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Far-Infrared Fourier Spectroscopy as a Method for Structure Determination in Chemistry.

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Far-Infrared Fourier Spectroscopy
as a Method for Structure Determination in Chemistry
New analytical
methods (4)
By Erich Knozinger[*I
Couched in the often confusing term "Fourier Spectroscopy" is the combined exploitation
of a fundamental physical concept, a simple mathematical principle, and use of modern data
technology. Introduction of this relatively young method into instrument technology has given
great impetus to nuclear magnetic resonance and infrared spectroscopy. The infrared spectroscopic investigation of low frequency molecular vibrations has especially profited : in this connection
one speaks of far infrared (FIR) Fourier Spectroscopy, which has opened up numerous interesting
applications in organic, inorganic, and physical chemistry.
1. Introduction
Nowadays, the methods ofvibrational spectroscopy---IRand
Raman spectroscopy-are used along with NMR and mass
spectroscopy for the elucidation of chemical structures". 411.
In principle they afford an almost complete overview of the
vibrational behavior of molecules, from which structural parameters can be determined qualitatively and quantitatively.
The two methods are distinguished by the complementary
nature of the information which they provide. Vibrations
accompanied by a strong change of dipole moment can be
observed particularly well in the IR spectrum (intense IR
absorption bands); vibrations accompanied by a strong change
in polarizability are readily observed in the Raman spectrum
(intense Raman lines). If a molecule has a center of symmetry
the vibrations are observable either in the IR spectrum only
(exclusively IR-active vibrations) or in the Raman spectrum
only (exclusively Raman-active vibrations). However, the ideal
case for vibration-spectroscopic analysis, in which the frequencies of all normal vibrations of a molecule can be determined,
seldom occurs. The reasons for this are far less theoretical
than practical ones-equipment parameters and methods of
sample preparation effect reduction in information quality,
particularly in the region of low frequency vibrations. In the
first place more or less pronounced difficulties are met withdepending on the measuring principle in the IR spectroscopic
investigation of low frequency vibrations-due
to the
smallness of the signals to be measured. In this connection
the Fourier method or Fourier spectroscopy as a measuring
principle has enabled considerable advances to be made over
the conventional dispersive methods. One refers to the spectral
region of electromagnetic radiation, which on the one hand
embraces the low frequency vibrations and on the other is
a region in which the advantages of the Fourier method
become particularly apparent, as the far IR or FIR region.
Its upper and lower limits lie at C N . 500 c m - ' (20pm; 1 . 5 ~
10'" Hz) and IOcm-' (1000pm: 3.3 x 10" Hz). respectively.
In the present review the.types of vibrations to be expected
in the FIR region are first briefly characterized. The wealth
of structural information which they disclose seems to justify
the considerable outlay on apparatus necessary for making
the FIR region accessible. Currently one already has the choice
of half a dozen commercially available FIR apparatus. They
all function, with one exception, on the same measuring prin~~
[*I
ciple: the Fourier method. In order to provide a fully illustrative account of this measuring principle and its more important
consequences the following review will deal with the most
striking advantages of the Fourier method in the FIR region
as well as the fundamental principles that it has in common
with conventional dispersive methods.
2. Applications of FIR Spectroscopy in Chemistry
What is the information that can be derived from the FIR
spectrum of a specific substance? It comprises information
about the rotational and vibrational behavior of molecules.
In this field the main accent is laid on vibrations since only
a very few small molecules such as H 2 0 , D 2 0 , H2S, CO.
NH3, HCI, etc.". show pure rotational transitions in the
FIR region. Apart from these exceptions the typical spectral
region for pure rotational transitions is the microwave region.
(For gaseous samples rotational transitions can of course
be ~uperimposed[~]
on vibrational transitions.)
If we assume a harmonic oscillator the frequency 0 (measured in cm l ) of the vibration of a diatomic molecule can
be calculated from the relationship:
where m, is the reduced mass, k the force constant, and c
the velocity of light. For polyatomic molecules the one vibration ofthediatomic molecule is replaced by a series of so-called
normal vibrations. In general the more complicated is the
structure of a molecule-and here we include giant molecules
such as exist in the form of crystals-the more complicated
becomes the calculation of the frequencies and types of its
vibrations. Equation (1) can be generalized for polyatomic
molecules as follows: The frequency or the, wave number
of an individual normal vibration is the smaller. the greater the
masses (for rotatory vibrations moments of inertia) concerned
in the vibration and the smaller the forces (for rotatory vibrations torques) that oppose the displacement of individual molecular components from the equilibrium positions. On the
basis of several decades of experience[*] with the assignment
of MIR spectra (MIR region: 4000 to CU. 400cm-') of organic
and inorganic substances one can extrapolate from this generalization of relation (1) to the FIR region. One can thus predict
.
.
Dr E. Knoringer
Lehrstuhl fiir Physikalische Chemie der Gesamthochschule
59 Siegen 21, Postfach 210209 (Gcrmany)
[*] T h e first absorption spectra
in
the I R region were meastired by W
I*. Cohlrnrz in 1905.
25
which molecules will undergo normal vibrations with frequencies in the FIR region.
The relevant types of vibration will be characterized in
the following sections and explained by means of examples.
The numerical values quoted for the force constants should
be regarded as only approximate.
In the present progress report it will not be possible to
deal with the numerous applications of FIR spectroscopy
in the field of physics particularly solid-state physics. For
this purpose the reader is referred to the book by M d k r
and Rorli,schi/d'21which contains, inter alia, a review of all
present-day physical applications of FIR spectroscopy.
2.1. Stretching Vibrations
Normal vibrations are described as stretching vibrations
if they lead predominantly to changes in the bond lengths.
This type of vibration is observed in the FIR region['] if
heavy constituents are present in the molecule and their movement actually contributes to the change in the relevant bond
length. In this connection the heavy constituents are considered--naturally only as a rule-to be the elements of the
fourth and higher periods of the Periodic Table. Typical
examples of application are the FIR investigations of carbonyl-["] and halo-metal complexes[' '. "].
