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Computation of Through-Space NMR Chemical Shift Effects

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### Computation of Through-Space NMR Chemical Shift Effects

Ned H. Martin

Department of Chemistry

University of North Carolina at Wilmington

Introduction to NMR

- In a strong magnetic field Bo, hydrogen nuclei have two possible spin states: aligned with or against the magnetic field.
- These states differ only slightly in energy.
- The energy difference between the two spin states corresponds (by Einstein’s equation: E = hn) to energy in the radiofrequency region of the electromagnetic spectrum.
- When hydrogen nuclei are irradiated with the appropriate radiofrequency in a strong magnetic field, they absorb energy and spin-flip. This is NMR.

Introduction to NMR

- Hydrogen nuclei are shielded from the full applied magnetic field Bo by the electrons surrounding them.
- Nearby electronegative atoms such as oxygen or chlorine attract electrons, thus reducing electron density and causing deshielding of nearby hydrogens.
- Each type of hydrogen has a unique position of absorption (called the chemical shift) in the NMR spectrum.

Estimation of Proton Chemical Shifts

- Proton chemical shifts are usually estimated based on additive through-bond substituent effects.
- However, in some instances, through-space (shielding or deshielding) effects may be more important.

Observed deviations from estimated chemical shifts caused

by through-space effects (- is shielding, + is deshielding):

+ 2.2 ppm

+ 0.2 ppm

- 0.3 ppm

- 3.1 ppm

Through-Space (de)Shielding

- Structures that exhibit NMR shifts that deviate from those predicted by substituent effects generally have one or more protons near a p bond.
- Theoretical predictions of through-space magnetic effects resulted in the familiar “shielding cones,” such as the one for the C=C shown below.

shielding

deshielding

deshielding

(q less than 54.7o)

shielding

Shielding Cones

- Shielding cones are based on the McConnell equation

which predicts the magnetic shielding increment at a point in space due solely to the magnetic anisotropy of the functional group (C=C in this case).

- Based on the McConnell equation, protons close to and over a C=C (within a 54.7º cone) should be shielded (shifted upfield); in fact they are deshielded and are shifted downfield.

Ds = 1/3 Dc (1 - 3 cos2q)/4pR3

McConnell Ds: +0.12

Observed Ds: -2.12

Our Group’s Reseach

- Our group’s research over the past eight years has focused on the use of ab initio quantum chemical calculations to:
- study through-space shielding effects of various functional groups
- Try to understand their origin and
- develop corrections to estimated shifts based on through-bond substituent effects.

Our Approach

- Our approach has been to use ab initio computational methods to calculate isotropic shielding values of protons in simple model systems incorporating functional groups that exert through-space effects.
- For instance, to examine the effect of a C=C bond, our model system uses methane as a probe in various positions over ethene, the simplest molecule containing a C=C bond.
- Subtraction of the isotropic shielding value of protons in an isolated methane gives the shielding effect of the C=C functional group.

Methodology

- The subroutine GIAO (gauge-including atomic orbital) in Gaussian was employed to calculate isotropic shielding values.
- HF/6-31G(d,p) calculations were performed on a simple model system composed of previously-optimized methane and ethene structures juxtaposed variously.
- Symmetry reduced the number of calculations required.

Methodology…

- Single-point calculations were done on a series of supramolecules each having methane at a different position over the plane of ethene.
- This process was repeated at several distances (2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5.0 Å) between the proximate proton of methane and the plane of ethene.
- The isotropic shielding values of the proximate proton of methane were extracted from the Gaussian output.
- The isotropic shielding valueof methane (by itself) calculated in the same way was subtracted from each of the above values. We define this difference as the shielding increment (Ds).

Methodology…

The shielding increment(Dd) for each H position was plotted against Cartesian coordinates to obtain a shielding surface at each distance above ethene.

- The

3.0 Å

2.0 Å

Positive values

are shielding;

negative values

are deshielding.

Methodology…

- A function was matched to each surface using TableCurve3D.
- The same form of mathematical function

. was found to give a good fit to the shielding surface at each of several distances of methane over ethene:

2.0 Å: Ds = – 2.73 + 1.88X + 2.20Y – 0.29X2 – 0.22Y2 – 0.77XY

2.5 Å: Ds = – 0.79 + 0.82X + 0.70Y – 0.22X2 – 0.14Y2 – 0.21XY

3.0 Å: Ds = – 0.12 + 0.35X + 0.23Y – 0.14X2 – 0.065Y2 – 0.038XY

(etc., up to 5.0 Å)

Ds = a + bX + cY + dX2 + eY2 + fXY

Methodology…

- The values of the constant a and coefficients b,c, d, e & f in the equations of the form: . varied smoothly as a function of distance.
- Each of these variables could be related to the distance above ethene using quadratic equations.

