Signal-to-noise (S/N)!
S/N = intensity of peak / rms noise level
S/N = 2.5 A / Npp
A
Npp
Noise: 99% of noise points fall within +/- 3 units of zero by
Gaussian distribution.
Signal-to-noise (S/N)!
What does this mean to you?
1.!
Signal increases with the number of scans (N).
2.!
Noise increases by N1/2.
S/N ! N/N1/2 = N1/ 2
16 X scans = 4 X S/N
Detection of Signal
SAMPLE
PROBE
The Signal is weak so it is amplified by the preamp.
The preamplfier can be tuned for selective signals.
Detection of Signal
SAMPLE
PROBE
- Signal
is in MHz (radio frequency) which we will convert
to an audio signal. This is done by stripping off the radio
frequency of the carrier leaving only a frequency
modulated signal.
- Audio signal carries information about offset from the
carrier frequency.
- Audio filters remove bands outside the spectral
bandwidth.
Time Domain Spectral Parameters
Spectral Width (SW): This is nothing more than setting the
audio filter.
Digitization: Rate, Resolution and Range.
-!Rate: A sine wave must be defined by two points in a
single period to be properly presented.
(a)!
To be properly represented, a signal of frequency ! must be sampled twice per cycle. (b) When sampled at
this rate, a signal of higher frequency, ! +!!, cannot be distinguished from (c) a signal at the lower
frequency, ! " !! .
Time Domain Spectral Parameters
Dwell time (DW): Time difference between two adjacent
points.
SW = 1/2 DW = Nyquist Frequency (!NQ).
* FT NMR assumes all peaks fall within ±!NQ. *
Time Domain Size (TD): Number of points of FID.
Acquisition Time (AQ): AQ = (DW) X (TD)
Time Domain Spectral Parameters
Correct
This peak folded
Quadrature Detection
This allows us to put carrier in the middle of region of
interest.
QD
rf
vs
rf
Advantage: Get half the noise so incresase sensitivity by
Problem: How do we distinguish ±! relative to carrier?
Quadrature Detection
Solution: Place two detectors out of phase by 90o.
Chemical Shift
So far we have assumed one nuclear resonance signal for
each nuclear species given by the larmor frequency:
"
v1 = "B0 2!
This is of very little practical use.
Fortunately:
- The resonances are influenced by the environment in
which the nuclei are present.
- Usually, the nuclei are surrounded by electrons and other
atoms.
Chemical Shift
In a diamagnetic molecule, the effective magnetic field
(Beff) is always less than the applied magnetic field (B0):
Beff = B0 (1 " ! )
"
# " the shielding constant and it is independent of magnetic
field strength.
New Resonance Condition is defined by:
v1 = # (1 $ " )B0 2!
Reference Compounds and the $ scale
%! = frequency difference between two signals.
-this difference will change as B0 changes.
Internal Standards (example TMS):
# =
v sample " v reference
v reference
! 10 6
Value expressed in parts per million (ppm).
Reference Compounds and the $ scale
If we replace vreference with the observing frequency of the
spectrometer:
$ = !v / observing frequency x 106
$ (TMS) = 0
- $ scale is referred to as chemical shift reference.
- It is independent of the magnetic field strength.
- For signals left of TMS $ is positive
- For signals right of TMS $ is negative.
Reference Compounds and the $ scale
Signals with lower values of $:
- low frequency, high field, more shielded, upfield shifted.
Signals with larger values of $:
- high frequency, low field, less shielded, downfield shifted.
12
10
8
6
4
2
0
-2 ppm
Chemical Shift Anisotropy
# is dependent on its orientation relative to the magnetic field B0.
In solution this is averaged out as
the result of rapid tumbling so:
! = (! 11 + ! 22 + ! 33 ) 3
The principal values of the carbon-13 screening tensor, #11, #22,
and #33, represented along three mutually perpendicular axes in a
laboratory frame for a molecule containing a 13C-X bond. One of
these axes, corresponding to #33, is shown as coinciding with the
13C-X bond, although in general it is not necessary that any of the
axes coincide with chemical bonds.
Chemical Shift: Shielding
What effects Shielding at a particular nucleus?
