron-withdrawing substituent or a reactive component in pericyclicreactions.

1.5 EFFECT OF SUBSTITUENTS ON FRONTIER ORBITALENERGIES AND COEFFICIENTS OF π SYSTEMS

A qualitative picture of the perturbation effects of different types of uents on the frontier orbital energies and coefficients ofπ systems is necessary

substit-to rationalize the features of reactivity and selectivity in cycloadditionsand other pericyclic processes The substituents are generally classified asfollows:

• c-Substituents: These are simple conjugating substituents such as vinyl,

Ph etc They can act asπ donors or as π acceptors based on the electrondemand of the parentπ system

• z-Substituents: These indicate conjugating and electron-withdrawingsubstituents such as COR, CO2R, CN, NO2, SiR3, BR2 etc Theyact asπ acceptors

• x-Substituents: These denote the electron-donating substituents such as

OR, NR2, R (alkyl) etc They act asπ donors

1.5.1 HOMO/LUMO Energies and Coefficients

of Substituted Alkenes

The unsubstituted alkene (ethylene) is the reference or unperturbed alkene

A perturbed alkene system is represented by c-, z- or x-substituted alkene.The patterns of frontier orbital energies and coefficients for the perturbedsystems vis-a-vis unperturbed alkene can be determined by choosing a rea-sonable model for each substituted alkene An all-carbon model for whichHMO energies and coefficients are known is the preferred choice to draw aqualitative inference

1.5.1.1 Perturbation by c-Substituents

Since a c-substituent is a neutral conjugating substituent (e.g CH]CH2), areasonable model for a c-substituted alkene is butadiene:

The energies and coefficients for HOMO and LUMO of butadiene andethylene as shown earlier are

Comparing the HOMO/LUMO energies between butadiene (a modelfor c-alkene) and ethylene, we have

EHOMO (c-alkene)>EHOMO (alkene)

ELUMO (c-alkene)<ELUMO (alkene)

Therefore, a c-substituent raises HOMO energy and lowers LUMO energy.The HOMO and LUMO energies were estimated by Houk from the exper-imental data of ionization potential and electron affinity, respectively.9These data indicating average or representative values will be shown later(seeFig 1.23)

Now, to determine the effect of c-substituent on the frontier orbital ficients, we consider the HOMO/LUMO coefficients of butadiene as amodel for c-alkene It is seen that there is a smaller coefficient (0.37) at theα-carbon carrying the substituent and a larger coefficient (0.60) at the unsub-stitutedβ-carbon in both HOMO and LUMO In the unsubstituted alkene,the coefficients are equal Therefore, a c-substituent leads to a large coefficient atβ-carbon and a small coefficient at α-carbon in both HOMO and LUMO The coef-ficient pattern for a c-substituted alkene is represented as

coef-1.5.1.2 Perturbation by z-Substituents

A z-substituent such as a C]O group in a z-substituted alkene imparts bothconjugating and electron-withdrawing character as a resonance hybrid:

Thus, a reasonable model of a z-substituted alkene is a hybrid model ofbutadiene (conjugating character) and allyl cation (electron-withdrawingcharacter):

The frontier orbital energies and coefficients for the relevant πsystems are

Comparing the energies, we see that the conjugating butadiene character

in the z-substituted alkene tends to increase the energy of HOMO[(α+0.62β)>(α+β)] but the electron-withdrawing allyl cation charactertends to decrease it [(α+1.41β)<(α+β)] The two effects thus act in oppo-sition leading to a very small effect on HOMO energy for z-alkene In con-trast, both butadiene and allyl cation characters act in concert to substantiallylower the LUMO energy of z-substituted alkene [(α0.62β)<(αβ),α<(αβ)] Therefore,

EHOMO z ð alkene Þ EHOMO alkene ð Þ

ELUMO z ð alkene Þ≪ELUMO alkene ð Þ

The Houk’s data show that HOMO energy of z-substituted alkene(10.9 eV) is slightly lower than that of unperturbed alkene (10.5 eV),but the LUMO energy is substantially lowered from 1.5 to 0 eV Therefore,

a z-substituent slightly lowers the HOMO energy and appreciably lowers theLUMO energy

