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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5925_Библиотеки_им_академика_М_И_Перельмана.pdf
10.2 Principle of NMR 441
Fig. 10.1 Schematic representation of nuclear spin distribution in NMR. The schematic shows the
distribution of nuclear spins during various stages of an NMR experiment. (a) In the absence of an
external magnetic field, nuclear spins are randomly oriented, exhibiting no preferred alignment. (b)
Upon application of an external magnetic field (H₀), the nuclear spins align either parallel (lower
energy) or antiparallel (higher energy) to the field direction. (c) After applying a radiofrequency
pulse, some spins are “flipped” into the higher energy state (antiparallel), creating an imbalance in
population distribution. This shift allows for the detection of nuclear magnetic resonance as the
spins relax back to their equilibrium state. The arrows represent the direction of the spins relative to
the magnetic field, while the circular yellow lines indicate the precession of the nuclei. The red
check marks highlight spins that are flipped to the higher energy state. (Image source: Google)
their lower energy state to a higher energy state. The absorption of energy during this
process, known as nuclear magnetic resonance, is highly dependent on the chemical
environment and properties of nuclei, providing crucial information about molecular
structure, composition, and dynamics. After the RF pulse is turned off, the excited
nuclei relax back to their lower energy state, emitting RF signals that are detected
and processed to generate NMR spectra. The princ
concept of magnetic resonance, which is the basis
iple relies on the fundamental
for this powerful analytical
technique widely used in chemistry, biochemistry, and other scientific fields for
structural elucidation and chemical analysis.
10.2.1 Resonance
In the context of NMR spectroscopy, resonance refers to the condition in which the
energy of an external RF pulse matches the energy difference between two quantized
spin states of a nucleus placed in a magnetic field.
Nuclear-spin states: Nuclei with nonzero spin (such as
two energy states when subjected to a strong external magnetic field:
• Lower energy state (α): When the nuclear magnetic moment is aligned parallel to
the magnetic field.
• Higher e
nergy state (β): W
hen the nuclear magnetic moment is aligned antipar-
allel to the magnetic field.
Energy differenc
e: The energy difference (ΔE) between these two states is
proportional to the strength of the magnetic field (B
1
) and is given by the equation:
0
H and
13
C) can exist in
442 10 Comprehensive Insights into Nuclear Magnetic Resonance Spectroscopy
ΔE = h × γ × B
0
where:
• h is Planck’s constant,
• γ is the gyromagnetic ratio (a property specific to the type of nucleus), and
is the strength of the external magnetic field.
• B
0
Resonance condition: To excite the nuclei from the lower energy state to the
higher energy state, the frequency of the applied RF pulse must match the resonance
frequency (V
When the RF frequency matches V
), which is determined by the energy difference:
0
ΔE
γ × B
V
=
0
h
, the nuclei absorb energy and transition to the
0
0
=
2π
higher energy state, a process referred to as resonance.
Relaxation and signal detection: After the RF pulse is turned off, the excited nuclei
relax back to their lower energy state, releasing energy in the form of an RF
signal. This emitted signal is detected by the NMR instrument. The relaxation
processes (T1 and T2) affect the timing and intensity of the detected signals.
Chemical shift and resonance: The resonance frequency can be influenced by the
electronic environment surrounding the nucleus, leading to shifts in the resonance
position know n as chemical shifts. These shifts provide valuable information
about the chemical structure and environment of the molecule.
Multidimensional resonance: In multidimensional NMR techniques, resonance can
also refer to the correlation between different types of nuclei or interactions,
allowing for more complex structural insights.
10.2.2 Spin
Spin is a fundamental property of atomic nuclei that plays a crucial role in NMR
spectroscopy. Spin is a quantum mechanical property of particles, including atomic
nuclei, that can be thought of as a form of intrinsic angular momentum. It is
characterized by a specific value, usually expressed in terms of the spin quantum
number (I). For instance,
spin of 1/2.
Magneti
oments: The spin of a nucleus generates a magnetic moment, which
c m
behaves like a tiny magnet. This magnetic moment is oriented in relation to the
applied magnetic field. Nuclei with nonzero spin (odd-numbered isotopes) can exist
in multiple orientations relative to an external magnetic field.
Orientation in a magnetic field: When placed in an external magnetic field (B
the magnetic mom ents of the nuclei align in one of two ways:
1
H has a spin quantum number of 1/2, while
13
C also has a
0
),
10.2 Principle of NMR 443
• Parallel alignment (lower energy state): The magnetic moment aligns with the
magnetic field, resulting in a lower energy state (α state).
