11. Giambiagi M, de Giambiagi MS, dos Santos CD, de Figueiredo AP (2000) Multicenter bond
indices as a measure of aromaticity. Phys Chem Chem Phys 2:3381–3392
12. Bultinck P, Ponec R, Van Damme S (2005) Multicenter bond indices as a new measure of
aromaticity in polycyclic aromatic hydrocarbons. J Phys Org Chem 18:706–718
13. Cioslowski J, Matito E, Solà M (2007) Properties of aromaticity indices based on the
one-electron density matrix. J Phys Chem A 111:6521–6525
14. Hückel E (1937) The theory of unsaturated and aromatic compounds. Z Elektrochem 43(752–
788):827–849
15. Baird NC (1972) Quantum organic photochemistry. II. Resonance and aromaticity in the
lowest
3
ππ* state of cyclic hydrocarbons. J Am Chem Soc 94:4941–4948
16. Mingos DMP (1984) Polyhedral skeletal electron pair approach. Acc Chem Res 17:311–319
17. Wade K (1971) The structural significance of the number of skeletal bonding electron-pairs in
carboranes, the higher boranes and borane anions, and various transition-metal carbonyl
cluster compounds. J Chem Soc D Chem Commun (15):792–793
18. Hirsch A, Chen Z, Jiao H (2000) Spherical aromaticity in icosahedral fullerenes: the 2(N + 1)
2
rule. Angew Chem Int Ed 39:3915–3917
19. Poater J, Solà M (2011) Open-shell spherical aromaticity: the 2 N
2 + 2 N + 1 (with
S = N + 1/2) rule. Chem Commun 47:11647–11649
20. Clar E (1972) The aromatic sextet. Wiley, New York
21. Solà M (2013) Forty years of Clar’s aromatic pi-sextet rule. Front Chem 1:22
22. Glidewell C, Lloyd D (1984) MNDO study of bond orders in some conjugated bi- and
tri-cyclic hydrocarbons. Tetrahedron 40:4455–4472
23. Herges R (2006) Topology in chemistry: designing Möbius molecules. Chem Rev 106:4820–
4842
24. Rzepa HS (2005) Möbius aromaticity and delocalization. Chem Rev 105:3697–3715
25. Rappaport SM, Rzepa HS (2008) Intrinsically chiral aromaticity. Rules incorporating linking
number, twist, and writhe for higher-twist Möbius annulenes. J Am Chem Soc 130:7613–7619
26. Hückel E (1931) Quantentheoretische Beiträge zum Benzolproblem I. Die
Elektronenkonfiguration des Benzols und verwandter Verbindungen. Z Physik 70:104–186
27. Doering WVE, Knox LH (1954) The cycloheptatrienylium (tropylium) ion. J Am Chem Soc
76: 3203–3206
28. Mayer I (2010) Analytical derivation of the Hückel “4n + 2 rule”. Theoret Chem Acc
125:203–206
29. Breslow R (1968) Small antiaromatic rings. Angew Chem Int Ed Engl 7:565–570
30. Hobey WD (1972) Free-electron molecular-orbital model of aromaticity. J Org Chem
37:1137–1141
31. Jiao H, Schleyer PVR, Mo Y, McAllister MA, Tidwell TT (1997) Magnetic evidence for the
aromaticity and antiaromaticity of charged fluorenyl, indenyl, and cyclopentadienyl systems.
