aromaticity: from organics to inorganics, from 2d to 3d

State Key Laboratory for Physical Chemistry of Solid Surfaces

厦门大学固体表面物理化学国家重点实验室

Aromaticity: From Organics to Inorganics, From 2D to 3D



吕鑫 (X. Lu)

2013. 07. 24



Outline Overview Practical Criteria of Aromaticity -aromaticity (2D) Möbius aromaticity Homoaromaticity -aromaticity Spherical aromaticity and 3D aromaticity



1. Overview

• Few concepts are as frequently used as AROMATICITY in the current chemical literature.

• Since 1981, ca. 300,000 papers dealing with the aromatic properties of chemical systems have been published.

• A thematic issue on Aromaticity: P. v. R. Schleyer, Chem. Rev. 2001, 101(5), 1115.

• A recent thematic issue on aromaticity: P. v. R. Schleyer, Chem. Rev. 2005, 105(10).



• The history of aromaticity can be traced

back to 1825 when M. Faraday isolated for

the first time benzene.

Benzene

(M. Faraday, 1825)



• The term “aromatic” was first used by chemists in the early 19th century to designate a specific class of organic substances (e.g., benzene), which are initially distinguished from those belonging to the aliphatic class by virtue of their pleasant olfactory properties.

• Aromaticity --- extra stability --- remarkable electron delocalization /conjugation.



1.1 Types of Aromatic Systems

• Before 1958, 2D planar polycyclic aromatic hydrocarbons (PAHs) reducible to molecules containing six -electrons, e.g.,

-aromaticity of PAH fulfilling

the Huckel 4N+2 or Clar sextet

(6N) rule



After 1958

1) Monocyclic hydrocarbons containing up to 30 -electrons, e.g., [n]annulenes

14 1810

Huckel & Möbius -aromaticity of annulenes



2) 3D boron and carborane cluster molecules based upon triangular face polyhedra, e.g.,

C2B3H5 B6H62- B7H7

2- B12H122-

C2B5H7C2B4H6 C2B10H12

3D aromaticity of clusters (ions)



3) Large carbon clusters illustrated by the famous buckminsterfullerene C60 and its homologues.



4) Analogues of PAHs containing metal atoms, such as gallium, or full metal clusters. E.g., metallabenzenes.

1) Thorn, D. L.; Hoffman, R. Nouv. J. Chim. 1979, 3, 39-45.

2) Elliott, G. P. et al. J. Chem. Soc., Chem. Commun. 1982, 811-813.

Predicted by Hoffman

in 1979.

Synthesized in

1982.



5) Molecules stabilized by -electron delocalization (-aromaticity), e.g., cyclopentane.

Dewar, M. J. S. Bul. Soc. Chim. Belg. 1979, 88, 957



6) transition-metal clusters stabilized by d-electron delocalization (-aromaticity), e.g.,

1) Tsipis et al. J. Am. Chem. Soc. 2003, 125, 1136.

2) Schleyer et al. J. Am. Chem. Soc. 2005, 127, 5701.

M4Li2 (M=Cu,Ag, Au)

CunHn (n=4,5,6)



1.2 Main developments about aromaticity

1980 Lu JX et al, quasi-aromaticity



1.3 Nature of the aromaticity concept

1) Like other useful and popular chemical concepts (chemical bonds, charges, electronegativities, hyperconjugations etc.), aromaticity is non-reductive, and lacks of clear physical bases.

2) Aromaticity is not a physical observable, having no precise experimental definition.

3) Aromaticity is just like to define beauty in our daily life!



• Easily to recognize (but not always)

• Many kinds

• Hard to compare

• Difficult to quantify

• Various opinions, no general agreement

• Interpreted differently

• Easily to recognize (but not always)

• Many kinds

• Hard to compare

• Difficult to quantify

• Various opinions, no general agreement

• Interpreted differently

Beauty (Aromaticity) is in the eye of the beholder!



4) Aromaticity is a time-dependent concept, of which new aspects are pending for discovery.

5) Aromaticity is a property associated with extra stability and many other unusual manifestation!!!



1.4 Main categories of criteria characterizing aromaticity• Structural - planarity and equal bond length tendencies

(simple, but unreliable!)

• Energetic – enhanced stability (indirect, but impractical!)

• Reactivity – lower reactivity, electrophilic aromatic substitution (neither direct nor reliable!)

• Spectroscopic– UV, proton chemical shifts, magnetic susceptibility exaltation (indirect, mostly reliable, but sometimes impractical!)



•Magnetic: ring current effectsa)Increased values of the magnetic

susceptibility (totb)Large magnetic anisotropies (aniso)c)Diamagnetic susceptibility exaltation ()

•Magnetic: ring current effectsa)Increased values of the magnetic

susceptibility (totb)Large magnetic anisotropies (aniso)c)Diamagnetic susceptibility exaltation ()

•Sructural bond length equalization •Sructural bond length equalization

1.39 1.47 1.34

•Chemical behavior: electrophilic aromatic substitution prefered to addition but C60addition, anthracene/phenantrene Diels-Alder !

•Chemical behavior: electrophilic aromatic substitution prefered to addition but C60addition, anthracene/phenantrene Diels-Alder !

•More stable than their acyclic analogues selection of reference systems, isodesmic or homodesmotic reaction !

•More stable than their acyclic analogues selection of reference systems, isodesmic or homodesmotic reaction !

Four classes of aromaticity criteria



1) Structural Criterion

Bond length equalization should not be used alone

as a criterion for aromaticity as some bond-

equalized systems are not aromatic. e.g.,

B3N3H6: isoelectronic with benzene, equalized B-N

bond lengths, not aromatic due to electron

localization on the N atoms.

Drawbacks exist with these criteria:



2) Energetic criterion.

• The aromatic stabilization energy (ASE) and

resonance energy (RE) have been well recognized

as the cornerstone of aromaticity.

• However, ASEs and REs of strained and more

complicated systems are difficult to evaluate.

• Such energy estimates vary significantly, strongly

depending on the equations used and on the

choice of reference molecules.



+ + 3

+ -32 kcal/mol3 2

3 CH3 CH3 -50 kcal/mol

Dewar Resonance Energy

(2)

(1)

-( )3 -21 kcal/mol

+ -35 kcal/mol3 2

+ -34 kcal/mol3 3

Aromatic Stabilization Energy

(3)

(4)

(5)

s-trans

cisoid

cisoid



3) Reactivity criterion

• The key characteristic reactivity feature: electrophilic aromatic substitution, not addition reaction.