• Antiparallel alignment (higher energy state): The magnetic moment aligns
against the magnetic field, resulting in a higher energy state (β state).
Energy levels and resonance: When an RF pulse is applied at a frequency that
matches this energy difference, nuclei can be excited from the lower energy state to
the higher energy state, a process known as resonance.
Relaxation processes: After excitation, nuclei return to their lower energy state
through relaxation processes:
• T1 relaxation (spin–lattice relaxation): Involves energy exchange between the
excited nuclei and the surrounding lattice (molecular environment).
• T2 relaxation (spin–spin relaxation): Involves loss of coherence among spins due
to interactions wi th nearby nuclei.
Applications of spin in NMR: The principles of spin are fundamental to
interpreting NMR spectra. The chemical shifts, coupling constants, and relaxation
times all depend on the spin properties of the nuclei involved. Understanding spin
dynamics allows researchers to probe molecular structures, conformations, and
dynamics in various fields, including chemistry, biochemistry, and medicine.
10.2.3 Spin–Lattice Relaxation
Spin–lattice relaxation, commonly referred to as T1 relaxation, is one of the two
primary relaxation processes in NM R spectroscopy. It describes the mechanism by
which excited nuclear spins return to thermal equilibrium with their surrounding
environment, known as the “lattice.” T1 relaxation is the process by which the
longitudinal magnetization of nuclear spins returns to its equilibrium state after
being disturbed by an external RF pulse. It is characterized by the time constant
T1, which represents the time required for the longitudinal magnetization to recover
approximately 63% of its equilibrium value.
Mechanism of T1 relaxation: When an RF pulse is applied, nuclear spins are
excited to a higher energy state, disrupting their equilibrium. During T1 relaxation,
the spins transfer energy to the surrounding lattice (the molecular environment),
allowing them to lose energy and return to their original state. Relaxation occurs
through interactions between the spins and the lattice, which can involve:
• Molecular motion:
tate energy exchange.
• Vibrational energy transfer: Spins may also interact with vibrational modes of the
surrounding molecules, aiding in the transfer of energy.
Rotational
and translational motions of molecules can facili-
444 10 Comprehensive Insights into Nuclear Magnetic Resonance Spectroscopy
Factors Affecting T1 Relaxation
• Temperature: Higher temperatures generally increase molecular motion, which
can lead to shorter T1 times as energy is transferred more efficiently.
• Chemical environment: The presence of different chemical groups and molecular
conformations can influence T1 relaxation times by altering interactions with the
lattice.
• Field strength: Higher magnetic field strengths often
lead to
longer T1 relaxation
times, as the energy gap between the spin states increases, reducing the probability of relaxation.
• Viscosity: In more viscous environments, molecular motion is restricted, poten-
tially leading to longer T1 times.
Importance of T1 relaxation: T1 relaxation times provide valuable information about
molecular dynamics and interactions within a sample. They can help characterize
different types of environments in complex mixtures, such as biological tissues or
chemical compounds. In medical imaging, particularly in magnetic resonance
imaging (MRI), T1 relaxation times are used to differentiate between various
tissues based on their relaxation properties. This differentiation helps in
diagnosing conditions and understanding tissue health.
T1 measurement: T1 relaxation times can be measured using various techniques
such as inversion recovery experiments. In these experiments, an initial inversion
pulse is applied to invert the spins, and the recovery of the longitudinal magnetization is monitored over time.
10.2.4 Spin–Spin Relaxation
Spin–spin relaxation, commonly referred to as T2 relaxation, is one of the two
primary relaxation processes in NMR spectroscopy. It describes how the coherence
among nuclear spins is lost over time due to interactions with neighboring spins. T2
relaxation is the process by which the transverse magnetization of nuclear spins
decreases due to interactions between nearby spins after an external RF pulse has
been applied. It is characterized by the time constant T2, which represents the time
required for the transverse magnetization to decay to approximately 37% of its initial
value after the RF pulse.
Mechanism
excited and aligned in the transverse plane, creating coherent magnetization. However, over time, the spins begin to precess at slightly different frequencies due to
variations in their local magnetic environments, primarily influenced by neighboring
spins. This loss of coherence among the spins leads to a decrease in the overall signal
intensity, resulting in T2 relaxation. T2 relaxation is fundamentally a result of spin–
spin interactions or dipole–dipole coupling, where the magnetic fields of nearby
spins influence each other.
of T2 relaxation: When an RF pulse is applied, nuclear spins are
10.2 Principle of NMR 445
Factors Affecting T2 Relaxation
• Molecular environment: The chemical structure and interactions of the molecules
can significantly affect T2 relaxation times. More complex environments with
strong interactions tend to lead to shorter T2 times.
