π-π (π-stacking) Interactions: Origin and Modulation
Larry Wolf
SED Group Meeting
01-18
18-11
π-Stacking
Stacking Geometries: An Electrostatic Tutorial
+
+
Hunter and Sander Rules: Geometry
Sandwich
Parallel displaced
Edge-to-face
Hunter, C. A.; Sanders J. K. M. J. Am. Chem. Soc. 1990, 112, 5525
Influence of differing pi electron density
Hunter, C. A.; Sanders J. K. M. J. Am. Chem. Soc. 1990, 112, 5525
Hunter and Sander Rules applied to Proteins (ala-ala)
(ala
Hunter, C. A. et al. J. Mol. Biol. 1991, 218, 837
Substituent effects parallel stacked
Kcal/mol
Rotation barriers were measured by line shape
analysis in H-NMR
Cozzi, F.; Siegel J. S.; et. al. J. Am. Chem. Soc. 1992, 114, 5729
Cozzi, F.; Siegel, J. S.; et. al. Phys. Chem. Chem. Phys. 2008, 10, 2686
Polar/π vs charge transfer
Free energy of activation determined from 2D NMR EXSY
pulse sequence
Charge transfer does not contribute
significantly to the interaction
Cozzi F.; Siegel, J. S.; et. al. J. Am. Chem. Soc. 1993, 115, 5330
Face-to-face or center-to-edge?
- Rotation barrier determined by 2D EXSY NMR
- Mode of stacking is not well characterized
- low sensitivity may be a result of decreased favorable
electrostatic orientation
MMFF
Cozzi, F.; Siegel, J. S.; et. al. Org. Biomol. Chem. 2003, 1, 157
Parallel Displaced and/or edge-to-face
face or T-shape
T
X=F
G = RTLn(2) – RTLn(syn/anti)
Interaction is strongest when both rings
contain e-withdrawing
e
groups?
OMe better fit with σ(meta)
Gung, B. W.; Xue, X.; Reich, H. J. J. Org. Chem. 2005, 70, 3641
Other pi-stacking Modes?
“The alternative T-shape
T
orientation is prohibited by the
triptycene skeleton.”
T-Shaped geometry?
Gung, B. W.; Xue, X.; Reich, H. J. J. Org. Chem. 2005, 70, 3641
Double Mutant Cycle: edge-face/T--shaped
NOEs
(ROESY)
Hunter, C. A. et al. Angew. Chem. Int. ed. 1996, 35, 1542
Double Mutant Cycle: edge-face/T--shaped
Combined (meta and para ) equation
Hunter, C. A.; et. al. Chem. Commun. 1998, 775
Hunter, C. A.; et. al. Chem. Eur. J. 2002, 8, 2848
Double Mutant cycle: face-face
Based on NOE and δ values
Hunter C. A.; et. al. J. Am. Chem. Soc. 2005, 127, 8594
Electrostatic or Dispersion?
Crystal structure:
X=NO2; CH3
NMR experiments in
CDCl3
-0.56 kcal/mol
-0.43 kcal/mol
Wilcox, C. G. et al. J. Am. Chem. Soc. 1998, 120, 11192
Benzene Dimer (Sandwich, T-Shaped,
Shaped, and Parallel Displaced)
Sandwich
T-Shaped
Parallel displaced
Energy
Distance
Sherrill, D. C.; et. al. J. Phys. Chem. A. 2004, 108, 10200
Decomposition of energetic components: Perturbation Theory
EA-B = Eelec + Eind + Evdw
van der Waals (Lennard-Jones)
Evdw = Edisp + Erep
Erep
Edisp
total
Sherrill, D. C.; et.al. J. Am. Chem. Soc. 2002, 124, 10887
Sherrill, D. C.; et. al. J. Phys. Chem. A. 2004, 108, 10200
Total Interaction energy and Dispersion
Eint traces a dispersive-like
potential with increasing distance
Sherrill, D. C.; et. al. J. Phys. Chem. A. 2004, 108, 10200
Sherrill D. C.; et. al. J. Am. Chem. Soc. 2004, 126, 7690
Sherrill D. C.; et. al. J. Phys. Chem. A. 2006, 110, 10656
Substituent effects
σp 0
σm 0
-0.37
0.12
-0.17
-0.07
0.06
0.34
0.66
0.56
S
T(2)
T
Kim K. S. et al. J. Am. Chem. Soc. 2005, 127, 4530
Substituent Effects
Type I
NO2, CN, Cl, OH, NH2
Type I
Type II
Sherrill D. C.; et. al. Phys. Chem. Chem. Phys. 2008, 10, 2646
Substituent effects in parallel-displaced:
displaced: energy profiles
All groups have a lower global
minimum than benzene
Energy decomposition
Dispersion: lowest change for F due to low polarizability, followed by OH then CN
Induction: slightly favors CN
Exchange:: minima represent minimal e-density
e
in center of ring, dominates in CN
Electrostatics:: Positive at large displacements due to overlap of electronegative
group with negative electrostatic potential
Sherrill D. C.; et. al. Phys. Chem. Chem. Phys. 2008, 10, 2646
Revisiting the “molecular torsion balance”
Experiments
performed in
C6D6 compared
to that of
Wilcox’s in
CDCl3
Desolvation and ESP:
Diederich, F.; et. al. Angew. Chem. Int. Ed. 2004, 43, 5056
Hunter, C. A. Angew. Chem. Int. Ed. 2004, 43, 5310
Desolvation or Eelec/Erep Modulation?
