Ned H. Martin

1
Computation of Through-Space NMR Chemical Shift
Effects

• Ned H. Martin
• Department of Chemistry
• University of North Carolina at Wilmington

2
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 Einsteins 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.

3
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.

4
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
- 0.3 ppm
- 3.1 ppm
0.2 ppm
5
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 CC
  shown below.

shielding
deshielding
deshielding (q less than 54.7o)
shielding
6
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 (CC in this case).
• Based on the McConnell equation,
  protons close to and over a CC
  (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 cos2 q)/4pR3
McConnell Ds 0.12 Observed Ds -2.12
7
Our Groups Reseach

• Our groups 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.

8
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 CC
  bond, our model system uses methane as a probe in
  various positions over ethene, the simplest
  molecule containing a CC bond.
• Subtraction of the isotropic shielding value of
  protons in an isolated methane gives
  the shielding effect of the CC functional group.

9
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.

10
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 value of 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).

11
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.
12
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
13
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
14
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 CC.
• 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

15
Discrepancy rel. to Mc Connell Eqn.

• Our results show deshielding over the center of a
  CC the McConnell equation predicts shielding.
• McConnells equation considers only the magnetic
  anisotropy of the CC (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.
16
McConnell Eqn. vs. Our Function
Calcd NMR shielding increments along the CC
bond axis of ethene (Blue shielding Red
deshielding)
McConnell Equation
Our Shielding Function
Martin et al., Int. J. Mol. Sci., 2000, 1,
84-91.
17
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.
18
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
- 0.3 ppm - 0.3 ppm
- 3.1 ppm - 3.0 ppm
0.2 ppm 0.3 ppm
19
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.
20
Results

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

of deshielding along the CO bond axis, with
shielding above the CO group. Our results differ
substantially
shielding
shielding
Martin et al., J. Mol. Graphics Mod. 2003, 22,
127-131.
21
Origin of NMR (de)Shielding Effects

• In collaboration with P.v.R. Schleyer (U. Ga.),
  IGLO-HF was used to analyze the localized orbital
  origins 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, McConnells 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.
22
Origin of (de)Shielding

• The strong deshielding of a proton in the face of
  a CC 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.
23
Polarization of C-H Bond

• 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.

24
Effect 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 constrained
  geometry-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.

25
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)

26
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.

27
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 probes position was moved 0.5 Å
  incrementally in the Z direction.
• Single point calculations were performed using
  GIAO in Gaussian 98.

28
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 CC bond). The distance
  between the probe and the dummy atom was fixed,
  but all other structural parameters were allowed
  to optimize.

29
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
• halfcc0.65746
• Constants
• hX2.0
• a90.0
• b180.0

30
Shielding over the Center of the Carbon-Carbon
Single Bond in Ethane
31
Shielding over the Center of the Carbon- Carbon
Double Bond in Ethene
32
Shielding over the Center of the Carbon-Carbon
Triple Bond in Ethyne
33
Shielding over the Center of the Carbon-Nitrogen
Triple Bond in HCN
34
Shielding over the Center of the Benzene Ring
35
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.

36
CH4 Shielding Surface over Cyclopropane, 2.5 Å
Top view
Ds
Positive (blue) is shielding Negative (red) is
deshielding.
Note vdW deshielding!
37
Comparison of Probes over Cyclopropane, 2.5 Å
CH4 probe
H2 probe
38
CH4 vs. 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.

39
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.
• H2 and 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.

40
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

41
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