View
4
Download
0
Category
Preview:
Citation preview
Chem 325 NMR Intro
1
Physical properties, chemical properties, formulas
Shedding real light on molecular structure:
Frequency νννν
Wavelength
Wavelength λλλλ
Frequency νννν
Velocity c = 2.998 ×××× 108 m⋅⋅⋅⋅s-1
λλλλ ×××× νννν = c
Energy of a photon: E = hνννν = hc/λλλλ
h = Planck’s constant = 6.626 ×××× 10-34 J⋅⋅⋅⋅s
The Electromagnetic Spectrum
Chem 325 NMR Intro
2
Emission and Absorption Spectroscopy
Nuclear Magnetic Resonance
Spectroscopy
Let’s go for a spin!
Electron Spin: A Fourth Quantum Number
The Stern-Gerlach Experiment
Chem 325 NMR Intro
3
Nucleus: nucleons: protons, neutrons
-these also have ‘spin’ properties: up, down
- spins add together in a complicated way to give total nuclear spin I, characteristic of a given type of nucleus
- some general guidelines….
oddoddevenodd
1H, 13C, 19F, 31P
(I = ½)
35Cl, 37Cl (I = 3/2)
127I (I = 5/2)
½, 3/2, 5/2, …
evenoddoddeven
2H, 14N (I = 1)
10B (I = 2)1, 2, 3, …oddevenoddodd
4He, 12C, 16O, 32S0eveneveneveneven
ExamplesTotal Spin
IZA#p#n
The net nuclear spin gives rise to a number of spin states
#spin states = 2I +1
Spin states characterized by mI or Izvalues:
For a given I value, mI = Iz = +I, I-1, I-2,..,-I+1, -I.
e.g. for I = 0, mI = 0 (only!)
for I = ½, ml = +½, -½
for I = 1, ml = +1, 0, -1
Normally all nuclear spin states are degenerate
→ same energy
-degeneracy can be removed by application of an external magnetic field
Chem 325 NMR Intro
4
Amount of splitting of the nuclear spin states, ∆∆∆∆E,
is directly proportional to the applied magnetic
field strength B0
is directly proportional to magnetogyric ratio γγγγ of
the particular nucleus type
νγπ
γ hBBh
)2
( E 00 ===∆ h
)2
( 0Bπ
γν =
νννν is the frequency of the EM radiation required for
the transition from the lower to the upper spin states
40.01.00251.719F
75.07.05
50.04.70
10.71.0067.2813C
6.51.0041.12H
300.7.05
200.4.70
42.61.00267.531H
Frequency νννν
(MHz)
Field
strength B0
(Tesla)
γγγγ
(106 rad/Tesla ×××× sec)
Nucleus
• Increasing B0 increases ∆∆∆∆E
• Increasing B0 results in a higher frequency νννν of EM radiation required to produce the transition
• For a given B0, different types of nuclei have different ∆∆∆∆E, thus different νννν values
• EM radiation with νννν values in MHz range are radio waves
• So far: allows us to identify which types of atoms our molecule has by monitoring which EM frequencies are absorbed at a given applied magnetic field strength (but limited to those nuclei with I ≠≠≠≠ 0!)
Precession
Interaction of the nuclear magnetic moment and the
applied field causes the rotational axis to precess about the
field axis (z-axis) (like a toy top)
H B0
ω
Precessional frequency or Larmor frequency ωωωω
For a given field strength B0, nuclei of
different types precess at different
Larmor frequencies according to their
magnetogyric ratio γγγγ values:
ωωωω = γγγγB0
Chem 325 NMR Intro
5
Mechanism of Absorption
When a photon of, say, νννν = 60 MHz encounters this spinning
charged system the two can couple and change the spin state
of the proton.
H
B0
ω
ν = ω/2ν = ω/2ν = ω/2ν = ω/2ππππ = = = = γγγγΒΒΒΒ0000/2/2/2/2ππππ
H
ω∆Ε∆Ε∆Ε∆ΕThis state is called nuclear magnetic resonance, and the nucleus is said to be in resonance with the incoming radio wave
Mechanism of Absorption
To observe a spectroscopic transition, need a population
difference between the two states involved.
The energy difference corresponding to 60 MHz (∆∆∆∆E = hνννν)
is 2.39 x 10-5 kJ mol-1.
Thermal energy at room temperature (298 K) is sufficient
to appreciably populate both energy levels.
The energy difference is small, so rapid exchange is
occurring between the two populations, but there is
always a net excess of protons in the lower energy state.
Mechanism of Absorption
From the Boltzman distribution equation we can
calculate the population of each energy state:
Nupper/Nlower = e-∆∆∆∆E/kT = e-hνννν/kT
@ 298 K the ratio is 1,000,000 / 1,000,009 !
There is an excess population of 9 nuclei in the lower
energy state!
Transitions
As the applied B0 increases, exchange becomes more
difficult and the excess increases:
In each case, it is these few nuclei that allow us to
observe NMR
96600
48300
32200
16100
1280
960
Excess
nuclei
Frequency
(MHz)
Chem 325 NMR Intro
6
When radio radiation is applied to a sample both
transitions upward and downward are stimulated.
If too much radiation is applied both states completely
equilibrate – called saturation – no NMR signal can
be observed.
Two mechanisms for relaxation:
1. spin-spin or transverse relaxation, exchange with
other nuclear spins, characterized by time constant T2
2. spin-lattice or longitudinal relaxation, transfer of
energy to surroundings (heat), characterized by time
constant T1
Shielding
• If all protons (1H nuclei!) absorbed the same
amount of energy in a given magnetic field, not
much information could be obtained.
