Spectroscopy(2) - U of L Class Index

Chemistry 3810 Lecture Notes
3.3
Dr. R. T. Boeré
Page 69
Vibrational Spectroscopy
Vibrational spectroscopy deals with changes in the vibrational energy levels in molecules. This term covers the two
common techniques, infra-red (IR) and Raman spectroscopy. We have already seen the effects of bond vibrations in UVPES, where ionizations that alter the bond order or the bond angle show vibrational fine structure. However, the vibrational
energy levels of bonds can be directly measured using two spectroscopic techniques: infra-red and Raman spectroscopy.
Note that only chemical bonds have vibrational spectra; pure ionic compounds will not display IR or Raman spectra and in
fact we often use ionic crystal as the sample holders for IR measurements. However, an entire crystal lattice will have a
certain vibrational frequency, and this frequency depends on the masses of the atoms in the lattice. As a consequences
different types of crystalline material have specific frequency ranges outside of which they do absorb infra-red radiation.
References: SAL 3.7 - 3.8, pp. 134 - 143
Butler and Harrod, Chapter 6.
R.S. Drago, "Physical methods in inorganic chemistry", Reinhold, 1965
3.3.1 What vibrational spectroscopy can tell us
Both IR and Raman spectroscopy deal with the interaction of vibrational energy levels in molecules with photons of
light. It is found that those photons which excite molecular vibrations are in the infra-red region of electromagnetic radiation.
That means photons with considerably less energy than visible light. These interactions are useful to chemists because they
can be used to diagnose chemical structure. The application of vibrational spectroscopy depends on the type of compound
being investigated. First and foremost, vibrational spectroscopy requires the presence of chemical bonds. Simple ionic solids
do not have IR spectra - an important fact which allows us to use ionic crystals as transparent windows for measuring spectra.
One key thing which you must learn in Chemistry 3810 is to learn to exercise judgement as to how to apply vibrational
spectroscopy to a particular compound.
a) Gas-phase spectra of small molecules
Typically, only small molecules will exist as gases at reasonably low temperatures, i.e. below the temperature at which
bonds break. At low pressures (<20 mmHg) we can observe essentially independent molecules in the gas phase with little or
no effect due to the interactions between molecules. Under these special conditions, it is observed that IR light not only
excites molecular vibrations, but also molecular rotation. Thus for gas-phase molecules, not only are the vibrational states
of molecules quantized, the way the whole molecule spins around its centre of gravity is also quantized.
Typically what one observes for gas-phase molecules are a small number of vibrational bands, but each of these are
usually split into many sub-bands due to the rotational behaviour, which occurs at considerably lower energy (!~ 20 cm-1)
than the vibrations (typically 100–4000 cm–1). A mathematical treatment of small molecules allows one to develop models
which "predict" IR spectra. By adjusting the models till they fit with experiment, it is possible for small gas-phase molecules
to determine the shapes of molecules and/or bond lengths. The bond length data comes from the rotational fine structure.
a) Solid and liquid samples of high symmetry or small size
The symmetry arguments which we will develop for gas-phase molecules also apply to solid and liquid samples.
However, due to intermolecular interactions, the rotational motion in such samples is normally completely quenched. This
means that IR bands in condensed phases are often sharper than they are for gases! When the molecules being observed are
relatively small, or have high symmetry, it is often possible to distinguish among possible structures or isomers by examining
the patterns of some of the IR or Raman bands, or by counting the number of bands present. Howe ver, since the rotational
lines are absent, no information is available on bond lengths from condensed-phase spectra.
c) Large solid and liquid samples with distinctive units
When molecules get very large, or have low symmetry, the number of bands can be so large, that it is impossible to
assign their structure from their vibrational spectra. However, specific types of bond units may absorb radiation within a
narrow range of possible energies. In the language of organic chemistry, these are often called functional groups. The identity
of a certain type of chemical species may be possible if the presence or absence of such functional groups can be determined.
Functional groups are just as important in inorganic chemistry, and a list of typical inorganic group frequencies is given in a
Table later in these notes.
d) Large solid and liquid samples without distinctive units
The unique combination of vibrational absorptions of a molecule or substance leads to a complex pattern of vibrational
bands that is found to be characteristic for only that specific compound. For technical reasons, the majority of bands for comp
. ounds composed of the 2nd period elements tend to fall in the region 500 cm- to 1500 cm-1, and this region is often called
the fingerprint region, because it can often be too complex to analyze precisely, but is a unique identifier of the compound.
Comparing the fingerprint region of a sample against a known standard is considered proof of identity for a chemical
compound.
The fingerprinting method represents the least sophisticated application of vibrational spectroscopy in chemistry,
requiring no theory at all! It is however very important, and can always be used if the above three methods cannot. I will say
nothing further about using the fingerprinting method, except to mention that chemists report vibrational data in the following
manner:
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 70
IR (KBr pellet): 1604(m), 1413(w), 1296(w), 1259(w), 1211 (s), 11 98(vs), I I 55(w), 1041(w), 924(m), 901(s), 847(w),
765(m), 686(w), 547(w), 289(m) cm–1.
Where (w), (m), (s) and (vs) stand for weak, medium, strong and very strong intensity. The intensity assignment is
approximate and is a matter of judgement.
3.3.2. Background theory to vibrational spectroscopy
Consider two atoms. The bond between them can be considered as a simple spring, with force constant k. The wellknown equation for a spring (called a restoring force in Physics) is:
F = −kx
When this is applied to a vibrating particle the frequency of the vibration is related to the masses of the particles and the force
constant k, which measures the stiffness of the chemical bond:
The term µ (in this context!) is called the reduced mass. We will use units of kg for mass, and thus the force constant will
have units of N/m, such that the term inside the square-root sign has units of (1/s)2. A table of some representative force
constants is given on the next page. Note that c is the velocity of light, and we arbitrarily choose that it be expressed in units
of cm s–1 so that the equation gives answers in the non-SI unit cm–1. The quantity ν is called the wavenumber, and its unit is
cm–1, which is actually a unit of energy. It is a very popular unit among spectroscopists, and another example of departure
from the SI unit of energy, the Joule. All modern IR and Raman instruments are calibrated in wavenumbers, which means
that they are frequency linear. However, older instruments and text-books record IR data in microns, and this is a wavelength
linear method. The same spectrum expressed in the two modes is shown below (l.h.s. and r.h.s. reversed in the two.)