A. Local diamagnetic currents about the nucleus (#dia)
B. Local paramagnetic currents about the nucleus (#para)
C. Current flowing in distant groups (#others)
1H
NMR: the B-component is small but C-component can
be significant.
13C
NMR: the B-component is also significant because of
low lying excited states.
Chemical Shift: Shielding
Chemical Shift Ranges:
1H, 2H!
13C
!
15N, 31P
59Co, 195Pt
1H
!
!
!
!
!
!
!
!
!10 ppm!
!300 ppm!
!500 ppm!
!10, 000 ppm!
Chemical Shifts: Inductive Effects
–! Electronegative groups cause deshielding of nuclei near
them.!
–! This effect falls off as the number of intervening bonds
increases.!
!
The correlation is by no means exact!!!!!
For methyl groups (CH3R) it is simple:!
CH3I = 2.16 ppm!
CH3Br = 2.68 ppm!
CH3Cl = 3.05 ppm!
CH3F = 4.26 ppm!
–!& EN of R you ' shielding.!
1H
Chemical Shifts: Inductive Effects
For ethyl groups (CH3CH2R) it is more complicated:!
!
In general with CH3CH2R:!
- At CH2 position as & EN of R you ' shielding but not as
rapidly as with corresponding methyl groups.!
- At CH3 position as & EN of R you ' shielding but to a
lesser degree.!
!
Fine but if R=X:!
The shielding of the CH3 protons increases with increasing
EN of the halide.!
Shielding by Magnetically Anisotropic Groups:!
General:!
Chemical bonds are usually magnetically anisotropic so they
have different susceptibilities along three directions."
In the case of axially symmetric charge distribution this can be
easily explained with two susceptibilities:"
"
"
"
"
"
"
"
"
#n = ((|| - ()) (1 – 3cos*)/3r34+"
Shielding by Magnetically Anisotropic Groups!
"
"
"
"
"
"
#n = ((|| - ()) (1 – 3cos*)/3r34+"
"
#n – depends on geometry and susceptibilities, not the
nuclide being observed.!
#n = 0 when * = 54.7°!
Shielding by Magnetically Anisotropic Groups!
Acetylenes:!
Classic example: by usual criteria of bond hybridization
and acidity, there should be a progressive deshielding of
protons from ethane to ethylene to acetylene.!
!
Ethane = 1.96 ppm!
Ethylene = 5.84 ppm!
Acetylene = 2.88 ppm!
Shielding by Magnetically Anisotropic Groups!
Ring Current Effects: Protons on aromatic rings resonate
at unexpectedly low fields.!
!
Due to circulation of +-electrons in the plane of the ring
giving enhanced diamagnetic susceptibility in a direction
perpendicular to the ring:!
Shielding by Magnetically Anisotropic Groups!
Mesomeric Effects of Aromatic Substitutions:!
- stronger at ortho and para positions!
- If there is an increase electron density in ring +M and if
there is a decrease electron density there is a –M.!
Shielding by Magnetically Anisotropic Groups!
Mesomeric Effects of Aromatic Substitutions:!
"
Electric Field Effects (#e)!
There are intramolecular electric fields associated with
groups like carbonyls and nitros.!
Protonation can also produce an electric field effect.
H-bonding and solvents (#i)!
Protons that are hydrogen bonded have particularly low
shielding values.!
!
They are effected dramatically by:!
- concentration!
- temperature
$+
$X-H,,,Y!
!
The hydrogen bond tends to draw H towards Y and
repel the X-H bonding electrons towards X resulting
in reduced electron density around Y.!
Chemical shift!
Beff = B0 (1- #)!
# = #dia + #para + #N + #R + #e + #i!
N- magnetic anisotropy of neighboring groups.!
R- ring current effects in arenes.!
e- electric field effect.!
i- effects of intermolecular interactions.
13C
Chemical shifts!
- covers ~200 ppm range!
- TMS is used as internal standard as with 1H chemical shifts
to establish $ scale.!
- Greater variability is attributed to the fact that there is
greater electron density about the nuclei.!
–! #para has a more significant role due to existence of low-lying
excited states.!