• However, aromaticity criteria based on chemical reactivity are not straightforward to apply!!



4) 1H NMR chemical shifts: ------- A magnetic criterion• A criterion most often used experimentally.

• Due to the ring current induced by an external magnetic field, the inner protons are shifted upfield, and the outer protons are downfield-shifted.



But !!!

O

H2

H1

H2 H3

H1H2

H3

H1

4-5antiaromatic H1: 6.10

H2: 7.71 nonaromatic

H1: 5.78H2: 6.26 H3: 6.36

4-membered ring is antiaromatic

H1: 8.6H2: 8.1 H3: 8.5

NonaromaticPW91/IGLOIII



Important criteria for aromaticity and key developments

Time Contributors Contributions Type

<1825 Aromatic smell

1825 Faraday isolation of Benzene, stable, but high unsaturation

1861 Loschmidt A ring of carbon atoms suggested for benzene.

1865 Kekulé Benzene structure

1866 Erlenmeyer Substitution is more favorable than addition for benzene.

R




1910 Pascal Increment system for diamagnetic susceptibility, aromatic exaltation

M

1922 Crocker Aromatic sextet

1925 Armit/

Robinson

Electron sextet and heteroaromaticity.

1931 Hückel Theory of cyclic (4n+2) systems

1933 Pauling et al. Resonance energy. R

1936 Pauling et al. Ring current theory M

1937 London et al. QM treatment of ring current, London diamagnetism, GIAO method

M




1953 Meyer et al. The difference in the proton magnetic shielding between benzene and noncyclic olefins observed

M

1956 Pople Ring current effects on NMR chemical shifts: deshielding of benzene protons– manifestation of moleuclar ring current induced by external magnetic field.

M

1969 Dewar Dewar resonance energy. E

1967 Garratt Define molecules with an induced diamagnetic ring current as diatropic

M

1967 Jug et al. Jug structural index S




1968 Dauben Diamagnetic susceptibility exaltaion as a criterion of aromaticity

M

1970 Flygare Microwave spectroscopy, aromatic systems shown diamagnetic anisotropies.

M

1971 Hess, Schaad Hess-Schaad resonance energy. E

1972 Clar Clar “aromatic sextet” rule

1972 Krygowski Harmonic oscillator model or aromaticity (HOMA) as structural index of aromaticity

S

1974 Fringuelli Fringuelli structural index S




1975 Aihara et al. Topological resonance energy E

1980 Kutzelnigg IGLO calculation of magnetic properties: chemical shifts, magnetic susceptibilities and magnetic susceptibility anisotropies

M

1981 Lazzeretti, Zanasi

Ab initio current density plots. M

1983 Jug Jug structural index S

1985 Pozharskki Pozharskki structural index S

1985 Bird Bird structural index S




1987 Mizoguchi Magnetic susceptibility of Huckel and Mobius annulenes show an opposite tendency

M

1988 Zhou, Parr, Garst

Hardness (low reactivity) as aromatic index

R

1990-1995

Schleyer Extensively using Li+ NMR to study aromaticity.

M

1994-1996

Schleyer, Jiao Extensively using magnetic susceptibility exaltation to study aromaticity

M

1994 Saunders et al. Experimental endohedral 3He NMR to measure aromaticity in fullerenes and their derivatives

M




1994 Buhl et al. Computed endohedral 3He NMR to measure aromaticity in fullerenes and their derivatives

M

1995 krygowski Bond alteration coefficient (BAC) structural index

S

1996 Schleyer Nucleus-independent chemical shifts(NICS)

M

1996 Fowler, Steiner

Extensive application of current density plots to study aromaticity

M

1997 Schleyer Dissected NICS for localized MOs M

1997 Bohmann, Weinhold, Farrar

NBO-GIAO dissected canonical MOs (CMO) and LMO NICS

M




1998 Bean et al. Application of NBO analysis to delocalization and aromaticity

1998 Chesnut Difference in ring proton shieldings between the fully unsaturated species and its monoene counterpart recommended as aromaticity measure

M

1999 Mo Block-localized wavefunction (BLW) method based on modern ab initio VB theory to approach the absolute RSE

E

1999 Sundholm Aromatic Ring-Current Shielding(ARCS)

M

2000 Thiel Computing NICS using MNDO M




2001 Herges Anisotropy of the current induced density (ACID)

M

2002 Schleyer Isomerization Stabilization Energy(ISE)

E

2002 Sakai CiLC(CI/LMO/CASSCF) analysis; index of deviation from the aromaticity (IDA)

2003 Schleyer et al. GIAO-CMO NICS M

2004 Heine et al. Induced magnetic field as aromatic index

M

2005 Sola Aromatic fluctuation index (FLU)



Aromaticity criteria

Aromaticity

Schleyer and Jiao, Pure Appl. Chem. 1996, 68, 209-218

aromatic smell(before 1825)

High carbon ratio(before 1865)

Discovery of benzeneFaraday (1825)

Substitution > additionErlenmeyer (1866)

Benzene structureKekulé 1865

Exalted diamagnetic susceptibility--Pascal

(1910)Electron sextet

Armit-Robinson (1925)4n+2 electronHückel (1931)

Ring current theoryPauling (1936)

electron to contribution to magnetic susceptibilty -- London (1937)

Ring current effect on NMR chemical shift--Pople (1956)

Magnetic sucseptibility exaltation --Dauben (1969)

Magnetic sucseptibility anisotropy -- Flygare (1970)

Nucleus-Independent chemical shift (NICS) --Schleyer (1996)

historicallyStructure criteriaReactivity criteriaEnergy criteriaMagnetic criteria



2 Key Criteria for Aromaticity

• 2.1.1 RE-Resonance Energy (VB theory).

RE or Edelocalization = E(LS) – E(DS)

Case study: Benzene

2.1 Energetic criteria

Delocalized Key Localized Structures

benzene Kekule Structures

Dewar Structures



HMO predictionsDelocalized Localized

benzene 1,3,5-cyclohexatriene

0

E

Edelocalized = |8-6= |2

HMO Predictions



Ab initio MO predictions

• The MO calculation on the “unrealistic” localized structure is impossible in practice.

