Download Notes for Classical/Semi-Classical/Quantum Outline of Basic NMR

Nuclear Magnetic Resonance Spectroscopy Notes
adapted by Audrey Dell Hammerich, October 3, 2013
Nuclear magnetic resonance (NMR), as all spectroscopic methods, relies upon the
interaction of the sample being examined with electromagnetic radiation, here in the low
energy range of radio frequencies (1-1000 MHz). To absorb a photon of electromagnetic
radiation the sample must exhibit periodic motion whose frequency matches that of the
absorbed radiation
ΔE sample = E photon = ħω = hν = hc/λ
(1)
The experiments will sample from the broad range of information accessible from NMR
interrogation of a sample, in particular how NMR frequencies can be used to obtain the
pKa of as well as structural information on a sample.
Angular Momentum and Spin
Classically a rotating particle possesses angular momentum. The nucleus of an atom
can be visualized as “rotating” and, consequently, has a spin angular momentum, I. This
angular momentum is intrinsic to the nucleus, rather than the angular momentum arising
from the nucleus physically rotating or spinning in space, and properly requires a quantum mechanical treatment. Nevertheless, employing an analogy of spin with that of a
rotating classical particle is instructive. The magnitude of the spin angular momentum is
given in quantum mechanics by
|I| = [I(I +1)] 1 / 2 ħ
I = 0, 1/ 2 , 1, 3/ 2 , …
(2)
where ħ is Planck’s constant h divided by 2π and I is the spin angular momentum quantum number or the “spin” of the nucleus. I has a quantized z-component
I z = mħ
m = −I, …, 0, …, I
(3)
where m is the magnetic quantum number with 2I +1 values. (The z-component is important as the direction of the static magnetic field is chosen as the z axis and the component of the magnetic moment which will interact with this magnetic field - generated by
the NMR spectrometer - lies along this axis.) Note the parallel between the orbital angular momentum quantum number l and magnetic quantum number ml for the electron in a
hydrogen atom and the I and m quantum numbers here.
Nuclei of all elements are composed of protons (p) and neutrons (n), both of which
have spin I = 1/ 2 . Thus the total nuclear spin is the resultant of the spin and orbital angular momenta of all the nucleons. The quantum treatment indicates that protons and neutrons pair up separately and that even numbers of either have zero spin angular momentum. The model leads to the three cases summarized in Table I.
Table I – Distinct Ways to Combine Spin of the Nucleons in an Atom
Spin
I=0
Nucleon Description
even numbers of both p and n
I = n (integer)
odd numbers of both p and n
I = n/2 (half integer)
even p (n) and odd n (p)
Examples
C: 6p, 6n
16
O: 8p, 8n
2
H: 1p, 1n, I = 1
10
B: 5p, 5n, I = 3
13
C: 6p, 7n, I = 1/ 2
23
Na: 11p, 12n, I = 3/ 2
12
Nuclear Magnetic Moment
Classically if a rotating particle is charged it generates a magnetic dipole which creates a magnetic field. The dipole has a magnetic moment. Nuclear spin angular momentum has an associated nuclear magnetic dipole moment μ which can interact with a
magnetic field
μ = γI
(4)
where γ is the magnetogyric ratio, a constant characteristic of each nuclide. The magnetic moment also has a quantized z-component.
μ z = γI z = mħγ
(5)
Protons and neutrons are actually not true elementary particles but consist of charged
fundamental particles known as quarks. Both nucleons (protons and neutrons) contribute
to the spin and also can contribute to the nuclear magnetic moment, μ . However I = 0
spins have no spin and, thus, no magnetic moment. Table II summarizes properties of
some nuclides.
Table II. Properties of Selected Nuclides
Nuclide
1
H
2
H
13
C
23
Na
1
I
1
/2
1
1
/2
3
/2
γ [× 107 rad (Ts)-1]
26.7519
4.1066
6.7283
7.0801
% Natural
Abundance
99.985
0.015
1.108
100
Resonance
Frequency1 [MHz]
100
15.351
25.144
26.466
relative to a proton frequency of 100 MHz
Nuclear Spin in an External Magnetic Field (Zeeman Effect)
There is no preferred orientation for a magnetic moment in the absence of external
fields. In the absence of Bo the magnetic moments of individual nuclei are randomly ori2
ented and all have essentially the same energy. Application of an external magnetic field
removes the randomness, forcing the nuclei to align with or against the direction of Bo.