The probability of finding a definite stretching vibration
in the FIR region is further increased by two effects:
- not only the masses of the atoms but also their ionic radii
increase from period to period. The larger the ionic radii
of the bonded atoms, the longer is the bond length and,
according to Badger's rule18],the smaller is the force constant.
- it is often not only the masses of the atoms directly involved
in a particular chemical bond but also larger masses that are
effective, as is shown when under certain conditions the
bonded atoms vibrate approximately in phase with the
ligands attached to them. In such cases, the term skeletal
vibrations is used (Section 2.3).
2.3. Skeletal Vibrations of Macromolecules
The skeleton of macromolecules consists in general of relatively light atoms, e. g. carbon atoms, but it undergoes forms
of vibration in which large groups of neighboring skeletal
atoms vibrating in phase vibrate in opposition to other such
groups. The force constant is then approximately of the same
magnitudeas in the stretching or bending vibrations of skeletal
atoms of a comparable smaller, e. g. triatomic, molecule; however, in general very much larger masses are concerned, as
they are-to a first approximation-the sums of the masses
of atoms vibrating in phase. Correspondingly, the wave
numbers for such skeletal vibrations are low.
A special case of these skeletal vibrations of macromolecules
is provided by the so-called one-dimensional lattice vibrations
of long-chain unbranched molecules. These include, for
example, the "accordion vibration" of unbranched aliphatic
hydrocarbon^['^^ "1, where the wave number is smaller than
220cm-' when ten or more carbon atoms are concerned;
admittedly, this vibration is Raman-active only when the chain
skeleton consists wholly of the same type of atoms (e.g. carbons) and when the substituents on the skeletal atoms are
all of the same type.
2.4. Skeletal Vibrations of Ringahaped Molecules
The skeletal vibrations of ring-shaped molecules generally
occur in the FIR region if there are only negligible changes
in the bond lengths and bond angles. Such vibrations are
observed in the case of planar or almost planar rings, if
the ring atoms swing out of the "ring plane". In the case
of four- and five-membered rings this form of vibration is
known as ring-puckering vibration (cf. Fig. 1).
/&
'*
26
/
I
I/
I
i
2.2. Bending Vibrations
Bending vibrations is the term applied to normal vibrations
in which mainly the bond angles change. They occur at lower
wave numbers than the comparable stretching vibrations, since
the forces that oppose displacement of molecular components
from their equilibrium positions are always stronger along
the direction of the bond than perpendicular to this direction.
Thus, bending vibrations are found in the FIR region for
all compounds whose stretching vibrations are to be found
in that region'"], e. g. carbonyl-["] and halo-metal complexes" "I. Furthermore, bending vibrations also appear
in the FIR region when light atoms (elements of the second
and third periods) are involved; as an example may be mentioned the bending vibration by which the COC angle in
methyl formate or methyl acetate is altered (325 or 303 cm- I ) .
Still lower wave numbers are recorded if whole groups of
atoms vibrate completely or approximately in phase with
the atoms under consideration; this can be shown e.g. for
alkyl formates when the alkyl group is larger than a methyl
group[131.In this case the term skeletal vibrations is also
used (see Section 2.3).
I
/
I
t--
I
----->
Fig. I . Schematic representation of the ring puckering vibration of a four-membered ring (for the sake of simpltcity the substituents on the ring atoms
have been omitted).
In the absence of double bonds the force constant for this
type of vibration is determined mainly by the interaction
forces between the substituents on the various ring atoms.
The magnitude of these forces is of the same order as that
of intermolecular interactions; this explains the low wave
numbers of ring-puckering vibrations which, for example, are
observed for oxetanes between 50 and 160 cm"I'']. Immediately double bonds are present in the ring, the respective vibrations occur at higher wave numbers.
2.5. Torsional Vibrations
In torsional vibrations (as in ring-puckering vibrations) the
bond lengths and bond angles also remain, to a first approximation, unchanged. What is changed is a dihedral angle (Fig.
2), i.e. the orientation of two parts of the molecule relative
A n g m . Chrm. I n r . Ed. Engl. 1 Vol. 15 ( 1 9 7 6 ) No I
to one another; here the only degree of freedom is the rotation
of the two parts of the molecule (AX2, BY2) around the
chemical bond (A-B) connecting them. The wave number
t for the torsional vibration depends on the reduced moment
of inertia I , and on the torque constant D :
If x molecules containing a total of n,=n.x atoms come
together to form an association, then N, normal vibrations
are observable where
N, = 3 n, - 6
Together with expression (3), this gives:
N X - x . N = 6 ( x - 1)
Here the reduced moment of inertia is obtained from the
moments of inertia of the two parts ofthe molecule analogously
to the way in which the reduced mass of a diatomic molecule
is obtained from the two individual atomic masses. Thus,
not only the mass of the atoms taking part in the vibration
but also their distance perpendicularly from the rotation axis
is responsible for the wave number 7 .
Y
Fig. 2. Schematic representation of the torsional vibration of a molecule
X2ABY, around the axis of the A -B bond.
In the case of a torsional vibration around a single bond
the torque constant with respect to this bond is determined
by the interaction between the substituents on one of the
bonded atoms (A) and those on the second atom (B); this
means that its value is determined by steric factors. Typical
examples are the torsion of methyl groups around C-C,
the torsion of OH
C-0, or C-N single bonds[’7-2’*271,
groups in aliphatic
and of NH2 groups in primary
amines’”31or hydrazines’*‘! The situation is different for torsional vibrations around a bond axis that has double-bond
character. The rotatability around such bonds is more restricted, and the torque constant can be determined largely
by the double-bond character. As has been shown by investigations of butadiene and glyoxal and compounds derived therefrom (C-C bond axes with partial double-bond chara ~ t e r ) [ ’ ~ . and
’ ~ ] of alkyl esters of carboxylic acids (C-0
bond axes with partial double-bond ~haracter)’~’~,
the wave
numbers for the corresponding torsional vibrations depend
largely on the properties of the substituents, which can exert
an effect through the reduced moment of inertia and the
torque constant (inductive and mesomeric effects).