• Isodesmic reactions were proposed to evaluate RE.

+ + 3

+ -32 kcal/mol3 2

3 CH3 CH3 -50 kcal/mol

Dewar Resonance Energy

(2)

(1)

An isodesmic reaction is a chemical reaction in which the type of chemical bonds broken in the reactant are the same as the type of bonds formed in the reaction product



• The ab initio MO-based RE depends strongly on the choice of isodesmic reactions.

• It is far from trivial to balance strain, hyperconjugative effects, as well as differences in the types of bonds and atom hybridizations, using energy evaluation schemes.

• Impractical for complex systems such as those with a large number of -electrons or -aromaticity.



VB treatment • VB/STO-6G

benzene

Kekule stable cyclohexatriene

VRE

B

TRE = VRE + B

Mo, Y et al, JPC, 1994, 98, 10048.

C-C RE(kcal/mol)

1 1.404

2 1.404 74.28

3 1.343/1.521

44.48



2.1.2 ASE (aromatic stabilization energy)

-( )3 -21 kcal/mol

+ -35 kcal/mol3 2

+ -34 kcal/mol3 3

Aromatic Stabilization Energy

(3)

(4)

(5)

s-trans

cisoid

cisoid Cryanski et al, Tetrahedron, 2003, 59, 1657.

Homodesmic reactions for the evaluation of ASE.

Homodesmic reactions are an improved form of isodesmic reactions in which all formal bonds and types of each carbon atoms are conserved in the reactants and products.



2.1.3 ISE (Isomerization stabilization energy): -------the difference between the total energies of a methyl derivative of the aromatic system and its nonaromatic exocyclic methylene isomer.

Schleyer, P. v. R.; Puhlhofer, F. Org. Lett. 2002, 4 , 2873.



2.2 Magnetic Criteria



Magnetic criteria of aromaticity

Aromaticity


Exalted diamagnetic susceptibilityPascal (1910)

Ring current theoryPauling (1936)

electron to contributionto magnetic susceptibilty

London (1937)

Ring current effect on NMR chemical shift

Pople (1956)

Magnetic sucseptibility exaltation

Dauben (1969)

Magnetic sucseptibility anisotropy

Flygare (1970)

Nucleus-Independent chemical shift (NICS)

Schleyer (1996)

Magnetic criteria

Induced magnetic field Heine (2004)



Why choose a Magnetic Criteria ?

Formation of molecular orbitals from

carbon's p atomic orbitals in benzene

electrostatic potential map of benzene

electrons in the system are evenly

distributed around the ring.

Circulation of -electrons give rise to ring current in

applied magnetic field

The ring current induces

magnetic shielding within the

ring, but deshielding out of the

ring.



2.2.1 Diamagnetic Susceptibility exaltation (MSE, )

• Pioneering work by Pascal in 1910

• Benzene and its derivatives exhibited larger diamagnetic susceptibilities than would be expected for them from the susceptibilities of other unsaturated compounds.

Pascal, P. Ann. Chim. Phys. 1910, 19, 5.



• Pacault handled the discrepancy of magnetic susceptibility in the “Pascal system” by introducing a special benzene-ring parameter called “exaltation”.

• Pink et al. hypothesized that the exaltation of diamagnetic susceptibility can be used to identify aromatic systems.

Pacault, A. Ann. Chim., Ser. XII. 1946, 1, 567.

Pink, R. C. Trans. Faraday Soc., 1948, 4, 407.



• Exaltation of diamagnetic susceptibility results from the presence of cyclic delocalization of electrons, i.e. ring current.

• Definition of exaltation of magnetic susceptibility:

• A systematic survey of MSE of aromatic hydrocarbons was done by Dauben in 1968.

Pacault, A. Ann. Chim., Ser. XII. 1946, 1, 567.

Dauben, H. J. Jr. et al. J. Am. Chem. Soc.1968, 90, 811.

M Msusceptibility delocalized system non delocalized isomerexaltation

' M Msusceptibility delocalized system non delocalized isomerexaltation

'



Magnetic susceptibility anisotropies

• The tensor component perpendicular to the aromatic ring is much larger than the average of the others two components

anis ( ) / 2zz xx yy anis ( ) / 2zz xx yy

Aromatic / Antiaromatic = negative / positive anis,



Calculation of magnetic susceptibility

• The magnetic susceptibility (MS) is a global property of the molecule.

• Calculation of MS can be readily computed with the CSGT (Continuous Set of Gauge Transformations) method available in the Gaussian package.



Example 1

Cyclopropane is -aromatic



Example 2: Double aromaticity in C6H3+

Schleyer, P. v. R. et al. J. Am. Chem. Soc. 1994, 116, 10129.

2e

plane: 6e

• In-plane: 2e



Schleyer, P. v. R. et al. J. Am. Chem. Soc. 1994, 116, 10129.



Schleyer, P. v. R.; Jiao, H. Pure Appl. Chem. 1996, 68, 209

Compounds which exhibit significant exalted diamagnetic susceptibility are aromatic. Those compound with exalted paramagnetic susceptibility may be antiaromatic.



Example 3: Calculated anis and




2.2.2 Li+ NMR Chemical Shift

• Lithium bonding is primarily electrostatic, experimental 7Li

chemical shifts generally shows little variation among

different compounds.

• Lithium cations, typically complex to the π faces of

aromatic (or anti-aromatic) systems.

• This complexation results in a significant shielding (or

deshielding) of the 7Li NMR signal due to ring current

effects.



2.2.2 Li+ NMR Chemical ShiftExperiments• Aromatic• Paquette, L. A. et

al, JACS, 1990, 112, 8776.

• Antiaromatic

• Sekiguchi et al, JACS, 1991, 113, 7081.



• Experimental 7Li NMR chemical shifts can be well

reproduced by modern computations.

• The clear advantage of using δ(7Li) as a theoretical

probe lies in the possibility to provide a comparison with 7Li NMR spectrum of experimental Li+ complexes.

• However, the number of Li+ complexes and therefore the

utility of Li+ as a computational probe are rather limited.



2.2.3 NICS (Nucleas-Independent Chemical Shifts)

• Motivated by the analysis of the ring current effects on 7Li+ chemical shifts.

• The ring current induced in aromatic molecules affects

the magnetic environment of nuclei quite sensitively.

• However, inversely the physical existence of the probe

nucleus could also affect the properties of the system

under consideration.