This change from a random state to an ordered state is known as polarization. Such polarization means there is a difference in the population of the various spin states. Furthermore the different spin states are no longer degenerate (the same) in energy.
Classically, in the presence of an external magnetic field Bo the energy of a magnetic
moment μ depends on its orientation relative to the field
E = − μ . Bo
(6)
being a minimum when the magnetic moment is aligned parallel to the magnetic field and
a maximum when it is anti-parallel. From the quantum mechanical prospective, when a
nucleus is introduced into a magnetic field its magnetic moment will align itself in 2I +1
orientations (number of values of the m quantum number) about the z direction of Bo
where the energy is given by
E m = − μ z B o = − mħγB  o
(7)
For an I = 1/ 2 nucleus there are only two orientations for the magnetic moment μ: 1)
a lower energy orientation parallel to Bo with a magnetic quantum number m = 1/ 2 often
referred to as the α spin state and 2) a higher energy anti-parallel orientation with m = −
1
/ 2 referred to as the β spin state.
β
anti-parallel to Bo
E β = 1/ 2 ħγB  o
α
parallel to Bo
E α = − 1/ 2 ħγB  o
Energy levels for a nucleus with spin quantum number I = 1/ 2
For an I > 1/ 2 nucleus there are more than two orientations. The physical description
can be portrayed in a vector diagram where the length of the angular momentum vector is
a constant whose magnitude |I| = [I(I +1)] 1 / 2 ħ and whose projection on the z-axis is Iz
= mħ. The number of possible orientations of this vector is given by the number of
values of the magnetic quantum number m. Note that even with the magnitude of the
vector and m known the uncertainty principle does not allow one to specify the vector I.
It can lie anywhere on the base of the cones about the z-axis as shown on the next page.
3
For clarity the vector is only shown for the highest and lowest values for m though all of
the cone bases are given.
Orientations of the spin angular momentum vector for I = 1/ 2 , 1, and 2 nuclei
Transition Frequencies
NMR spectroscopy induces transitions between adjacent nuclear spin energy states
(the selection rule is Δm = ±1). The energy change for a nucleus undergoing an NMR
transition from the spin state characterized by the magnetic quantum number m to the
state with quantum number m − 1 is
ΔE = E m − 1 – E m = [−(m−1)ħγB o ] – [−mħγB o ] = ħγB o
(8)
Equation (8) follows from the previous discussions. The difference between the
z-component of the angular momentum of adjacent m states is ħ [Eq. (2)]. This difference is multiplied by γ to obtain the difference in the magnetic moment z-component [Eq.
(5)]. This result is then multiplied by the magnetic field strength to obtain the energy difference between adjacent m states in a magnetic field [(Eq.7)].
The frequency ν of the electromagnetic radiation used to induce an NMR transition
between adjacent m levels in an external magnetic field Bo is found from Eq. (1)
ν = ΔE/h = ħγB o /h = γB o /2π
(9)
The units of frequency (ν) are cycles/second, hertz (Hz) in SI units. In NMR spectroscopy, it is often more convenient to use angular frequency (ω) with units of radians/second. Since one cycle equals 2π radians,
4
ω ≡ 2πν
(10)
As cycles and radians are not SI units, both ν and ω have the same SI units (s−1). The angular frequency of an NMR transition is more commonly written as
ω o = γB o
(11)
which is the Larmor equation. Note that the use of ω eliminates the occurrence of 2π in
the Larmor equation.
The Larmor frequency has two important physical interpretations. It is the frequency
of the electromagnetic radiation that induces a transition between nuclear spin quantum
states in the magnetic field. It is also the precessional (or rotational) frequency of the nuclear magnetic moment about the magnetic field. While the actual origin is quantum mechanical and involves the Heisenberg uncertainty principle, this precession has a classical analogy. The interaction between a magnetic field and a magnetic dipole
moment produces a torque on the dipole that makes it
revolve around the direction of the magnetic field at a
fixed angle, sweeping out a conical surface. This
precession is illustrated on the right for an I = 1/ 2
nucleus and shows the two allowed orientations of the
spin vector I (and, by Eq. (4), its associated magnetic
moment μ). The length of the vector is ħ√ 3/ 2 , Eq. (2),
and its projection on the z-axis is either 1/ 2 ħ or – 1/ 2
ħ, Eq. (3).