Next, we examine the coefficient data Butadiene HOMO contributes asmall coefficient (0.37) at α-C and a large coefficient (0.60) at β-C, whilethe allyl cation HOMO contributes in opposite sense that is, a large coefficient(0.71) atα-C and a small coefficient (0.50) at β-C The net effect is expected to

be a small difference in coefficient at the two termini in the HOMO ofz-substituted alkene As estimated by Houk, the coefficient atβ-C is slightlylarger than that atα-C In contrast, for LUMO, both butadiene and allyl cationcontribute larger coefficients atβ-C reinforcing each other Therefore, a z-substituent leads to a slightly larger coefficient atβ-carbon in HOMO, but a much largercoefficient atβ-carbon in LUMO This pattern is represented as

Problem 1.2

Assuming the model of z-substituted alkene to be a 1:1 mixture of butadiene and allyl cation, estimate its HOMO/LUMO energies and coefficients Answer

EHOMO (zalkene)¼ [½ (α+0.62β +α+1.41β)]¼α+1.02β This energy

is slightly smaller than that of ethylene.

ELUMO (zalkene) ¼ [½ (α0.62β +α)]¼α0.31β This LUMO energy

is much smaller than that of ethylene.

(The above coefficients estimated for z-substituted alkene are not true coefficients as the sum of the squares of coefficients on all atoms of z-alkene including z-substituent would not be unity The estimated values show qualitatively a pattern of large/small coefficients.)

1.5.1.3 Perturbation by x-Substituents

An x-substituent is π donating through a lone pair on the heteroatom orthrough aσ bond (usually CdH):

Thus a reasonable model of x-substituted alkene is a hybrid model ofethylene and allyl anion:

The frontier orbital energies and coefficients for ethylene and allyl anion are

It is seen that allyl anion component tends to increase the energy ofHOMO [α>(α+β)] as well as the energy of LUMO [(α1.41β)>(αβ)] in proportion to its contribution to the hybrid Thus

EHOMO (x-alkene)>EHOMO (alkene)

ELUMO (x-alkene)>ELUMO (alkene)

Therefore, an x-substituent raises the energy of both HOMO and LUMO.The coefficient values indicate that the allyl anion HOMO contributeszero coefficient atα-C and a large coefficient (0.71) at β-C The resultanteffect would be a larger coefficient at theβ-C than at α-C in HOMO of

an x-substituted alkene For LUMO, allyl anion and ethylene contributeequal coefficient (0.71) at theα-C, but allyl anion contributes smaller coef-ficient (0.50) than ethylene (0.71) atβ-C The net effect would be a smallercoefficient at β-C in LUMO of an x-substituted alkene Therefore, anx-substituent leads to a larger coefficient at β-carbon in HOMO and at α-carbon

in LUMO This coefficient pattern is represented as

Problem 1.3

Assuming that the model for an x-substituted alkene is a 1:1 mixture of ethylene and allyl anion, estimate its HOMO/LUMO energies and coefficients Compare the results with the unsubstituted alkene.

EHOMO (x-alkene) ¼ [½ (α+α+β)¼(α+0.5β)]>EHOMO (alkene)

ELUMO (x-alkene) ¼ [½ (α1.41β +α β)¼(α1.21β)]>ELUMO (alkene)

(The above coefficients calculated for x-alkene are not true coefficients, and indicate a qualitative pattern of large/small coefficients.)

1.5.1.4 Summary

The perturbation effects of c-, z- and x-substituents on frontier orbital gies and coefficients of alkeneπ system are summarized inTable 1.2.The energy diagram for the unsubstituted and c-, z- and x-substitutedalkenes using Houk’s data of frontier orbital energies and the coefficient pat-tern is shown inFig 1.23.9,10

ener-Table 1.2 Perturbation effects of the substituents on frontier orbital energies and coefficients of alkene

c Raises HOMO energy Larger coefficient at β-carbon in

HOMO Lowers LUMO energy Larger coefficient at β-carbon in

LUMO

1.5.1.5 Alkyneπ System

Alkynes have a shorter CdC bond length than alkenes, which results in astronger overlap of p orbitals Thus, the alkyneπ system has a lower energyHOMO which is generally found to be 0.4–0.9 eV (0.7 eV on average)lower than the HOMO energy of alkene as measured by photoelectronspectroscopy However, the LUMO energy of alkyne is almost same as that

of alkene as shown by UV spectroscopy The effects of c-, z- andx-substituents on the coefficients of alkyne are similar to those on alkenecoefficients