2.6. Intermolecular Vibrations
The number N of normal vibrations of a nonlinear molecule
composed of n atoms can be calculated from the formula:
N=3n-6
A i y e w . Chem. / ! i t .
(3)
Ed. Etlyl. i Vol. 15 ( 1 9 7 6 ) N o . 1
(4)
In the association there are thus 6(x- 1) normal vibrations
more than in the total of x isolated molecules. Where d o
these 6(x- 1) vibrations come from?
The total number of degrees of freedom concerned with
rotation, translation, and vibration is constant for a system
of n . x atoms independently of how these atoms are combined
into molecules and associations. On combination of x molecules to form an association 3 (x- 1) rotational degrees of
freedom and 3 (x- 1) translational degrees of freedom disappear. An individual molecule can no longer undergo translation or rotation independently of the others; only the association as a whole has the possibility of this type of movement.
These 6(x - 1) lost rotational and translational degrees of
freedom have become the above mentioned 6(x - 1) additional
vibrational (librational and translational vibrations) degrees
offreedom in the association. They correspond to the so-called
intermolecular vibrations in which the individual molecules
vibrate as more or less rigid structures. In this process relatively
large masses, namely those of the molecules, move in opposition to relatively weak forces, namely the intermolecular interactions; and this results in low-frequency vibrations generally
found in the region below 300cm-’. The force constants
have values between 1.0 and 0.001 mdyne/A and are thus
normally smaller by orders of magnitude than the force constants of principal valence bonds (ca. 20 to 1 mdyne/A).
As is well known, the influence of intermolecular interactions
on single molecules can be studied by various spectroscopic
methods such as MIR, UV/VIS, and NMR spectroscopy.
All these methods, however, have in common the feature
that they supply only part of the Information-they indicate
how the skeleton and the electron distribution of a molecule
change under the influence of specific intermolecular interactions, but information about the nature of these interactions
themselves is obtained only by investigation of the lower-frequency vibrations, i. e. by FIR spectroscopy and Raman spectroscopy. Applications of FIR spectroscopy for such purposes
are described in Sections 2.6.1 to 2.6.4.
2.6.1. Hydrogen Bonding
Association by means of hydrogen bonding is observed
for water, alcohols, carboxylic acids, amines, etc..[*’l and for
their
with other polar compounds in the liquid
and solid phase, and frequently also in the gaseous phase.
The force constants for vibrations of the individual molecules
in the direction of the H bonding are between 1 and
0.1 mdyne/A; the force constants of the other so-called Hbonding “vibrations” are correspondingly smaller. Study of
H bonding by FIR spectroscopy has been particularly detailed
for carboxylic acidsL2’ 3”1. Intramolecular H bonding is
regarded as a special case of this type of intermolecular interaction: as a kind of intermolecular interaction it is observable
27
in the FIR spectrum only in the form of intramolecular vibrations. Investigations of compounds of the salicylic acid type
are still in progress[32!
2.6.2. "Weak" Intermolecular Interactions
Dispersive forces and dipole-dipole interactions etc. belong
to this group. The force constants are generally smaller by
1 or 2 orders of magnitude than those for H bonding, and
the wave numbers of the corresponding vibrations are therefore
very low (less than 100cm
34! Under the usual conditions the absorption bands observed are strongly broadened
because of the multivarious intermolecular force constants
in solid and liquid samples (cf. Fig. 3). Of particular interest
in this connection are rc-electron-rich (dispersive forces!) and
strongly polar substances (dipole-dipole interaction !). TO
exhaust the information content of the FIR spectrum additional experimental work (matrix isolation techniquel8'1) is
necessary.
2.6.4. Lattice Forces in Molecular Crystals
Molecular crystals can be regarded as associations in which
a very large number of molecules are joined together, whereby
various types of interaction force can be observed. The intermolecular vibrations of such a crystal are known as lattice
vibrations. Only those lattice vibrations in which neighboring
primitive unit cells vibrate in phase can be observed by means
of IR and Raman spectroscopy. This means that when the
number of intermolecular vibrations of a molecular crystal
observable in IR or Raman spectra is being determined, only
the number of molecules combined in one' primitive unit cell is
taken into account; this number replaces the x in Eq. (4). I n
this case equation (4) must be modified further. Thus, not only
the librational and translational vibrations within a primitive
unit cell but also the three in-phase librational vibrations of the
whole primitive unit cell around the three spatial axes can be
observed in the IR and/or the Raman spectra. This is. ofcourse.
not the case for the three in-phase translational vibrations of
the whole primitive unit cell in the direction of the three spatial
axes; these correspond to translatory movement of the whole
crystal. The number of lattice vibrations of a molecular crystal
that can be observed by the methods of vibration spectroscopy
thus amounts not to 6(x- 1 ) [Eq. (4)]. but to 6s-3. The spectral region corresponding to these lattice vibrations lies below
2(jocm-lL33.3X1
The crystalline portions of polymers provide a special problem in crystal structure; in polyethylene, for example, the
crystalline portions give rise to a lattice vibration at
72 cm- 1[3q. 401
hr'
If the masses of crystalline components are sufficiently large
then, of course, also the lattice vibrations of valence and
ionic crystals lie in the FIR region (e. g. alkali metal halides
such as KBr etc.).
3. The Importance of FIR Spectroscopy in Chemistry
and its Problems
I
I
500
.m
100
3W
t-w i i e
I
200
1w
20
number [ m11
Fig. 3. FIR spectra of a ) chloroform and b) benzene (liquid' layer thickness
I m m ) and c) of acetonitrile (dissolved in CCI,, c % 10 moI-",<;; layer thickness
1 mm).