Boltzmann Statistics
In the presence of an external magnetic field different nuclear spin states (with different values of m) have different energies. The energy difference is proportional to B o .
At thermal equilibrium, these states will also have different populations, their ratio given
by the Boltzmann equation
N high
N low
= e
− Δ E / kT
(12)
with N high and N low the respective populations of the upper and lower spin states (such as
β and α for an Ι = 1/ 2 nucleus), ΔE = E high − E low the energy difference between the two
states, k the Boltzmann constant, and T the absolute temperature. In currently achievable
magnetic fields, the difference between nuclear spin energy levels ΔE is much smaller
than kT, implying that N low is only very slightly in excess of N high. For 1H in a 9.4 tesla
field (400 MHz) and 300 K one obtains a population ratio N(α)/N(β) of 1.000064, i.e.,
for one million spins in the upper β state there are one million and sixty-four in the lower
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energy α state! It is the excess 64 spins that respond to
the NMR experiment and create the net magnetization
M o (as shown on the left with the double precessional
cone characteristic of a spin 1/ 2 nucleus). To summarize, the larger B o is the greater the energy difference
ΔE between the levels and the larger the ΔE the more
excess population exists in the lower energy state
(waiting to be excited to the higher level).
The NMR Spectrometer
The major components of
an NMR spectrometer are a
strong magnet with associated
electronics to control the field
homogeneity and stability,
probe,
RF
electronics,
computer, and a coil of wire
which serves as an antenna for
radiofrequency
transmission
and
detection.
Older
continuous wave instruments
employed two coils, one for the
transmitter and one for the
receiver.
Note how the
terminology is similar to that of
an FM radio as both rely upon
RF! The magnet is a solenoid
whose
wiring
becomes
superconducting
at
liquid
helium temperatures (4 K). To
facilitate continuous cryogenic
operation, a liquid nitrogen (77
K) dewar surrounds the He
dewar providing a heat sink
and minimizing loss of the more expensive liquid helium.
Pulse NMR Experiment and Fourier Transform NMR
When a sample is placed in the magnetic field the field causes the spins to become
polarized creating a Boltmann distribution where slightly more spins exist in the lower
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energy state. The excess of nuclear spins in the α spin state is illustrated below on the far
left.
ωo
ωo
ωo
ωo
ωo
ωo
In the presence of the B o magnetic field the precessing spins are distributed equally about
the z-axis. Their precessional frequency ω o is given by the Lamor equation [Eq. (11)].
The vector sum of the individual μ vectors [Eq. (4)] yields a net equilibrium magnetization M o along the positive z-axis. (Due to the precession about the z-axis, the x and y
components of the individual μ vectors sum to zero, leaving only the z component μ z
[(Eq. (5)]). Excitation of the nuclei from the lower energy α spin state to the higher energy β spin state is achieved with an oscillating radio frequency magnetic field B1 applied
with a transmitter coil as a short duration pulse along the x-axis (RF pulse). The oscillating magnetic field can be viewed as a rotating magnetic field. When the rotating frequency of B1 is equal to the precession frequency of the nuclear moments (ω o ), B1 excites nuclei in the α spin state to the β spin state. This causes the net magnetization Mo
to rotate about the x-axis tipping it from the z-axis into the yz-plane. (One can completely transform the z magnetization into y magnetization if the duration of the pulse is
the length of a π/2 pulse, a 90° pulse.) The component of the magnetization in the xy
plane, initially along the y-axis (M y ) precesses about the z-axis at the precession
frequency ω o . The net magnetization along the y-axis is detected with an antenna coil
illustrated with an eye in the figure above.
