CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
1. INTRODUCTION.
This course lasts for ten lectures and aims to extend your knowledge of techniques such as
NMR spectroscopy and to introduce techniques which you will not have encountered to date,
such as EXAFS, X-ray crystallography and Electron spin resonance. There is not time to give
an in depth treatment of any of the techniques, since each one could easily be the subject of a
ten lecture course (or more!). Some background theory will be covered in each case to give an
overview of how the technique works and what information it can give, followed by some
examples from the literature to illustrate this. Most of the examples will be from a variety of
areas of inorganic chemistry.
Reading List:
1.
2nd year Identification and Analysis notes.
2.
3rd year spectroscopy notes.
3.
“Structural Methods in Inorganic Chemistry” Cradock, E.A.V. Ebsworth and D.W.
Rankin, Blackwell Scientific Publishers Ltd. 2nd Edition.
4.
Other references to specific examples will be given at the appropriate point.
So where are we coming from?
Preparative chemistry is all about the reaction of known materials to give novel compounds.
Why make novel compounds?
a) new structural types give understanding of fundamentals of chemistry while also
stimulating the development of.....
b) new applications (or improvements on existing applications).
So when a reaction is performed we obtain a series of products...
A + B

C ( + D + E......)
The hope is for a single product in quantitative yield, but this is rarely the case! The initial
action therefore is separation of the components by well known techniques, crystallisation,
distillation (sublimation), chromatography etc.
Next on the agenda is identification: knowledge of what the compounds are (structure) and it
properties (reactivity). Having produced a compound from a reaction we need to ask a
number of questions (in roughly the following order)...
1.
2.
3.
4.
5.
6.
7.
8.
Does the material contain any known compounds which can be identified?
Is the material pure?
What is the elemental composition (empirical formula)/molecular weight (molecular
formula).
What functional groups are present?
We know what went in - are the same functionalities present or have they been
changed?
How are the functional groups linked (connectivity)
What is the molecular symmetry?
What is the molecular geometry?
What is the electronic structure?
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
There is an increasing degree of sophistication as we go down the list of questions. The first
four questions can be asked of a mixture of compounds, but questions 5-8 are only
meaningful when dealing with a pure compound.
There is a whole battery of techniques available to the modern chemist to begin to answer
these questions. (See handout 1) and these can also be graded in terms of degrees of
sophistication.
At the lowest end are fingerprint techniques. These are generally used to compare with
known examples of related compounds and don’t give a complete characterisation of the
compound. Examples with which you should be familiar include infra-red spectroscopy for
organic compounds and UV-visible (electronic) spectroscopy for transition metal compounds.
Next we need to determine composition using elemental analyses to establish an empirical
formula, and techniques such as cryoscopy and/or mass spectrometry to give a value for the
molecular mass of the compound. We can also use techniques such as IR and NMR to give
information about functional groups present.
Having determined the composition of the compound we ideally wish to know its structure as
well. We can find information regarding symmetry from a number of techniques. For
instance, the infra-red and Raman activity of various bands is related to molecular symmetry,
while in NMR spectroscopy the equivalence of resonances also implies the presence of
symmetry. X-ray crystallography also gives symmetry information – the way in which a
compound crystallises reflects the symmetry within that molecule.
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
2. NMR SPECTROSCOPY
2.1 Introduction
You will be familiar with the basics of NMR spectroscopy and how to interpret spectra (2nd
Year: 13 279 – Identification and Analysis). Dr Dunkin’s 3rd year course Interpretive
Spectroscopy also gives extensive treatment of NMR spectroscopy. If you need to refresh
your memory, the notes are available in PDF form from SPIDER. The aim in this course is to
take your understanding of the technique further and to open up new applications. We will
revise the basis of Fourier Transform methods, multipulse operation, multinuclear NMR, and
in particular consider the information to be gained from quadrupolar nuclei, coupling, line
widths and chemical shifts.
2.2 The Basis of Fourier Transform NMR
2.2.1 Nuclei in a magnetic Field.
In order to be NMR active a nucleus must have a nuclear spin, I ≠ 0. Such a
nucleus has a magnetic moment, , which can interact with an external
magnetic field. Note that  is a vector quantity, having both magnitude and
direction. Normally these magnetic moment vectors are randomly orientated,
but in a homogeneous magnetic field a torque is exerted on the magnetic
moment, tending to align it perpendicular to the field, Bo. The result is that
the magnetic moment rotates in a cone around the direction of the field. The
motion is like that of a gyroscope and is generally referred to as precession,
and specifically in this instance is known as Lamor precession (Figure 2.1).