Fig (A) – SO2 in gas phase frequency linear
Fig (B) – SO2 in gas phase wavelength linear
Consider the example spectra in the notes which are presented in both formats (Fig. A and B). Do you see the difference?
Actually, since most of the specific information is in the fingerprint region, which is much expanded in the micron format
one could make a very valid argument that the older form of presentation is more useful for chemical characterization by IR!
The main advantage of the wavenumber method is its more direct correlation with the energy of the vibration, which for a
given set of nuclei (i.e. constant m1 and m2) is a direct measure of the force constant k. Some examples of force constants are
given in the Table on the following page.
The key point of this equation is that the frequency of a vibrational band for a bond depends in an interrelated manner
on:
(1) mass of attached nuclei
(2) strength of the bond.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 71
Increase the masses, and ν decreases; increase the bond strength, and ν increases.
So far we have touched on the choice in the presentation of the x-axis, i.e. in frequency or wavelength. The other choice
deals with the y-axis, for which we may choose either %-transmittance, or absorbance. In days gone by, many
spectrophotometers were calibrated in transmittance (e.g. the Spectronic 20's used in the Freshman labs) because these
instruments has very simplistic electro-mechanical readouts. Modem spectrometers, however, read out directly in absorbance,
since this is linear with concentration. Remember the definition of these terms in the Beer-Lambert law:
%T =
I
I0
and
I 
A = log10   = ε bc
 I0 
However, most IR data is still presented in the old fashioned manner. Fig. (C) shows the same gas-phase spectrum Of
SO2 in both the %T and absorbance modes. With the advent of FT-IR there has been a concerted movement towards the
presentation of IR data as absorbance. Raman data has almost always been presented in this mode. It has the disadvantage of
emphasizing the stronger bands at the expense of the weaker bands, but it is linear with concentration. Absorbance is also
normally used in electronic spectroscopy, where one is often interested in quantitative analysis.
Table of Some typical force constants for chemical bonds
–1
Molecule
k(N m –1)
ν (cm )
HF
HCl
HBr
HI
N2
CO
C=C in alkynes
CO in metal carbonyl complexes
C=C in alkenes
NO
C–C in alkanes
F2
C1 2
Br2
I2
3962
2886
2558
2230
2331
2143
~2150
~2000
~1600
1876
~1350
892
557
317
213
885
480
390
290
2240
1860
1500
1700
1000
1550
800
450
320
250
170
Two older units for force constant that are still found in the literature are dyn cm-1 and mdyn ? -1. Ffor example, for H, the corresponding values are 8.85 dyn
cm-1 or 8.85 mdyn ? -1. Data taken chiefly from J. B. Lambert et. al., Organic Structural Analysis. New York: Macmillan, 1976.
Figure (C) %Transmittance (top) and Absorbance (bottom) traces for the IR spectrum of gaseous SO2
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 72
3.3.3 Harmonic and anharmonic oscillator
The equation introduced earlier is called the equation for the classical harmonic oscillator:
ν =
1
2π c
k
mm
, µ= 1 2
m1 + m2
µ
Such an oscillator follows a plot or energy vs. internuclear separation given by the left hand plot below. To apply in a
valid manner to molecules, we need two major corrections: quantization and anharmonicity.
a) The quantum-mechanical harmonic oscillator
Quantum-mechanics applies to most chemically bonded vibrations. We can treat quantization as an add-on to the
classical oscillator. Remember that E = hv, which is the basic concept of quantization of electromagnetic radiation by Planck.
Here ? (the Greek letter, nu) is the frequency, while h is Planck’s constant. If we now solve the Schrödinger equation for
harmonic oscillator, we get the following result:
1 h
Eν = (ν + )
2 2π c
k
, ν = 0, 1, 2,....
µ
In this equation, ? is the vibrational quantum number. It has some surprising results. First of all, there are only certain
allowed frequencies (energies) of vibration. Secondly, there is a minimum energy of vibration. This is seen by choosing the
lowest vibrational quantum number, i.e. when ? = 0:
1 h
k
E0 = ( )
2 2π c µ
This is called the zero-point energy, and is lowest vibrational energy state of the bond. In other words, all bonds are predicted
to vibrate, even at when they have no thermal energy at all.
We are more interested, however, in the possible changes in vibrational energy. For the purpose of vibrational
spectroscopy, it has been shown that there is a selection rule: ? ? = ±1. Hence all absorptions for harmonic oscillators lead to
the same absorption peak, and the energy of the transition is actually given by the original classical equation! Selection rules
express the probability of transitions between quantized states.
b) The quantum-mechanical anharmonic oscillator
At high-enough energy, bonds will of course break. This means that they are not true harmonic oscillators. In fact they
are anharmonic oscillators. However, as the figure shows, there is considerable similarity left between the two models at low
energy. At higher energy, however, the spacing between the levels decreases as the potential well gets wider.
The practical consequence of anharmonicity is that instead of all the absorptions overlapping to give a single sharp peak,
multiple peaks at slightly off-set energies occur, which in practice leads to line-broadening, always seen towards the lowenergy side of the absorption peak. This is most significant for light elements: the distortion may be as much as 100 cm–1 for
E—H bonds, yet be as little as 1 cm–1 for heavy-element bonds. Another consequence is the breakdown of the strict selection
rule. Hence there is a small probability that some transitions will occur with ? v = ±2, ±3, etc. Such bands are called
overtones, which are always found at 2×, 3× , etc. the frequency of the primary band. Overtones are always of much weaker
intensity than the fundamental vibration peaks. However, if the principal band is very intense, its overtones can be stronger
than some weak principal lines in the same spectrum.