• Magnetic field strength: Higher magnetic fields can enhance the
resonance
frequencies, potentially leading to longer T2 times, although this is not
separation of
always straightforward.
• Viscosity: In more viscous solutions, molecular motion is restricted, which can
lead to longer T2 times as spins remain more coherent.
• Temperature: Generally, higher temperatures increase molecular motion and
interactions, which can lead to shorter T2 relaxation times.
Importance of T2 relaxation: T2 relaxation times are crucial for understanding
molecular dynamics and interactions in samples. They can provide insights into
molecular motion, conformational changes, and the effects of different
environments. In MRI, T2 relaxation times are used to differentiate between
various tissues and conditions. Tissues with shorter T2 times appear darker on
T2-weighted images, while those with longer T2 times appear brighter.
T2 measurement: T2 relaxation times can be measured using techniques such as
spin–echo experiments. In these experiments, an initial RF pulse is applied,
followed by a second pulse that refocuses the spins, allowing for the measurement
of transverse magnetization decay over time.
10.2.5 Spin–Spin Coupling
Spin–spin coupling, also known as J-coupling, is a phenomenon in NMR spectroscopy that arises from interactions between nuclear spins. This interaction leads to the
splitting of NMR signals into multiple peaks, providing valuable information about
the structure and dynamics of molecules. Spin–spin coupling refers to the interaction
between the magnetic moments of nonequi valent nuclear spins that are in close
proximity to each other. This interaction affects the resonant frequencies of the
nuclei, causing splitting of their signals in the NMR spectrum.
Mechanism of spin–spin coupling: The coupling occurs through magnetic dipole–
dipole interactions or through indirect interactions mediated by chemical bonds
(known as through-bond coupling). When two nuclei are coupled, the magnetic
field generated by one nucleus influences the effective magnetic field experienced by
the other nucleus. As a result, the resonant frequency of the coupled nuclei is
modified based on their relative orientations and the distance between them.
Types of Coupling
• Scalar coupling (J-couplin
where the interaction occurs through bonds. The coupling constant J (measured in
Hz) quantifies the strength of the coupling.
g): The most common form of spin–spin coupling,
446 10 Comprehensive Insights into Nuclear Magnetic Resonance Spectroscopy
• Dipolar coupling: A direct interaction between the magnetic moments of two
nuclei, significant in solid-state NMR but usually averaged out in solution due to
molecular motion.
Multiplet formation: In the presence of spin–spin coupling, NMR signals are split
into multiple peaks, creating multiplets. The number of peaks in a multiplet is
determined by the number of neighboring equivalent spins, according to the n + 1
rule. If a nucleus has n equivalent neighboring nuclei, its signal will split into n + 1
peaks. The relative intensities of the peaks in the multiplet can also provide information about the number of neighboring spins.
Coupling constants (J values): The coupling constant J is a key parameter in
spin–spin coupling, representing the interaction stre ngth between coupled spins. It
can vary depending on:
• The type of nuclei involved (e.g.,
1
H–H, 1 H–
13
C),
• The nature of the chemical bonds and molecular geometry, and
• The chemical environment surrounding the spins.
Applications of spin–spin coupling: Spin–spin coupling is essential for deducing
molecular structures from NMR spectra. The pattern of splitting, the number of
peaks, and the coupling constants provide insights into the connectivity and arrangement of atoms in a molecule. It is particularly useful in identifying functional groups,
determining stereochemistry, and analyzing complex molecular systems.
Example of spin– spin coupling: In a simple molecule such as ethyl acetate (CH₃–
COO–CH₂–CH₃), the proton signals from the methyl (CH₃) and methylene (CH₂)
groups exhibit splitting due to coupling with neighboring protons:
• The CH₃ has three equivalent
protons
that couple with the two protons of the
adjacent CH₂, resulting in a triplet (n + 1 = 2 + 1= 3).
• Converse ly, the methylene group (CH₂) is split into a quartet due to coupling with
the three protons of the adjacent methyl group (n + 1 = 3 + 1 = 4).