Bo

Figure 2.1 Lamor
Precession
We have only referred so far to the effect on single magnetic moments. The resultant of an
ensemble of magnetic moments is a random distribution of the magnetic moments around the
field direction, Bo. This results in an overall magnetic moment, the
Bo
vector sum of all the magnetic moments, known as the magnetisation.
The magnetisation in this case is along the direction of Bo, since all
the components in the directions perpendicular to the field (x, y)
mI = +1/2
cancel each other out. We can also include quantisation in this model,

by allowing the cone angle to be determined by the quantum number
mI, such that cosθ = mI / [I/(I+1)]½. So for an nucleus with I = ½, mI
takes values of -½ and +½, giving two cones as shown (Figure 2.2,
mI = -1/2
right).
Figure 2.2
2.2.2 Pulses and Relaxation
In order to observe an NMR spectrum the system must be perturbed from its equilibrium
state. This is achieved by irradiating the nuclei with a short pulse of radiofrequency radiation,
typically of length 1 – 50 s. The length of the pulse, p, is dependent on the field and the
magnetogyric ratio of the nucleus, and pulse lengths of (/2)B (referred to as a 90º pulse)
and of length B (referred to as a 180º pulse) are most commonly used.
z
A 180º pulse results in a net magnetisation M in the opposite
direction – ie the populations of the energy levels characterised by
mI = ½ and mI = - ½ are inverted. Restoration to the equilibrium
state is achieved by a process called spin-lattice relaxation
characterised by a relaxation time T1. A 90º pulse is used to
observe a standard NMR spectrum. It results in a net
Bo
Figure 2.3 90º Pulse
mI = +1/2
My
mI = -1/2
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
magnetisation in the y-direction, My (Figure 2.3), which arises from a “bunching” of the
magnetic moments of the nuclear spins. Most of the spins remain randomly distributed
around the precession cones, but a small number bunch together – this is more properly
termed phase coherence.
The 90º pulse is followed by a relaxation to equilibrium, known as transverse relaxation,
which is exponential in nature. The magnetisation in the y-direction at time t (My(t)) is given
by the following equation:
My(t) = My(0) exp (–t / T1)
2.2.3 The FID and its Fourier Transform
The decay is accompanied by an emission of energy which is detected in the receiver coils of
the spectrometer. The plot of this signal intensity with time is known as the Free Induction
Decay or FID. If all the spins being measured are identical and the energy of the
radiofrequency pulse (carrier frequency) is coincident with the energy separating the mI = ½
and – ½ states then a simple exponential decay will be observed. In practice, the carrier
frequency is generally off resonance, resulting in a sinusoidal modulation, shown
schematically in figure 2.4.
The FID contains all the information of a conventional spectrum and it was shown in 1966
that Fourier transformation of an FID indeed does give a spectrum with lines corresponding to
the different frequencies represented in the FID. The Fourier transform takes the FID which is
in the time domain and converts to it frequency domain equivalent. It is a mathematically
simple process, but tedious. It is readily computerised and is routinely used in modern NMR
spectrometers.
If more than one spin environment is present in the sample the FID is further complicated by
the superimposition of the different resonances, giving a complex interferogram (Figure 2.5).
Figure 2.5. Left, FID and corresponding Fourier transform.
Above, FID for 1H NMR of cholesterol.
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
2.2.4 Multi-pulse Operation
The major advantage of Fourier Transform (FT) NMR is multi-pulse operation. Since the
information recorded is digitised multiple scans can be performed and the FIDs summed. The
pulse sequence is summarised in the schematic below:
The radiofrequency pulse is followed by a short delay after which the FID is acquired.
Finally, a second, much longer delay (it should be approximately 10 times T2) allows the
system to fully relax to equilibrium before the next pulse is initiated. This prevents saturation
of the excited state, which leads to a loss of signal intensity.
The result of multi-pulse operation is an improvement in the signal-to-noise ratio. Essentially,
the genuine signal due to the resonance of the sample is ever present and is reinforced, while
the random noise arising from various sources (mostly instrumental) is gradually cancelled
out. Doubling the number of scans improves the signal to noise ratio by a factor of 2,
allowing the measurement of dilute samples and samples of nuclei with low natural
abundances.
