Nuclear Magnetic Resonance an analytical tool in Physical Chemistry

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Nuclear Magnetic Resonance-an analytical tool in
Physical Chemistry-

• Todays lecture
• Physical underpinnings to NMR
• Integration and quantitative aspects
• The Chemical Shift
• The interplay of kinetic and equilibria phenomena
  in NMR measurements.
• The investigation of an equilibrium behavior in
  the Physical Chemistry Lab. Before class/lab,
  read and understand the lab writeup for the NMR
  experiment.

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Background Reading

• Go to the link below
• http//astro.temple.edu/7Edebrosse/
• Here, read specifically
• the UserGuide for the Inova300
• Guide to moving NMR data to PCs
• UserGuide for NUTS, the offline NMR data
  processing software
• Also read
• The PChem lab writeup NMRPchemLab.doc

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What is NMR Spectroscopy?

• Nuclear Magnetic Resonance
• Radio Frequency Absorption Spectra of atomic
  nuclei in substances subjected to magnetic
  fields.
• Spectral Dispersion is Sensitive to the chemical
  environment via coupling to the electrons
  surrounding the nuclei.
• Interactions can be interpreted in terms of
  structure, bonding, reactivity

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NMR-What is it Good For?(absolutely everything!)

• Solving structures of compounds like synthetics,
  impurities, natural products
• Identifying metabolites
• Stereochemical determination
• Follow reactions
• Validating electronic theory trends within
  series of compds.
• Kinetics
• Extended structure, e.g. protein nmr
• Molecular interactions e.g. ligand binding
• Acid-base questions
• Purities
• Mechanisms, e.g. isotope distributions, other
  effects
• Questions about the solid state
• Imaging
• Todayss focus, NMR as an Analytical Tool for
  quantifying mixtures

Based on what you know from sophomore organic,
you would think that NMR is really just for
fingerprinting organic structures, and
determining their structures!
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What are the Measurables in NMR?

• Intensity (analytical parameter, proportional to
  molarity)
• Chemical Shift (the electronic surroundings)
• Couplings (scalar J and dipolar D bond paths,
  angles connectivity and distances)
• Relaxation parameters (motions, distances)

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Origin of the NMR Effect

• Nuclei with other than A(protonsneutrons) and
  Z(protons) both even numbers, possess net spin
  and associated angular momenta
• Reveals itself only in magnetic field. As usual,
  such momenta are quantized
• States have different energies, populated
  according to Boltzmann distribution
• States are 1/2, 3/2, 5/2for A odd number and
  integer if A even number and Z odd number
• Transitions of individual nuclei between spin
  states is possible (both directions) leading to
  an equilibrium of populations
• Number of states is 2I 1
• Many elements have NMR active nuclei.
• Those elements like 1H, 13C, 31P, 19F are the
  most popular and accessible because they have
  spin I 1/2, and this makes their NMR signals
  narrow and relatively easy to measure and
  interpret.

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Why NMR?

• Unmatched versatility as an Analytical technique
• High on chemical information content
• Significant interpretability
• Interpretable at several levels of sophistication
• Response related to molar preponderance
• These attributes are true for solids, liquids,
  mixtures, and to a small extent, gas phase
• More than half the periodic table has at least
  one NMR active isotope

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But on the other Hand

• NMR is one of the least sensitive analytical
  methods
• Characterized by long relaxation time constants,
  limiting experimental efficiency in real time
• Sometimes too much information. Can be demanding
  on interpretation skill
• Relatively Expensive compared with other
  analytical methods
• As with other methods NMR has blind spots and
  cannot serve as an analytical panacea

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The Chemical Shift

• The Chemical shift makes NMR useful in Chemistry
  (they named it after us)
• Arises from the electrons surrounding our nuclei,
  responding to a magnetic field.
• Induced circulation of electrons, Lenzs law
  this circulation generates a small magnetic field
  opposed to H0
• The small negative field diminishes the H0
  experienced by a nucleus. This differentiates
  sites, based on chemical nature
• Effect grows directly proportional to H0

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A Picture of this
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How many signals do we Expect in an NMR Spectrum?

• The Chemical shift implies that we see
  (potentially) a different signal for every
  different chemical environment.
• Chemical environment here is the electronic
  structure (electrons, hybridization, charge,
  polarizability etc.) These are all things able
  to be predicted to some extent by theory.
• What do we mean by different? (hint symmetry
  is key!)