3.3.4 IR spectroscopy - instrumentation
The IR frequency range is considered to be 4000-30 cm–1. The Bomem 102 instrument can detect signals in the range
4000-200 cm–1. Below 200 cm–1, the optical materials of the instrument absorb all the light (CsI). The range above 4000 is
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 73
called the "near-visible" range, which contains many overtone bands, but none of the principal bands of IR spectroscopy.
The Bomem 100 instrument can record data from 6000-450 cm–1. Its optics are manufactured from KBr, which absorbs
below 450 cm–1. Below 200 cm–1 requires special instrumentation that is very rare in a routine chemical laboratory (but
Raman can easily go down to as low as 50 cm–1.) The Nicolet Avatar is also limited to 450 cm–1 as the lowest frequency,
again because of the optical materials of construction.
Older instruments were analog devices that are called scanning (or dispersive) spectrometers, where a grating or a prism
is slowly turned through the spectrum, and the intensity of transmitted light is measured. A newer technique is the Fourier
transform, in which all the wavelengths of light are detected simultaneously. However, half the light is rendered out-of-phase
with the other half, and the degree of this phase shift is altered by moving a mirror inside the instrument. The resulting
pattern is called an interferogram. This can by analyzed by the mathematical technique of the Fourier transform, in which the
shape of the interferogram is ratioed to the speed at which the mirror moves. The computer then presents the data in the
traditional way. The advantage is speed. In our runs we typically do 10 scans, in which the true signal is additive, but
background noise tends to cancel out. We get a much better quality spectrum. Currently all our instruments are FTIR’s.
3.3.5 IR spectroscopy - sampling techniques
a) Gases
Gases are measured at low pressure in long-path length cells which can hold a vacuum. The path length most common is
10 cm, although for special purposes paths of several meters can be devised!
b) Liquids
Liquids are usually measured as smears (thin films) held between two plates of alkali halide, sometimes with a spacer to
get a definite path length. They can also be measured as solutions using a solvent with suitable “open window”.
Table of regions in which various solvents transmit at least 25% of the incident radiation (so-called Open Regions)
(A) For Cells of 1 mm path
(B) For Cells of 0.1 mm path
Solvent
Open Region Solvent
Open Region
(cm–1)
(cm–1)
CCl 4
4000-1610
CS2
4000-2200
1500 1270
2140-1595
1200-1020
1460- 650
960- 860
C6H6
4000 - 3 1 00
CHCl 3
4000-3100
3000-1820
2980-2450
1800-1490
2380-1520
1450-1050
1410-1290
1020- 680
1155- 940
910- 860
CCl 4
4000- 820
720- 650
CH2Cl2
4000-3180
2900-2340
CHCl 3
4000-3020
2290-1500
3000-1240
1130- 935
1200- 805
CS2
4000-2350
CH2Cl2
4000-1285
2100-1640
1245- 900
1385- 875
890- 780
845- 650
750- 650
Cl2C=CCl2
4000- 1375
Cl2C=CCl2
4000- 935
1340-1190
875- 920
1090-1015
745- 650
Solvent
CH3CN
Open Region
(cm–1)
4000 3700
3500-2350
2250- 1500
1350-1060
1030 930
910- 650
CH3NO2
4000 3 1 00
2800-1770
1070- 925
910- 690
C5H5N
4000-3500
3000-1620
1400-1230
980- 780
4000-3000
2700-1780
1020- 870
860- 680
2800- 1500
1370 1150
970- 700
NC(O)N(CH3)2
CH3OH
c) Solids
Solids can be measured by three common methods:
1. Mulls
Grind the sample to particles to = ? (wavelength) i.e. to several micrometer in size. This means vigorous
grinding in a hard mortar like agate. Then scrape the fine solid off with a spatula. To minimize dispersion of the
light, mix with oils like Nujol or Fluorolube to the consistency of a thick paste. Spread a thin film of this paste
between the plates.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 74
2. Nujol is a hydrocarbon oil, with strong absorption around 2900 and 1400 cm–1. Fluorolube is a completely
fluorinated oil, giving a clear window above 1600 cm–1, and a huge mess below this value. The two kinds of
mulls are complementary and by combining them it is possible to observe almost the whole IR spectral region.
3. KBr pellets
Grind both the KBr powder (oven dry and desiccator storage) and the sample (1-2% only required) to the same
size as for mulls. Load into the pellet press, and apply 20 tons pressure for 5 minutes. Remove the thin pressed
pellet (or plate) into the appropriate sample holder. KBr pellets avoid the bands caused by Nujol or Fluorolube,
and generally give the best IR spectra. However, in some cases bands can be distorted by crystal effects as the
molecules are squeezed into the ionic crystal lattice of KBr. Reaction with the Br – ions can also occur.
4. Solutions
Choose a solvent with a clear window in the region you wish to measure. Avoid solvents with a strong affinity
for water, because these will damage the alkali halide cells! On FTIR instruments, this is always a two step
procedure. Run as a reference an empty cell compartment. Then run the cell containing the selected solvent
using single beam mode. Then make a solution of your compound in that solvent, and run this as a transmittance
or absorbance spectrum, but again in single beam mode. After this it will be necessary to run a spectral
subtraction, in which the spectrum of
pure solvent is subtracted from that of
the solution.
The subtraction
parameter almost always requires
adjustment by the operator. This will
have the effect of subtracting the
solvent peaks out of the spectrum.
However, the regions where the
solvent absorbs most strongly may
have funny noise peaks. This is
because so little IR light gets through
in this region that the detector gets a
little fooled. The Table above gives
useful information on the "open
regions" for common IR solvents.