With respect to the eye, y-axis magnetization rises and falls in a sinusoidal manner as
the vector precesses about the z-axis. The amplitude of the signal decays with time as the
phase coherence between the precessing magnetic dipoles is lost in a process known as
nuclear spin relaxation (spin-spin relaxation of next section). If the molecule has only a
single chemical shift, the signal appears as a simple decaying sine wave and the shift in
hertz is the frequency of the sine wave relative to a reference frequency. Most molecules
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have many nuclei with many different chemical shifts and correspondingly many
different precession frequencies. The B1 field actually contains a broad band width of
frequencies that excite all nuclei in a molecule at the same time. Since the RF pulse is on
the order of microseconds, the time-energy uncertainty principle (ΔEΔt = ħΔωΔt ≥ ħ)
shows that the pulse will consist of a range of frequencies Δω able to simultaneously
excite all the spins of a given nuclide. The net magnetization along the y-axis is then the
sum of the magnetization of each set of equivalent nuclei, all precessing at different
frequencies. The resulting waveform is called the free induction decay (FID) or the time
domain spectrum. It is a measure of y-axis magnetization M y as a function of time after
the B1 pulse. A Fourier transformation (FT) of the signal yields the individual precession
frequencies or chemical shifts, the frequency domain spectrum or simply the NMR
spectrum:
+∞
spectrum = signal(ω) = M y (ω) =
∫
−∞
M y (t )e
−i ω t
+∞
dt =
∫
signal(t )e
−i ω t
dt
(13)
−∞
Nuclear Spin Relaxation
The precession of spins in the xy-plane does not last forever. It decays due to three
distinct effects:
1. The magnetic field is not perfectly uniform. Nuclei in different parts of the sample precess at slightly different frequencies and get out of phase with one another, thereby
gradually decreasing the net magnetization of the sample.
2. Spin-Lattice (or Longitudinal) Relaxation, T1 (mechanism which involves a
net transfer of energy from spin system to surroundings to reestablish Boltzmann
distribution – an enthalpy effect). The applied RF pulse and consequent rotation of the
net magnetization M o from the z-axis is a disruption of the thermal equilibrium of the
spins. The system responds to reestablish equilibrium by transferring energy from the
spin system to the environment (lattice) until the populations of the energy states regain
the Boltzmann distribution given in Eq. (12). The process is attributable to electromagnetic interactions between the nuclei and the surrounding particles which cause transitions between the spin states (α and β when I = 1/ 2 ). As it is the coherent combination of
these spin states that contribute to the magnetization rotating in the xy-plane, the result is
a gradual decay of these coherent combinations and a return to the state of equilibrium in
which the magnetization is in the z-direction and no longer capable of inducing a signal
8
in the antenna coil. How fast the spins regain equilibrium is a measure of the coupling of
the spins to their environment. Bloch assumed that the nonequilibrium distribution of M z
moves toward the equilibrium distribution M o by a first order rate process
d Mz
= − k (M z − M o )
dt
(14)
where the reciprocal of the rate constant k is the
spin-lattice or longitudinal relaxation time T1.
Making this substitution the equation can be
integrated from time zero to some time t to yield
M z (t ) = M o + [M z (t = 0) − M o ]e − t/ T1
(15)
an exponential approach to equilibrium.
3. Spin-Spin (or Transverse) Relaxation, T2 (mechanism which adiabatically
redistributes the energy of the spin system without a net transfer of energy to the
surroundings – an entropy effect). After an RF pulse tips the net magnetization M o
from the z-axis, the magnetic moments interact with one another by magnetic dipole interactions. Nuclei are generally located in several different molecular environments, each
with a slightly different B o due to molecular motion or chemical exchange. In
each of these regions the precession frequency will be perturbed to a slightly different
extent. The result is a collection of regions rotating at slightly different frequencies producing a gradual loss of phase coherence (precession as a group) and a decay of the resultant magnetization (the spin vectors become evenly distributed in xy-plane). Bloch
also assumed that Mx and My lose their magnetizations in first order rate processes
d Mx
= − k Mx
dt
and
d My
dt
= −k My
(16)
where the reciprocal of the rate constant k is the
spin-spin or transverse relaxation time T2
(characterizes the exponential decay of the FID).
With this substitution the equations can be
integrated from time zero to some time t to yield
M x (t ) = M x (t = 0) e − t/T2
(17)
M y (t ) = M y (t = 0) e
In the figure Mxy denotes either Mx or My.
9
− t/T2
The spin-spin relaxation time does not exceed the spin-lattice relaxation time, T2 ≤
T1. Since the relaxation times are reciprocals of rate constants this implies that spin-lattice relaxation processes are not faster than spin-spin relaxation processes. In many
cases, the same physical relaxation mechanisms determine T1 and T2 so that they are then
equal. In spectroscopies involving higher energy excitation such as in the ultraviolet or
visible region of the electromagnetic spectrum, the return to the ground state of an excited molecule is very rapid. The situation is quite different in NMR where the small energy difference between nuclear spin states means that spontaneous emission is very
slow. (The lifetime of an unperturbed excited nucleus is in the range of years!) Consequently the excited nucleus must be induced to flip its spin and return to the ground state
by some external means. An analysis of the interaction of electromagnetic radiation with
matter shows that a spin subjected to a fluctuating magnetic field will be induced to undergo transitions between all available energy levels at a rate that is proportional to the
intensity of the field. The principal sources for producing fluctuating magnetic fields are
the movement of spins in space due to molecular motion or due to molecular rotation.
