NMR Spectroscopy Short Course 2016
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Special Reading Assignment will be posted here. 1.
A Brief Introduction to NMR Technique Development Nuclear
Magnetic Resonance spectroscopy has been developed from experiments performed to
accurately measure nuclear magnetogyric ratio sixty-five years ago. The
technique depends on the fact that some atomic nuclei possess a nonzero spin
angular momentum. A spinning charge generates magnetic field associated with its
angular momentum. This phenomenon has long been known in molecular beams and has
yielded a great deal of information on nuclear properties. Two independent
groups in 1945, Purcell et al. at Harvard and Bloch et al. at Stanford reported
the first observation of nuclear magnetic resonance in bulk matter. They were
jointly awarded the Nobel Prize for physics in 1952 for this discovery.
In 1949 and 1950, Pake noted that nuclei of the same species absorbed
energy at different frequencies. In 1951, Arnold’s discovery of three
magnetically nonequivalent protons in ethyl alcohol paved the way for NMR to
become a powerful tool for chemists. The importance of NMR spectroscopy is
paramount in the fields of organic, inorganic and analytical chemistry for the
investigation of molecular structure and dynamics. New developments have been
applied to biochemistry, materials and medicine research. As a natural
consequence of continuous development both in NMR instrumentation and
methodology, more and more scientists will employ. Over
the last decade we have witnessed a substantial increase in the range and power
of NMR experiments, which allow chemists to gain an order of magnitude more
information than that provided by standard or traditional experiments. Three
developments were necessary for this revolutionary change. First, spectrometer
hardware including fast computing and networking had to become very reliable.
Second, the software had to become easy to use and fast enough to control all
experimental parameters by a keyboard and a mouse. Third, the superconducting magnet had to reach the
highest field ever. The 900MHz NMR instrument is available now. Continuing
efforts have been made to develop methods to obtain more information from NMR
measurements such as COSY, NOESY, ROESY, TOCSY, HETCOR, J-Resolved Spectroscopy,
INADEQUATE, HMQC, Multiquantum Filter COSY etc. for liquids and CRAMPS, CP/MAS,
TOSS, DOR, REDOR etc. for solids. One recent advance is Pulsed Field Gradient
NMR. This technique can measure molecular diffusivities in a variety of samples
such as liquids, solids and polymers. It can also be used to select specific
coherence pathways and provide the NMR spectroscopists with a powerful method to
improve the efficiency of multidimensional techniques and to obtain new
information. Nowadays,
NMR probably is the most important technique for structure elucidation, material
characterization and studying molecular motion.
As practicing chemists who are not NMR spectroscopists begin to consider
using these NMR techniques in their work, they are almost immediately confronted
by a series of questions. In this book those questions have been collected and
organized along with appropriate answers. 2.
Basic Theory of NMR A.
Magnetization of Nuclei in Magnetic Field All
nuclei carry a charge. In some nuclei this charge spins around the nuclear axis.
This spin generates a magnetic dipole along the axis. The spin angular
momentum is decried in terms of the spin quantum number I.
If the sum of protons and neutrons is even, the spin quantum number, I
will be 0, 1, 2, etc. For example, the 2H nucleus has one proton and
one neutron. I is 1. If the sum of
protons and neutrons is odd, I will
be 1/2, 3/2 ...etc. For example, 13C nucleus has six protons and
seven neutrons. I is ½. If both
protons and neutrons are even numbers, I
will be zero and then it is NMR insensitive.
Figure 2 - 1. A spin with nonzero spin angular momentum m. There
are a large number of nuclei, such as 1H, 13C, and 31P,
they have a nonzero spin angular momentum,
I ¹
0, then Ih/2p
¹ 0. The
Zeeman Hamiltonian for a spin with quantum number I
in a magnetic filed is:
Where
g is the magnetogyric ratio, a characteristic
of the nucleus and it could be either positive or negative and B0 is
the magnetic filed chosen by convention to be the z axis of the laboratory
coordinate. For a spin I under the
influence of a fixed magnetic field, the energy levels split into (2I + 1)
sublevels, which are represented in Figure 1-2. The energy difference between
neighboring levels can be expressed by:
Where
mI takes values ±I,
±(I-1), ...... ±1/2
or zero depending on whether I is a
half-odd integer or an integer.
Figure 2 - 2. The energy level splits into (2I +1) levels under the influence of a magnetic field. Zeeman
energy levels are displaced by a constant value, ghBo/2p, which generally can be expressed in
frequency unit and is called the Larmor frequency of the isotope in the field of
Bo. This resonance frequency is found to vary in direct
proportion to the applied field, thus the larger the magnetic field, the higher
the resonance frequency. For proton we can represent this effect as in Figure
2-3.
