Modeling Remote Interactions
Docking, p-Stacking, Stereorecognition,
and NMR Chemical Shift Calculations
Remote Interactions Include:
‘Docking’ of a ligand to its host
 p-Stacking of aromatic compounds
 Stereorecognition in chiral chromatography
 NMR chemical shift calculations

1. Docking
Docking Software

Sculpt
–

GRASP
–

http://www.intsim.com/
http://tincan.bioc.columbia.edu/Lab/grasp/
AutoDock
–
http://www.scripps.edu/pub/olsonweb/doc/autodock/AutoDock
2. Aromatic p-Stacking
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!

Benzene p Complexes: 3 Forms!
H
H
H
‘T’
‘stacked’
‘offset’
The ‘T’ form is lower in energy than ‘stacked’ form which
is lower than ‘offset’; benzene crystallizes in ‘T’ form.
‘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.

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.

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.)

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)
All calculations of the AB complex are
made at the geometry of the complex

This value (BSSE) is added to the calculated
interaction energy of the complex.
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.
Interaction Energy of p-Stacking
‘Aligned’ form
Interaction Energy
1,3,5-Trisubstituted:
Trinitrobenzene-Mesitylene
(Uncorr. for BSSE):
Energy, kcal/mol
2.5
(CH3)3
(NO 2)3
2.4 kcal/mol
'ortho'
'aligned'
0
0
5
10
15
Interaction Energy
(Corr. for BSSE):
-2.5
Distance between rings, Angstroms
1.4 kcal/mol
(not shown)
Modeling Aggregation Effects
on NMR Spectra


N-Phenylpyrrole has
a concentrationdependent NMR
spectrum, in which the
protons are shifted
upfield (shielded) at
higher concentrations.
We hypothesized that
aggregation was
responsible.
Modeling Aggregation Effects
on NMR Spectra...
Two monomers were modeled in different positions
m  p o
parallel to one another, and the energy
was plotted vs. X and Y. The NMR of
the minimum complex was calculated.
7.8
7.6
7.4
m
o

mean dimer
(calc'd.)
7.2
7.0
 6.

p
mean monomer
(calc'd.)
8.2
8.0
7.8
7.6
7.4
7.2
7.0 
3. Stereorecognition
R-2-Phenylethanol/S2500 Model
This complex is nearly 2 kcal/mol higher in energy
than the complex formed by the S enantiomer.
S-2-Phenylethanol/S2500 Model
4. NMR Shift Calculations
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)

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.
Examples of GIAO-Calculated
NMR Chemical Shifts
H
H
H
H
H
Observed:
Calculated:
H
H
4.12 
4.16 
H
Observed: -0.50 
Calculated: -1.04 
H
H
H
H
H
H
H
R
H
R
Observed: -0.50 
Calculated: -0.10 
H
H
Mapping a Shielding Surface
Over the Face of a Benzene Ring
H
C
H
H
H
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, D, at each
point X, Y, Z relative to the center of benzene.
H
C
H
H
NMR Shielding Surface
3.0 Angstroms above Benzene
The surface (colored mesh) is the graph
of the function 1/D = a + bx2 +cy2
Fit of Calculated Shielding
Increment to Function
Distance above
benzene (Å)
r2
2.5
3.0
3.5
4.0
4.5
5.5
0.65
0.96
0.91
0.95
0.91
0.91
rms Deviation
(ppm)
0.19
0.09
0.05
0.03
0.02
0.04
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 D = 2.1 ppm @ 2.5 Å vs. 0.25 @ 5.5 Å
–
–
Orbital interactions between methane and
benzene (see next slide).
Other functions might fit the data better.
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).