The principal mechanisms by which these fields are produced are
• dipole-dipole interactions with other nuclei – generally dominant mechanism in
solution; most important for I = 1/ 2 nuclei with nearby protons
• chemical shift (or shielding) anisotropy – molecular tumbling of a nonspherical
distribution of electron density causes the local magnetic field acting on a nucleus
to change the shielding of the B o field
• scalar interactions – indirect spin-spin coupling of nuclear spins through electrons; the nuclei are either involved in chemical exchange or one of the magnetic
moments is that of an electron (and thus requires a quadrupolar nucleus)
• spin-rotation interactions – molecular collisions interrupt the coupling between
rotational angular momentum of the electrons and nuclear spin
• quadrupolar interactions – nuclei with I > 1/ 2 have a nonspherical nuclear
charge distribution and possess an electric quadrupole moment that can interact
with electric fields
Attributes of 1H NMR Spectroscopy
NMR Chemical Shifts
chemical shift, ppm δ =
(frequency of signal − frequency of reference) in Hz
× 10 6
spectrometer frequency in Hz
The chemical shift is the position on the δ scale (in ppm) where the peak occurs. In
proton and 13C NMR the reference at 0 ppm is the chemical shift of tetramethylsilane,
(CH3)4Si (i.e., TMS).
10
Table III – Proton Chemical Shifts
There are two major factors that influence chemical shifts:
• deshielding due to reduced electron density (e.g., due to electronegative atoms)
• anisotropy due to magnetic fields (e.g., those generated by π bonds)
Shielding in NMR
Nuclei are shielded by valence electrons surrounding them which circulate in an applied magnetic field producing a local diamagnetic current in the opposite direction. This
diamagnetic shielding will affect the frequency of radiation necessary to cause a nucleus
to spin flip (the resonance frequency). Therefore nuclei will absorb radiation of slightly
different frequency depending upon their local magnetic environment which is determined by the structure of the compound. Hence magnetically different types of nuclei
will occur at different chemical shifts. This is what makes NMR so useful for structure
determination; otherwise all nuclei would have the same chemical shift. Some important
factors include:
• inductive effects by electronegative groups
• magnetic anisotropy
Electronegativity
Electrons around the nucleus create a magnetic field that opposes the applied field.
This reduces the field experienced at the nucleus. Since the induced field opposes the
applied field the electrons are said to be diamagnetic and the effect on the nucleus is re-
11
ferred to as diamagnetic shielding. Since the field experienced by the nucleus defines the
energy difference between the different spin states, the frequency and hence the chemical
shift δ will change depending on the electron density around the nucleus. Electronegative
groups decrease the electron density around the nucleus, and there is less shielding (i.e.
deshielding) so the chemical shift increases.
Magnetic Anisotropy
Magnetic anisotropy means that there is a non-uniform magnetic field. Electrons in
π systems (e.g. aromatics, alkenes, alkynes, carbonyls, etc.) interact with the applied field
which induces a magnetic field that causes the anisotropy. As a result, the nearby nuclei
will experience three fields: the applied field, the shielding field of the valence electrons,
and the field due to the π system. Depending on the position of the nucleus in this third
field, it can be either shielded (smaller δ) or deshielded (larger δ), which implies that the
energy required for and the frequency of the absorption will change
Magnetic Anisotropy
Different ways to express the relative chemical shifts are summarized in Table IV.
12
Table IV. Nomenclature to Express Relative Peak Positions in NMR
low field
down field
deshielded
less electron density
high frequency
large δ (ppm)
high field
up field
shielded
more electron density
low frequency
small δ (ppm)
Chemical Shifts in 1H NMR
Magnetically different types of nuclei will occur at different chemical shifts resulting
in an NMR spectrum which contains peaks for each of these different types of nuclei.
Coupling in 1H NMR
Spectra generally have peaks that appear in clusters due to coupling (referred to as
scalar, spin-spin, or J-coupling) with neighboring protons The coupling constant J
(measured in frequency units, Hz) is a measure of the interaction between a pair of protons and is independent of the magnetic field strength. The interaction is through chemical bonds via coupling of the nuclear spins with the spin of the electrons and rapidly decreases with the number of bonds.
