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Hückel	
  MO	
  theory:	
  Is	
  it	
  s3ll	
  useful?	
  
Brno,	
  May	
  2012	
  
Erich	
  Hückel	
  (09.08.1896	
  Berlin	
  -­‐	
  16.02.1980	
  Marburg)	
  
Postdoc	
  with	
  Max	
  Born	
  in	
  GöNngen	
  and	
  Peter	
  Debye	
  in	
  Zürich	
  (Debye–Hückel	
  
theory,	
  Habilita3on	
  1925)	
  
The	
  HMO-­‐Model	
  and	
  its	
  applica3ons:	
  Basis	
  and	
  Manipula3on,	
  	
  
E.	
  Heilbronner	
  and	
  H.	
  Bock,	
  English	
  transla3on,	
  1976,	
  Verlag	
  Chemie	
  
(P.	
  Klán	
  and	
  J.W.,	
  Photochemistry	
  of	
  Organic	
  Compounds)	
  
•  Father	
  Armand	
  (MD)	
  inherited	
  –	
  decided	
  to	
  go	
  for	
  private	
  
research	
  (smallpox)	
  in	
  GöNngen,	
  where	
  his	
  son	
  Erich	
  visited	
  
school	
  and	
  studied	
  physics	
  
•  P.	
  Debye,	
  liq.	
  crystals	
  PhD	
  1921	
  (Debye	
  -­‐>	
  ETH)	
  
•  Ass.	
  D.	
  Hilbert,	
  M.	
  Born	
  	
  
•  1922:	
  Zürich	
  Debye	
  (electrolytes),	
  hab.	
  1925	
  
•  1929	
  Leipzig	
  N.	
  Bohr	
  (QM	
  double	
  bond)	
  
•  1931	
  hab.	
  Benzene	
  (MO	
  vs	
  VB)	
  [L.	
  Pauling	
  “Nature	
  chem.	
  
bond:	
  VB,	
  “resonance”]	
  4n	
  +	
  2	
  
•  1937	
  a.o.	
  Prof.	
  Marburg	
  	
  
•  1962	
  emer.	
  
Schrödinger	
  equa3on	
  
Molecular	
  orbitals	
  cannot	
  (adequately)	
  
describe	
  many-­‐electron	
  systems:	
  
P[(d1	
  =	
  1)	
  and	
  (d2	
  =	
  4)]	
  =	
  P(d1	
  =	
  1)	
  x	
  P(d2	
  =	
  4)	
  
=	
  1/6	
  x	
  1/6	
  =	
  1/36	
  	
  	
  
Boiling	
  down	
  QM	
  (HMO)	
  
•  Only	
  electronic	
  wavefunc3on	
  (B–O	
  approxima3on)	
  
•  Product wavefunction of MO’s (correlation)
•  Consider only π-electrons (highest in energy, frozen core)
•  Neglect electronic interactions altogether (!)
•  HMO’s constructed as linear combinations of 2pz-AOs (LCAO:
•  Treat matrix elements H as parameters
•  No physics left, only topology (connectivity) as input
Determina3on	
  of	
  LCAO-­‐coefficients	
  	
  
(e.g.,	
  cyclobutadiene)	
  
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HMO	
  of	
  cyclobutadiene	
   Pauli	
  principle,	
  Hund’s	
  1st	
  rule	
  
The Fermi “hole”: electronic interaction as an afterthought
Electronic	
  configura3ons	
  
Calculate: …
The “physical” basis of “bow-and-arrow” chemistry
Heilbronner,	
  Helv.	
  Chim.	
  Acta	
  45,	
  1962,	
  1722.	
  	
  
	
   The	
  complete	
  set	
  of	
  unexcited	
  VB	
  structures	
  that	
  
can	
  be	
  wrisen	
  for	
  an	
  even	
  π-­‐electron-­‐system	
  
containing	
  only	
  six-­‐membered	
  rings	
  and/or	
  linear	
  
chains	
  of	
  orbitals,	
  defines	
  a	
  matrix	
  which	
  is	
  the	
  
inverse	
  of	
  the	
  Hückel-­‐matrix	
  of	
  the	
  same	
  system	
  
See	
  also:	
  	
  
Herndon,	
  Tetrahedron,	
  29,	
  1973,	
  3.	
  