2.6.3. Interactions between Adsorbed Molecules and the
Adsorbent
Investigatlon of the vibrations of adsorbed molecules with
respect to the adsorbent enables some conclusions to be made
about the nature of the interactions between them"'- 371.
Inter aha, H bonding, dispersive forces, and dipole-dipole
interactions may play a part here.-Such studies are important
for surface chemistry and heterogenous catalysis. As examples
may be cited studies on the adsorption of ~ a t e r ' ~ ' . "and
~ of
organic molecules[3510; silica gel. Admittedly, the information
content of the FIR spectra is usually greatly reduced because
of the heterogeneity of the surface concerned and the resulting
band broadening.
28
All compounds that absorb in the FIR region exhibit absorption bands with considerably higher absorbance coefficients c
in the mid IR (MIR) and/or in the UV/VIS region; e.g. in
the MIR region E assumes maximum values of about
2000 I/mol .cm, whereas the corresponding values in the FIR
region are smaller by a factor of at least 1/5; naturally, this
makes itself apparent, on the one hand by the amount of
sample required and on the other-so as to ensure an acceptable signal-to-noise ratio in the spectrum-by
increased
demands on the apparatus. Even more pronounced are the
differences in absorbance coefficients on comparing the FIR
with the UV/VIS region. It thus follows that quantitative
analyses can be carried out with very much higher sensitivity
and-as regards equipment-more favorable detection limits
in these shorter wavelength regions. Consequently, FIR spectroscopy is resorted to only in exceptional cases for the purpose
of qualitative analysis and identification of unknown substances. Its main area of application is in structural elucidations.
Although the content of information in the FIR region
is undoubtedly smaller than that in the MIR region for many
compounds, in particular organic ones, the importance of
the FIR region in chemistry, including organic chemistry,
is not to be underestimated. The reason is that the assignment
A n y r x . Cheni.
Iilr.
Ed. Engl.
I
Vul. I5 ( l Y 7 6 ) No. 1
of an FIR spectrum provides access to important physical and
physicochemical information:
100
The structure of many compounds that contain one or
more heavy atoms can be determined with the aid of vibration-spectroscopic methods only if the FIR spectrum is
taken into consideration.
- For normal coordinate analysis the information about the
vibrational behavior of molecules must be as complete as
possible; the low-frequency region cannot be arbitrarily
excluded, for the solution is then no more than approximate.
- For determination of thermodynamic functions it is precisely
the low-frequency normal vibrations that play a decisive
role'"'].
- Facts about the potential barriers in interconversion of
conformers are closely related to the wave number of torsional and ring-puckering vibrations, which are found exclusively in the FIR region.
-- Intermolecular interactions, which are often responsible for
the conformation of a compound and decisively determine
its physical behavior, can be investigated directly in the
FIR region.
The problems of assignment in the FIR region reside in
the facts that a large number of different types of vibration
(see Sections 2.1 to 2.6) can be observed next to one another
and that the concept of group frequencies, which so greatly
assist the assignment in the MIR region, is applicable only
in exceptional cases in the FIR region. The reason for this
is that the low-frequency normal vibrations generally involve
a relatively large number of atoms with non-negligible amplitude. This is immediately apparent for skeletal, torsional, and
intermolecular vibrations; for example, in a torsional vibration
around a specific bond axis there is movement of all the
atoms in the molecule except those that occur along this
axis. In the case of torsional vibrations one can therefore
speak of a group frequency only when the reduced moment
of inertia is almost identical with the moment of inertia of
the group under study referred to the torsion axis; i. e. when
this moment of inertia is small in comparison with the corresponding moment of inertia of the other part of the niolecu1e.An additional complication in the interpretation of the FIR
spectrum arises through the increasing intensity of "hot bands"
with decreasing wavelength (at 500 cm- and room tempel-ature already w. 1'10 of the molecules investigated are in the
first excited state!l4l1)andthrough band-splitting which occurs.
ir7rrr trfitr. in torsional vibrations and has its origin in special
Moreover
potential curLes having two or three minima"
as in the MIR region- difference bands, combination bands.
and overtones can interfere: they usually lead. of course, to weak
intensity bands.
How varied the information in the FIR region can be,
even for purely organic molecules (only light bonded atoms),
is shown in Fig. 4, in which the FIR spectra of some alkyl
acetic esters have been c ~ l l e c t e dThe
~~~
assignment
~.
naturally
requires the additional introduction of Raman spectroscopy.
Further difficulties arise when attempting to extract the
maximum of information from the FIR spectrum in the region
around and below 100cm-'. The reasons for this are as
follows:
50
-
-
"Hot bands"ofconsiderab1e intensity occur at room temperature in this region of low-frequency vibrations.
500
k%d
a1
LOO
-Wave
300
200
100
0
number [cm-'l
Fig. 4. FIR spectra of a l k k l esters of acetic acid, CI-I,COOR ( d i s d v e d
in C J i , L , c :5 to IOmol-",,: layer thickness 2 m m ) : a ) R=CH.,. h) R = C L H i r
c) R = i - C , H - . d ) R=t-C,Hq.
Low-frequency intramolecular vibrations are strongly
influenced by intermolecular interactions.
- The low-frequency vibrations corresponding to the intermolecular interactions in solid and--particularly-liquid
phases are usually characterized by a large variety of different force constants.
As a result, a single broad absorption band is found below
100 c m - for many substances, particularly in the liquid phase
(cf. Fig. 3). The information content of this band can possibly
be made accessible to the chemist by the matrix isolation
technique["]. This opens up a broad and very interesting
field of application for FIR Fourier spectroscopy where, however, because of fundamental difficulties (high radiated power
on cooled sample!), the Raman spectrum is no longer expected
to have its usual importance as a supplementary source of
information.