Window materials for vibrational spectroscopy:
NaCl 6000 – 600 cm–1
KBr 6000 – 450 cm–1
CsI 6000 – 200 cm–1
Polyethylene < 600 cm–1
3.3.6 Group frequency method
Where the detailed analysis is not possible, we
can sometimes use the group frequencies
approximation. This use is common in organic
chemistry, where certain regions of the spectrum are
associated with certain organic functional groups. In
the Table at right are some typical “inorganic”
group frequencies. Use this to assign your
laboratory spectra.
The basic assumption of the group frequencies
is that a certain normal mode of vibration of the
molecule will be dominated by motion in the bond
of interest. Also, it will dominate in all or most
derivatives with that same functional group. E.g. the
C=O stretch in acetone dominates one normal
mode. This frequency can be used to identify other
C=O groups in other molecules, where this is again
a dominant contributor.
In general the group frequencies approach is
valid so long as the normal mode is 80-90%
dominated by the group being identified. Be
particularly aware of special bonding scenarios
which might alter this assumption (e.g. a strong
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
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contribution by another resonance isomer in the Lewis structure.)
Going back to the original force-constant equation, recognize that all 3 rd period and over atoms are very heavy (22 mass
units or more!) As a rule, the element-ligand stretch will be found as a weak set of peaks at very low wavenumber. (The
exception will be for metal hydrides, i.e. with a direct M—H bond.) Also remember that many of the constituents of your
molecules will be "organic" fragments, which may have very similar vibrations to their parent organic compounds.
3.3.7 Raman spectroscopy: principles and techniques
Raman spectroscopy is named after its inventor, and Indian physicist who detected the phenomenon with very simple
apparatus and using a focussed beam of sunlight as his light source. After the invention, the technique lay dormant for many
years until lasers became routinely available for use in scientific experiments. An intense, monochromatic light from the
laser is directed through the sample; a detector is mounted at 90° using careful optics, so that the direct beam of light is not
detected. This is the same optical path used in fluorescence spectroscopy, which you may be familiar with.
Some of the light is scattered by the sample, and this occurs at the molecular level, which actually involves the absorption
and re-emission of the light by the compounds in the sample. Most of the light is re-emitted at the same wavelength as the
incident light. This is called Rayleigh scattering, which typically has in any given direction in space an intensity about
1/1000 of the incident beam.
A very small amount of the re-emitted light is returned with slightly different wavelength. Let's talk in terms of
frequency. The light whose frequency is less than the incident has lost part of its energy to vibrational excitement of the
molecule. This is called the Stokes scattering.
Also some of the light is re-emitted with higher frequency. This light has gained energy from the vibrations of the
molecule. This is called the anti-Stokes scattering. The intensity of anti-Stokes lines is usually lower, since more molecules
are in the ground vibrational states near room temperature. Only molecules in excited vibrational states can give off
vibrational energy, and there are normally less of such molecules around than those that absorb from the direct beam. The
combination of the two sets of lines is called the Raman scattering of the molecule, and these lines typically have intensities
1000-fold smaller than that of the Rayleigh scattering, i.e. about 1/10–6 that of the incident beam.
The principle behind the technique can be illustrated by the following figure, which is a room temperature spectrum of
liquid CC1 4.
A spectrum that looks like this is extremely rare. Almost all Raman spectra show only the Stokes lines (they are the
more intense.) Furthermore, the intense Rayleigh line is normally omitted, although sometimes the tail of this band is visible
at the edge of the spectrum. Thus the spectra can look surprisingly like an IR spectrum (in absorption mode), even though
the light used is of much higher energy. In Raman spectroscopy, it is the difference between the frequency of the Rayleigh
line and that of the Stokes line that defines the “energy” of the band. Depending on the optical quality of the spectrometer
and how sharp the laser line is made, it is often possible to measure Raman lines right down to about 20 cm–1 from the origin.
A more typical Raman spectrum is shown below. In this figure, an organometallic compound of manganese has been
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 76
recorded by both IR and Raman spectroscopy. In the Raman, the lines are very weak compared to the Rayleigh line, but by
reducing the intensity, bands right down to low energies from the incident wavelength can be detected. Some of the more
important weak bands, on the other hand, have been enlarged to emphasize them.
By comparing the two, you will immediately recognize that the spectra are not the same. Indeed, as a rule, the bands that
show up in the IR and Raman spectra will be different. In some cases, there may be overlap, with some bands occurring in
either technique. In other cases, there will be no ove rlap. This depends on the symmetry point group of the molecule.
Hence chemists use Raman specifically as a complimentary technique to IR spectroscopy. Before we can talk meaningfully
about such an analysis, we need to introduce another consequence of molecular symmetry.
3.3.8 Degrees of Freedom and Normal-mode analysis
The total number of degrees of freedom for the motion of any molecule is 3N,
where N is the number of atoms in the molecule. This is simply the result of
allowing x,y,z motion for each atom in the ensemble. Let us illustrate this for a
simple bent molecule such as water, as shown in the diagram at left. In a water
molecule, the three atoms are joined by chemical bonds. What happens when we
apply x,y,z motion to each atom, as illustrated by the pictures by the red vectors?
For water there will be 3 × 3 = 9 degrees of motional freedom. The six shown here
lead to either overall movement of the molecule (on the left of the diagram), or to
rotation about an inertial axis (as shown at the left). This result is general for most
molecules. There will always be three degrees of freedom associated with moving
the whole molecule, what theorists call translation. For a non-linear molecule,
there will also be three degrees of rotational freedom. However, for linear
molecules, only two variables are required to express all possible rotations, namely
rotation of the linear axis, and rotation about the linear axis. This leads to some
very important consequences for molecular vibration. The total number of
vibrational degrees of freedom is expressed by:
3N – 6 for non-linear molecules, and
3N – 5 for linear molecules.
We will consider the vibrational motion for the water molecule shortly, but first it is worth mentioning that IR and
Raman spectroscopy are not able to observe translational motion, but they are able to observe quantized rotational motion.