13
Before addressing the coupling, examine the peak assignments in the above spectra:
• δ = 5.9 ppm, integration = 1H; deshielded: agrees with the −CHCl2 unit
• δ = 2.1 ppm, integration = 3H; agrees with −CH3 unit.
What about the coupling patterns? Coupling arises because the magnetic field of
adjacent protons influences the field that the proton experiences. To understand the implications of this, first consider the effect the −CH group has on the adjacent −CH3. The
methine −CH can adopt two alignments with respect to the applied magnetic field, one
which deshields neighboring protons and the other which shields them. As a result the
methyl −CH3 is split
into a doublet, two
lines of equal intensity
due to the equal probability of the methine
proton being aligned
either parallel or antiparallel to the applied
field. Remember that
the excess of spins in
the lower energy state
is only very, very slightly larger than the number in the higher energy state. When considering coupling patterns, for practical purposes, they can be considered to be equal.
Now consider the effect the −CH3 group has on the adjacent −CH. The methyl -CH3
protons have 8 possible combinations with
respect to the applied
field, only four of
which are magnetically distinct. The resulting signal for the
adjacent
methine
−CH is a quartet, four
lines with the intensity ratio 1:3:3:1.
14
n + 1 Rule
As protons on a
carbon atom experience
the magnetic field of
protons
on
adjacent
carbon atoms the signal
for a particular proton will
be split by these protons
into n + 1 peaks where n
is the number of adjacent
protons. This rule can be
extended to any spin 1/ 2
nucleus.
Pascal’s Triangle
The relative intensities of the lines in a
coupling pattern are given by a binomial
expansion or more conveniently by Pascal's
triangle. Individual resonances are split
due to coupling with n adjacent protons.
The number of lines in a coupling pattern is
given, in general, by 2nI + 1 for coupling
with n spin I nuclei.
Interpreting 1H NMR Spectra
What can be obtained from a 1H NMR spectrum:
1. number of equivalent types of H – number of groups of signals in the proton
NMR spectrum
2. types of H – chemical shift of each group; protons found in chemically identical
environments are chemically (and usually also magnetically) equivalent; chemically equivalent protons will have the same chemical shift.
3. number of H of each type – NMR spectrometer can integrate all peaks (determine the area under each peak) to determine the relative numbers of protons responsible for all peaks.
4. connectivity – spin-spin splitting (J coupling with the n + 1 rule); coupling pattern gives what is adjacent to each group of protons
15
Chemical shift
• position on the δ scale (in ppm) where the peak occurs
• major factors influencing shifts: 1) deshielding due to reduced electron density
(electronegative atoms) and 2) anisotropy (magnetic fields generated by π bonds).
Integration
• area of a peak is proportional to the number of H that the peak represents
• integral measures the area of the peak
• integral gives the relative ratio of the number of H for each peak
Coupling
• proximity of other n H atoms on neighboring carbon atoms, causes the signals to
be split into n +1 lines (to first order).
• this is also known as the multiplicity or splitting of each signal.
Table V. Magnitude of Some Typical Coupling Constants1
1
Magnitude of the coupling constant is independent of the strength of the applied field.
16
Attributes of 13C NMR Spectroscopy
It is useful to compare and contrast 1H NMR and 13C NMR:
12
•
C isotope does not exhibit NMR behavior (nuclear spin I = 0)
13
•
C isotope has a natural abundance of 1.108% (of all C atoms)
13
1
• Magnetogyric ratio γ for C is approximately four times smaller than γ for H
13
1
• As a result, a C nucleus is about 400 times less sensitive than an H nucleus in
•
•
•
•
•
•
•
NMR spectroscopy
13
C - 13C coupling is seldom observed due to the low natural abundance of 13C
Chemical shifts measured with respect to tetramethylsilane, (CH3)4Si (i.e., TMS)
Chemical shift range is normally 0 to 220 ppm
Similar factors affect the chemical shifts in 13C as in 1H NMR
13
C spectra are normally broadband proton decoupled, removing J coupling between 13C and 1H, so peaks appear as single lines
Number of peaks indicates the number of distinct types of C
Long T1 relaxation times (excited state to ground state) mean no meaningful peak
area integrations
The general implications of these points are that 13C take longer to acquire, though they
tend to look simpler. Overlap of peaks is much less common than for 1H NMR which
makes it easier to determine how many distinct types of C are present.