1.5.2 HOMO/LUMO Energies and Coefficients

of Substituted Dienes

1.5.2.1 1-Substituted Dienes

The effects of c-, z- and x-substituents on the frontier orbital energies andcoefficients of 1-substituted dienes can be determined using similar argu-ments as advanced for alkenes with the models given below

Fig 1.23 Estimated frontier orbital energies and coefficient pattern for unsubstituted and c-, z- and x-substituted alkenes.

The substituent effects on HOMO/LUMO energies and coefficientsusing the above models give similar trends as observed for alkenes (seeTable 1.2) (The substituted dienes are drawn in an s-cis conformation;the pattern of change in s-cis and s-trans conformations is expected to be sim-ilar.) The Houk’s data9of estimated frontier orbital energies and the coef-ficient pattern at the terminal carbons C-1 and C-4 are shown inFig 1.24.The effect of the substituent at the unsubstituted terminal (C-4) of the dienes

Fig 1.24 Estimated frontier orbital energies and coefficient pattern of 1-substituted dienes.

(cf.β-carbon in alkenes) is indicated Remember that HOMO has oppositephase signs and LUMO has the same phase sign at C-1 and C-4.

1.5.2.2 2-Substituted Dienes

The trends for frontier orbital energies and coefficients of dienes with c-,

z-or x-substituent at C-2 can also be rationalized using the perturbation tern for c-, z- or x-substituted alkene moiety present in a 2-substituteddiene To illustrate, let us consider a 2-c-substituted diene In an unsubsti-tuted diene, there are equal coefficients on the terminal atoms C-1 and C-4

pat-in HOMO/LUMO In a 2-c-substituted diene, a c-substituent on thealkene moiety tends to raise the coefficient at the β-carbon (i.e C-1 ofdiene) in HOMO (or LUMO) as shown inFig 1.25 As a result, the coef-ficients at the terminal carbons of a 2-substituted diene become unequal,with a larger coefficient at C-1 in HOMO/LUMO Similar argumentsapply to other 2- substituted dienes

Fig 1.25 Effect of the c-substituent on the frontier orbital coefficient of a 2-substituted diene.

Fig 1.26shows the frontier orbital energies and the coefficient pattern of2-substituted dienes.9Note that the substituted alkene moiety is placed in abox to highlight the substituent effect It may be mentioned that the explicitmodels for 2-substituted dienes could also be formulated using similar argu-ments as used for alkenes (try for yourself ), which would provide similarresults as shown inFig 1.26.

1.6 TRIMETHYLENEMETHANE AND FULVENE SYSTEMS

Trimethylenemethane (TMM)1.1 and fulvene 1.2 do not belong to linearconjugatedπ systems but represent cross-conjugated systems

Fig 1.26 Estimated frontier orbital energies and coefficient pattern of 2-substituted dienes.

As shown, TMM is usually drawn as a diradical and is referred to as methylenemethane diradical (TMM diyl) which is a cross-conjugated sys-tem of four p orbitals The energy diagram of its π MOs is shown inFig 1.27.11It is seen thatψ1is a bonding MO;ψ2andψ3constitute a degen-erate pair of nonbonding MOs; andψ4is an antibonding MO.

tri-The TMM diyl is a reactive intermediate and can exist in triplet and glet states Triplet TMM with theπ electron configuration ψ12ψ21ψ31behaves

sin-as a diradical The singlet TMM hsin-as the π electron configuration ψ12ψ22or

ψ12ψ32 However, between ψ2 and ψ3, ψ2 as the HOMO can explain thecourse of pericyclic cycloadditions (seeChapter 4, Section 4.4) The LUMO

is thenψ3

Fulvene is a cross-conjugated system of six p orbitals It can be lated as a combination of butadiene and ethylene, and the perturbation anal-ysis gives six π MOs of fulvene whose energies increase in the order

formu-ψ1<ψ2<ψ3<ψ4<ψ5<ψ6(Fig 1.28).12

Fig 1.27 The π MOs of TMM.