–! There is not a lot of other information in 13C spectrum.!
–! More spread out then the 1H spectrum so sometime trickier
to figure out.!
1H
Signal Intensities!
Area under the curve is proportional to the number of protons
(Integration)!
13C
Signal Intensities!
-!areas are distorted due to low natural abundance and
sensitivity.!
!
- if decoupled signals are proportional to the number of
directly bonded hydrogen atoms.!
Relationship Between the Spectrum
and the structure!
-! Equivalent nuclei have the same resonance frequency.!
-! Coupling between equivalent nuclei is not seen in first order
spectra.!
Relationship between the spectrum
and the structure!
Relationship between the spectrum
and the structure!
Chiral Molecules:!
Enantiomers: give identical NMR spectra!
Diastereomers: give different NMR spectra!
"
The case of CH2:!
Homotopic: two fold axis of symmetry(C2),!
protons are equivalent.!
Enantiotopic: two protons appear equivalent in the NMR but
they are not (prochiral).!
"
Relationship between the spectrum
and the structure!
Diastereotopic: two protons are not equivalent in NMR.!
Indirect spin-spin coupling!
1J:
coupling between directly bonded nuclei.
2J:
geminal coupling; -CH2 protons.
3J:
vicinal or three-bond coupling.
3 + nJ
: long-range coupling.
Indirect spin-spin coupling!
Magnitudes of coupling constants:
Table 3.1.
General summary of the orders of magnitude and signs of H,H, C,H and C,C coupling constants.
1J
2J
3J
3J+ nJ
a) For H2
J(H,H)
[Hz]!
Sign
276a)
0—30
0—18
0— 7
positive
positive
usually neg.
positive
positive
pos./neg.
J(C,H)
[Hz]!
Sign
125—250
— 10 to +20 pos./neg.
1—10
<1
J(C.C)
[Hz]!
30—80
<20
0—5
<1
Signb)
positive
pos./neg.
positive
pos./neg.
pos./neg.
b) Determined in only a few cases
Indirect spin-spin coupling"
Factors that Influence Coupling constants:
1. The hybridization of the atoms involved.
2. Bond angles and torsion angles.
3. Bond lengths.
4. The presence of neighboring +-bonds.
5. Substituent effects.
J-coupling is observed in the spectrum only if the spin
orientation of the coupling nuclei in B0 are maintained for
a time longer than -j = l/J.
Indirect spin-spin coupling!
How does it occur?
•! the result of slight polarization of spins and orbital
motions of the valence electrons.
•! since only s atomic states have finite electron density it can
be expected that nuclear couplings will depend to some
degree on the fraction of s character in the bond.
•! they are not affected by the tumbling of the molecule and
are independent of B0.
•! splitting depends on the probability of paired nuclei
finding the others spin to be oriented with or against the
applied field.
•! usually limited to no more than three intervening bonds.
•! couplings between equivalent nuclei or groups of
equivalent nuclei are not directly observable.
Indirect spin-spin coupling!
Order of Spectrum:
Zero- spectrum which contains only singlets.
First- %! >> J
Higher- larger values of J/%!"
•! zero order are usually the result of decoupling.
•! first order can be analyzed according to rules.
•! higher order can be analyzed but much more
complicated.
AX system!
AX spin system: large difference in chemical shifts of signals relative to
coupling value.
•! can be analyzed according to first order rules
•! two frequencies !a and !x, if they are coupled we will see two signals for
both frequencies.
•! chemical shift always corresponds to the middle of the doublet which is
the position of the signal if there was no coupling.
•! Coupling values depend on nuclear magnetic moments (µ) thus the
values are independent of field strength (B0) so they are always given in
Hz.
AB System!
AB System:
- J/%v becomes larger
- signals are closer together in spectrum.
-!analysis of the data becomes more difficult. (it becomes less
realistic to assign each nucleus a specific quantum number).
Calculated AB spectra!
For J= 10 Hz:!
a)J/"!=0.20!
!
b)J/"!=0.25!
!
c)J/"!=0.33!
!
d)J/"!=0.50!
!
e)J/"!=0.75!
AXn systems!
M=n+1
M = multiplicity of the NMR signals, number of lines in a
multiplet.