Why not use the absolute chemical shielding of a virtual nucleus to probe

(the ring current effects of) aromaticity? --Schleyer et al, JACS, 1996, 118, 6317.

Why not use the absolute chemical shielding of a virtual nucleus to probe

(the ring current effects of) aromaticity? --Schleyer et al, JACS, 1996, 118, 6317.



Ab initio calculations of NICS

• NICS indices correspond to the negative value

of the magnetic shielding computed at chosen

points in the vicinity of molecules.

• Typically computed at ring centers, at points

above, and even as grids in and around the

molecule.



NICS(0) and Aromaticity

NICS Magnetism Ring Current Aromaticity

Significantly Negative

Magnetically Shielded

Diatropic Aromatic

Positive Magnetically Deshielded

Paratropic Anti-aromatic

Around Zero Non-Aromatic



Computation of NICS with Gaussian

Request an NMR type calculation

Optimize the molecule structure

Place "dummy" (Bq) atoms at the positions where NICS should be computed



Case Study: Benzene (GIAO-B3LYP/6-311+G**)



C6H6 vs. C4H4

• The NICS grid plot of benzene and cyclobutadiene at the GIAO-B3LYP/6-311+G*//B3LYP/6-311+G* level of theory. The red and green dots denote diatropic (aromatic) and paratropic (antiaromatic) ring currents, respectively.



NICS experimental validation

Endohedral 3He Chemical Shifts (ppm) of Fullerenes.Cages B3LYP/6-31G* He) C60 (1, Ih) -2.8 –6.3b

C70 (1, D5h) -27.2 -28.2c

C606-

(1, Ih) -50.0 -48.7c

C706- (1, D5h) 10.3 8.3c

C76 (1, D2) -16.2 -18.7e

C766-

(1, D2) -18.2 -20.6f

Bühl, M. Chem. Rev. 2001, 101, 1153.



More Examples



Bergman cyclization = aromatization reaction

P. Schreiner J. Am. Chem. Soc. 1998.

NICS [ppm]

TS -17.9 2 -19.0B3LYP/6-311+G*Schleyer J. Org. Chem. 2002.



Iso-Chemical-Shielding Surfaces (ICSS)

• The shape of the magnetic shielding function provides the same information about electron delocalization and molecular aromaticity.

• ICSS are actually isosurfaces of NICS values.

Klod, S et al. J. Chem. Soc. Perkin Trans. 2, 2001, 1893.



• Calculated ring current effect of benzene. (shielding surfaces at 0.1 ppm in yellow, at 0.5 ppm in green, at 1 ppm in green-blue, at 2 ppm in cyan, and 5 ppm in blue, respectively; deshielding surface at 0.1 ppm in red). View from perpendicular to the molecule and in the plane of the molecule.



Advantages of NICS1. Does not require reference standards, increment

schemes, calibrating, and calibrating (homodesmic ) equations for evaluation.

2. Importantly, in several sets of related molecules, NICS correlates well with other aromaticity indexes based on energetic, geometric, and other magnetic criteria.

3. Much less size-dependent than diamagnetic susceptibility exaltation.

4. Easily computed with standard QM packages, such as Gaussian, ADF, DeMon etc.

The numbers of citations of the original NICS paper Schleyer, P. v. R. J. Am. Chem. Soc. 1999, 121, 6872.



Disadvantages of NICS1. The total NICS does not depend purely on the system, but also on other magnetic shielding contributions due to local circulations of electrons in bonds, lone pairs and core electrons.

2. Refined alternatives of the original NICS technique are highly desirable to offer a better control of the contributions.



2.2.4 Dissected NICS• By definition, the chemical shielding tensors can be

described by a sum of partial chemical shifts arising from occupied molecular orbitals (MOs). So do the NICS tensors.

occ occ

0 0 0 13 32

diamagnetic term paramagnetic term

( )1 2| ( )

2N N N

k k k kk kN N

c c

rr I r r Lσ ψ

r R r R

where

and N N

N N

L r

r r R

Eschrig, H.; Seifert, G.; Ziesche, P. Solid State Commun. 1985, 56, 777.



Two alternative ways of Dissected NICS

• Localized MO-NICS (LMO-NICS

• Canonical MO-NICS (CMO-NICS)

Schleyer, P. v. R.et al. J. Am. Chem. Soc. 1997, 119, 12669.

Heine, T.et al. PCCP. 2003, 5, 246; JPCA 2003, 107, 6470.

Bohmann, T.et al. JCP. 1997, 107, 1173.



LMO NICS

NICStot= NICSC-C()+NICSC-H+NICSLP

+NICS



NICS(tot), NICS () and NICS () at the ring centers

• SOS-DEPT-IGLO/III//B3LYP/6-311+G**

Molecules R NICS() NICS() NICS(tot)

C6H6 (D6h) 1.396 -20.7 13.8 -8.9

Si6H6 (D6h) 2.217 -15.0 0.6 -13.1

Si6H6 (D3d) 2.240 -11.2

Ge6H6 (D6h) 2.305 -15.0 -1.5 -14.6

Ge6H6 (D3d) 2.384 -10.0

B3N3H6 (D3h) 1.431 -12.0 11.4 -2.1



Application of CMO-NICS

+

In-plane aromaticity3c-2

Schleyer 1979

NICS =-42.6 ppmDouble aromaticity

PW91/IGLO-III

MO-NICS(ppm)

-21.95

-5.3

-5.4



3 2D -Aromaticity

3.1 Benzene & other 6-e aromatics

3.2 PAHs (Polycyclic aromatic hydrocarbons)

3.3 [n]Annulenes

3.4 [n]Trannulenes



3.1 Benzene & other 6e aromatics

2-

X

(X=O,S,NH)

X

(X=N)



Benzene: MO-NICS Analysis

• Poater, J. et al. Chem. Eur. J., 2003, 9, 1113.

-5.1

-15.2



NICS(total) RB3LYP/6-311+G** values for aza pyrroles.



NICS(total) RB3LYP/6-311+G** values for phospha pyrroles.



NICS(total) RB3LYP/6-311+G** values for aza thiophenes.



NICS(total) RB3LYP/6-311+G** values for azapyridines.



3.2 PAHs

(Randic, M. Chem. Rev. 2003, 103, 3449.)



Misuse of circle notation!

