Modeling Remote Interactions

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

Remote Interactions Include:

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

1. Docking

Docking Software

Sculpt– http://www.intsim.com/

GRASP– http://tincan.bioc.columbia.edu/Lab/grasp/

AutoDock– http://www.scripps.edu/pub/olson-web/doc/aut

odock/AutoDock

2. Aromatic -Stacking

Modeling Stacking Interactions

Aromatic 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 Complexes: 3 Forms!

‘T’ ‘stacked’ ‘offset’

The ‘T’ form is lower in energy than ‘stacked’ form whichis lower than ‘offset’; benzene crystallizes in ‘T’ form.

H

H

H

‘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 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)

This value (BSSE) is added to the calculated interaction energy of the complex.

All calculations of the AB complex aremade at the geometry 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 theindividual 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 -Stacking

1,3,5-Trisubstituted: Trinitrobenzene-Mesitylene

-2.5

0

2.5

0 5 10 15

Distance between rings, Angstroms

En

erg

y, k

cal/

mo

l 'ortho'

'aligned'

(CH3)3

(NO2)3

‘Aligned’ form

Interaction Energy(Uncorr. for BSSE):

2.4 kcal/mol

Interaction Energy(Corr. for BSSE):

1.4 kcal/mol

(not shown)

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.

Modeling Aggregation Effects on NMR Spectra...

p

mean dimer (calc'd.)

m o

pmean monomer (calc'd.)

m o

8.2 8.0 7.8 7.6 7.4 7.2 7.0 6.8

7.8 7.6 7.4 7.2 7.0 6.8

Two monomers were modeled in different positions parallel to one another, and the energywas plotted vs. X and Y. The NMR of the minimum complex was calculated.

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

Observed: 4.12 Calculated: 4.16

H HH

H

HH

H

H H

H

H

HH H

RR

H H

H

H

Observed: -0.50 Calculated: -1.04

Observed: -0.50 Calculated: -0.10

Mapping a Shielding Surface Over the Face of a Benzene Ring

C

HH

H

H

CH H

H

Methane was ‘moved’ incrementallyacross the face of a benzene ringat distances of 2.5, 3.0, 3.5, 4.0, 4.5 and 5.5 Angstroms above benzene.

Isotropic shielding values were calculatedfor the three protons closest to the benzenering, and these were subtracted from the value of the shielding tensor of methane toobtain a shielding increment, , at eachpoint X, Y, Z relative to the center of benzene.

NMR Shielding Surface3.0 Angstroms above Benzene

The surface (colored mesh) is the graphof the function 1/ = a + bx2 +cy2

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

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 = 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).