Figure 2 - 3. The energy difference between two adjacent levels depends on the strength of applied magnetic field B0 (Tesla or Gauss. 1.00 T = 10,000 G). For
an ensemble of nuclear spins I, the (2I + 1) allowed energy levels are populated
in thermal equilibrium in accordance with the Boltzmann distribution. For a spin
I=1/2, the ratio of the number of spins in the higher energy state (b) compared to the lower energy state (a) is given by:
Where
e =ghB0/2pT. In principle, a bulk magnetization, M,
is directly proportion to the net population difference between energy levels:
Where
m=ghI/2p. The value of the magnetization, M, can be
shown to determine the signal intensity. From the equation it is shown that the
concentration of nuclei in the sample, the strength of the magnet field B0,
the magnetogyric ratio
of the nuclei under the observation are directly proportion to the NMR signal
intensity. However, increase sample
temperature T will reduce the NMR signal intensity. B.
The Larmor Frequency A
typical magnetic field strength used for NMR is 9.395 Tesla. For proton and
carbon, the resonance frequencies can be calculated by: wo=
gBo
(2 – 5)
Where
g is the magnetogyric ratio, and B0
is the strength of the magnetic field. If a magnetic field B1
(typical strength 7.34 ´ 10-4 T) is placed along the X’ axis, a 90 degree pulse
width can be calculated by:
Figure 2 – 4. A 90 degree flip of a spin under magnetic field B1 along the X axis. C.
Spin-Lattice and Spin-Spin Relaxation When
a sample is inserted into the magnetic field B0, the
Boltzmann distribution of spins occurs between the energy levels. The
equilibrium is established by means of specific relaxation process and gives
rise to a small excess of nuclei in the lower state. We can apply an oscillating
field, B1 perpendicular
to the B0 axis,
to manipulate this spin system. After B1 is removed, there are two
different mechanisms that allow spins return to equilibrium of the longitudinal
and transverse components. The spin-lattice relaxation is a process whereby non-radiative
energy transfer takes place from “excited” spins to the surrounding of the
molecules. These relaxation
processes can be described by the Bloch equations:
Where
T1 is the spin-lattice relaxation time and T2 is the
spin-spin relaxation time. The magnitude of T1 and T2 is
related to the relaxation efficiency that is a property of the molecule. T1
and T2 are also related to the structure and mobility of the
molecule. D.
Chemical Shift When an atom is placed in a magnetic field,
its electrons circulate about the direction of the applied magnetic field. This
circulation causes a small magnetic field at the nucleus that opposes the
externally applied field.
Figure 2 – 5. A water molecule is placed in a magnetic filed. Its electrons cause a small magnetic field that opposes the applied filed. The magnetic field at the nucleus (the
effective field) is therefore generally less than the applied field by a
fraction.
B
= Bo
(1-s)
(2 – 9)
So
the Larmor frequency of the nucleus under observation is smaller. w=gB.
We use TMS as an chemical standard, its frequency under the filed refer to wo=gBo,
or fref.
In an NMR spectrum, each nucleus has a characteristic frequency or chemical
shift. It is defined as:
The
chemical shift is a finger printer of a nucleus in the molecule. It relates to
nucleus’s environment and relative position in the molecule. For the proton
NMR, 1ppm is equal to 500 Hz under the static filed of 11.74 Tesla (500MHz NMR
instrument). However, under the static filed of 4.70 Tesla (200 MHz NMR
instrument), 1ppm is equal to 200Hz.
Figure 2 - 6. Two spins coupled each other with a coupling constant J. The chemical shift d, 1ppm is equal to 60, 200 and 500 Hz respect to the static field of 60, 200 and 500 MHz instruments. The J is a constant in different field, however, Chemical shift between peaks d (in Hz) is increased as field strength increasing, so the two pair of peaks will be resolved in a spectrum acquired in a high field while overlapped in lower filed. Chemical
shifts arise from the simultaneous interaction of a nucleus with an electron and
the electron with the applied static magnetic field. It is practically
impossible to calculate a chemical shift value from the screening factor due to
the complexity of the mechanisms that give rise to it.
E.
Spin-Spin Coupling (Scalar Coupling or J-Coupling) Spin-Spin
coupling is the coupling of spins through the bonding electrons. It results in
the multiple peaks observed in the NMR spectra. The distance (in Hz) between the
multiple peaks (JH-H or JH-X) provides important molecular
structure information. If
two protons are magnetically inequivalent, there are two peaks in the spectrum
for each proton. If these two protons are scalar coupled, then the other senses
the spin states of one nucleus. Since
proton (I=1/2) has two energy levels (+1/2, -1/2), the coupled proton will be
splited to two lines relative to the two energy states.
If one of the nuclei has a spin of one (I=1), then the nucleus to which
it is coupled become split into three lines because the nucleus has three energy
levels (+1, 0, -1). A good example
is CDCl3, the carbon spectrum will have a triplet with equivalent
intensity since deuterium has spin of one (I=1).