• But protons (1H nuclei!) are surrounded by
electrons that shield them from the external field.
• Circulating electrons create an induced magnetic
field that opposes the external magnetic field.
Electronic Motion
A permanent magnet will induce a current carrying
loop to spin:
Shielding
In the same way, electrons in orbitals will start to
circulate when the molecule is placed in an external
magnetic field. This circulation of electrons creates
another magnetic field that opposes the external field.
B0
Chem 325 NMR Intro
7
Shielding
Magnetic field ‘felt’ at the nucleus:
BN (= Beff = Blocal) = B0 - σσσσB0 = B0(1-σσσσ)
where σσσσ is the shielding constant
Thus the local field is modulated by the local
electronic or chemical environment of the nucleus.
Known as the chemical shift.
Shielded Nuclei
Magnetic field strength must be increased for a shielded proton to flip at the same frequency.
7.0459 T A small, but NOTICABLE, effect!
Protons in a Molecule
Depending on their chemical environment,
protons in a molecule are shielded by different
amounts.
The Chemical Shift
mos
t des
hiel
ded
leas
t de
shie
lded
high fieldlow field
Chem 325 NMR Intro
8
NMR Signals
• The number of signals shows how many different
kinds of protons (H atoms!) are present.
• The location of the signals shows how shielded or
deshielded the proton is.
• The intensity of the signal shows the number of
protons (H atoms!) of that type.
The NMR Spectrometer There are two types of NMR
spectrometer, continuous
wave (CW) sweep and
Fourier Transform (FT). CW
instruments have been almost
entirely phased out.
RF (MHz) oscillator
Magnet
RF Detector
Magnetic Field Strength
Field Strength Magnet Type Frequency
1.41T permanent 60 MHz
2.35T electromagnet 100 MHz
4.70T superconducting 200 MHz
7.05T 300 MHz
............ ............
21.2T 900 Mhz
Frequency is that required to observe 1H signals
Modern NMR
Recall the concept of precession of the spinning nuclear magnet in the applied magnetic field:
H B0
ω
µ = magnetic moment
Chem 325 NMR Intro
9
Behaviour of a collection of spinning nuclei:
Spin population difference
Net moment or magnetization
Application of a second magnetic field
B1 (magnetic field of EM radiation)
matching Larmor frequency
Phase coherence of spins
Transfer of magnetization from
z-axis to x,y-plane
The x,y component of the magnetization is detected
electronically as the ‘resonance’ signal
Rather than show the magnetization vectors
precessing about the z-axis, we will now make the
x- and y-axes rotate about the z-axis with the
Larmor frequency.
Transfer from the stationary laboratory coordinate
system to a rotating coordinate system.
-Initial alignment of net magnetization M along z-axis
-Apply a pulse of B1 along x-axis
-Causes phase coherence of spins and rotation of M by angle
θθθθ, value depends on pulse duration
Magnetization along the y-axis after 90°°°° pulse
Free Induction Decay “FID”
Chem 325 NMR Intro
10
- the magnetization along the y-axis decays by spin-spin
relaxation, time constant T2
- the magnetization along the z-axis subsequently
reappears by spin-lattice relaxation, time constant T1
-So far, only one type of nucleus, one frequency
-Real sample, different H’s, different frequencies due to
shielding effects
-Coordinate system rotating at one fixed frequency
-Some H magnetizations rotate in the x,y-plane
-The magnetization along the y-axis (detector) oscillates
between + and – values with a cosine dependence on time
-Overall decay still that of spin-spin relaxation, T2
-Horizontal difference between two peaks is inverse of
frequency difference between B1 and the Larmor
frequency
FID
CH3
C
CH3
O
CH3
C
O
OCH3
CH3
CH
CH2
C
OH
O
OH
Chem 325 NMR Intro
11
• The FID is magnetization as a function of time.
• Need to transform the time-domain data into frequency-domain data.
• The Fourier Transform
• Mathematically simulate the FID with a number of sine waves, distance between the peaks is related to the frequency of the signal
frequency
Fourier Transform
0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
t1 sec
FT
time
The NMR Graph
Peak positions (x-axis scale):
1. Field strength: 1.500000000 versus 1.500002085 T
cumbersome and depends on resonance frequency!
2. Resonance frequency at constant field strength:
60000000 versus 60000089 Hz
cumbersome and depends on magnetic field strength!
The NMR Graph
Use a reference and quote all field strengths or
frequencies relative to the field or frequency of the
reference peak.
The δδδδ Scale: 6-
ref
sampleref10 1.39
01.50000000
50.00000208
B
B -B δ ×===
6-
6
ref
sampleref10 1.39
Hz 10 63.87
Hz 88.8
- δ ×=
×==
ν
νν
i.e. The sample signal is shifted by 1.39 ppm relative to the reference.
The chemical shift is 1.39 ppm.
Sample signal is at δδδδ = 1.39 relative to the reference (δδδδ = 0).
OR
δδδδ values INDEPENDENT of applied field or frequency
Chem 325 NMR Intro
12
Tetramethylsilane
“TMS”
• TMS is added to the sample (internal standard).
Soluble in most organic solvents.
• Since silicon is less electronegative than carbon,
TMS protons are highly shielded. Signal defined
as zero.
• Organic protons absorb downfield (to the left) of
the TMS signal.
• All 12 H’s identical, strong signal.
• Also used for 13C spectra.
Si
CH3
CH3
CH3
H3C
Chemical Shift
• Measured in parts per million.
• Ratio of shift downfield from TMS (Hz) to total
spectrometer frequency (Hz).
• Same value for 60, 100, or 300 MHz machine.
• Called the delta (δδδδ) scale.
Delta Scale
Recommended