The assignment of an FIR spectrum is only possible when
the sample to be examined has been suitably prepared. For
the problems arising in this connection and their solution
the reader is referred to the literature[63,- 3 - 8 2 1 ,
--
4. Principles of the Fourier Method
4.1. The General Problem in Optical Spectroscopy
The general problem in optical spectroscopy, irrespective
of the spectral region, is to determine the intensity I of electromagnetic radiation as a function of the frequency v , the wave
number 0 or the wavelength A. The fact that especially in
29
IR spectroscopy the transmittance T($,=I(?, I,,,,,, or its negative common logarithm, the absorbance, is used. is of secondary
importance and arises because a substance-specific datum
is called for that must be independent of the apparatus-specific
intensity distribution lo,?). For thedetermination ofan intensity
distribution the series of waves with different wave numbers
contained in a polychromatic light wave must be separated
from one another in some wayt42! For this purpose a code
is needed in which, in accord with information theory[431,
a set of values of some measurable quantity A , is assigned
to the set of values of the wave number 0, :
Thus the intensity is measured as a function of this measurable quantity A,, and the dependence I,?,,is finally determined
on decoding.
When choosing the code [Eq. (S)], the properties of electromagnetic radiation must be taken into account. For an unambiguous description of a nonpolarized, monochromatic, electromagnetic wave in a vacuum four quantities are available:
Intensity I
Wave number 0
Direction of propagation 7f
Phase state cp
I is one measurable quantity of interest here, and 0 is
the other. There are thus two determinable quantities still
free that can be used for coding, namely ?and cp.
CO,)-(Z,)
(54
(0,)-(cp,)
(5 b)
The problem of coding solves itself if an apparatus is available for use as a light source by means of which monochromatic
radiation of variable wave number can be produced. The
wave number 0, can then always be related to a specific
setting X , of one parameter of the apparatus:
The decision for or against one or the other form of coding
depends on the following criteria:
- Unambiguity :
- Accuracy;
The apparatus required;
- The radiation flux through the measuring equipment.
The far infrared lies between the microwave region
( < 10 cm - ')and the mid IR region ( > 500 cm- '). The question
is whether the methods of coding customary in these last
two spectral regions and of long-proved value are applicable
and useful in the FIR region.
The microwave region is a domain of nondispersive spectroscopy. Electronically controllable high-frequency tubes are
used, e. g. reflex klystrons, which act as sources of monochromatic light.
For the medium IR region the so-called conventional dispersive spectroscopy is used. By means of a monochromator
each wave train is assigned a specific propagation direction
?, corresponding to its wave number 0,. In practice, we use
for this purpose:
- the wave-number dependence of the angle of refraction
of light in a suitable prism or
the wave-number dependence of the angle of diffraction
of light by a suitable grating
At a specific distance from the dispersive element (prism
or grating) one can thus, given suitable imaging optics, measure
the intensity I,& corresponding to each direction of propagation by means of an aperture diaphragm and, behind it, a
detector. The intensity distribution I,<,, is then obtained by
means of the well-known code (5a). Assessed by the previously
mentioned criteria, this method of coding is satisfactory except
in one respect: the radiation flux from the light source to
the detector is considerably reduced. There are two reasons
for this reduction:
- To a first approximation, the aperture diaphragm in front
of the radiation detector allows the passage only of light
with a specific propagation direction and thus with a specific
wave number Oi. All light waves with 0+Oi are kept away
from the detector.
Deflection of the light at the dispersive element occurs
in one dimension ; accordingly, the diaphragm aperture delimiting the radiation flux muxt be a slit. The finer the details
of the intensity distribution I , ; , that are to be recorded,
the smaller must be the slit width. The radiation flux is
thus reduced in comparison with that from a comparable
circular aperture (see Section 4.2). A circular aperture can
always be used if the code (5a) is not required, i.e. if the
wave trains of differing wave numbers all have the same
direction of propagation.
So long as both intense light sources and sensitive detectors
are available for the spectral region under study, the reduction
of the light flux is really disadvantageous (that is the signalto-noise ratio is unpdvorable and,'or the time of the measurement is prolonged) only in exceptional circumstances. These
exceptions occur:
when there is a strong background absorption ( e . g . by
the solvent),
- in investigations involving high-resolution conditions, and
in the investigation of microsamples.
Spectral regions, in which the conventional dispersive
method, i. e. code (Sa), leads in most cases to useful results,
are the near-IR and the UV/VIS as well as the mid IR.
-
~
~
4.2. Principle of the Fourier Method Regarding Its Use in
FIR Spectroscopy
~
30
The nondispersive spectroscopy practised in the microwave
region is not applicable to the FIR region; electronically
controllable high-frequency tubes are available only up to a
maximum of a few 100 GHz (100 GHz 5 3.3 cm-'). It
can be expected, however, that in a few years controllable
lasers in the FIR region will take over the function of electronically controllable high-frequency tubes in the microwave
region.-If conventional dispersive spectroscopy is introduced
in the FIR region [coding according to relation (Sa)], the
reduced radiation flux is disadvantageous even under normal
conditions, since only light sources of relatively weak intensity
and relatively insensitive radiation detectors are available for
the spectral region below 500cm '.