This happens whenever vibrational and rotational motion are coupled, and the resulting spectra are known as the rovibrational spectra. These typically occur when molecules exist at relatively low pressure in the gas phase. On the other
hand, quantization of rotational motion is rapidly quenched by inter-molecular motions in condensed phases. Thus the
vibrational bands in IR or Raman are often observed to be sharper for liquids than for gases. A very important practical
consequence of all this is that to observe gas-phase spectra, a spectrometer should have the highest possible resolution in
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
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energy. Our spectrometers are only capable of 1 cm–1 (Bomem) or 0.5 cm–1 (Nicolet), but research spectrometers can be 100
times higher in resolution. On the other hand, for liquids and solids, resolution of greater than 4 cm–1 is pointless, and our
spectrometers are normally run at this resolution for all condensed matter applications. For quantitative IR, as used in
industry, the resolution can be reduced much further, and quant IR is often run at 16 cm–1 resolution to
simplify and speed up the measurements. Accuracy limitation: note that if the spectrometer is set to a
4 cm–1 resolution, the peaks should never be quoted to an accuracy of more than ±1 cm–1!
Let us now return to the problem of the vibrational degrees of freedom of water. The figure at left
shows the remaining three vectors for possible move ment of the atoms in water. These motions have
been carefully defined to that they do not lead to overall motion (translation) nor to net rotation of the
molecule about its inertial axis. These three motions can be classified as vibrations which (1) stretch
both bonds at once, (2) ones which stretch one while compressing the other, and (3) vibrations which
bend the molecule more or less. These are called the symmetric stretch, asymmetric stretch and
scissoring vibrations. In the water molecule, these bands are shown in the picture. The labelling
scheme is based on a convention derived from Group Theory, and thus ?1 is the symmetric stretch, ?2 is
the scissoring vibration, and ?3 is the asymmetric stretch. Note that, as is common, the highest energy
vibration is that due to the asymmetric stretch ?3. By the way, these bands of water can be observed
anytime you run an IR spectrum during the scanning of the background. The broad, multi-line spectra
that you see are the rovibrational bands of water vapour, showing hundreds of rotational lines. For
water, ? 1 and ?3 overlap in the 3600 cm–1 region, but ? 2 is by itself at 1595 cm–1. The band at 2351 cm–1
is the asymmetric stretch of CO2 vapour.
2.8
2.6
2.4
2.2
Arbitrary units
2.0
1.8
1.6
CO2
1.4
v2 of water vapour
1.2
1.0
0.8
v1 and v3 of water overlapping
0.6
-4
10
4000
2000
Wavenumbers (cm-1)
It is possible to develop a scheme of similar idealized vibrations which fully describe the vibrational degrees of freedom
for all molecules. More importantly, it is possible to organize these possible vibrations using symmetry. This is the second
major application of point group symmetry that we will use in Chemistry 3810. These unique vibrations are called the
normal modes of vibration, which are an "orthogonal" set of vibrations express all the possible motion of the molecule.
a) Application of normal-mode analysis to SO2 vapour
For a small molecule like water, or in this case, SO2, normal mode analysis can be used to determine molecular structure
using vibrational spectroscopy by itself. When coupled with measurement of the rotational lines, is its possible to determine
the momement of inertia also, and from this bond lengths can be determined.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
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When the motions described by these normal modes are
analyzed by Group Theory using the character tables, each
mode can be assigned to an irreducible representation, and
can then be identified by its Muliken label. As in the case of
symmetry adapted orbitals, we will not learn how these
labels are determined as that requires a detailed knowledge
of Group Theory. However, we will be able to use the
results in a simple and powerful manner. For water, the ?1
and ?2 modes have A1 symmetry, while the ?3 mode has B1
symmetry. In the character table for C2v, these Mulliken
labels are associated with the mathematical functions z and x, respectively. Whenever the symmetry of a vibration matches
x, y, or z, the vibration will be observed in the IR spectrum. It is said to be IR active. On the other hand, whenever a
vibration matches a squared term, e.g. x2 or xy, etc., it will be observed in the Raman spectrum. It is said to be Raman
active. In the case of SO2, we can compare the results from the IR spectrum with the symmetry analysis. We see that all
three normal modes of vibration are IR active in the C2v point group. The full analysis of the gas phase spectrum can now be
given. The full spectrum is shown here again, with the peaks labelled. Unlike water, the bands do not overlap.
Band, cm–1
519
506
1151
1361
1871
2305
2499
Assignment
?2
?2 + ? 1
?1
?3
?2 + ? 3
2 ?1
?1 + ? 3
Comments
A fundamental band; rotational lines resolved*
A combination band; weak, obscured by ?2
A fundamental band, rotational lines resolved*
A fundamental band; intense, rotational lines are not well resolved*
A combination band; very weak, not observed
A weak "overtone" band of ?1.
A weak combination band.
The presence of low intensity overtone and combination bands is due to anharmonicity, as mentioned above. Their
frequencies can be obtained by adding or multiplying those of the fundamentals, so that for example, 2?1 is found at 2305 cm–
1
, which is very close to 2 × 1151 (?1) = 2302 cm–1. Usually, stretches have higher energy than bends, and this is clearly the
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 79
case for SO2, where ?2 has about half the energy of either ?1 or ?3. Detailed studies have been done on SO2 to confirm the
above assignments.
In this gas-phase spectrum, each vibrational band shows rotational fine structure, some well-resolved as in ?1, others not
resolved as in ?3. The bands fall into two classes, the so-called P-Q-R and the P-R patterns. This can best be seen on the
following spectrum which zooms in on just ? 1 and ?3.
The P-Q-R pattern is observed for ?3,while ?1 shows the P -R pattern. These are known as the branches of a rovibrational
spectrum. By convention, the P branch is always to higher energy, and R to lower. P and R show the rotational fine
structure. The P branch of ?3 has the rotational lines merged into one broad band – it is not resolved on this spectrometer.