Ds = a + bX + cY + dX2 + eY2 + fXY

Methodology…

- Substitution of these quadratic equations into the general shielding surface equation resulted in one equation (18 terms; too big to show!) for predicting the through-space shielding increment as a function of Cartesian coordinates relative to the center of the C=C.
- This increment is useful as a correction for estimated chemical shifts.

Fcn. Calc. Ds - 0.28 - 0.30 - 1.99

Obs. Dev.Ds - 0.24 - 0.27 - 2.12

Discrepancy rel. to Mc Connell Eqn.

- Our results show deshielding over the center of a C=C; the McConnell equation predicts shielding.
- McConnell’s equation considers only the magneticanisotropy of the C=C (or other functional group); it disregards all other factors that affect the chemical shift!

Martin et al., J. Am. Chem. Soc. 1998, 120(44), 11510-11511.

McConnell Eqn. vs. Our Function

Calc’d NMR shielding increments along the C=C bond axis

of ethene; (Blue = shielding; Red = deshielding)

McConnell Equation

Our Shielding Function

Martin et al., Int. J. Mol. Sci., 2000, 1, 84-91.

Results…

- We have reported results of such computational studies of the NMR shielding (or deshielding) surfaces over aromatic rings1,2 and alkenes3.

benzene rings1,2 and alkenes3.

Positive values

are shielding;

negative values

are deshielding.

1. Martin et al.,J. Mol. Struct. (THEOCHEM) 1998, 454, 161-166.

2. Martin et al., J. Mol. Graphics Mod. 2000, 18(3), 242-246.

3.Martin et al., Struct. Chem. 1998, 9(6), 403-410, Struct. Chem.

1999, 10(5), 375-380, J. Molec. Graph. Mod. 2000, 18(1), 1-6.

Results…

- The function-predicted through-space shielding increment compares favorably to the observed deviation from the estimated chemical shifts (based on additive substituent effects).

Observed deviations from estimated chemical shifts

(Here, - is shielding, + is deshielding)and

Function-computed chemical shift increments:

+ 2.1 ppm

+ 2.0 ppm

+ 0.2 ppm

+ 0.3 ppm

- 0.3 ppm

- 0.3 ppm

- 3.1 ppm

- 3.0 ppm

Results…

- We have also reported on the NMR shielding surfaces of the ethynyl, cyano, and nitro groups using CH4 as a probe, with good prediction of chemical shift effects.

Chemical shifts

Predicted: 8.7d 8.7d 8.7d

Adjusted: 9.8d 10.9d 8.2d

Observed: 9.9d 10.3d 8.1d

Martin et al., J. Mol. Graphics Mod. 2002, 21, 51-56.

Results…

- Our most recently published NMR shielding surface study was of the carbonyl group, C=O.
- The traditional (McConnell) shielding cone picture of the carbonyl group in textbooks shows a cone of deshielding along the C=O bond axis, with shielding above the C=O group. Our results differ:

of deshielding along the C=O bond axis, with shielding above the C=O group. Our results differ substantially:

shielding

shielding

Martin et al., J. Mol. Graphics Mod. 2003, 22, 127-131.

Origin of NMR (de)Shielding Effects

- In collaboration with P.v.R. Schleyer (U. Ga.), IGLO-HF was used to analyze the localized orbitalorigins of the through-space shielding effects due to the ethenyl, ethynyl, cyano, nitro and carbonyl groups.
- The results indicated that in each of these systems, the proximate C-H bond of the methane probe accounts for over 40% of the shielding increment.
- Thus, McConnell’s approach, based solely on magnetic anisotropy of the functional group can not be expected to predict chemical shift effects accurately.

Martin et al., Org. Lett. 2001, 3(24), 3823-3826.

Origin of (de)Shielding

- The strong deshielding of a proton in the face of a C=C may be the result of mutual perturbation of the interacting orbitals of the probe and the test molecules.
- An indication of this is seen in the representation (right) of the HOMO of ethene(wiremesh) superimposed with the HOMO of a methane-ethene pair (solid), separated by 2.0 Å

Martin et al., in “Modeling NMR Chemical Shifts: Gaining

Insights into Structure and Environment," ed. Facelli, J.C

and deDios, A.C., ACS, Washington, D.C., 1999, 207-219.

Such a perturbation should be accompanied by a change in the calculated atomic charge.

NPA charges were calculated for the proximal H of the probe methane over each functional group and also for the Hs on isolated methane.

The difference between these was plotted vs. distance of the proximal H above ethene.