• Belloli, R. C. J. Chem. Educ. 1983, 60, 190.

Circle notation

Wrong!!!

Chrysene

Kekule Structures

Clar Structures



Electron Rules for PAHs

Clar 6n rule versus Hückel (4n+2) rule• Hückel (4n+2) rule holds strictly for monocyclic

aromatic systems.

• Clar 6n rule holds faithfully for benzenoid PAHs having 6n -electrons which always show extra stability.

Clar, E. The Aromatic Sextet; J. Wiley & Sons: London, 1972.



Clar Sextet Structures of PAHs

Each circle represents 6 -electrons exclusively!

1 2 3 4

5 6 7

•Extra stability

•Large HOMO-LUMO gap

•Unusually high excitation energy



Giant Benzenoids

Müllen, K. et al, Chem. Rev. 2001, 101, 1267; Angew. Chem. Int. Ed., 1997, 36, 631, 1604, 1607.

All fulfill Clar 6n rule.



Further Support for Clar’s Aromatic Sextet

• Clar sextet rings have large negative NICS values. ----Moran, D.et al, J. Am. Chem. Soc. 2003, 125, 6746.

NICS grid of C42H18




NICS Hexaradical Clar formula

Fully Benzenoid Clar formula

C48H24

Moran, D.et al, J. Am. Chem. Soc. 2003, 125, 6746




For all PBHs, there is perfect agreement between Clar and NICS electron topologies.

Moran, D.et al, J. Am. Chem.

Soc. 2003, 125, 6746.



Clar Sextet model for SWCNTs

• Length-dependence of finite armchair (n,n) SWCNTs.

a) Kekule b) Incomplete Clar c) Complete Clar

(3m+1)-layered (3m+2)-layered 3m-layered

Matsuo, Y.; Tahara, K.; Nakamura, E. Org. Lett. 2003, 5, 3181



HOMO, LUMO and G of finite (5,5) SWCNTs (PM3 predictions)

HOMO

LUMO

G

The finite (n,n) tubes having complete

Clar aromatic sextet structures have

smaller HOMO-LUMO gaps!



Clar Sextet model for infinite (n,m) SWCNTs

R(n,m) Conductivity Clar VB Model

0 Metallic complete Clar sextet & fully benzenoid

1, 2 Semiconductor Incomplete Clar Structure with a seam of double bonds.

R(n,m) = n- m modulo 3

Ormsby, J. L.; King, B. T. J. Org. Chem., 2004, 69, 4287.



Clar VB representation of (12,9), (12,8), (12,7) and (19,0) SWCNTs

(12,9) (12,7) (19,0)(12,8)



Important application of Clar VB

• The Clar VB models of SWCNTs were demonstrated to be consistent with the patterns exhibited by SMT images.



3.3 [n]Annulenes

• Examples of aromatic [n]annulenes



• Examples of antiaromatic [n]annulenes



ISE of Aromatic [n]annulenes

• Wannere, C. S.; Schleyer, P. v. R. Org. Lett. 2003, 5, 865.



HH

H

HH

H

H

HH

H

H

H

H

H H

H

H

HHH

H

HH

H

H

HH

H

H

H

H

H H

H

H

H

The twelve outside hydrogens resonate at = 9.0 ppmThe twelve outside hydrogens resonate at = 9.0 ppm

The six inner hydrogens resonate at =-3.0 ppmThe six inner hydrogens resonate at =-3.0 ppm

Upfield of TMS !!!

Nucleus-Independent Chemical Shifts(ppm)

Nucleus-Independent Chemical Shifts(ppm)

1996 Schleyer: Nucleus-Independent Chemical Shifts (NICS): J. Am. Chem. Soc. 1996, 118, 6317.

Magnetic properties of [18]-annulenes



Calculated Properties of [n]annulenes

• B3—B3LYP/6-31G* ; HF – HF/6-31G*

Wannere, C. S.; Schleyer, P. v. R. Org. Lett. 2003, 5, 865.

Schleyer, P. V. R. et al., Chem. Rev. 2005, 105, in press.



• However, large annulenes such as [54]- and [66]-annulenes behave more like long chain cyclic polyenes.

Wannere, C. S.; Schleyer, P. v. R. Org. Lett. 2003, 5, 865.

Schleyer, P. V. R. et al., Chem. Rev. 2005, 105, in press.



3.4 [n]Trannulenes • [n]trannulenes --- all-trans-[n]annulenes with in-

plane p-orbital conjugation.

Annulenes(all cis-) or cis,trans-

Annulenes(cis,trans)

Trannulenes(all-trans)



Dodecahedrapentaene & [10]trannulene

McEwen, et al. J. Org. Chem. 1986, 51, 4357.

Fokin, et al. J. Am. Chem. Soc. 1998, 120, 9364.

NICS= -16.5 ppm

NICS= -14.0 ppm

Predicted model molecules



1. The [n]trannulenes, CnHn, have uniform configurations (Dn and Dnd symmetries) and are

higher in energy than the corresponding [n]annulenes.

2. All of the [n]trannulenes follow the Hückel rule exactly.

4n + 2 electron singlets--------aromatic

4n singlets ------------------antiaromatic

4n triplet ---------------------- aromatic.

Aromaticity of [n]trannulenes

Fokin, et al. J. Am. Chem. Soc. 1998, 120, 9364.

Burley, et al., Angew. Chem. Int. Ed., 2005, 44, 3176.



Magnetic Properties of Aromatic [n]Trannulenes (B3LYP/6-31G*)Magnetic Properties of Aromatic [n]Trannulenes (B3LYP/6-31G*)

Formula Sym. NICS (H)

C10H10 D5d -29.3 -14.0 2.0

C14H14 D7d -105.8 -17.2 1.8

C18H18 D9d -232.5 -17.9 1.0

C22H22 D11d -426.9 -17.9 0.4

C26H26 D13d -705.0 -17.8 -0.1

C30H30 D15d -1082.3 -17.8 -0.5



Magnetic Properties of Antiaromatic [n]Trannulenes (B3LYP/6-31G*)


C12H12 D6 113.7 35.7 10.6

C16H16 D8 221.3 27.8 10.7

C20H20 D10 349.0 21.6 10.3

C24H24 D12 487.4 17.0 9.8

C28H28 D14 619.6 13.4 9.1



Magnetic Properties of Triplet-aromatic [n]Trannulenes (B3LYP/6-31G*)


C12H12 D6d -58.9 -15.3 2.7

C16H16 D8d -157.4 -17.2 1.5

C20H20 D10d -315.6 -17.6 0.6

C24H24 D12d -548.9 -17.7 0.2

C28H28 D14d -874.9 -17.7 -0.1



Synthesized [n]Trannulenes

[18]trannulenes----Derivatives of C60

Wei et al., Angew. Chem. Int. Ed. 2001, 40, 2989.