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Consider the Molecule of Interest for this
Investigation
OH
CH3
Because of the asymmetric carbon center at Ha,
the other ring H are potentially all at different
shifts (each is either on same, or opposite face
from Ha)
O
O
N
H?
H?
H?
H?
H?
H?
H?
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A Vector Picture

• Chemical shift is the ultimate precessional
  frequency of the vector component of M in the
  plane perpendicular to H0

Precesses at a frequency ? This is in units of
(radians)/sec At some time, has distinct angle
and as a vector in x,y can be resolved into x, y
components. The receiver works by counting how
many times this electric vector whizzes past in a
unit of time
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Free Precession, Rotating Frames and the Chemical
Shift

• Our vector picture can help

Now, more than one chemical shift wil move with
just a difference from ?H0
Rotates at ?H0 MHz
Stands Still!
What if we could contrive to measure once every
?H0 seconds? Strobe effect Is The Rotating Frame
Dont have to distinguish 25000002 from 25000005
Hz, but 2 cf. 5
Imagine a blinking eyeball, (strobe effect)
blinks at Larmor frequency
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Practical Theory

• The real triumph of the shift theory is in its
  relationship to electronegativity and
  hybridization and easy prediction of trends based
  on qualitative notions from structural theory.
• Withdrawing electron density diminishes the
  screening ability of the electron cloud and the
  absorbance of the nucleus goes to lower field.
• Feeding in electron density sends nucleus to
  higher field.
• Moving electrons have some real consequences on
  nearby chemical shifts.

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Anisotropic Shielding Near ? Electrons
Pronounced effect for aromatic, in line with e
circulation
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Other Anisotropic Shielding Cones
Nitriles, acetylenes isonitriles
Above, below plane shielded




In plane deshielded



Carbonyl, alkene

• Effects are ca. 2 ppm at most.
• Most Significant when a nucleus is fixed in
  geometry with respect to the neighboring field.
• Best description is in
• L.M. Jackman, S. Sternhell, Applications of
  Nuclear Magnetic Resonance Spectroscopy in
  Organic Chemistry, Pergamon Press, (1969) ch.2

Small pos
C
O
Polarized effect
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This chemical shift anisotropy is the basis for
the separation, and the direction of the
separation of signals in the Lab exercise on
acetylproline
Predict that the H signals for the ? protons will
move to higher shift values when the CO is
pointed at them, compared with the other form
Important point one would have to identify which
signals these are in the spectrum
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What are Spin Systems?
A network of protons of which the members are
mutually J-coupled to some (not necessarily all)
of the nearby protons, via contiguous bonds.
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How Do these Various Features show up in an NMR
Spectrum?
Every different hydrogen in the molecule has (or
is entitled to have) its own chemical shift value
The amount of this value is reflective of the
chemical influence of nearby heteroatoms,
electron deficency etc.
The signals have extra splitting superimposed on
them. This is coupling, caused by the
neighboring Hs. Helps identify which H is which.
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Integration of Signal areas in NMR
Integration as the area under a curve Units are
arbitrary, as the user defines the area
scale. The real units would be mV x Hz but these
numerically are unwieldy. Areas are taken
relative to each other. Generally a recognized
signal known to arise from one 1H is defined as
1.00. Can also add a weighed amount of an
internal reference compound assign an area to
one of its signals, and compare the other signals
to the reference.
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Integrating Spectra
Area is given by the rise between the two level
lines. Here we have used the software to reset
the integral baseline between the two signals
Inegral trails
Signals
Repeated measurements can give us the precision
(rsd)
Then, we use the software scale setting tool to
define the peak at 8 ppm to be 3 units (H). The
value for the other signal is then normalized and
scaled so we know it is about 1 bigger.
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More on Integration
Areas are proportional to molar ratios. Within a
compound, if one signal is 3x another the signals
represent atom counts of 13, e.g a CH, CH3. For
mixtures, if we compare ratios of areas, these
are the molar ratios Can convert to wgt by
multiplying by MW Must compare signals from same
number of Hs or normalize to correct. Example Say
we have a mixture and want to quantify two
components by NMR. If we compare a CH3 group
from compound A with a CH2 group from compound B,
the comparison is not appropriate. (unless we
know that those two signals are CH3 and CH2, and
divide the areas by 3, and 2 respectively before
making the comparison.)
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NMR of Mixtures

• Potentially all the hydrogen atoms are equal to
  each other as chromophores
• Compare with the situation of an HPLC analysis
  detected by means of a UV monitored flow-cell
  (monitoring a given wavelength). To interpret the
  areas of the HPLC peaks, one has to either know
  the response factors for all the compounds at
  that wavelength, (measure in a separate
  experiment) or assume that the responses are all
  identical on a molar basis (dubious at times).
• NMR is good for mixture analysis also because you
  see everything that has hydrogen atoms. If you
  can locate signals that are not overlapped among
  the ingredients in the mixture, you can
  integrate, and obtain ratios of the molar amounts
  present.