J Am Chem Soc 119:7075–7083
32. Fowler PW, Steiner E, Jenneskens LW (2003) Ring-current aromaticity in triplet states of 4n π
electron monocycles. Chem Phys Lett 371:719–723
33. Poater J, Duran M, Solà M, Silvi B (2005) Theoretical evaluation of electron delocalization in
aromatic molecules by means of atoms in molecules (AIM) and electron localization function
(ELF) topological approaches. Chem Rev 105:3911–3947
34. Bader RFW (1991) A quantum theory of molecular structure and its applications. Chem Rev
91:893–928
35. Feixas F, Matito E, Solà M, Poater J (2008) Analysis of Hückel’s [4n + 2] rule through
electronic delocalization measures. J Phys Chem A 112:13231–13238
36. Feixas F, Matito E, Solà M, Poater J (2010) Patterns of π-electron delocalization in aromatic
and antiaromatic organic compounds in the light of the Hückel’s 4n + 2 rule. Phys Chem
Chem Phys 12:7126–7137
37. Rosenberg M, Dahlstrand C, Kilsa K, Ottosson H (2014) Excited state aromaticity and
antiaromaticity: opportunities for physical and photochemical rationalizations. Chem Rev
114:5379–5425
12 Rules of Aromaticity
333
indices as a measure of aromaticity. Phys Chem Chem Phys 2:3381–3392
12. Bultinck P, Ponec R, Van Damme S (2005) Multicenter bond indices as a new measure of
aromaticity in polycyclic aromatic hydrocarbons. J Phys Org Chem 18:706–718
13. Cioslowski J, Matito E, Solà M (2007) Properties of aromaticity indices based on the
one-electron density matrix. J Phys Chem A 111:6521–6525
14. Hückel E (1937) The theory of unsaturated and aromatic compounds. Z Elektrochem 43(752–
788):827–849
15. Baird NC (1972) Quantum organic photochemistry. II. Resonance and aromaticity in the
lowest
3
ππ* state of cyclic hydrocarbons. J Am Chem Soc 94:4941–4948
16. Mingos DMP (1984) Polyhedral skeletal electron pair approach. Acc Chem Res 17:311–319
17. Wade K (1971) The structural significance of the number of skeletal bonding electron-pairs in
carboranes, the higher boranes and borane anions, and various transition-metal carbonyl
cluster compounds. J Chem Soc D Chem Commun (15):792–793
18. Hirsch A, Chen Z, Jiao H (2000) Spherical aromaticity in icosahedral fullerenes: the 2(N + 1)
2
rule. Angew Chem Int Ed 39:3915–3917
19. Poater J, Solà M (2011) Open-shell spherical aromaticity: the 2 N
2 + 2 N + 1 (with
S = N + 1/2) rule. Chem Commun 47:11647–11649
20. Clar E (1972) The aromatic sextet. Wiley, New York
21. Solà M (2013) Forty years of Clar’s aromatic pi-sextet rule. Front Chem 1:22
22. Glidewell C, Lloyd D (1984) MNDO study of bond orders in some conjugated bi- and
tri-cyclic hydrocarbons. Tetrahedron 40:4455–4472
23. Herges R (2006) Topology in chemistry: designing Möbius molecules. Chem Rev 106:4820–
4842
24. Rzepa HS (2005) Möbius aromaticity and delocalization. Chem Rev 105:3697–3715
25. Rappaport SM, Rzepa HS (2008) Intrinsically chiral aromaticity. Rules incorporating linking
number, twist, and writhe for higher-twist Möbius annulenes. J Am Chem Soc 130:7613–7619
26. Hückel E (1931) Quantentheoretische Beiträge zum Benzolproblem I. Die
Elektronenkonfiguration des Benzols und verwandter Verbindungen. Z Physik 70:104–186
27. Doering WVE, Knox LH (1954) The cycloheptatrienylium (tropylium) ion. J Am Chem Soc
76: 3203–3206
28. Mayer I (2010) Analytical derivation of the Hückel “4n + 2 rule”. Theoret Chem Acc
125:203–206
29. Breslow R (1968) Small antiaromatic rings. Angew Chem Int Ed Engl 7:565–570
30. Hobey WD (1972) Free-electron molecular-orbital model of aromaticity. J Org Chem
37:1137–1141
31. Jiao H, Schleyer PVR, Mo Y, McAllister MA, Tidwell TT (1997) Magnetic evidence for the
aromaticity and antiaromaticity of charged fluorenyl, indenyl, and cyclopentadienyl systems.
J Am Chem Soc 119:7075–7083
32. Fowler PW, Steiner E, Jenneskens LW (2003) Ring-current aromaticity in triplet states of 4n π
electron monocycles. Chem Phys Lett 371:719–723
33. Poater J, Duran M, Solà M, Silvi B (2005) Theoretical evaluation of electron delocalization in
aromatic molecules by means of atoms in molecules (AIM) and electron localization function
(ELF) topological approaches. Chem Rev 105:3911–3947
34. Bader RFW (1991) A quantum theory of molecular structure and its applications. Chem Rev
91:893–928
35. Feixas F, Matito E, Solà M, Poater J (2008) Analysis of Hückel’s [4n + 2] rule through
electronic delocalization measures. J Phys Chem A 112:13231–13238
36. Feixas F, Matito E, Solà M, Poater J (2010) Patterns of π-electron delocalization in aromatic
and antiaromatic organic compounds in the light of the Hückel’s 4n + 2 rule. Phys Chem
Chem Phys 12:7126–7137
37. Rosenberg M, Dahlstrand C, Kilsa K, Ottosson H (2014) Excited state aromaticity and
antiaromaticity: opportunities for physical and photochemical rationalizations. Chem Rev
114:5379–5425
12 Rules of Aromaticity
333