Modeling Remote Interactions Docking,  -Stacking, Stereorecognition, and NMR Chemical Shift Calculations

Remote Interactions Include: n ‘Docking’ of a ligand to its host  -Stacking of aromatic compounds n Stereorecognition in chiral chromatography n NMR chemical shift calculations

1. Docking

Docking Software n Sculpt – n GRASP – n AutoDock – web/doc/autodock/AutoDock web/doc/autodock/AutoDock

2. Aromatic  -Stacking

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

Benzene  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.

‘T’ Preference is Computed n MO calculations indicate that the ‘T’ form of benzene is lower in energy than the stacked and offset. n 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 n The stabilization (lowering of energy) due to non- covalent intermolecular interaction is called the interaction energy. n The range of the reported interaction energy for benzene dimer is from 1.6 to 2.8 kcal/mol (experimental and computational data) n This is roughly one-fourth to one-half of the magnitude of a typical H-bond.

Computational Concerns n When computing the interaction of two (or more) molecules, MO computations introduce an error called the basis set superposition error (BSSE). n This is because 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 n 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 simple method. n This energy value (the BSSE, a negative number) is subtracted from the calculated (uncorr.) interaction energy of the complex to obtain a better interaction energy.

BSSE Correction  E (uncorr for BSSE) = E ab AB – E a A – E b B To correct for the ‘extra’ basis functions in the complex, a correction is made using the ‘counterpoise’ method of Bernardi and Boys: E BSSE A = E ab A – E a A (this is the amount of energy by which A is computed to be stabilized by having access to the orbitals of B in the complex; it is a negative value) (where ‘A’ means molecule A, ‘ a ’ means the basis set of A, and ‘ ab ’ means the combined basis functions of molecules A and B) Likewise, E BSSE B = E ab B – E b B (this error is stabilizing; that is, it is a negative number; it must be subtracted from the  E to correct for basis set superposition) A + B = A … B (a weak complex)

BSSE Correction  E (uncorr for BSSE) = E ab AB – E a A – E b B  E (corr. for BSSE) = E ab AB – E a A – E b B – E BSSE A – E BSSE B = E ab AB – E a A – E b B – (E ab A – E a A ) – (E ab B – E b B ) = E ab AB – E a A – E b B – E ab A + E a A – E ab B + E b B  E (corr.) = E ab AB – E ab A – E ab B (however, this ignores relaxation…geometry change upon complexation)

Interaction Energy of  -Stacking ‘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 N-Phenylpyrrole has a concentration- dependent NMR spectrum, in which the protons are shifted upfield (shielded) at higher concentrations. n We hypothesized that aggregation was responsible.

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.

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 n Gaussian 03 has a subroutine GIAO (gauge invariant atomic orbital) which computes isotropic shielding values. n 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 n 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. n GIAO calculations involve extensive sets of integrals (~45 million integrals for toluene), and are computationally quite costly.

Examples of GIAO-Calculated NMR Chemical Shifts HH H H Observed:  Calculated:  Observed:  Calculated: 

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, , at each point X, Y, Z relative to the center of benzene.

NMR Shielding Surface 3.0 Angstroms above Benzene The surface (colored mesh) is the graph of the function 1/  = a + bx 2 +cy 2

Fit of Calculated Shielding Increment to Function Distance above rms Deviation benzene (Å) r 2 (ppm)

Reasons for Poorer Correlation at Closer Distances n The closer the distance, the lower the correlation. – Relative deviations may be comparable (closer distance, larger shielding vs. further distance, weaker shielding). Maximum  = Å vs. 5.5 Å – Orbital interactions between methane and benzene (see next slide). BSSE. – Other functions might fit the data better.

Orbital Interactions n 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).