However, rotational quantization is still present, or else the entire P branch would be missing. In the R branch, some fine
structure is just visible. Such distortions of bands are quite common in IR spectra of real molecules. On the other hand, a Q
branch will never have rotational fine structure, and gives just a single sharp vibrational band, indeed Q gives the frequency
of the vibration. In a P-R pattern, the frequency of the vibration is measured at the mid-point where the intensity is zero!
A Q branch is observed whenever the vibration induces a change in dipole moment which is perpendicular to the
principal axis of rotation Cn. A Q branch is not observed whenever a vibration induces a change in dipole moment that is
parallel to the principal axis of rotation Cn. In SO2, ?1 and ?2 are symmetric w.r.t. to the C2 axis, hence the dipole changes
parallel to this axis, and no Q branch is seen. However, ?3 is asymmetric w.r.t. the C2 axis, and hence the dipole changes
perpendicular to the axis, and a strong Q branch is seen. Note that for diatomics such as H—Cl, which is studied in Chem
3730, a Q branch is never observed.
We could now ask the question: what if SO2 were linear, instead of bent. In that
case, what would its vibrational spectrum look like? The vibrations of a symmetric
linear diatomic in the D8 h point group are shown in the diagram at the right. Now there
will be four vibrational bands (why?) However, its pretty obvious that the two bending
motions differ only in orientation, and hence you will not be surprised to learn that
these two motions are degenerate, i.e. they occur at the same energy and hence are
responsible for the same band in the IR spectrum. The symmetries of the bands are S g+
for the symmetric stretch, Su+ for the asymmetric stretch, and ? u for the set of two
symmetric bends. A consideration of the point group tables (next page) shows clearly
that only Su+ and ? u will be IR active, and hence there will only be two fundamental
bands in the IR spectrum of CO2. One of these, Su+, can be seen in the IR spectrum of
air shown two pages back.
Hence we have shown how a consideration of the symmetry of the molecular
vibrations can be used to determine the shapes of molecules. When combined with
rotational fine structure, it may be possible to determine both the shape and the bond
lengths for small molecules. In the Chem 3810 lab, this is done for GeH4. Large
molecules, which do not give vapour phase spectra and are measured as liquids,
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 80
solutions or solids, lose the rotational fine structure. However, it may still be possible to distinguish between different
structural possibilities using vibrational spectroscopy and symmetry. However, success in this endeavour generally requires
the use of Raman spectroscopy in conjunction with IR spectroscopy.
b) Limitations of normal-mode analysis
Large molecules simply have too many bands to make assignments possible. Remember that we have NOT gone into the
work involved in assigning the bands in SO2. This process becomes too complex to solve for large molecules. As an example,
consider the number of normal modes one gets for a medium-sized molecule such as ethane:
This 8-atom molecule already has 12 normal modes. You can imagine how this grows with the size of the molecule.
Also, the more bands there are, the more they overlap, and you soon get the familiar "fingerprint" complexity of the IR
spectra of a typical organic molecule. In general, for large molecules only certain prominent features can be fully analyzed in
the IR spectrum. The group frequency approach already mentioned is valuable whenever on functional group in a molecule
is found to dominate one of the normal modes of vibration, and this happens often enough that for similar groups of
molecules detailed tables of IR correlation tables have been established. All such tables, however, are empirical and will
only be valid so long as the molecules you study share considerable similarity with the model compounds used to derive the
correlation in the first place. In summary, one can say that: small molecules can at times be completely characterized by their
IR spectra, usually in the gas phase. Complex molecules can be analysed (1) by the group-frequency approach or (2) by the
fingerprint method.
3.3.9 Applications of Raman and IR together to solve structure
An IR absorption will only occur if the molecular vibration involved in some way alters the net dipole moment of the
molecule. Diatomic molecules have only one vibrational degree of freedom. If they are symmetrical, vibration will not alter
the bond dipole. Hence any symmetrical diatomic cannot absorb IR radiation, and this is the reason that the air molecules N2
and O2 do not absorb IR. A good thing this is, or else your TV remote would not be able to function! Look back at the
background IR spectrum shown a few pages back. Note that water and CO2 show up strongly, even though each is only a
few percent abundant in air. If nitrogen and oxygen absorbed, then all IR radiation would be absorbed and the spectrum
would be a straight line at 0%T.
Raman scattering occurs only when the net polarizability of the molecule is altered during the vibration. The two
techniques are therefore complementary. I have already pointed out that IR vibration is associated with the vector functions
x, y, z in symmetry Character tables. Raman spectra are associated with the tensor functions xy, xz, yz, x2, y2 and z2.
Qualitatively Raman measures changes in the “fatness” of molecules; vibrations that alter the overall size of the electron
cloud are Raman active, while vibrations that change the extension of the cloud are IR active.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 81
The exclusion rule states that if a molecule has a centre of inversion, i, then none of its vibrational modes can be both IR
and Raman active. Hence knowing the point group of a molecule can tell you something specific about the spectra of the
compound. Conversely, if you have to choose between two possible geometries, one with i and the other without i, then it
may be possible to determine the structure simply by measuring both the IR and the Raman spectra, and seeing if any bands
are common to the two kinds of spectra.
a) Structure determination for trigonal molecules: BF3
BF3 (which is a mixture of 10BF3 {19%} and 11BF3 {81%}, has two reasonable structures, i.e. trigonal pyramidal C3v, and
trigonal planar, D3h. VSEPR predicts the latter, but what evidence is there for this assignment?
Step 1: Look at the normal modes of vibration for the two possibilities:
Step 2: Tabulate the results and assign the activity from the character tables:
Mode
?1
?2
?3
?4
C3v
A1
A1
Ee
E
activity
IR-Raman
IR-Raman
IR-Raman
lR-Raman
D3h
A1’
A2”
E’
E’
activity
Raman
IR
IR-Raman
IR-Raman
Step 3: look at the spectra to see what is observed.
