Modeling Remote Interactions

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Modeling Remote Interactions

• Docking, p-Stacking, Stereorecognition, and NMR
  Chemical Shift Calculations

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Remote Interactions Include

• Docking of a ligand to its host
• p-Stacking of aromatic compounds
• Stereorecognition in chiral chromatography
• NMR chemical shift calculations

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1. Docking
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Docking Software

• Sculpt
• http//www.intsim.com/
• GRASP
• http//tincan.bioc.columbia.edu/Lab/grasp/
• AutoDock
• http//www.scripps.edu/pub/olson-web/doc/autodock/
  AutoDock

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2. Aromatic p-Stacking
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Modeling p Stacking Interactions

• Aromatic p complexes, sometimes termed
  charge-transfer complexes, have been known for
  many years.
• Only recently have computational chemists begun
  to study them.
• Several surprises have resulted from these
  studies!

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Benzene p Complexes 3 Forms!
T stacked
offset
The T form is lower in energy than stacked
form which is lower than offset benzene
crystallizes in T form.
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T Preference is Computed

• MO calculations indicate that the T form of
  benzene is lower in energy than the stacked and
  offset.
• Substituents on benzene complicate the situation
  some calculations on toluene show that the
  stacked form is nearly as stable as the T
  form, and that the offset form is not much
  higher in energy.

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Interaction Energy of p Stacking

• The stabilization (lowering of energy) due to
  non-covalent intermolecular interaction is called
  the interaction energy.
• The range of the reported interaction energy for
  benzene dimer is from 1.6 to 2.8 kcal/mol
  (experimental and computational data)
• This is roughly one-fourth to one-half of the
  magnitude of a typical H-bond.

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Computational Concerns

• When computing the interaction of two (or more)
  molecules, MO computations introduce an error
  called the basis set superposition error (BSSE).
• In the complex, orbitals of both molecules are
  available for electron occupation, which
  artificially lowers the energy. (Recall that
  electrons are lower in energy in large,
  delocalized orbitals.)

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Correction for BSSE

• Corrections for BSSE are usually done by the
  counterpoise method of Bernardi and Boys. This
  is not an accurate correction, but is is
  generally accepted as the best method.
• BSSEAB EAB - EA(B) - EB(A)
• This value (BSSE) is added to the calculated
  interaction energy of the complex.

All calculations of the AB complex are made at
the geometry of the complex
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Interaction Energy (Corr. For BSSE)

• Interaction EnergyAB
• I.E. EA EB - EAB BSSE
• where EA, EB, and EAB are the energies of
  the individual molecules A and B, the AB
  complex.
• or, a mathematically equivalent expression
• I.E. EA EB - EA(B) - EB(A)
• where EA(B) and EB(A) are the energies of each
  molecule A B in the complex including the basis
  set of the other.

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Interaction Energy of p-Stacking

• Aligned form
• Interaction Energy
• (Uncorr. for BSSE)
• 2.4 kcal/mol
• Interaction Energy
• (Corr. for BSSE)
• 1.4 kcal/mol
• (not shown)

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Modeling Aggregation Effects on NMR Spectra

• N-Phenylpyrrole has a concentration-dependent
  NMR spectrum, in which the protons are shifted
  upfield (shielded) at higher concentrations.
• We hypothesized that aggregation was responsible.

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Modeling Aggregation Effects on NMR Spectra...
Two monomers were modeled in different positions
parallel to one another, and the energy was
plotted vs. X and Y. The NMR of the minimum
complex was calculated.
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3. Stereorecognition
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R-2-Phenylethanol/S2500 Model
This complex is nearly 2 kcal/mol higher in
energy than the complex formed by the S
enantiomer.
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S-2-Phenylethanol/S2500 Model
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4. NMR Shift Calculations
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NMR Chemical Shift Calculations

• Gaussian 03 has a subroutine GIAO (gauge
  invariant atomic orbital) which computes
  isotropic shielding values.
• These can be converted to chemical shift values
  by subtracting the isotropic shielding value of
  the nucleus (any NMR active nucleus!) in question
  from the isotropic shielding value of a reference
  substance (e.g., TMS)

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NMR Calculations in Gaussian 94

• Keyword NMR
• the default method is GIAO others are also
  available in Gaussian 03.
• GIAO gives good estimates of chemical shifts if
  large basis sets are used.
• GIAO calculations involve extensive sets of
  integrals (45 million integrals for toluene),
  and are computationally quite costly.

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Examples of GIAO-Calculated NMR Chemical Shifts
H
H
H
H
Observed -0.50 d Calculated -0.10 d
Observed -0.50 d Calculated -1.04 d
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Mapping a Shielding Surface Over the Face of a
Benzene Ring
Methane was moved incrementally across the face
of a benzene ring at distances of 2.5, 3.0, 3.5,
4.0, 4.5 and 5.5 Angstroms above benzene.
Isotropic shielding values were calculated for
the three protons closest to the benzene ring,
and these were subtracted from the value of the
shielding tensor of methane to obtain a shielding
increment, Dd, at each point X, Y, Z relative to
the center of benzene.
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NMR Shielding Surface3.0 Angstroms above Benzene
The surface (colored mesh) is the graph of the
function 1/Dd a bx2 cy2
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Fit of Calculated Shielding Increment to Function

• Distance above rms
  Deviation
• benzene (Å) r2 (ppm)
• 2.5 0.65 0.19
• 3.0 0.96 0.09
• 3.5 0.91 0.05
• 4.0 0.95 0.03
• 4.5 0.91 0.02
• 5.5 0.91 0.04

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Reasons for Poorer Correlation at Closer
Distances

• The closer the distance, the lower the
  correlation.
• Relative deviations may be comparable (closer
  distance, larger shielding vs. further distance,
  weaker shielding).
• Maximum Dd 2.1 ppm _at_ 2.5 Å vs. 0.25 _at_ 5.5 Å
• Orbital interactions between methane and benzene
  (see next slide).
• Other functions might fit the data better.

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Orbital Interactions

• HOMO of benzene alone (wiremesh) compared to HOMO
  of benzene with methane 2.0 Å above the
  plane. Visualization generated from SP
  HF/6-31G(d,p).