Troshin, et al. Angew. Chem. Int. Ed. 2005, 44, 234.

Chiang et al., J. Am. Chem. Soc. 2005, 127, 26.



4 Möbius Aromaticity

• Möbius Strip: A ribbon with a 180 twist, named after the theoretical astronomer and mathematician August F. Möbius (1790-1868).



• Craig-type -conjugation & aromaticity: Möbius topologies in electronic wave functions, i.e., introducing the essential 180°() half-twist into a cyclic array of atomic orbital (AO) basis functions.

HMO calculations by Craig et al. revealed that in such planar cyclic (AB)n, n=3,4, molecules with equal numbers of p- and d-functions, the delocalization energies were smooth functions of n, and leading in the limit of large rings to the same delocalization energy per -electron as p-p overlaps.

Craig, D. P. et al. Nature 1958, 181, 1052; J. Chem. Soc. 1959, 997.

A B A B

phase inversion



Heilbronner-type Möbius Aromaticity

Heilbronner, E. Tetrahedron Lett. 1964, 1923.

• In 1964, Heilbronner predicted that singlet [4n]annulenes would be aromatic systems in twisted conformations where the p orbitals lie on the surface of a Möbius strip.

C2



-system of Benzene

A Möbius -system with a 180°twist --- Heilbronner-type

Möbius aromaticity

C2


Critical Features in Geometry &

Electronic Structure



(a) planar 4n+2 (b) planar 4n (c) one-half twisted 4n

-MO occupations




C9H9+

( = -188.8)

Mauksch, M. et al. Angew. Chem., Int. Ed. 1998, 37, 2395.



Möbius [4n]annulenes

C12H12

NICS = -14.3 ppm

Castro, C. et al.. Org. Lett. 2002, 4, 3431

C16H16

NICS = -14.5 ppm



Synthesized Möbius-type [16]annulene

Ajami, D. et al. Nature 2003, 426, 819.



Is this molecule möbius-aromatic ?

Castro et al. J. Am. Chem. Soc. 2005, 127, 2425.

• This möbius-shaped [16]annulene is nonaromatic and that any aromatic character of it is confined to the benzene rings!!

• The goal of preparing an unambiguously aromatic neutral Möbius [4n]annulene remains to be realized!!

NICS= -3.4 ppm



New metallacycles of Craig-Möbius aromaticity

Xia, H.P. et al, Nature Chem. DOI: 10.1038/NCHEM.1690.

Resonance of VB

structures

arising from 8c-8e d-p -conjugation.

C2



Trend for d-p conjugation within fused ring compounds with one transition metal atom

• Simplified as a [n]-polyenic chain + a TM atom! (n =odd)

• The occupied -MOs of a [n]-polyene (n=odd) is always aligned as, ne, (n-1)/2 MOs doubly occupied

and one non-bonding SOMO! E

E1

E2

E(n+1)/2

E(n+3)/2

… ……

1

2

E(n-1)/2 (n-1)/2

(n+3)/2

Symm.

Asymm.

LUMO

SOMO

n= 4k+1 n= 4k+3

Symm.

Asymm.

Symm.

Asymm.

(n+1)/2= 2k+1 (n+1)/2= 2k+2(n+1)/2

(n+3)/2= 2k+2 (n+3)/2= 2k+3



• Based on HMO theory, the [n]polyene (n=odd) has a nn bond,

whose SOMO adopts the form,

Simplified diagram of SOMO:n=4k+1 n=4k+3

C C C C CH21 2 3 4 5

Cn

1531

n

kSOMO ...)(A φφφψ

Symm. Asymm.

• To form a closed ring system with d-p (n+1)c(n+1)e conjugation, the symmetry of d(AO) of the TM atom should be compatible with that of the SOMO of [n]polyenic fragment. Thus,

1

35

1

35

7

1

357

9 1

357

911

A-Huckel B Mobius C partially Mobius hypothetically Huckel

n=11n=5 n=7 n=9

D Mobius



5. Homoaromaticity• In 1959 Winstein introduced the term

"homoaromatic" to describe compounds that display aromaticity despite one or more saturated linkages interrupting the formal cyclic conjugation.

•Winstein, S. J. Am. Chem. Soc. 1959, 81, 6524 & 6523.

•Williams, R. V. Chem. Rev. 2001, 101, 1185.



Homoaromaticity & Homoantiaromaticity

Hückel-type:

•Homoaromaticity: homoconjugative interaction(s) with

cyclic delocalization of (4n+2) electrons.

•Homoantiaromaticity: homoconjugative interaction(s)

with cyclic delocalization of 4n electrons.

Similarly, Möbius-type homoaromaticity arising from

Möbius-manner homoconjugation involving 4n electrons.

•Williams, R. V. Chem. Rev. 2001, 101, 1185.



The first suggestion of homoaromatic system

cholesteryl p-toluenesulfonate

Homoallylic cation

Winstein, S.; Adams, R. J. Am. Chem. Soc. 1948, 70, 838.



Types of Homoaromaticity

Homoaromatic

Bishomo-aromatic

Monohomo-aromatic

Trishomo-aromaticity

Tetrahomo-aromaticity

Number of saturated insertions

1

2

3

4



Criteria for Homoaromaticity

• The presence of homoconjugative interaction(s) (either through-bond or through-space) closing cyclic conjugation.

• Electron delocalization.

• 4n+2 Huckel rule

• RE > 2 kcal/mol.

• exceptional magnetic properties.

Note that through-bond homoconjugation invloves the hyperconjugation around the saturated linkage!



5.1 Cationic homoaromaticity

5.1.1 2e systems:

Homocyclopropenium cation

Applequist, D. E. et al. J. Am. Chem. Soc. 1956, 78, 4012.

monohomoaromatic



Cationic homoaromaticity

Bishomoaromatic

bishomocyclopropenium cations

Winstein, S. Chem. Soc. Spec. Publ. 1967, 21, 5.

non-homoaromatic



More examples of 2e-bishomoaromatics

• Laube, T. Acc. Chem. Res. 1995, 28, 399.