Dewar,	
  Longuet-­‐Higgins,	
  Proc.	
  Roy.	
  Soc,	
  A214,	
  1952,	
  
482	
  
“Resonance” theory Aroma3city	
  (4n+2)	
  
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Photoelectron	
  spectroscopy	
   Correla3on	
  with	
  HMO-­‐orbital	
  energies	
  
Perturba3on	
  theory	
  for	
  HMO’s	
  
π
HMO	
  Heteroparameters	
  
Perturba3on	
  of	
  ethylene	
  
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1st-­‐Order	
  perturba3on	
  of	
  degenerate	
  orbitals	
  
Need to use symmetry-adapted LCMOs (any LC is equally valid)
Pairing	
  theorems	
  
Coulson–Rushbrooke theorems for alternant hydrocarbons (AHs)
(Hold also for π-SCF calculations (PPP)
Pairing	
  theorems	
   Back-­‐of-­‐envelope	
  NBMO’s	
  
The NBMO coefficients* on all atoms attached to an atom with
cNBMO° = 0 must add up to 0 (always choose * for the larger set):
Fused	
  systems:	
  Perinaphthenyl	
  
Perinaphthenyl anion has no excess charge in the center!
Biradicals:	
  Singlet	
  or	
  triplet	
  ground	
  state?	
  
Borden,	
  Davidson,	
  JACS	
  99,	
  1977,	
  4587	
  
Can	
  the	
  NBMOs,	
  if	
  necessary	
  by	
  appropriate	
  LC,	
  be	
  confined	
  to	
  
different	
  sets	
  of	
  atoms	
  (“disjoint”)?	
  
Cyclobutadiene: disjoint (singlet GS)
Trimethylenemethane: non-disjoint (triplet GS)
Calculate:
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Electronic	
  excita3ons	
  (π,π*)	
   Excited state charge distributions and bond orders
Bond orders of 1,3-butadiene:
Zimmermann’s meta-rule:
Excited state charge distributions and bond orders
p-­‐Band	
  of	
  aroma3c	
  hydrocarbons	
  
Why is azulene blue?
Linear	
  chains	
  
x all-trans linear polyenes
+ polyacetylenes
Blue	
  carrots?	
  
• Linear carbon chains HC2nH+• (radical cations)
O Linear carbon chains HC2n+1H+ (triplet ground state)
☐ symm.cyanines Me2N(CH=CH)n/2–3–CH=N+Me2
Electronic	
  spectra	
  of	
  ion	
  radicals	
  and	
  their	
  molecular	
  orbital	
  
interpreta;on.	
  III.	
  Aroma;c	
  hydrocarbons	
  
T.Shida,	
  J.	
  Am.	
  Chem.	
  Soc.,	
  1973,	
  95,	
  3473	
  
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Radical	
  ions	
  of	
  alternant	
  HCs	
  
Nonalternant	
  HC	
  
Transi3on	
  moments	
  and	
  their	
  direc3ons	
  
Mel = er1,2/2
Transition moments can be determined using linearly polarized light and oriented
molecules (photoselection, stretched polymer sheets, doped crystals).
The	
  benzene	
  catastrophe	
  
Neglect of electronic correlation and symmetry
Naphthalene	
  
Cycl[3.3.3]azine	
  
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Aza-­‐subs3tuted	
  cyl[3.3.3]azines	
  
PMO	
  theory	
  (Dewar)	
  
If there are several ways to divide AHs into two odd AHs, then the one that
gives the smallest interaction is best.
“Mirror image of GS”
General rules for excited state reactivity are often
opposite to those of ground state reactivity
•  Woodward–Hoffmann; Zimmerman’s meta-rule
•  PMO (Dougherty, JACS 1971, 93, 7187)
The photoproduct is
often less stable than
the starting material
Conclusions
Hückel theory has helped me enormously to
• understand and predict trends
• interpret electronic spectra
• interpret the output of “black-box” ab initio calculations
• provide general principals and guidelines
I hope this lecture has increased your awareness of
the merits of the HMO model.
The HMO model rectifies some problems of resonance
theory (cyclobutadiene) and, in contrast to resonance theory,
it is useful to consider electronic structures and reactivities
of excited states.