IR 10B
1505
IR 11B
1454
791
482
691
480
Raman 10B
1505
888
Raman 11B
1454
888
482
480
Assignment
?3
?1
?2
?4
Step 5: We see that the spectrum has only one exclusively IR
active band, 1 exclusively Raman active band, and two which are IR
& Raman active. This clearly fits only the D3h point group, and not
with the C3v point group. We conclude the molecule probably is
trigonal planar, as the VSEPR theory predicts.
You were wondering…
1) What is the difference in positions of 10B and
11
B bands due to?
2) Why does ?1, not show this difference?
b) A large molecule example: Ni(CO)4
Sometimes this kind of analysis can also be applied to molecules
where the group frequency approximation holds. A very famous
example is in the spectra of transition metal carbonyl complexes.
For example, consider the vibrational spectroscopic data for the C=O
stretches in Ni(CO) 4. Many four-coordinate nickel complexes are square
planar in geometry, but some are also known to be tetrahedral. Which is it
for nickel carbonyl? In the intense carbonyl region as measured in a dilute
solution using a non-interacting solvent, generally between 1850 and 2100
cm–1, Ni(CO)4 has a single, sharp IR band, but displays two sharp Raman
bands. We must consider the normal modes of vibration, which for
tetrahedral Ni(CO) 4 are shown in the diagram.
There are only four mode s to consider, because we can decouple the
vibrations between C and Ni (these do occur, but at much lower energy; the
effective triple bonds of the CO group have a very high force constant,
pulling their vibrations to the carbonyl region.) However, in the point group
Td, three of them are found to be degenerate. When we consult the character
tables, we find that the A1 mode is Raman active, while the T2 mode is both
IR and Raman active. Hence the observed spectra fit for tetrahedral.
Conversely, using the exclusion rule, in D4h there is a centre of
inversion, i, and hence it is not allowed that the same band is observed in
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 82
both the IR and the Raman spectrum. Conclusion: Ni(CO)4 is one of the rather rare examples of tetrahedral nickel
complexes, and is definitely not square planar as is often observed for nickel. A closer examination of the data suggests that
the square planar form is most common when nickel is in the +2 oxidation state, while for the 0 oxidation state tetrahedral or
something close to tetrahedral is more common. Ni(CO)4 is an example of a zero-valent nickel complex.
3.4
Mass Spectrometry
Notice the change in terminology: a mass spectrum is recorded on a mass spectrometer, not a mass spectroscope, since
electromagnetic radiation is not used. Instead, masses are measured, hence “metry”, by the variation in the applied voltage to
an electromagnet.
3.4.1 Instrumentation
It’s useful to consider the instrumentation, because this explains the technique. The sample is introduced through a tiny
port into a high-vacuum chamber. Here it can be heated if necessary to volatilize it. In a typical electron impact experiment,
the sample is bombarded with high energy electrons, which strip off even more electrons to make positive ions:
M + e–
à
M+ + 2e–
The mass of the positive ion is then measured by analyzing its kinetic energy, e.g. by relative curvature of the path
through a bent magnetic field. Some instruments use electric quadrupoles, others measure time-of-flight. The results are the
same. We end up getting the mass-to-charge ratio of the ions produced in the source.
It is also possible to perform mass spectroscopy with negative ions, and there are many different ways to generate the
charged state. This accounts for the profusion of mass spectroscopic techniques on the marketplace, and much of the recent
development has been aimed at making mass spectroscopy possible for species of biological interest.
The units of mass spectroscopy are then properly:
m/e–
This means that a doubly charged ion will appear half as heavy in the mass spectrometer. In practice, the instrument is
carefully controlled so as to avoid as much as possible the production of these confusing “half-mass” ions.
We call the M+ ion the parent ion. Usually, these ions are unstable and we also see signals due to many fragment ions in
the spectrum. For well-established chemistries, as in standard organic chemistry, the nature of the fragments produced can be
used to distinguish, e.g. among different isomers of compounds with the same molecular mass. Such rules are empirical in
nature, and should be used with caution, just as the group frequency approach in IR spectroscopy, and many deviations exist.
3.4.2 Accuracy
We will consider two kinds of mass spectra: so-called low resolution, and so-called exact mass or high resolution
spectra. Low resolution spectra generally give peaks to the nearest whole atomic mass unit, while exact mass spectra
measure peaks to the nearest 10–4 amu. Often the low resolution spectra are adequate so long as the elements in the sample
have a non-trivial isotopic distribution.
In exact mass spectrometry, the mass of both the parent and daughter ions can be compared to the sum of the exact
isotopic masses of all the constituent atoms in a given fragment. A match within 10 ppm of the calculated and measured
mass is considered to be an exact identification of the unknown fragment.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 83
3.4.3 Spectra and interpretation
The best way to learn mass spectroscopy is to interpret examples. The key thing is to reme mber that mass spectrometry
is an isotope sensitive technique. Information on isotopes is most easily gotten by looking in the Table of Isotopes in the
CRC handbook. This is a detailed table tucked in between the tables of inorganic and organic compounds in this
handbook. We will do one example in detail to show the method of using mass spectroscopy in inorganic chemistry.
Mass spectrum of CF 3CN2Se2
A spectrum of this type is normally analyzed by recognizing that a whole cluster of peaks is associated with the isotopes
of one kind of ion. The major diversity in the isotope distribution comes from selenium. There are in all six naturally
occurring selenium isotopes, of which the major contributors are 78Se (24% abundant) and 80Se (50% abundant). When there
are two selenium atoms in one molecule, the combinations 78Se + 78Se = 156 (0.242 = 0.06), 78Se + 80Se and 80Se + 78Se =
158 (2 × 0.24 × 0.50 = 0.24) and 80Se + 80Se = 160 (0.502 = 0.25) mass units must be taken into consideration, with the
indicated approximated intensity ratio’s. Hence the tall “doublet” with a two amu separation seen at 269, 174 and 160 amu
are indicative of two seleniums. All the other fragments do not contain the two selenium atoms.