10.2.6 Nuclear Overhauser Enhancement
Nuclear Overhauser enhancement (NOE) is a phenom enon in NMR spectroscopy
that allows for the enhancement of the NMR signals of certain nuclei through
interactions with neighboring nuclei. It is a powerful tool for elucidating threedimensional structures of molecules and understanding molecular dynamics. NOE
refers to the increase in the intensity o f an NMR signal of a nucleus when the
population of its neighboring nuclei is selectively manipulated through RF pulse.
This enhancement occurs due to cross-relaxation between spins, leading to a transfer
of magnetization from one nucleus to another.
10.2 Principle of NMR 447
10.2.6.1 Mechanism of NOE
The mechanism behind NOE involves two main processes:
• Spin–lattice relaxation (T1): When a nucleus experiences a change in its popula-
tion due to an RF pulse, it can influence the relaxation of nearby nuclei. This
influence can enhance the population difference of the observed nucleus.
• Dipole– dipole interactions: NOE relies on the spatial proximity of nuclear spins,
typically within 5 Å. The interactions between spins in close proximity lead to
changes in the relaxation rates of the nuclei involved.
10.2.6.2 Types of NOE
• Positive NOE: Occurs when the enhancement of the observed signal of a nucleus
is due to the presence of a neighboring nucleus. This often happens when the
observed nucleus is in a favorable spatial arrangement relative to the enhancing
nucleus.
• Negative NOE: Occurs when the intensity of the observed signal of a
decreases
the neighboring spins are in anticorrelation or when the populations are inversely
related.
due to the manipulation of a neighboring nucleus. This can occur when
nucleus
10.2.6.3 Applications of NOE
• Structure elucidation: NOE is particularly useful in determining the three-
dimensional structure of molecules, especially in proteins and other
biomolecules. By observing the NOE between specific nuclei, researchers can
infer spatial relationships and interactions.
• Distance measurement: NOE can be used to estimate distances between
non-bonded atoms in a molecule, providing valuable information about
conformations and interactions.
• Dynamic studies: NOE can reveal information about molecular dynamics and
conformational changes by monitoring how the NOE pattern changes under
different conditions (e.g., temperature, solvent).
10.2.6.4 NOE Experiments
Common experimental techniques that utilize NOE include:
• NOESY (nuclear Overhauser effect spectroscopy): A 2D NMR technique that
provides information about the spatial proximity of nuclei. It is particularly useful
in studying large molecules and biomolecules.
• ROESY (rotating frame Overhauser effect spectroscopy): Similar to NOESY but
provides different kinds of information, particularly useful in cases where fast
molecular motion occurs.
10.2.6.5 Limitations of NOE
• Distance dependence: NOE is most effective for measuring distances within
approximately 5 Å, beyond which the effect diminishes.
448 10 Comprehensive Insights into Nuclear Magnetic Resonance Spectroscopy
• Complexity in interpretation: In complex mixtures or large biomolecules,
interpreting NOE data can be challenging due to overlapping signals and multiple
interactions.
10.3 Nuclear Shielding
Nuclear shield ing is a fundamental concept in NMR spectroscopy that describes how
the electronic environment surrounding a nucleus affects its resonant frequency in an
external magnetic field. This phenomenon is crucial for understanding chemical
shifts and interpreting NMR spectra. Nuclear shielding refers to the reduction of the
effective magnetic field experienced by a nucleus due to the presence of surrounding
electrons. This effect alters the resonance frequency of the nucleus in an external
magnetic field.
10.3.1 Mechanism of Nuclear Shielding
In the presence of an external magnetic field, electrons surrounding a nucleus
generate their own magnetic fields due to their motion. The magnetic fields created
by these electrons can partially oppose the external magnetic field, leading to a
decrease in the effective field experienced by the nucleus. This results in the
shielding of the nucleus.
Chemical shifts: The degree of nuclear shielding is reflected in the chemical shift,
which is the difference in resonance frequency of a nucleus relative to a standard
reference (typically tetramethylsilane, TMS, for
frequency (ν) of a nucleus is influenced by its shielding constant (σ): ν(observed) = ν(reference) × (1 - σ).
When a nucleus is more shielded (higher electron density around it), its resonance
frequency decreases, resulting in a lower chemical shift value (more downfield).
Conversely, when a nucleus is less shielded, it experiences a higher frequency
(higher chemical shift).
1
H and
13
C NMR). The resonance
10.3.2 Factors Affecting Nuclear Shielding
• Electronegativity of surrounding atoms: Nuclei adjacent to highly electronegative
atoms (such as oxygen or nitrogen) are typically deshielded because these atoms
attract electrons, reducing electron density around the nucleus.