Figure 2 – 7, (A). The proton a and proton b are not
coupled. (B). The proton a and proton
b are coupled. (C). The carbon is
coupled with D (I=1) and the carbon
spectrum will be a triplet. F.
Dipole-Dipole Coupling Dipole-Dipole
coupling is the coupling of spins through the space. They are not necessary
bonded. The Dipole-Dipole interaction is an important source of relaxation
effect but not necessary broaden the lines in liquids. In solids, however, it is
the dominant source of line broadening. If there are two spins, I and S, an
approximate dipolar Hamiltonian can be written as:
Where
q is the angle between the internuclear vector
and the applied field, r is the distance between two nuclei.
In liquid, due to the random motion of molecules, q
is a random value. The average value of (1-3cos2q)
is zero for all possible directions. In solids, the (1-3cos2q)
is not zero since molecule can not move freely. Hd-d is the major
line-broadening factor. In order to narrowing the line, the CP/MAS (Cross
Polarization/ Magic Angle Spinning) probe is designed so that the angle between
sample tube and field is 54.7 degree. The term (1-3cos2q)
in the equation will be zero when q
is equal to 54.70
(Refer to Magic Angle) G.
Cross Polarization (CP) The
presence of strong dipole coupling between rare spin (such as 13C)
and abundant spin (such as 1H) in solids or the presence of scalar J
coupling (JC-H) in liquids can be used to enhance the sensitivity of
the rare spin observation under an appropriate conditions. Cross
Polarization or Polarization Transfer is very important technique to observe
chemical shift correlation between two different nuclei, to observe very
insensitive nuclei coupled to proton, such as 15N.
The key to this type of experiment is that the signal of the nucleus that
we observe in t2 in somehow modulated by the chemical shift of one or more other
nuclei through the polarization transfer.
H.
Nuclear Overhauser Effect (NOE) A
change in the integrated NMR absorption intensity of a spin when the NMR
absorption of another spin is saturated is know as the Nuclear Overhauser Effect
(NOE). It depends on the observing field and mobility in solution of the
molecule under study. The NOE is a very important tool for determination of the
distance between spins. The
NOE is characterized by an enhancement factor:
Where
I0 is the intensity of a peak without irradiation of the other spin,
and I with irradiation. The maximum NOE in liquid is:
Where gi is the magnetogyric ratio of irradiating nucleus; go is that of observed nucleus. For homonuclear, the maximum NOE is 0.5. For heteronuclear, the NOE depends on the value of g and its sign. One very important application of NOE is enhancement of S/N when the go is low. In some case, even if the observing nucleus is not directly connected to protons, it could help to develop a potential intermolecular NOE enhancement by dissolving the compound in a protonated solvent, rather than a pure deuterated solvent. Table
of Magnetogyric Ratio
I.
Magnetic Field Strength and Transmitter Frequency The
nature action of a nuclear spin in a magnetic field, whether a static field (The
magnetic field generated by a DC current in a coil) or an oscillatory field (The
magnetic field generated by an AC current in a coil) is that of precession,
likes a top. The frequency of precession depends on the strength of the field.
For example, a TMS proton signal will be at the frequency of 100,000,000 Hz in a
static field (2.34874 Tesla), a water proton will be at the frequency of
100,000,480 Hz (100,000,000 + 4.80ppm ´ 100Hz). If the instrument has a 100,000,000
Hz transmitter, then the TMS signal will be at the frequency of 0.0 Hz, i.e. on
resonance (at 0.0 ppm) and the water signal has a frequency of 480Hz.
The difference between two signals is 4.8 ppm. If the static magnetic
field is 2.3380 Tesla, transmitter frequency is set to 99.6 MHz. If we still set
reference to TMS as 0.0 ppm, the water signal will still 4.8 ppm away from TMS,
but at this filed 1 ppm is equal to 99.6 HZ, rather 100 Hz. At this point we
know it is important when a internal reference is selected. In most case, the
residual amount of CHCl3 in CDCl3 is enough as reference. Sometimes, however the
signals may overlap, it is hard to determine the reference peak. A good practice
is inert a external reference by using coaxial tube.
J. Laboratory Frame and Rotating Frame A
laboratory Frame is refer to XYZ axis. In convention, the spin precesses along
the Z axis with Larmor Frequency in a magnetic field. Rotating Frame is an
imaginary frame refer to X’Y’Z’ axis which precesses as the same frequency
as an observe spin. In the other words, the spin in the rotating frame is
stationary in a fixed magnetic field. When a B1 along the X axis is
applied to the spin, the spin will rotate around the X’ axis. So the spin
manipulation is much simplified comparing with in the laboratory frame.
Figure 2 - 8. (A) Spins process in a static magnetic field under the laboratory frame; (B) Spins process in a static magnetic field under rotating frame; (C) Spins rotate in an oscillatory field along the X’; (D) Spins rotate in an oscillatory field along the Y’. The w1 is the frequency depending on the strength of the filed of B1.
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