For the FIR region we thus need a different kind of codingC4',4h1. This is provided by relation (5 b), in which a specific
phase or phase difference is unambiguously assigned to each
wave number while, however, all the wave trains of different
~
wave number retain the same direction of propagation. The
concept of phase difference makes it immediately clear that
there must be two waves between which the phase difference
exists. Hence the light wave to be investigated must be divided
into two partial waves. Let us first assume-for the sake
of simplicity-that a monochromatic plane light wave is present and that it has been divided into two partial waves
of the same intensity I,i),same direction of propagation, and
same state of polarization. After we have produced a variable
phase difference cp between them, we now make these partial
waves overlap. The cp-dependent intensity is then measured
in the overlap region:
If cp=O or an integral multiple of 271, then I(,+) assumes
its maximum value of 41(?,. If cp is an odd multiple of n,
then
has the lowest possible value, namely zero. 11,) is
called the interferogram, and the cp-dependent component
in formula (6) is called the interferogram function:
For the production of the variable phase difference between
the two planar light waves the latter are allowed to traverse
different but well-defined paths. The phase difference cp
depends on theoptical path difference x and on the wavelength
h or wave number 0:
X
cp1.,=2n- = 2 n 0 x
h
(8)
Thus, the desired coding is achieved: according to Eq. (S),
the wave number 0 is unambiguously assigned a phase difference cp as a function of the optical path difference x. In
the present experiment there is thus, according to Eqs. (7)
and (S), for the monochromatic light wave under study, a
corresponding experimentally measurable harmonic function-the interferogram function F,,,-whose amplitude is
proportional to the desired quantity I , i , and whose argument
is equal to the phase difference cpl,,=27c0x:
If, in place of monochromatic light, we are dealing with
polychromatic light having any desired continuous intensity
distribution, the interferogram functions corresponding to the
individual wave numbers overlap without distortion with a
fixed phase relationship, given by Eq. (S), between them. For
a n optical path difference x = O all the wave trains, irrespective
of the wave number 0,give an interference maximum. Mathematically speaking, the overlap of the interferogram functions
corresponding to the different wave numbers implies integration of the “monochromatic interferogram function” (7 a) over
all possible values of 0:
Here Ilelhas the meaning of a n intensity density, i. e. exactly
the quantity that one wishes to determine in spectroscopic
investigations. In Fig. 5 the interferogram functions for polyA t l g r ~ Chwi. Int. E d . Enyl.
I_
lie/.
i j (1976) No. 1
chromatic light having a continuous intensity distribution and
for monochromatic light are placed side by side. It will be
seen that in the former case the amplitudes become smaller
and smallerwith increasingabsolute valueof the path difference
x and finally reach zero; the cause of this is explained in
Section 4.3.
x:a
Optical
I
~
path differencex
Fig. 5. lnterlerogram functions (sections) for polychromatic light having a
continuous intensity distribution (above) and for strictly monochromatic
light (below): the ordinate scales are not all the same.
After its experimental determination, the “polychromatic
interferogram function” [Eq. (9)] must be investigated for
its harmonic components (characterized by the wave number
0 ) whose amplitudes all afford the desired value I(cj. The
procedure that makes this possible is none other than a mathematical filtering of the function F based on the property
of orthogonality of harmonic functions (cf. standard works
on higher mathematics):
The method outlined here for investigating an intensity
distribution I,cjthus differs in fundamentals from conventional
dispersive spectroscopy only in that the optical filtering of
the polychromatic light wave (in the monochromator) has
been replaced by mathematical filtering of the “polychromatic
interferogram function” provided by the interference experiment.
Independently of whether the filtering is carried out by
the optical or the mathematical method, we are always dealing
with a Fourier analysis. The method in which the filtering
is mathematical is called Fourier spectroscopy or Fourier
transformation spectroscopy (FTS), because here, in the determination of an intensity distribution, the procedure of Fourier
analysis or.Fourier transformation clearly emerges in its own
right.-In both methods interference experiments are carried
out (in dispersive spectroscopy with multibeam interference,
in Fourier spectroscopy with two-beam interference). In both
methods the desired intensity distribution is provided by evaluating the interference pattern. Both methods require Fourier
analysis; in conventional dispersive spectroscopy this procedure is effected by the analog monochromator/detector system,
in Fourier spectroscopy by a digital or analog computer after
or during the recording of the experimental quantities by
31
Parabolic mirrui
I
Sample
position
II
_---______-_-------
Golay
detector
-
,-Light
- source with aperture
I
I
I
I
diaphragm
!I
1
I
I
‘
!
I
Blackened
polyethylene
lens
I
I
II
1
/‘
I
I
I
1
I
I
I
I
I
.
~
I
I
1
I
Fixed mirror
I
I
I
Oetector
unit
I
Beam splitter
.‘
Light source
housing
Reduction
optics
Beam splitter
unit
Sample
space
Fig. 6. Construction and optical path of a Michelson interferometer for spectroscopy in the FIR region.
the detector. The physical and mathematical bases of the
Fourier method have been clearly described by, inter a h ,
Gunzel, Geick, Hurley, Grossu, and H o r l i ~ k [ ~” I ~. .S~pec~ific aspects of Fourier spectroscopy are dealt with in the proceedings of the “Aspen International Conference on Fourier
Spectroscopy I 970‘521.
What, then, are the advantages of the Fourier method over
the conventional dispersive method?
- In the first place, all wave trains with their different wave
numbers reach the detector simultaneously and not in succession. This difference in comparison with conventional
dispersive spectroscopy is called “the multiplex advantage”
(“Fellgett advantage”).
- Secondly, there is no need for the diaphragm aperture to
be in the form of a slit, since all the wave trains with
their different wave numbers have the same propagation
direction. With a circular aperture a radiation flux at least
two orders of magnitude higher than with a slit aperture
can be achieved for optical systems having the same resolving power (cf. Section 4.3) and the same collimator parame441. In this connection one
ters (focal length,
speaks of “throughput advantage” (“Jacquinot advantage”,
“etendue advantage”, “aperture advantage”). The throughput advantage is naturally partly or wholly lost as soon
as-e. g. in the investigation of microsamples-the preset
aperture of the apparatus is reduced.
Only through the Fourier method has FIR spectroscopy
attained its present importance in chemistry for structural
determinations. Besides the above-mentioned advantages over
the conventional dispersive method, it should be noted that
the problems of optical filtering are more easily solved and
especially that the optical systems are comparatively simpler
(Fig. 6). In this respect the Fourier method is also superior
to Hadamard transformation
46. 31 which
otherwise is, or at least could be, of equal value. It remains,
however, to explain why the Fourier method is not also generally used for the IR and UV/VIS regions.