• Evans, W. J. et al. J. Am. Chem. Soc. 1995, 117, 12635.



Double bishomoaromatics

• Prakash, G. K. S.et al. J. Am. Chem. Soc. 1987, 109, 911.

Bishomoaromatic



Trishomocyclopropenium Cations

Trishomoaromatic

Szabo, K. J. et al. J. Org. Chem. 1996, 61, 2783



Pagodane Dications

4c2e homoaromatics(C…C distance 2.3~2.4 Å)

Prinzbach, H.et al. Pure Appl. Chem. 1995, 67, 673.

Etzkorn, M. et al. J. Org. Chem. 1998, 63, 6080.

Prakash, G. K. S. et al. Chem. Commun. 1999, 1029.



Syn-Periplanar Bisdiazene-Tetroxide Dication

Exner, K. et al. J. Am. Chem. Soc. 1999, 121, 1964.

2.55

-2e



5.1.2 6e systems

Homotropylium cations

a) equalized C-C bonds

b) equalized (13C)

c) NICS(0) = 11.3 ppm

Reindl, B.et al. JPCA 1998, 102, 8953.



5.1.3 dehydroadamantyl dication

• 4c2e Tetrahomoaromatic

Bremer, M. et al. ACIE. 1987, 26, 761.

Schleyer, P. v. R. JACS, 1996, 118, 6317.

NICS = 50.1

= -50.1



5.1.4 Antihomoaromatic Cations

• Jiao, H.et al. In AIP Conference Proceedings 330: E.C.C.C. 1, Computational Chemistry; American Institute of Physics: Woodbury, NY, 1995; p 107.



5.2 Neutral Homoaromatics

• Hypothetic neutral homoaromatics



• Few examples of neutral homoaromatic molecules has been predicted theoretically.

• Thus far, neutral homoaromaticity has been widely recognized in the transitions states of a lot of chemical pericyclic reactions, such as Diels-Alder, 1,3-dipolar cycloaddition, cope rearrangement and so on.!



5.3.1 Diels-Alder reactions

• Evans, M. G..; Warhurst, E. Trans. Faraday Soc. 1938, 34, 614.

• Cossio, F. P. et al. J. Am. Chem. Soc. 1999, 121, 6737.

6e homoaromaticity

5.3 Aromaticity of Transition States of Pericyclic Reactions & Homoaromaticity



5.3.2 Sigmatropic shifts

• Jiao, H.; Schleyer, P. v. R. J. Phys. Org. Chem. 1998, 11, 655.

6e homoaromaticity



5.3.3 Cope rearrangements

• Navarro-Vazquez, A. et al. Org. Lett. 2004, 6, 2981.

6e homoaromaticity



5.3.4 Claisen rearrangements

• Yoo, H. Y.; Houk, K. N. J. Am. Chem. Soc. 1997, 119, 2877.

6e homoaromaticity



5.3.5 Electrocyclic reactions

• Jiao, H.; Schleyer, P. v. R. J. Phys. Org. Chem. 1998, 11, 655.

6e homoaromatic TSs



5.3.6 Ene reactions

• Loncharich, R.; Houk, K. N. J. Am. Chem. Soc. 1987, 109, 6947.

6e homoaromaticity



5.3.7 Reactions involving TS’s of Möbius Homoaromaticity

• Jiao, H.; Schleyer, P. v. R. Angew. Chem., Int. Ed. Engl. 1993, 32,1763.• Lee, P. S. et al. J. Am. Chem. Soc. 2003, 125, 5839.

4ne Möbius homoaromaticity

[1,7] Sigmatropic Shift Ring opening of cyclobutene



6 -Aromaticity

•Dewar, M. J. S. Bul. Soc. Chim. Belg. 1979, 88, 957.

•Exner, K. et al, J. Phys. Chem A 2001, 105, 3407.

•Moran, D. et al. Org. Lett. 2003, 5, 23.NICS

Grid



• Dissected NICS data of cycloalkanes.



Super -(anti) aromaticity

• Moran, D. et al. Org. Lett. 2003, 5, 23.

Cage

3MR

4MR

-48.3

-46.1

-0.1

-33.0

-0.8

Symm. Td D3h

+23.1

+13.1

Oh

NICS



Related Inorganics: P4 and P8

PP

P

P

Cage

3MR

4MR

-59.7

-57.4

Symm. Td

P

P

P

P

PP

P

P

+43.4

+26.6

Oh

NICS



7 Spherical Aromaticity

• Fullerenes

• Polyhedral boranes and carboranes

• Other inorganic cage compounds and Clusters

• Aihara, J. J. Am. Chem. Soc. 1978, 100, 3339.

• Bühl, M. ； Hirsch, A.; Chem. Rev. 2001, 101, 1153.

• King, R. B. et al, Chem. Rev., 2005, 105, in press.



7.1 The Sphericity of Fullerenes

Tang, A. C. et al. Chem. Phys. Lett. 1994, 227, 579.

Reiher, M.; Hirsch, A. Chem. Eur. J. 2003, 9, 5442.

-MOs of C60

The spherical harmonic pattern for

C60 MOs



Noble-gas configuration of C6010+

2(N+1)2 electron-counting rule for spherical aromaticity of Ih fullerenes, e.g., C20

2+ and C6010+

• Hirsch, A. Angew. Chem, Int. Ed. 2000, 39, 3915-3917

NICS(C202+) = -73.1 ppm

NICS(C6010+) = -81.4 ppm



7.2 Duality of Fullerenes and Deltahedral Boranes

• Fullerene polyhedra and borane deltahedra have an interesting dual relation ship.

• A given polyhedron P can be converted into its dual P* by locating the centers of the faces of P* at the vertices of P and the vertices of P* above the centers of the faces of P.