Arrow indicates position of the reported chemical shift.
AMX system!
Three non-equivalent nuclei.
2J:
Geminal proton-proton couplings!
2J
couplings can vary greatly and can be positive or
negative:
- protons on a CH2 group must be non-equivalent.
- sp3 hybridized groups are usually negative
- sp2 hybridized groups are often positive.
-!values highly dependent on angle between the two
protons. and increases (algebraically) as angle increases.
1
2
3
Dependence of geminal coupling constants on the bond angle !."
2J:
Geminal proton-proton couplings!
I#n substituted ethylenes EN substituents at . position
cause a negative contribution.
3J:
Vicinal proton-proton couplings!
What affects them?
-!substituents although less than in geminal case.
-!variation in geometry (torsion or dihedral angle).
-!distance between two carbon atoms concerned.
3J:
Vicinal proton-proton couplings!
Table 3-5: Ranges and typical values of vicinal H,H coupling constants.
Compound
Range b)
3J (H,H) [HzI
Typical valueb)
Cyclopropane
cis trans
6-10
3- 6
8
5
Cyclobutane
cis
trans
6-10
5- 9
Cyclohexane
a, a
a,e
e,e
6-14
3- 5
0- 5
3
3
3
Benzene
ortho
6-10
9
Pyridine
2,3
3,4
5- 6
7- 9
8
8
H—C—C—H
0-12
7
=CH—CH=
9-13
10
5-14
11-19
10
16
>CH—CHO
1- 3
3
=CH—CHO
5- 8
6
CH—NHa)
4- 8
5
CH—OHa)
4- 10
5
CH—SHa)
6- 8
7
—CH=CH2
a) Not exchanging.
cis
trans
b) All values are positive.
3J:
Vicinal proton-proton couplings!
Karplus Curves:
- the fact that these couplings are through bonds is best evidence in
olefinic double bonds, if through space one would expect cis coupling
to be stronger than trans.
-!Karplus gave a valence-bond interpretation of these results and
concludes that the vicinal coupling of two protons on adjacent sp3
orbitals should depend on /, the dihedral angle by the following
equations:
J = 8.5cos2/ - 0.28(Hz)
0° < 0 < 90°
and
J = 9.5cos2/ – 0.28(Hz)
90° < 0 < 180°
Values are largest when / = 0° and 180° and they are smallest when /
= 90°.
3J:
Vicinal proton-proton couplings!
Karplus Curves:
10
9
8
7
6
5
4
3
2
1
0
-1
0o
20o
40o
60o
80o
/"
100o
120o
140o
180o
3J:
Vicinal proton-proton couplings!
There are three rotamers 2 gauche and 1 trans:!
"
"
"
"
"
"
"
"
"
3J
= 1/3 ( 23Jg + 3Jt) !
"
This is ~ 7Hz if three populations are equal (fast rotation).!
If populations vary:!
3J = x J + x Jt + x J !
!
!
I g
II
III g
"
3J:
Vicinal proton-proton couplings!
Substituent Effects:!
- in general electronegative substituents slightly reduce
the coupling.!
"
"
!
!3J = 8.0 - 0.8(Ex -EH)!
3J:
Vicinal proton-proton couplings!
More dramatic effects seen with ethylene derivatives:!
"
"
"
"
"
"
"
"
"
"
"3Jcis = 11.7 - 4.7(Ex -EH)!
!
!
!3Jtrans = 19.0 - 3.3(Ex -EH)!
"
C, H coupling constants!
Principal structural significance is that they depend on
the s character of the bonding carbon orbitals:!
!
!
!1J (C,H) = 500s!
!
!
!
!
!
2J (C,H)- Smaller that 1J(C,H) and show some
dependence on s character.!
!
3J (C,H)- Show some dependence on dihedral angles but
many other factors are involved. They are hard to
predict.!
C, C coupling constants!
- There is only a 1:8300 probability of two 13C’s at
natural abundance.!
- They are dependent on hybridization of bonding
orbitals.!
!
"
"
"
"
"
"
"
Couplings in proteins!
"
"
"
"
"
"
"
"
"
Important 1J and 2J couplings