An important reason for this-among o t h e r ~ [ ~ ~ ] - the
is
existence of problems with precision, which are not very impor4s3
32
’
tant between 20 and 1000pm (the FIR region) but become
greater with decreasing wavelength; the shorter the wavelength
of the light under study, the greater is the precision needed
SO as not to exceed a definite relative limit of error in the
determination of the abscissa values for F,,, [see Eq. (9)].
It follows that even in the mid IR region (between 2.5 and
20 pm) very much greater technical effort must be expended[54]
to obtain the full advantage of the Fourier method over the
conventional dispersive method.
The important components of a Fourier spectrophotometer
are the interferometer, which produces the experimental function
or I ( x ) and
, the system for evaluating the interferogram
data. It is not the purpose of this review to go into details
of apparatust6*s6 62, 641 (see also Refs. [2-41) or questions
of evaluating the interferogram (Fourier transformation)[s7,65-69.
721;here we shall only relate the theory discussed in this section to practice.
Figure 6 shows schematically the construction of an interferometer used for FIR spectroscopy (Beckman IR-720) and
the optical path of the radiation. It functions on the Michelson
principle. The two partial waves with the properties described
above are produced by splitting the wave amplitude of a
plane light wave in the beam splitter unit-this is the only component of the interferometer that is important for the explanation of the principle outlined above. (It can naturally also
be the wave front that is split, as occurs in the lamellar
grating interferometer[60-62!) The beam splitter itself is a
film that absorbs as weak]; as possible in the spectral region
of interest and which permits part of the incident light to
pass through while reflecting the remaining part. The light
transmitted through the beam splitter falls on a fixed plane
mirror parallel to the wave front. The light reflected from
the beam splitter falls on another plane mirror, also parallel
to the relevant wave front. Unlike the first mirror, however,
the second mirror is movable in the direction normal to
the wave front of the beam incident upon it, and its position
determines the phasedifference between the beams transmitted
and reflected at the beam splitter. After respectively reflection
and transmission through the splitter the two partial beams
~
Angrw. Chern. inr. Ed. Engl. j Vol. I S ( 1 9 7 6 ) No. I
finally reach a region (to the left of the splitter in Fig. 6)
where they can overlap (see Section 4.3). Their intensities
are exactly the same, since, given ideal mirrors and optimal
adjustment, they have the same history. In the region where
the two partial beams overlap the resulting intensity can be
measured and related to the position of the movable mirror,
i. e. the interferogram I,,, can be measured. Thence the interferogram function F(x, is obtained by simply subtracting a
constant value (which is equal to the integral intensity of the
two partial beams), and finally the spectrum 1 , ~by
) subsequent
mathematical filtration (Fourier transformation) of F(x).
All other commercially available FIR Fourier apparatus
(Polytec Model FIR-30, Digilab/Cambridge Instruments
Models FTS-16 and FTS-18, Bruker-Physik Model IFS-114,
Coderg Model FS-4000, and Grubb Parsons Models IS-3
and Mark 11)-in one or other variant-also function on
the Michelson principle.
Such a grating produces very broad interference maxima.
This means that generally speaking a very large number of
diffraction maxima must be passed through before the first
occasion is encountered where the maximum for one spectral
line coincides with the minimum of the other, which is the
prerequisite for the fact that the existence of two adjacent
spectral lines is at all observed in this experiment. As implied
in Eq. (Ila), the grating order n must be the higher, i.e.
the optical path difference n.h between the two interfering
beams must be larger, the closer together are the two spectral
lines, i. e. the smaller is A5.
This result can be applied to the Fourier method: in place
of n.h we set the maximal optical path difference xmaX
between
the two light waves that are made to overlap:
4.3. The Resolving Power of the Fourier Method
The resolving power A obtainable by means of a grating can
be calculated from the expression :
0
In order that two infinitely sharp spectral lines separated
by A 5 can just be resolved, x
, must have the value prescribed
by Eq. ( l l c ) :
A=-=nN
A0
where A 5 is the distance [measured in cm-’) between two
infinitely sharp neighboring spectral lines that are just resolved,
5 is the mean wave number for these two lines, N is the number
of lines of the grating, and n is the grating order.
xm.x
1
2A0
= __
A0 can of course also be regarded as the experimental
broadening, depending on the value of x,,,, of an infinitely
From
l i g h t source
Lattice with
2 Lines
Detect
Or
-
‘
I
Beam splitter
I
Movable mirror
;
I
I
,1
A\ _ _ ,
2-,
__
11x1
h
f i x e d mirror
Fig. 7. Schematic representation of the phenomenon of two-beam interlerence on a grating with two lines (above) and in the
Michelson interferometer (below). On the right is sketched the interferogram produced in both cases for strictly monochromatic
light
In the Fourier method a two-beam experiment (cf. Fig.
7: beams 1 and 2) is carried out. So far as the resolving
power is concerned this amounts to a diffraction experiment
with a grating (Fig. 7) containing only two lines (N=2); in
this case we have:
A I I ~ Y I I Cheiii.
.
l n r . Ed. Engl. f Vol. 15 ( 1 9 7 6 ) No. I
sharp spectral line. This is the quantity that in conventional dispersive spectroscopy is usually given as the “spectral slit width”.
In practice the spectral lines are never infinitely sharp,
a fact that is connected with the finite breadth of the energy
levels between which the light emission processes take place.
33
The question arises how the finite breadth of the spectral lines
is expressed in the interferogram function. For this purpose
the Heisenberg uncertainty principle provides an answer:
where Ap is the uncertainty in momentum and Aq the uncertainty in the position of a particle (e.g. a photon) and h
is Planck’s constant. Taking into account that
where AF,,, represents the half-width of the emission lines
studied, it follows from relation (12) that:
to exactly half of the maximal possible interferogram value (at
x = 0). The continuous decrease in the interferogram function,
which originates in the limited coherence length of the light
wave, is called the “seIf-apodization”[’ ‘ I .
So far only more or less sharp emission lines have been
discussed. In vibrational spectroscopy, however, one has to
do mostly with continuous emissions weakened by absorption
in specific areas. What, then, is the value of the coherence
length Ifor such an intensity distribution, absorption occurring
only within a specific spectral interval of width 2A\O,,, (Fig.