Table VI. Carbon Chemical Shifts
Note the importance of hybridization in the shielding of 13C chemical shifts in the order:
sp2 < sp < sp3. In the following are three examples of the simplicity of 13C spectra over
1
H spectra which also illustrate the large range of the carbon chemical shifts.
17
CH3−CH2−OH
There are four alcohols with the formula C4H10O.
H
Which one produced the 13C NMR spectrum on the right?
Interpreting 13C NMR Spectra
The following information can be obtained from a typical broadband decoupled 13C
NMR spectrum (all coupling with 1H removed):
1. number of equivalent types of C – number of signals (peaks) in the 13C NMR
spectrum
2. types of C – chemical shift of each signal; 13C nuclei found in chemically identical environments are chemically (and usually also magnetically) equivalent;
chemically equivalent nuclei will have the same chemical shift.
18
NMR Experiments to Aid Spectral Interpretation
Each dimension of an NMR experiment represents a different observable nucleus.
Normal 1H and 13C NMR examine a single type of nucleus at one time by plotting intensity versus frequency. One can examine multiple nuclei simultaneously using the Fourier
transform (FT) technique coupled with a computer capable of directing RF pulses on both
nuclei during the same time period. In such experiments intensity is plotted as a function
of two frequencies generally in the form of a contour plot. This part of the NMR lab will
examine three one-dimensional techniques, normal 1H and 13C NMR and DEPT, and two
two-dimensional NMR techniques, HETCOR and COSY.
A. DEPT: 1D experiment used for enhancing the sensitivity of carbon signals and
for editing 13C spectra. The sensitivity gain comes from starting the experiment with
proton excitation and transferring the magnetization onto carbon (via the process of
polarization transfer). The gain arises due to the larger population differences associated
with 1H, which are four times those of 13C (γ is four times larger). The editing feature
alters the amplitude and sign of the carbon resonances according to the number of
directly bonded protons:
• 45o decoupler pulse - carbon spectrum contains only carbons with protons attached (quaternary carbons are not observed).
• 90o decoupler pulse - carbon spectrum contains only carbons with a single attached proton, methine CH
• 135o decoupler pulse - carbon spectrum with methyl (CH3) and methine (CH) carbon peaks up, methylene (CH2) carbon peaks down (negative).
B. HETCOR (HMQC): 2D experiment used to identify couplings between
heteronuclear spins separated by one bond. Most often employed to correlate carbons
with their directly bonded protons by the presence of cross-peaks in the 2D spectrum. It
relies on scalar coupling (spin-spin or J coupling) between the different nuclei. The
HETCOR spectra in our experiments plot proton versus carbon with the 1D spectra
displayed along the appropriate axes. The 2D peaks show which protons are coupled to
which carbons.
C. COSY: 2D experiment used to identify nuclei that share a scalar (J) coupling. The
presence of off-diagonal peaks (cross-peaks) in the spectrum directly correlates the coupled partners. Generally used to analyze coupling relationships between protons but may
be used to correlate any high-abundance homonuclear spins. The COSY spectra in our
experiments plot the proton spectrum versus itself. The 2D peaks show which 1H are
coupled over three bonds.
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A. DEPT: Distortionless Enhancement by Polarization Transfer
A 1D experiment that utilizes polarization transfer from a nucleus with a relatively
larger magnetogyric ratio γ to one with a smaller γ to increase the signal from the latter
nucleus, here from 1H to 13C. By changing the length of the last proton pulse from 45 to
90 to 135o the multiplicity of the carbon nucleus can be determined.
Observed 13C signals are modulated by the 13C−1H coupling conconstant so that when 1) θ = 45o
signals from all CH, CH2, and CH3
carbons are observed (no quaternary C or C attached to D, as in a
deuterated solvent), 2) θ = 90o signals seen from only CH carbons,
and 3) θ = 135o signals from all
CH, CH2, and CH3 carbons but the
CH2 signals are negative.
Pulse sequence:
On the right are the proton decoupled 13C spectrum and DEPT spectra
at 45, 90, and 180o for
the compound on the
left. DEPT 45 only
shows C with a directly
bonded H, DEPT 90
CH, and DEPT 135
shows carbon with a directly bonded H but
peaks for CH2 carbon
atoms are negative.
