Resonancia magnética nuclear de protones y carbono 13

Elucidation of Chemical Structures
Summary
• Nuclear spin states
• The mechanism of absorption (resonance)
• The chemical shift and shielding
• The nuclear magnetic resonance spectrometer
• Chemical equivalence
• Integrals and integration
• Chemical environment and chemical shift
• Local diamagnetic shielding
• Magnetic anisotropy
• SPIN–SPIN SPLITTING (n + 1) RULE
• The origin of spin–spin splitting
• Pascal’s triangle
• The coupling constant
Bibliography
Introduction to Spectroscopy (2015) Donal L. Pavia, Gary M. Lampman and James R. Vyvyan
Fifth Edition, Editorial: Cencage learning. EEUU. Chapter 5. Pages 215-288.
Unit IV: NMR spectroscopy

Nuclear Magnetic Resonance (NMR)
• Nuclear magnetic resonance (NMR) is a physical phenomenon based on the
quantum-mechanical properties of atomic nuclei.
• It is a technique used mainly in the elucidation of chemical structures.
• The phenomenon of resonance only manifests itself in the presence of a magnetic
field that differentiates in terms of energy the possible orientations of the nuclear
magnetic moment.
• The amounts of energy involved are extremely small and are only measurable when
the magnetic field is very strong. The electromagnetic radiation used corresponds
to radio waves.

Nuclear spin states
• Many atomic nuclei have a property called spin: the nuclei behave as if they were spinning. In fact, any atomic
nucleus that possesses either odd (impar) mass, odd atomic number, or both has a quantized spin angular
momentum and a magnetic moment.
• For each nucleus with spin, the number of allowed spin states it may adopt is quantized and is determined by its
nuclear spin quantum number I.
• For each nucleus, the number I is a physical constant, and there are 2I + 1 allowed spin states with integral
differences ranging from +I to −I. The individual spin states fit into the sequence:

Nuclear magnetic moments
• However, the spin states are not of equivalent energy when a magnetic field is applied because the nucleus is a charged particle
and any moving charge generates a magnetic field of its own.
• The nucleus has a magnetic moment µ generated by its charge and spin.
• A hydrogen nucleus may have a clockwise (+½) or counterclockwise (-½) spin, and the nuclear magnetic moments (µ ) in the two
cases are pointed in opposite directions. In an applied magnetic field, all protons have their magnetic moments either aligned
with the field or opposed to it.
• Hydrogen nuclei can adopt only one or the other of these orientations with respect to the applied field. The spin state +½ is of
lower energy since it is aligned with the field, while the spin state -½ is of higher energy since it is opposed to the applied field.

Absorption of energy
• The phenomenon of nuclear magnetic resonance occurs
when nuclei aligned with an applied field are induced to
absorb energy and change their spin orientation with respect
to the applied field.
• Energy absorption is a quantized process, and the energy
absorbed must be equal to the energy difference between
the two states involved.
• In practice, this energy difference is a function of the strength
of the applied magnetic field B0.The stronger the applied
magnetic field, the greater the energy difference between
the possible spin states.
• The magnitude of the separation of the energy levels also
depends on the nucleus in question. Each nucleus has a
different ratio between magnetic momentum and angular
momentum, since each has a different charge and mass. This
ratio, called the magnetogyric ratio γ, is a constant for each
nucleus and determines the energy dependence of the
magnetic field.
• Therefore this constant must be considered in the equation.
Moreover the angular momentum of the nucleus is quantized
in units of h/2∏, if we solve for the frequency of the
absorbed energy the final equation takes the form of:

Absorption of energy

The mechanism of absorption (resonance)
Protons absorb energy because they begin to precess in an applied magnetic field, i.e. to move like a spinning
top. When the magnetic field is applied, the nucleus begins to precess around its own spin axis with an
angular frequency, which is called its Larmor frequency. The precession frequency of a proton is directly
proportional to the strength of the applied magnetic field; the stronger the applied field, the higher the rate
(angular frequency w) of precession. Since the nucleus has charge, precession generates an oscillating electric
field of the same frequency. If radio frequency waves of this frequency are supplied to the precessing proton,
the energy can be absorbed. That is, when the frequency of the oscillating electric field component of the
incoming radiation matches the frequency of the electric field generated by the precessing nucleus, the two
fields can couple and energy can be transferred from the incoming radiation to the nucleus, thus causing a
spin shift. This condition is called resonance, and the nucleus is said to have resonance with the incoming
electromagnetic wave.
B0