2.3 NMR of Nuclei other than 1H and 13C:
2.3.1 The Spin-½ Nuclei.
A very significant number of the elements have one or more NMR active nuclei. Most NMR
texts list these nuclei, along with some of their properties. An extract from such a table for
some of the more commonly studied I = ½ nuclei is given below…
Isotope
1H
13C
15N
19F
29Si
31P
77Se
103Rh
109Ag
119Sn
183W
195Pt
205Tl
207Pb
Natural
Abundance,
C (%)
99.985
1.108
0.37
100
4.70
100
7.58
100
48.18
8.58
14.40
33.8
70.5
22.6
Magnetic
Moment,
/N
4.83724
1.2166
-0.4903
4.5532
-0.96174
1.9601
0.925
-0.153
-0.2260
-1.8119
0.2025
1.043
2.8187
1.002
Magnetogyric
Ratio
 / 107 rad T-1 s-1
26.7520
6.7283
-2.712
25.181
-5.3188
10.841
5.12
-0.846
-1.250
-10.021
1.120
5.768
15.589
5.540
NMR
Frequency
 / MHz
100.000 000
25.145 004
10.136 783
94.094 003
19.867 184
40.480 737
19.071 523
3.172 310
4.653 623
37.290 662
4.161 733
21.414 376
57.633 833
20.920 597
Standard
Dp
Dc
SiMe4
SiMe4
MeNO2 or NO3CCl3F
SiMe4
85% H3PO4
SeMe2
mer-[RhCl3(SMe2)3]
Ag+(aq)
SnMe4
WF6
[Pt(CN)6]2TlNO3 (aq)
PbMe4
1.000
1.76  10-4
3.85  10-6
0.834
3.69  10-4
0.0665
5.3  10-4
3.16  10-5
4.92  10-5
4.51  10-3
1.06  10-5
3.39  10-3
0.140
2.01  10-3
5.670  103
1.000
2.19  10-2
4.73  103
2.10
3.77  10-2
3.01
0.179
0.279
25.6
5.99  10-2
19.2
7.91  102
11.4
The magnetic moment and magnetogyric ratio are intrinsic properties of each nucleus, while
the NMR frequency, , is dependent on the magnitude of the applied field, B, and the
magnetogyric ratio, , as given by:
 = ( / 2) B
Thus there is a linear relationship between field strength and the resonant f requency.
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
The standard (or reference) chosen for a nucleus should satisfy a number of criteria. It should
i) contain only one chemical environment of the nucleus to be studied so that its NMR
spectrum contains a single sharp line;
ii) give an intense signal for only a small amount of compound;
iii) give a resonance in a region of the spectrum away from the signals of most
common chemicals; and
iv) where possible be stable and chemically inert.
The last two columns are the relative receptivities, the sensitivity of a nucleus relative to the
1
H (DP) and 13C (DC) nuclei. The maximum peak height of a resonance is given by the
following equation:
Smax  | 3 Bo2 N (T2 / T T1) |
where  is the magnetogyric ratio, Bo is the applied field, N is the number of nuclei present,
T1 and T2 are the relaxation times and T is the temperature in Kelvin. T1 and T2 are
approximately equal for a non-viscous fluid, while Bo and T are essentially constant in the
NMR experiment. The equation therefore reduces to:
Smax  | 3 N |
which can be written as:
Smax = C | 3 N|
The constant, C, can be set using the parameters for the 1H nucleus such that Smax = 1 and
then used to give relative values for other nuclei. The number of nuclei, N, is dependent on
concentration (which is assumed to be constant) and on the isotopic abundance of the nucleus
in question. Thus, for the 1H nucleus:
Smax = C  (26.7520)3  0.99985
If Smax = 1 then C = 5.224  10-5. Then consider another nucleus, namely 119Sn. The
receptivity relative to the proton, DP, may then be calculated using the value obtained for the
constant C and the values of  and isotopic natural abundance in the table:
DP = 5.224  10-5  (10.021)3  0.0858
= 4.51  10-3
Compare the value obtained here with that given in the table above. A similar strategy will
also yield values of DC, the receptivity relative to the 13C nucleus. The value of the multipulse operation possible on a Fourier transform spectrometer now becomes apparent, with
most nuclei being very significantly less sensitive than the proton.
The spin-½ nuclei tend to give sharp resonances. The width of a line is described as the line
width at half the height of the line, 1/2, and is given by:
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
1/2 = 1 / T2 Hz
The line width will typically be of the order of a few Hz or less unless chemical exchange
between equivalent sites is taking place. The corollary of the narrow linewidths can be very
long relaxation times. Thus 109Ag nuclei in silver complexes can have relaxation times of
over 100 seconds. This can be a problem in the measurement of the NMR spectrum, since it
is necessary to put in a delay of 10  T2 in order to allow equlibration of the spin states prior
to the next pulse. This problem can be overcome by adding a chemically inert paramagnetic
ion, known as a relaxation agent. The paramagnetism of the compound encourages rapid
relaxation via interaction with the unpaired electron spin. The most commonly used
relaxation agent is the complex [Cr(acac)3] (acac = acetylacetonate).
2.3.2 The Quadrupolar Nuclei.
Quadrupolar nuclei are those which have a nuclear spin, I > ½. At the simplest level they
differ from spin-½ nuclei in the distribution of the charge within the nucleus. Spin-½ nuclei
have a spherical distribution of charge in the nucleus, whereas quadrupolar nuclei have a nonspherical distribution of electric charge in the nucleus. Consequently their properties are quite
different.