Similar results were observed over ethyne; a similar pattern but with less charge difference was seen over HCN and over benzene.

Polarization of C-H BondEffect of Choice of Probe?

- Several referees and researchers in this field have suggested using other probes, such as a ghost atom (Bq in Gaussian ), a H atom, or a He atom.
- It was also suggested that constrainedgeometry-optimized probe-test supramolecules (as opposed to the single point calculations we had performed) would give more accurate results.
- Our most recent work has involved investigating alternative computational probes of through-space NMR shielding effects to assess their validity and computational efficiency.

Methodology

- The following probes were used to calculate the through-space shielding effect of several test molecules:
- Bq(ghost atom)
- H atom (single point)
- H atom (geometry optimized)
- He atom(single point)
- He atom (geometry optimized)
- H2 molecule(single point)
- H2 molecule (geometry optimized)
- CH4 (single point) (the probe used in our previous work)
- CH4 (geometry optimized)

Methodology…

- The test molecules, simple structures containing common organic functional groups, included:
- We are also examining the effect of the choice of probe over some small-ring hydrocarbons. Of these, only cyclopropane will be discussed today.

Single Point Calculations

- Each HF/6-31G(d,p) geometry-optimized probe (Z) was placed over the HF/6-31G(d,p) geometry-optimized test structures in separate Cartesian coordinate input files.
- The probe’s position was moved 0.5 Å incrementally in the Z direction.
- Single point calculations were performed using GIAO in Gaussian 98.

Geometry-optimized calculations

- Each HF/6-31G(d,p) geometry-optimized probe (Z) was placed over the HF/ 6-31G(d,p) geometry-optimized test structures in separate Z-matrix input files.
- A dummy atom X was placed at the reference point (here, the center of C=C bond). The distance between the probe and the dummy atom was fixed, but all other structural parameters were allowed to optimize.

Z-Matrix Description of He over Ethene

0 1

X

C1 X halfcc

He X hX C1 a

C2 X halfcc He a C1 b

H1 C1 1.076 X 121.7 He1 90.0

H2 C1 1.076 X 121.7 He1 -90.0

H3 C2 1.076 X 121.7 He1 90.0

H4 C2 1.076 X 121.7 He1 -90.0

Variables:

halfcc=0.65746

Constants:

hX=2.0

a=90.0

b=180.0

CH4 Shielding Surface over Cyclopropane

- NMR shielding increments over cyclopropane were computed using CH4 as a probe and using H2 as a probe in much the same way that the shielding increments over ethene and other models for functional groups were obtained.
- The resulting shielding increments were plotted vs. Cartesian coordinates to provide shielding surfaces.

CH4 Shielding Surface over Cyclopropane, 2.5 Å

Top view

Ds

Positive (blue)

is shielding;

Negative (red)

is deshielding.

Note vdW deshielding!

CH4vs.H2 Probe

- The shielding surfaces obtained using the two different molecular probes are very similar.
- They differ slightly in the magnitude of shielding.
- The ratio of the isotropic shielding values for the two probes (H2/ CH4) was 0.84, regardless of the test molecule and independent of the position over the test molecule in the systems studied (ethane, ethene, ethyne, benzene, HCN).
- Both probes provide good agreement with experimental chemical shift effects in example structures.
- The H2 probe is considerably easier to employ and is more economical computationally.

Summary of Shielding Probes

- Bq (ghost atom) gives the poorest agreement with observed chemical shift effects. It completely ignores the mutual perturbation of orbitals.
- Monatomic probes (H and He) are not much better.
- There is no appreciable difference between single-point calculations and geometry-optimized calculations.
- H2and CH4 give generally similar results, with H2 providing isotropic shielding values 0.84 of those obtained with CH4.
- CH4 has been found previously to give accurate predictions of chemical shift effects of through-space shielding; H2 (with or without a minor correction) can do so also.
- H2 is simpler and cheaper computationally.

Ongoing Research

- We have begun to study the NMR shielding surfaces of molecules and complexes of biochemical interest, modeling through-space NMR shift effects that are operative in peptides:

Acknowledgments

- Student collaborators:
- Noah W. Allen, III; Luong Vo; Jill C. Moore; Everett K. Minga; Sal T. Ingrassia; Justin D. Brown; H. Lee Woodcock; David M. Kmiec, Jr.; Kimberly H. Nance; Dustin C. Wade; David M. Loveless; Kristin L. Main.
- The donors of the American Chemical Society Petroleum Research Fund for support of this research (1996-2003)
- The (former) North Carolina Supercomputing Center
- The UNCW Information Technology Services Division
- The UNCW College of Arts and Sciences
- The UNCW Department of Chemistry

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