Diederich:
Diederich
Wilcox:
Hunter C. A.; et. al. Chem. Commun. 2006, 3806
Diederich F. et al. Chem. Commun. 2008, 4031
Desolvation counters
Based on (α + αs) between CDCl3 and C6D6, a large
sensitivity difference is not antipicipated
Hunter C. A.; et. al. Chem. Commun. 2009, 3961
Sandwich interaction in [4+2] cycloaddition
Me
OMe
Br
Houk, K. N. et al.; Swager T. M. et al. J. Am. Chem. Soc. 2010, 132, 3304
Substituent effects on ESP
Politzer, P.; Murray, J. S. In Reviews in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B.,
Politzer
Eds.; VCH Publishers: New York, 1991; Vol. 2
Molecular Electrostatic Potential (Multipole Expansion)
ESP vs ρ
Are substituent effects on ESP manifested by
polarization of π-electron density?
Compare ESPA and ESPB
with Hodgkin index (HAB)
Wheeler, S. E.; Houk, K. N. J. Chem. Theory Comput. 2009, 5, 2301
Hodgkin, E. E.; Richards, G. W. Int. J. Quantum Chem. 1987, 32, 105
Wheeler, S. E.; Houk, K. N. J. Chem. Theory Comput. 2009, 5, 2301
Examples
Application of Method: Cation/π & Anion/π
Anion/
Cation/π
Anion/π
Wheeler, S. E.; Houk, K. N. J. Am. Chem. Soc. 2009, 131, 3126
Wheeler, S. E.; Houk, K. N. J. Phys. Chem. A 2010, 114, 8658
Sandwich: minus one pi-surface?
Is all the variation in structure
that accounts for the observed
Eint be derived from the just the
substituent?
Attributed to Dispersion
(~-0.5 kcal)
Wheeler, S. E.; Houk, K. N. J. Am. Chem. Soc. 2008, 10854
Substituent Additivity
3F
3 CN
6F
6 NH2
6 CN
Dispersion forces are likely contributing
Wheeler, S. E.; Houk, K. N. J. Am. Chem. Soc. 2008, 10854
Sherrill, D. C. et al. J. Am. Chem. Soc. 2009, 131, 4574
Edge-to-Face aryl-aryl interactions
Wheeler, S. E.; Houk, K. N. Molecular Physics 2009, 107, 749
Global vs local dipole moment
Global dipole moment is insignificant
relative to individual dipoles
Wheeler, S. E.; Houk, K. N. Molecular Physics 2009, 107, 749
Conclusions
• Electrostatic-only
only (rather than donor-acceptor)
donor
considerations illustrate
much of the observed experimental results (stacking orientation and
substituent effects)
• Substituent effects generally follow that predicted by the polar/
polar/ model
in the absence of significant dispersion contributions
• Gas phase calculations: dispersion forces are considered to be the
principle contributor to the overall interaction
• Relative role of desolvation and dispersion forces in solution (eg.
(
CHCl3
and C6D6) is inconclusive
• Origin of electrostatic interaction may primarily result from throughthrough
space interactions with the substituents for the majority of stacking
configurations