Example: Cube Octahedron dualization



Dualization of C60 and B32H322-

C60

(v = 60, e = 90, and f = 32)

B32H322–

(v = 32, e = 90, and f = 60)

Dual



7.3 Aromaticity of fullerenes

Symmetry Ne l NICS

C284- Td 32 3 -35.5

C32 D3 32 3 -53.2

C482- (199)C2 50 4 -40.4

C6010+ Ih 50 4 -81.7

C808+ Ih 72 5 -82.9

** GIAO-SCF/6-31G*



3He@Cn 3He2@Cn

C60 -6.40 -6.40

C606- -49.27 -49.17

C70 -28.82 -28.81

C706- +8.20 +8.04

Chemical Shifts of Endohedral 3He in C60 and C70



7.4 Aromaticity of boranes and derivatives

• The deltahedral closo-boranes BnHn–2 (6 ≤

n ≤ 12) and their carboranes are well-accepted as aromatic.



NICS(B5H52-) = -28.1 ppm

NICS (N2B3H5) = -10.1 ppm

• Schleyer, P. v. R. et al. J. Am. Chem. Soc. 1996, 118, 9988



NICS of Boranes and derivatives(CSGT-B3LYP/6-311+G**)

BnHn2- CBn-1Hn

- NBn-1Hn

6 vertex -26.5 -26.6 -25.9

7 vertex -19.7 -20.3 -15.7

8 vertex -16.7 -16.8 -14.7

9 vertex -21.1 -20.2 -16.7

10 vertex -27.5 -24.9 -20.0

11 vertex -26.2 -24.0 -19.4

12 vertex -28.4 -28.0 -26.3

Najafian K.et al. Inorg. Chem. 2003, 42, 4190.



7.5 Other inorganic clusters7.5.1 E4

q (q=0, E=N,As,Sb,Bi; q=-4, E=Si,Ge,Sn,Pb)

Both the and MO shells of P4 fulfill the 2(N+1)2 rule, attaining daul spherical aromaticity.

Hirsch, A. ACIE 2000, 39, 3915



NICS (ppm) of E4q clusters

P4 As4 Sb4 Bi4

NICSa -54.6 -55.3 -40.3 -37.3

Si44- Ge4

4- Sn44- Pb4

4-

NICSb -41.9 -39.3 -32.3 -29.1

a GIAO-MP2/6-31G*; b GIAO-MP2/LANL2DZp

Hirsch, A. et al. Angew. Chem, Int. Ed. 2001, 40, 2834.



7.5.2 Zintl ions

E94- (E= Si, Ge, Sn, Pb) and Bi9

5+

>

double spherical aromaticity = 32 () + 8 ()

Corbett, J.D. Angew. Chem. Int. Ed. 2000, 39, 670



E9q Clusters (GIAO-MP2)

Symmetry NICS Erel(kcal/mol)

Si94- closo(D3h) -87.7 0.0

nido(C4v) -86.7 1.1Ge9

4- closo(D3h) -81.0 0.0nido(C4v) -80.3 0.8

Sn94- closo(D3h) -68.9 0.0

nido(C4v) -68.2 0.8Pb9

4- closo(D3h) -68.9 0.0nido(C4v) -68.3 1.0

Bi95+ closo(D3h) -28.1 0.0

nido(C4v) -28.1 0.4Kuznetsov, A. N. et al. Chem. Eur. J. 2001,7,2821.



7.6 Spherically aromatic gold clusters

• King, R. B. et al. Inorg. Chem. 2004, 43, 4564.

NICS=-36 ppmNICS=-36 ppm



MOs of Au20(Td)

• King, R. B. et al. Inorg. Chem. 2004, 43, 4564.

Spherically Aromatic



icosahedral “golden” fullerene Au32

The dual of C60 The dual of C60

• Johansson, M. P. et al. Angew. Chem., Int. Ed. 2004, 43, 2678.

32 -electrons 32 -electrons

Spherical

-aromaticity

NICS=-100ppm

Spherical

-aromaticity

NICS=-100ppm



8. Aromaticities in Metal Clusters

• Ga32-

• Li, X. W. et al. J. Am. Chem. Soc.,1995, 117, 7578.

• Xie, Y. M. et al. J. Am. Chem. Soc. 1996, 118, 10635.

NICS(0) =-45.4 ppm

NICS(1) =- 23.5 ppm



Hg46-

• A 2e aromatic inorganic cluster

• Kuznetsov, A.E. et al. Angew. Chem., Int. Ed. 2001, 40, 3369.



Au5Zn+

• 6e aromatic

• Tanaka, H. et al, J. Am. Chem. Soc. 2003, 125, 2862.



8 Through-space Aromaticity of Inorganic Ions

Zhang, Q.; Lu, X. et al. Inorg. Chem., 2006, 45, 2457. JACS, 2009, 131, 9781.

E

LUMO

HOMO

HOMO-1

HOMO-6

HOMO-7

HOMO-11

Selected MOs of Se2I42+

10e homoaromatic

8.1 Pericyclic Transition-State-Like Aromaticity



Three VB structures of Se2I42+

The resonance of these VB structures results in 6c10e through-space conjugation!



(I2+)2 with PTS-like

aromaticity



8.2 S2I42+ with dual

PTS-like aromaticity



8.3 Bishomoaromatic Inorganic Ions

MO descriptionVB description

S

S

S

S

S

S

SS

S

S

S

S

S

SS

S

S

S

S

SS

S

S

S

6c10e through-space homoconjugation



8.4 Neutral Bishomoaromatic Inorganics

1,5-diphoshadithiazocines

6c10e homoconjugation

14aa 14bb 14ca

S….S

(Å)

2.62

(2.55)

2.77

(2.53)

2.62

(2.53)

NICS

(ppm)

-18.4 -18.7 -17.3

ppm cgs

-135.8 -251.9 -235.6

a B3LYP/6-311+G(3df); b B3LYP/6-31G(d);



8.5 Spherically Aromatic TS Conjugation

Te64+

6c8e spherical through-space conjugation



Concluding Remarks

Aromaticity is a time-dependent concept, of which new aspects are pending for

discovery.



厦门大学校主 --陈嘉庚先生



Questions

• 同芳香性和常规芳香性体系的异同点有哪些 ?

• Möbius芳香性区别于 Hückel芳香性的关键特征有哪些 ?

• 上述 Nature Chem文献中的Metallapentalyne为何在杂金属后具有Möbius芳香性 ? 当金属原子不位于其中间桥位时是否仍可能具有类似的Möbius芳香性？

aromaticity: from organics to inorganics, from 2d to 3d

Documents

aromaticity conceptlike

aromaticity of pah

history of aromaticity

d aromaticity of clusters

d boron

transitionmetal clusters

term aromatic

time benzene