• Hybridization: The hybridizat
example, sp-hybridized carbons are more deshielded than sp
• Steric effects:
The spati
tion and thus the degree of shielding.
• Conjugation and
resonance: Delocalization of electrons through conjugated
systems can lead to changes in shielding.
ion state
of the atom can influence shielding. For
2
or sp3 carbons.
al arrangement of atoms can affect the electronic distribu-
10.4 Chemical Shielding 449
10.3.3 Applications of Nuclear Shielding
• Structure determination: Analyzing chemical shifts in NMR spectra allows
chemists to deduce information about molecular structures, functional groups,
and the electronic environment of specific nuclei.
• Functional group identification: Different functional groups exhibit characteristic
chemical shifts, aidi
the identification of compounds.
ng in
• Dynamic studies: Changes in shielding can provide insights into molecular
dynamics, conformational changes, and interactions within a molecule.
10.3.4 Shielding and Deshielding Effects
• Shielding : Increased electron density around a nucleu s leads to a lower chemical
shift (more shielded). For example, a CH
• Deshielding: Decreased electron density leads to higher
is typically more shielded than a C=O.
3
chemical
shifts (less
shielded). For example, protons on a carbon adjacent to an electronegative atom
will appear downfield due to deshielding.
10.4 Chemical Shielding
Chemical shielding is a specific aspect of nuclear shielding in NMR spectroscopy
that refers to the effect of the electronic environment surrounding a nucleus on its
resonance frequency. It plays a crucial role in determining chemical shifts and
interpreting NMR spectra. Chemical shielding describes how the local electron
density surrounding a nucleus affects its effective magnetic field when exposed to
an external magnetic field. The degree of shielding influences the resonance frequency of the nucleus, leading to variations in the chemical shifts observed in NMR
spectra.
10.4.1 Mechanism of Chemical Shielding
When an external magnetic field is applied, electrons surrounding a nucleus generate
their own magnetic field due to their motion. This induced magnetic field can either
enhance (shield) or oppose (deshield) the external magnetic field experienced by the
nucleus:
• Shielding : When
the induce
the effective field experienced by the nucleus, resulting in a lower frequency of
resonance and a smaller chemical shift.
• Deshielding: Conversely,
field, the nucleus experiences a higher effective field, leading to a higher frequency of resonance and a larger chemical shift.
d magnetic field opposes the external field, it reduces
if the induce d magnetic field enhances the external
450 10 Comprehensive Insights into Nuclear Magnetic Resonance Spectroscopy
10.4.2 Chemical Shifts and Shielding Constants
The δ is a quantitative measure of the resonance frequency difference of a nucleus
relative to a standard reference, often expressed in ppm. It can be affected by the
chemical shielding constant (σ):
reference
- V
observed
ðÞ=V
δ = V
reference
× 10
6
A higher σ indicates greater electron density around the nucleus, leading to a
lower chemical shift (more shielded). Conversely, a lower shielding constant
indicates reduced electron density and a higher chemical shift (less shielded).
10.4.3 Factors Affecting Chemical Shielding
• Electronegativity of nearby atoms: Nuclei adjacent to electronegative atoms (such
as oxygen or halogens) are typically deshielded due to electron withdrawal,
resulting in downfield shifts.
• Hybridization: The hybridization state of carbon can affect chemical shifts. For
example:
– sp-hyb
ridized carbons
are generally more deshielded than sp
2
or sp3 carbons
due to greater s-character.
• Conjugation and resonance: Delocalization of electrons in
conjugated
systems
can lead to changes in shielding, often resulting in distinctive chemical shifts.
• Steric effects: The spatial arrangement of atoms and the presence of bulky groups
can affect the electronic environment and consequently the shielding.
10.4.4 Applications of Chemical Shielding
• Molecular structur e determi nation: Analyzing chemical shifts in NMR spectra
helps chemists infer the structure and functional groups present in a molecule.
• Functional group identificati
on: Differe
chemical shifts, aiding in compound identification.
• Dynamic s
tudies: Monit
oring changes in chemical shifts can provide insights into
molecular dynamics, conformational changes, and interactions.
nt functional groups have characteristic
Example
of chemical shielding: In a simple molecule such as ethanol (CH₃CH₂OH),
the protons on the CH₃ are more shielded than the protons on the OH due to the
electronegativity of oxygen. As a result, the chemical shift of the hydroxyl proton
appears downfield (higher ppm) compared to the methyl protons.