1. 1H and 13C NMR Spectroscopy in Organic Chemistry
Basics, Parameters,
Internuclear Interaction and Applications
Helmut Duddeck
Institute of Organic Chemistry

2. Contents Basics The NMR Parameters Stereochemistry
Internuclear Connectivity
Exercises

3. Basics

4. The NMR Experiment Excitation: DE = E1 – E0 DE = h · n = h · c/l
with c = n · l

5. Electromagnetic Spectrum

6. The Spin Some nuclei have a mechanical spin P, i.e. the sum
of all spins of the nucleons in the nucleus is not
equal to zero.
This results in a magnetic moment m. The relation
between those properties is:
m = g · P
When such nucleus is placed into a static
homogeneous magnetic field B0, is can adopt several
orientations the number of which is given by the spin quantum number I.
In the case of 1H and 13C: I = ½
i.e. those nuclei can adopt two orientations.

7. How Do Spins React to B0? The interaction between
two vectors is described by the
vector product.
This results in a rotation of m about B0:
d m /dt = m x B0
( Bloch equations)

9. How Do Spins React to B0? Precession w0 = 2 p n0 = - g · B0
(Larmor Equation)
Bruker Avance 400
Hannover
[ g(1H)  4 · g(13C) ]

10. Excitation of an Individual Spin
Boltzmann distribution: N1/N0 = e-DE/kT

11. M = Macroscopic magnetization
The Vector Model
M = Macroscopic magnetization

12. Rotating Frame and Irradiation
a = g · B1 · tp

13. Longitudinal (Spin-Lattice) Relaxation, T1
dMz/dt = -(Mz – M0)/T1

14. Longitudinal RelaxationM M0

15. Transversal (Spin-Spin) Relaxation, T2
dMx´/y´/dt = -Mx´/y´/T2
T2  T1

16. “Real“ T2 Times NMR Line Widths
1/T2* = 1/T /T2(inhom)
NMR Line Widths
w1/2 = 1/(2pT2*)

17. „Classical“ PFT-NMR Experiment

18. Pulse and FID
resonance range

19. Transversal Magnetization My‘
Dn = n0 - n1 = 0 ; 900 pulse (p/2)
y´-Magnetization decays exponentially.

20. Free Induction Decay

21. Fourier Transformation of an FID
FT of an exponentially decaying curve gives a Lorentzian.
analytical form:
However:
the freq.-domain spectrum consists of two sections:
(1) real part (see curve);
(2) imaginary part)

22. Transversal Magnetization My‘
Dn = n0 - n1 > 0

23. FID as Function of Dn
Dn = 15 Hz
Dn = 65 Hz and 114 Hz, resp.

24. FID as Superposition

25. Digitization dwell time td
number of data points is mostly a multiple of 1 K (kilo)
= = (nearly 1000)

26. Digital Resolution Examples: 13C NMR, resonance frequency 100.6 MHz,
typical d range of 250 ppm
250 ppm is ca Hz = 25 kHz,
FID collected with 32 K data points;
in the real spectrum 16 K =
Digital resolution = 1.5 Hz/point (= ppm)!
Good enough for chemical shifts but not for coupling constants.
1H NMR, resonance frequency MHz,
typical d range of 10 ppm; 10 ppm is ca Hz = 4 kHz.
FID collected with 64 K data points;
in the real spectrum 32 K =
Digital resolution = 0.12 Hz/point (= ppm)!
Very good for chemical shifts but not for coupling constants:
Precision > 0.2 Hz!

27. Spectral Window; Nyquist-Frequency
Given a data point train; <2 points per period
=> ambiguity !

28. Spectral Window; Nyquist-Frequency
Given a data point train; <2 points per period
=> ambiguity !

29. Spectral Window; Nyquist-Frequency
Given a data point train; <2 points per period
=> ambiguity !

30. Which is the Folded Signal?
Quadrature detection

31. Data Manipulation Akkumulation
Signal-to-noise ratio after n accumulations:
S/N = n / n = n
13C signals of a phenyl group:
NS = 4
NS = 16
NS = 64

32. Data Manipulation Exponential Multiplication
FID:
FID + exponential multiplication:

33. Data Manipulation Exponential Multiplication

34. Data Manipulation Exponential Multiplication
13C signals of a phenyl group:

35. Data Manipulation Resolution Enhancement
FID and spectrum before (left) and after Lorentzian-Gaussian transformation (right)

36. Data Manipulation Resolution Enhancement
Example: 13C-Signal () of 1-trifluoromethyladamantane:
plus
Lorentz-Gauß-
transformation
from the
original FID

37. Data Manipulation Resolution Enhancement
Sucrose
mind the wiggles (apodization)!

38. Data Manipulation Truncation
What happens when FID are truncated after decaying to zero ?
Signal is not affected and S/N ratio is improved.

39. Data Manipulation Truncation
What happens when FID are truncated before decaying to zero (apodization) ?
Signal is affected by wiggles.

40. Data Manipulation Zero Filling
What happens when a fully decayed FID is supplemented by zeros
(data points with zero information)?
Better digital resolution
without loss of signal information.