The differences are very small, in the parts per million range

Population densities of nuclear spin states
The thermal energy resulting from the ambient temperature is sufficient to populate
these two energy levels, since the energy separation between the two levels is small.
However, there is a slight excess of nuclei in the lower energy spin state. It is the excess
nuclei that allow the resonance to be observed. When radiation is applied, not only are
upward transitions induced, but also downward transitions are stimulated. If the
populations of the upper and lower states are exactly equalized, we do not observe any
net signal. This situation is called saturation. Care must be taken to avoid saturation when
performing an NMR experiment. Saturation is quickly reached if the power of the RF
signal is too high.Therefore, the very small excess of nuclei in the lowest spin state is quite
important for NMR spectroscopy, and we can see that very sensitive NMR instrumentation
is required to detect the signal.

Population densities of nuclear spin states
• If we increase the operating frequency of the NMR
instrument, the energy difference between the two
states increases, which causes an increase in this
excess. Table 5.3 shows how the excess increases
with operating frequency. It also clearly shows why
modern instrumentation has been designed with
increasingly higher operating frequencies.
• The sensitivity of the instrument is increased, and
the resonance signals are stronger, because more
nuclei can undergo transition at higher frequency.
Before the advent of higher-field instruments, it was
very difficult to observe less-sensitive nuclei such as
carbon-13, which is not very abundant (1.1%) and
has a detection frequency much lower than that of
hydrogen

The chemical shift and shielding
Diamagnetic anisotropy—the diamagnetic shielding of a nucleus
caused by the circulation of valence electrons.
Bef = B0 - Bin
Bo – applied magnetic field
Bin – induced magnetic field
Bef – effective magnetic field

The chemical shift and shielding

The nuclear magnetic resonance spectrometer
It consists of four parts:
1. A stable magnet, with a driver that produces a
precise magnetic field.
2. A radio frequency transmitter, capable of emitting
precise frequencies.
3. A detector to measure the RF energy absorption
of the sample.
4. A computer and a recorder to make the graphs
that make up the NMR spectrum.

The Continuos Wave Instrument
• The CW NMR spectrometer uses a constant-frequency RF signal and varies the magnetic field strength.
• As the magnetic field strength is increased, the precessional frequencies of all the protons increase. All protons are different!
• When the precessional frequency of a given type of proton reaches 60 MHz, it has resonance.
• In the case of 1H nuclei, each distinct type of proton (phenyl, vinyl, methyl, and so on) is excited individually, and its resonance peak
is observed and recorded independently of all the others. As we scan, we look at first one type of hydrogen and then another,
scanning until all of the types have come into resonance.
The sample is dissolved in a solvent containing no interfering protons (usually CDCl3), and a small amount of TMS (IR).
The RMN spectrometer
angular frequency ω

The Pulse Fourier Trasnform Instrument
• An alternative approach is to use a powerful but short burst (ráfaga
corta) of energy, called a pulse, that excites all of the magnetic
nuclei in the molecule simultaneously. All of the nuclei are induced
to undergo resonance at the same time.
• Ex: an instrument with a 2.1 Tesla magnetic field uses a short (1 to
10 μsec) burst of 90-MHz energy to accomplish this. The source is
turned on and off very quickly, generating a pulse.
• The pulse actually contains a range of frequencies centered about
the fundamental.
• This range of frequencies is great enough to excite all of the distinct
types of nuclei in the molecule at once with this single burst of
energy.
• When the pulse is discontinued, the excited nuclei begin to lose
their excitation energy and return to their original spin state, or
relax. As each excited nucleus relaxes, it emits electromagnetic
radiation.
• Extract the individual frequencies due to different nuclei by using a
computer and a mathematical method called a Fourier transform
(FT) analysis is applied to obtain the spectrum.
• The pulsed FT method has several advantages over the CW method:
is more sensitive and faster

Resonancia magnética nuclear de protones y carbono 13

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