Fig 1.28 The interaction energy diagram of fulvene.

Fulvene has six electrons Therefore, HOMO isψ3and LUMO isψ4.The diagram suggests that fulvene HOMO (ψ3) is the butadieneψ2orbital,

so the p orbitals at C-1 and C-6 of fulvene do not contribute to its HOMO

In contrast, all p orbitals contribute to fulvene LUMO (ψ4) It is also seenthat the NLUMO (next-lowest unoccupied molecular orbital) of fulvene

isψ5, and this orbital is the butadieneψ4orbital, and so C-1 and C-6 havezero coefficient in NLUMO Dimethylfulvene participates in a variety ofpericyclic cycloadditions The frontier orbital energies and coefficients ofdimethylfulvene are shown inFig 1.29.13,14(Note that only the front lobe

of each p orbital is drawn.)

1.7 CYCLIC CONJUGATED π SYSTEMS15

1.7.1 H€uckel System

H€uckel theory assumes that the cyclic π system is planar and a regular gon with equal sides The solution for the energies ofπ MOs of a monocy-clic conjugated system is given by

where n is the total number of p orbitals

First, we consider benzene as a cyclic conjugated system of six p orbitals(n¼6) The possible j values are 0, 1, 2, 3, 4 and 5 Using Eq.(1.6), the ener-gies of sixπ MOs (ψ0– ψ5) of benzene are estimated as

MO energy diagram of benzene is shown inFig 1.30in which the functions are labelled by j values in both notations The sixπ MOs of ben-zene are classified into three bonding and three antibonding MOs.

wave-Theπ electron configuration of benzene is ψ02ψ12ψ12 which indicatesthat all bonding orbitals are completely filled This configuration represents

a closed-shell system and hence is stable

In general, the total number of electrons for a closed-shell system

¼ no of electrons in the filled lowest nondegenerate level+the total

no of electrons in filled degenerate bonding levels (n pairs)

different contexts: in Eq.(1.6), n denotes the total number of p orbitals whilefor 4n + 2 electron system, n is zero or a positive integer.)

Theπ MO wavefunctions (ψj) for benzene as linear combinations of pAOs (ϕr) are obtained as

ψ0¼ 1ffiffiffi6

p ϕð 1+ϕ2+ϕ3+ϕ4+ϕ5+ϕ6Þ

ψ1¼ 1

2 ffiffiffi3

p 2ϕð 1 ϕ2ϕ3+ 2ϕ4 ϕ5 ϕ6Þ

ψ2¼1

2ðϕ2 ϕ3+ϕ5 ϕ6Þ

ψ3¼ 1ffiffiffi6

p ϕð 1 ϕ2+ϕ3 ϕ4+ϕ5ϕ6ÞTheπ MOs of benzene are drawn schematically inFig 1.31 (Note thatonly the top lobe of each p orbital is shown.) A nodal plane perpendicular

to the planar ring is indicated by a broken line The number of nodes

Fig 1.31 Schematic drawing of the π MOs of benzene.

(nodal planes) increases with energy The lowest energy bonding MO (ψ0)has no node; the two degenerate bonding MOs (ψ1,ψ1) have one node;the degenerate antibonding MOs (ψ2,ψ2) have two nodes; and the highestenergy antibonding MO (ψ3) has three nodes.

Next, we consider cyclobutadiene with four p orbitals (n¼4) The gies of the fourπ MOs (j¼0, 1, 1, 2) are estimated as

The ground state π electron configuration of cyclobutadiene is

ψ02ψ11ψ11 , which represents an open-shell system and also a triplet state.Cyclobutadiene is thus expected to be much less stable In general, the totalnumber of electrons for an open-shell system¼4n (2 less than 4n+2, sincethe two orbitals in a degenerate level are half-filled) These (4n)π systems(n¼1, 2,…) with open-shell configuration are called antiaromatic.The above results for H€uckel π systems to be aromatic or antiaromatic areknown as the H€uckel rules and are summarized as

Number of electrons H€uckel system

Fig 1.32 Energy diagram for the π MOs of cyclobutadiene.