The sensitivity of the nuclei, for instance, are now also dependent on the nuclear spin of the
nucleus, IX, as given by:
Smax  | 3 N | IX(IX + 1)
Again, values relative to the 1H and 13C nuclei (DP and DC) can be calculated.
Linewidths are also very significantly influenced by the quadrupolar nature of the nucleus.
We define a linewidth factor, ℓ, where
ℓ = Q2(2I + 3) / [I2(2I-1)]
and Q is the nuclear quadrupole moment and I is the nuclear spin. Both I and Q are intrinsic
properties of the nucleus and the linewidth factor gives a direct comparison of the likely
linewidths of a resonance, all other things being equal (which of course they rarely are!) and
thus an indication of the likely suitability of a nucleus for NMR study).
The linewidth is similar to that for spin-½ nuclei, only it is now inversely proportional to the
quadrupolar relaxation time, TQ:
½ = 1 / TQ
This expression may be expanded as follows:
3 2 I  3  e 2 q Q
    10 I 2 (2 I  1)  zz 
2
c
where I = nuclear spin, e = unit charge, qzz = electric field gradient, Q = nuclear quadrupole
moment and c is the correlation time, given by:
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
c = V / 6kT
where  = viscosity and V = molecular volume. There are three main terms which need to be
minimised in order to obtain reasonable linewidths in quadrupolar nuclei, namely: the
linewidth factor, the electric field gradient and the correlation time.
The linewidth factor is dependent only on the intrinsic nuclear properties and so is unaffected
by chemical or experimental parameters. Some quadrupolar nuclei are simply better than
others for NMR observation.
The electric field gradient is dependent on the symmetry around the nucleus being studied.
Cubic symmetry (either tetrahedral or octahedral geometry) gives zero electric field gradient –
although small local variations in symmetry mean that the linewidth is never zero. (See
examples later on). So choice of chemical system can very considerably influence the ability
to observe an NMR resonancefor a given nucleus.
The correlation time is dependent on experimental conditions, primarily the viscosity and the
temperature. It is a measure of molecular tumbling (and thus averaging of nuclear anisotropy)
in the magnetic field. The correlation time is approximately the time required for the
molecule to turn through 1 radian. Bigger molecules tumble less rapidly, while higher
viscosity also results in slower tumbling. Finally temperature also plays a part, since
molecules possess higher rotational energy at higher temperatures.
So, the ideal situation is to choose a nucleus with a small quadrupole moment in a small
molecular compound with the highest possible symmetry at high dilution and elevated
temperatures! Despite these apparently stringent conditions, it is often possible to make
sufficient compromises to enable spectra to be observed even for quite unfavourable nuclei.
2.3.3 Chemical Shifts
It was discovered early in the history of NMR spectroscopy that the exact frequency at which
a given nucleus resonates is dependent on the chemical environment. While the proton
chemical shift range is fairly restricted (-30 to +20 ppm) in normal circumstances other
elements, and particularly the metallic elements are able to give very large chemical shift
ranges. For instance 59Co has a chemical shift range of some 18000 ppm.
Let us examine the reasons for this. Chemical shifts arise from local variations in the field in
the vicinity of the nucleus being studied:
Bx = Bo (1 - )
where  is the shielding parameter, which in turn may be expressed as:
 = d + p
where d is a diamagnetic contribution to the shielding, arising from electrons in closed
shells, and p is a paramagnetic contribution arising from the presence of unpaired electrons.
In the majority of organic, s-block and upper p-block compounds the paramagetic term is
negligible. However, in compounds which have low energy paramagnetic excited states (eg in
CH407/CH507 INTERPRETATIVE SPECTROSCOPY
Dr M.D. SPICER
the transition metals and lower p-block metals) the paramagnetic term can become very large
and dominate the shielding of the nucleus.
In the case of 59Co NMR this is well documented and an expression for the paramagnetic
term has been derived:
32  B r 3 
p 
E
where B is the Bohr magneton, <r-3> is a measure of the mean distance of an electron in the
metal p-orbital from the nucleus,  is the nephelauxitic parameter (a measure of covalency)
and E is the d-orbital splitting, or more properly, the energy of the lowest energy electronic
transition. The smaller the value of E, the higher the level of occupation of the first excited
state (cf Boltzmann distribution), hence the greater the value of p and thus the greater the
chemical shift. The magnitude of E depends very strongly on the ligand donor set around the
metal centre (remember the spectrochemical series) and so the chemical shift correlates well
with the donor set and can be diagnostic of the coordination environment of the metal.