The DEPT 90 and 135
spectra on the left are
sufficient to identify
which of A-E below is
the structure of the
compound. On top is
the normal 1H decoupled 13C spectrum.
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B. HETCOR: HETeronuclear CORrelation (also 13C/1H COSY or 13C/1H HMQC)
A 2D heteronuclear correlation experiment where cross peaks yield information
about the connectivity of two different spin coupled spin 1/2 nuclei, here protons with 13C
nuclei. The experiment takes advantage of the large one-bond heteronucler J coupling for
polarization transfer between the 1H and 13C nuclei. The experiment can be modified to
give coupling information over more than one bond.
Pulse sequence:
1D 1H NMR
plotted vs. 1D
13
C
NMR;
cross peaks observed at intersection of the x
and y values
denoting
the
CH
interactions. Peak A
shows that the
H at ~ 4 is
bonded to the
C at ~ 60 ppm.
Peak B shows
that H at ~ 1.8
ppm is bonded
to C at ~ 18
ppm. The quaternary C is
identifiable as
no cross-peak
appears (*).
The HETCOR experiment
involves
13
1
C− H correlation by
polarization transfer. It
encodes the proton
chemical shift information into the observed
13
C signals and yields
cross signals for all 1H
and 13C nuclei that are
connected by 13C−1H
coupling over one
bond.
1
H NMR
Spectrum
13
C NMR
Spectrum
*
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C. COSY: COrrelation SpectroscopY
A 2D homonuclear correlation experiment where cross peaks yield information on
the protons which are spin-spin coupled to each other. The experiment uses polarization
transfer between the coupled spins. The technique can be modified to yield COSY spectra for four-, five-, and occasionally six-bond couplings.
Pulse sequence:
COSY experiment involves
1
H−1H correlation by polarization transfer. It encodes
the proton coupling information into the observed 1H
signals and yields cross
signals for all 1H that are
coupled over three bonds.
1
H NMR
Spectrum
1
H NMR
Spectrum
22
1D 1H NMR plotted vs.
1D 1H NMR generating a 2D xy plot. If a
signal on the x-axis has
an interaction with a
signal on the y, a crosspeak is observed at the
intersection of the x
and y values, denoting
the interaction. The
peaks on the diagonal
represent the 1H spectrum and the COSY is
symmetric with respect
to the diagonal. Peak
A indicates that the
peak at ~ 6.9 ppm is
proton coupled to the
peak at ~ 1.8. Peak B
indicates that the peak
at ~ 4.2 ppm is coupled
to the 1H at ~ 1.3.
Web References
1. Jim Clark
http://www.chemguide.co.uk/analysis/nmrmenu.html#top
2. Joseph P. Hornak, Rochester Institute of Technology
http://www.cis.rit.edu/htbooks/nmr/bnmr.htm
3. Ian Hunt, University of Calgary
http://www.chem.ucalgary.ca/courses/351/Carey5th/Ch13/ch13-2dnmr-1.html#cosy
On-Line Learning Center for "Organic Chemistry" (Francis A. Carey), University of Calgary, http://www.chem.ucalgary.ca/courses/351/Carey/Ch13/ch13-nmr-1.html
4. Tad Koch, University of Colorado
http://orgchem.colorado.edu/hndbksupport/nmrtheory/main.html
5. Brent P. Krueger, Hope College
http://www.chem.hope.edu/~krieg/Chem348_2002/NMR/Principles_of_NMR_Spectrosc
opy.html
6. Arvin Moser, Advanced Chemistry Development, Inc (ACD Labs)
http://acdlabs.typepad.com/elucidation/hsqchmqc
7. Tom Newton, University of Southern Maine
http://www.usm.maine.edu/~newton/Chy251_253/Lectures/DEPT/DEPT.html
8. Hans J. Reich, University of Wisconsin
http://www.chem.wisc.edu/areas/reich/chem605/index.htm
9. William Reusch, Michigan State University:
http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/nmr/nmr1.htm#nmr1
10. http://lucas.lakeheadu.ca/luil/nuclear-magnetic-resonance-nmr-facility
11. http://www2.warwick.ac.uk/fac/sci/physics/research/condensedmatt/imr_cdt/
students/stephen_day/relaxation
12. http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Magnetic_Resonance
_Spectroscopies/Nuclear_Magnetic_Resonance/NMR%3A_Theory
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