The spectra are normally reported only for those signals with the highest abundance isotope, e.g. in this case for 1H, 12C,
14
N, 19F and 80Se. On this basis the parent ion C2F3N2Se2+ has mass 269 (tallest peak in the heaviest cluster), 174 is then only
conceivably due to the NSe2+ ion, and the Se 2+ ion can be seen at 160. The remaining peaks are mono-selenium (94 = SeN+
and 80 = Se +) or non-selenium (69 = CF3+). The weak lines are ignored, as they maybe random impurities. Note that the
numbers reported are one less than suggested by the scale on the diagram. This is because the output cuts off the decimal
region, rather than rounding up the number.
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 84
The isotopic pattern for the parent ion can be accurately constructed by adding the masses of the all the constituent
isotopes. This has been done by computer in the following diagram:
The incredible agreement between this pattern and the observed peak is a virtual “fingerprint” for the molecular
formula, and by itself establishes the molecular formula of the compound. The mass spectrum is successful for CF3CN2Se2.
Finally, for a high-resolution mass spectrum, the agreement predicted for a particular formula using the highly-accurate
exact masses of each isotope (compiled in the CRC Table of the Isotopes to a precision of 8 or 9 significant figures) can be
used to compare the measured and calculated peak position and hence get an essentially unique identification by mass.
Here this is done for the parent ion: the peak at “268” on the spectrum is actually 268.8347 amu as measured. The computer
output identifies the desired formula CF3CN2Se2+ as being only 0.9 ppm different from the calculated value. This serves as
definitive proof of identification for this ion, and hence for the formula of the parent, neutral, compound.
Chemistry 3810 Lecture Notes
3.5
Dr. R. T. Boeré
Page 85
Electronic Spectroscopy
Electronic spectroscopy as the name implies involves changes in the state of the electrons in a molecule (or atom, ion,
etc.) Changing electronic states generally requires a large amount of energy, such that electronic spectroscopy is most often
effected using high-energy radiation such as found in visible light photons or in the ultra-violet. However, this is not
exclusively true, and some electronic spectroscopy is done with near infra-red light. Commonly you will see this technique
referred to as “UV-vis”, and by this is usually meant “electronic absorption spectroscopy using ultra-violet or visible light
sources”. Other forms of electronic spectroscopy include UV-PES, atomic absorption (AA), atomic or molecular emission,
circular dichroism or optical rotatory dispersion spectroscopy.
3.5.1 Electronic transitions
An atom or molecule can absorb a photon of energy if the photon exactly matches the energy
difference between a filled and an empty, higher lying, orbital. Upon the absorption, the electron is
promoted to the higher lying energy level. In molecules, we call the most energetic filled orbital the
HOMO, and the least energetic empty orbital the LUMO. Thus the electronic absorption band of
lowest energy (longest wavelength) corresponds to the HOMO-LUMO transition.
From the lengths of the arrows it is clear that the lowest energy transition is that between the
HOMO and the LUMO. It is generally much harder to assign any other bands in the spectrum, as
they may be HOMO to LUMO+1, but could also be HOMO-1 to LUMO, etc. A confident
assignment is normally only possible for the lowest energy band. However, from the literature it
may be possible to find a full assignment for an electronic absorption spectrum.
3.5.2 Lambert-Beer law
Most measurements of electronic absorption spectroscopy involve a measurement of the wavelength of the absorption
maximum, ?max, as well as the intensity of the signal. The latter is expressed in terms of the molar absorptivity, e, using the
Lambert-Beer law:
%T =
I
I0
and
I 
A = log10   = ε bc
 I0 
Most UV-visible spectrophotometers read-out directly in absorbance units, since that is linear with concentration. We
typically use precision fused quartz cells with path-lengths of exactly 1.00 cm. That makes the calculation of e very easy, i.e.
e = A/c, the latter in molarity units. Note that UV-visible bands in the condensed phase are usually very broad, Gaussian-type
curves. We measure A at the ?max point only, and ignore the wide spectral enve lope entirely.
3.5.3 UV-vis Absorption Spectra - Some Examples
Most molecules other than saturated hydrocarbons absorb somewhere in the UV or the vis or near-IR ranges, where
electronic spectra are measured. If visible light is absorbed, the compound will be coloured. Transition metals are very often
coloured in their positive oxidation states. Some representative spectra of metals ions are shown below; in Chemistry 3820
the treatment of such spectra is dealt with in great detail.
[Ti(H2O)6]3+
[MnO4]– with vibrational fine structure
[Pr(H2O)8]3+
Chemistry 3810 Lecture Notes
Dr. R. T. Boeré
Page 86
Since the spectra measure electron promotion from filled to empty MO's, an MO diagram is used to explain the
phenomenon. Here are two examples of closely related inorganic ring compounds, one of which has higher symmetry (S3N3–
) and therefore shows only a single band due to the 2e"→2a2" promotion, and the other has lower symmetry (Me2PN3S2), so
that two bands are observed close together in energy (in this case corresponding to 3b1→4b1 and 2a2→4b1 transitions. The
HOMO-LUMO gap in the second compound is significantly smaller than in the first, so that the 2a2→4b1 transition is found
at lower energy (18400 cm–1 compared to 28000 cm–1 in S3N3–.
S
N
N
S
S
N
A note on units: ε is the Absorbance per unit concentration, while A is the absorbance of the actual sample (use Beer's
law). The x-axis is usually measured in nanometers (nm), but is often converted to wavenumbers (cm–1) for purposes of
presentation or analysis, since the latter are energy units and thus directly comparable to the gaps in the MO diagram.
Sometimes the cm–1 are themselves converted to eV.