Aromaticity:Beyond Hückel’s Rule

E. Adrian HenleGroup Meeting

2014.06.25

Aromaticity

• No single, concise definition of what makes an “aromatic” molecule

• Origin of term unclear (Hofmann 1855?)• Defined via inference, on basis of

observables:– Thermodynamics– Geometry– Ring current

Hofmann Proc. R. Soc Lond. 1856 8 1-3

Generalized Definition

Aromatic molecules:– Have empty or singly-occupied atomic orbitals

aligned in phase– Demonstrate electron delocalization– Are diamagnetically anisotropic

Quantification

• Empirical:– 3He encapsulation NMR– 1H, 13C shielding/deshielding– Aromatic Stabilization Energy (ASE)

• Semi-Empirical:– Magnetic susceptibility exaltation (Λ)– Harmonic Oscillator Model (HOMA)– Nucleus-Independent Chemical Shift (NICS)

1H, 13C, 3He Chemical Shift

• Direct measurement of magnetic environment “inside/outside” molecule

• Limitation: target nucleus must be present and resolvable

• Susceptible to convolution by induction, nearby heavy atoms

Gomes & Mallion Chem. Rev. 2001 101 1349-1384Rabinovitz, et al. J. Am. Chem. Soc. 2002 124 8786-8787

NMR Shift Examples

Aromatic Stabilization Energy

• Compare heats of hydrogenation– Full hydrogenation of

• Requires synthesis of partially-hydrogenated derivatives

• Neglects steric contribution

Example: 1,2-Azaborine

Liu, et al. J. Am. Chem. Soc. 2010 132 18048-18050

NBH

tBuNBH

tBu

NBH

tBuNBH

tBu

NBH

tBu

H2

NBH

tBu

-30.0 kcal/mol

-22.7 kcal/mol

-23.9 kcal/mol

H2

H2

ASE = 16.6 kcal/mol

Magnetic Susceptibility Exaltation

• Compares measured diamagnetism to value calculated from increment table

• Pro: all values calculated from same increment table fairly comparable

• Con: increment tables make assumptions/approximations

• Con: difficult to perform measurements

Pascal Ann. Chim. Phys. 1910 19 5

Harmonic Oscillator Model

• Quantifies aromaticity by deviation from “ideal” C-C bond length in ring (1.397Å)

• 퐻푂푀퐴 = 1 − . ∑ (푥 − 1.397)

• 퐻푂푀퐴 = 0 for Kekulé benzene퐻푂푀퐴 = 1 for true benzene structure

• 푛 ≝ number of C-C bonds푥 ≝ length of rth C-C bond

Kruszewski & Krygowski Tetrahedron Lett. 1972 36 3839-3842

NICS

• Either semi-empirical or ab initio• Quantum mechanical calculation of

diamagnetic susceptibility at fixed point• Pro: can calculate aromaticity in difficult or

inaccessible systems• Pro: generally agrees with other methods• Con: “In silico coniecto”

Hückel’s Rule

• Doering 1951: defined a rule for predicting aromatic behavior in ring systems

• Derived from Hückel’s 1931 work• Planar, fully conjugated systems• Aromatic: 4n+2 π-electrons• Anti-aromatic: 4n π-electrons

Doering & Detert J. Am. Chem. Soc. 1951 73 876-877Hückel Z. Phys. 1931 70 204-286; 72 310-337

Benzene

• 6π e- (n=2), planar, fully conjugated• Aromatic, as expected

Cyclooctatetraene (COT)

• 8π e- (n=2), fully conjugated• Anti-aromatic; distorts to break conjugation

Homotropylium

• 6π e- (n=2), but not fully conjugated• VSEPR predicts a planar structure• Distorts to give a “7-membered” arene!• Homoaromaticity (first described for tris-

homocyclopropenium)

Winstein, et al. J. Am. Chem. Soc. 1959 81 6523-6524

Pyrene

• 16π e- (n=4); Hückel’s rule predicts non-planarity to break conjugation

• Aromatic! 4n+2 rule fails in polycycles

Corannulene

• 20π e- (n=5)• Non-planar: surely cannot be aromatic• Aromatic! Hückel’s rule does not apply

Clar’s Rule

• The aromaticity of fused rings is determined by the number of π sextets

• The resonance form with the most sextets contributes the most character

Clar Polycyclic Hydrocarbons Academic Press: New York, 1964

3D Aromaticity

• Fullerene: aromatic for 2(n+1)2 π e-

– Ih symmetric fullerenes spherically symmetric– C60 non-aromatic; C50, 72, 98, etc. aromatic

Hirsch, et al. Angew. Chem. Int. Ed. 2000 39 3915-3917

Möbius Aromaticity

• Hückel’s rule is based on circular topology• Möbius topology allows for 4n πe-

aromatic systems• First Möbius arene isolated in 2003

Herges, et al. Nature 2003 426 819-821

Möbius Arene Synthesis

Hückel and Möbius Isomers

Summary

• Hückel’s rule is a gross oversimplification!• Aromaticity is both hard to define and

difficult to quantify• Methods for quantification are hit-or-miss• There is a huge diversity of non-classically

aromatic molecules (and they are cool!)