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Practical Consequences of Relaxation times for
Quantitative Interpretation
Time constant that limits the repeat rate for NMR
scans. Real concern in comparing disparate
molecular sizes. Solvents vs. moderate size
organics, common example
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A Recent Example from the Chem 314 Lab
Data is the integrated intensity of NMR signals
from Ibuprofen vs an internal std of methylene
chloride. Plots are for varying the delay time
between successive pulses.
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Mixtures at equilibrium
The NMR spectrum would likely show peaks from
compound A, compound B and compound C. Some of
these peaks could be overlapped. The proportions
of these peaks for A, B, C would be related to
how much the scientist put in the sample, and on
the value of Keq
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The Mixture of Interest Here
Every hydrogen in the compound gives a
potentially different signal for the cis, and
trans forms. For these, we can see and integrate
the areas for the two forms as major, minor
components.
(Solvent)
Note here that the Hg, Hb happen to overlap. We
cannot conveniently integrate these separately,
or evaluate the major/minor ratio
Acetyl CH3
Hd
Ha
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A Closer look at the fine structure
The individual peaks within these clusters are
the fine structure due to couplings to nearby Hs
An Expansion of the NMR spectrum for the Ha
region. Each of the compounds two forms shows its
own a hydrogen at a separate chemical shift.
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Assessing Equilibria
The integrated areas, normalized for the number
of contributing signals, can be taken as
proportional to the molarity. All the components
are in the same volume of solution. To use the
example for this lab exercise cis
trans
There are only two compounds in the mixture.
Conc of each is proportional to int. area for
each, normalized.
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Energies and dipole moments of NAcProline
Conformers From ab initio (density functional at
B3LYP/6-31G level of theory) calculations
6.02 debyes -553.8072 h
5.74 debyes -553.5800 h
3.03 debyes -553.8136 h
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Systems Approaching Chemical Equilibrium
A Collorary A system of chemically related
species may or may not be equilibrated. If you
take a repeat spectrum are the ratios unchanged?
Get time distribution curves at different
Temperatures, e.g. Care must be taken that the
time for the measurement is not significant
w.r.t. the chemical time scale.
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Chemical Reactions and Kinetics and NMR
Spectroscopy

• NMR is a powerful technique for exploring
  reactions
• Equilibrium and Kinetics are both accessible
• In solution, we get total chemical picture (of
  NMR active atoms)
• Can evaluate chemical exchange that is not
  accessible through other methods
• Like any mechanistic study, requires controls,
  temperature regulation, careful integration,
  thoughtful interpretation

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Systems in Chemical Equilibrium
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NMR and Kinetics a great fit but
?? (Hz) in NMR is a chemical shift difference
related to the 2 chemical environments
? (Hz) in kinetics is a reciprocal chemical
lifetime
B
A
??
Spectra are affected when the 1/(chemical
lifetime) becomes similar to the ?? that
separates the chemical shifts of the atoms in
exchange. Important corollary Since the chemical
shifts of these two are what is observed, ?? for
the same process will vary with magnet strength.
The same sample, same process, same NMR tube,
same temperature can give two different-appearing
spectra, at two different fields. Chemical
process can be rotation, proton exchange,
isomerization, rearrangement, dissociation or
almost any reaction. Lifetime (sec) can be
expressed as rate. The chemical and the NMR ??s
different numbers!!!
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What is the Picture?
Imagine a chemical species A, in chemical
equilibrium with B, and that they have different
NMR signals (can be proton, carbon phosphorus,
etc.)
A and B are separated in the Spectrum by some
number of Hz. What gives us the ability to see
these as separated peaks? Hint, Hz is a
reciprocal lifetime
Hz?
A
B
Is k near in value to ???
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What is meant by The NMR Time Scale?

• Imagine two signals that are chemically changing
  their identities.
• They have chemical shifts, ?1, ?2
• These shifts are also separated by a given number
  of Hz (???1-?2)
• Remember, that Hz has units of 1/sec.
• The chemical shift difference in Hz can be
  compared to a chemical lifetime or its
  reciprocal the reaction rate constant k. k has
  units of 1/sec.
• If the reaction rate k is faster than ??, we can
  only observe a signal at the average of the two
  chemical shifts. Intensity will be the sum.
• We can address this experimentally by making k
  smaller (lower the temperature) or making ??
  bigger (use a higher field NMR magnet)
• Practically, the relevant time scale for exchange
  here is 10s of msec.

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Take home message
The NMRs ability to see different signals for
compounds that are in chemical exchange is
limited. The limit is determined by the
comparison of the rate (1/lifetime) for the
chemistry, with the separation in Hz of the
related signals.