9, top) and there has the form prescribed by the transmittance
IT;?,? The coherence length can be determined by carrying
out the interference experiment described in Section 4.2 and
thus measuring the region in which the interferogram function
depends on the optical path difference.
t
For photons we can replace A4 by the length of the wave
train under consideration, namely the coherence length 1. It
follows that
The coherence length of a light wave is the greater, the
smaller the half-width of the sharpest of the spectral lines
corresponding to the light wave.
m
x- 0 :
;J,+ A? ”2
So- A?,,?
Fig. 9. Determination of the coherence length of light corresponding to
a continuous intensity distribution weakened in a narrow spectral interval
Z A G , , (for explanation see text).
The interferogram function for the intensity distribution discussed here has the following mathematical form [see also
Fig. 9 and Eq. (9)]:
x = I’
2’
La_q2al
Fig. 8. Schematic representation of the overlap region between two wave
trains of coherence length I in dependence on the optical path difference
Y.
The two partial waves produced from the light wave to
be studied (cf. Section 4.2) can only interfere if they overlap
completely or partially. Complete overlap occurs (see Fig.
8) when the optical path difference x is zero. The larger is
x, the smaller the overlap region becomes and the less marked
are the interference phenomena. Accordingly, the modulation
amplitude of the interferogram function decreases continually
with increasing optical path difference (Fig. 5, upper part),
until it becomes zero as soon as the optical path difference
equals or exceeds the coherence length (x 2 1). In the region
where x> I, the interferogram assumes a constant value which
is independent of the optical path difference and corresponds
34
The subscript k refers to the unweakened continuous intensity
distribution.
This equation can be rearranged to:
Angrw. Chem.
I I ~ IEd.
. Enyl.
,
&I/.
15 (1976) N o . 1
Fix1
cI
with
Fig 10. Determination of the sampling intervals (for explanation see t e x t )
and
In order to be able to calculate Zlv) from F,:, by Eq. (10)
one must care for numerical acquisition of FIX,between x=O
and x=xmax,which is not possible continuously but only
at specific intervals Ax (Fig. 10). This procedure in which
Eq. (15) is used with m=O, 1,2...
we obtain
(1 5 )
x=m.Ax
The interferogram function F,,, thus has two additive components :
- the contribution Fk(xl,
which corresponds to the broad-band
continuous intensity distribution (Fig. 9, upper part) and
which decreases “rapidly” to zero (Fig. 5, upper part), and
- the contribution
FA^] 21n), which, except for the minus
sign, corresponds to an emission band with the intensity
distribution z k ( v ) ( 1 - 7&,) and half-width AF1.2 (Fig. 9, lower
part) and which decreases to zero the more “slowly”, the
smaller is A? ,2 (half-width of the absorption band).
The coherence length 1 of a light wave that corresponds
to a continuous intensity distribution weakened in the interval
2AF1‘2 by absorption (Fig. 9, upper part) can thus be estimated
[Eq. (13)] if an indication of the half-width of the sharpest
absorption bands to be expected is available. For solid, liquid,
or dissolved samples under normal conditions, experience
shows that the half-width achieved is less than 10cm-I only
in exceptional cases. With this standard factor Eq. (13) leads
to a value of ca. 1 mm for the coherence length. If the maximal
optical path difference is chosen as xmax=2mm,then the
total region O < x < l in which the interferogram function
depends on the optical path difference is usually covered.
If xmax< [, then, as when the spectral slit width in conventional
dispersive apparatus is made too large, experimental broadening of the absorption lines is observed, as well as disturbing
artefacts-though the latter can be reduced mathematically
(by apodization)“’, ’‘I. If xma.> 1, then the measurement time
is increased without any gain in spectral information, and
in the region I<x<xrnaxadditional noise is recorded which
contributes through the Fourier transformation to a worsening
of the signal-to-noise ratio throughout the entire spectrum.
is called digitization of the function F,x,, Ax the sampling
Due to the digitization of the interferogram
function it is, of course, necessary to convert the integral
in Eq. (10) into a sum. After the choice of Ax’ the upper
limit of the spectral region to be measured is already fixed
because, according to the sampling theorem of information
theory, harmonic functions can be characterized unambiguously in digital form only when at least one ordinate value
per half-period is sampled. The Fourier transformation of
F ( x ican thus be effected unambiguously only if this condition
is fulfilled for all harmonic functions making up F,,). Since,
however, the periods of these harmonic functions are exactly
equal to the wavelengths of the polychromatic light studied,
only light of wavelength h>h,,, may contribute to the measured signal Z,Kl; we have:
or
Wave trains with F>Fmax contribute intensity to the wave
trains with F < F,,,; this means that the form of coding [relation
( 5b)] is not unambiguous. Unambiguity can, however, be
brought about if all the intensity contributions with wave
numbers 0>Om,, are eliminated by optical or electrical filtering.
The contributions with wave numbers Fz>F,,,
to the
intensity expected at wave numbers 0 <,F
,,
can be determined
as follows: The “monochromatic interferogram function”
F
Z cos 2 T ~ S1,x
is assigned to the wave number F1. From this, with allowance
for Eqs. (15) and (16), we obtain
4.4. Spectral Region for Measurement by the Fourier Method
mnFl
F1,,,= zcos 7
The spectral region usable for measurements is determined,
as in every spectroscopic method, by the characteristics of
the radiation from the light source, the sensitivity characteristics of the detector, and the type and efficiency of the optical
apparatus. A further aspect, however, also plays an important
part in the Fourier method.
Aagru.. Cheiii. I n t , E d EngI. ! Vol. 15 ( 1 9 7 6 ) N o . I
Vmax
Then we determine all those “monochromatic interferogram
functions”
vmnx
35
that with F2>Fmaxhave the same value as Fl,mlat the same
m ; after digitization they can no longer be distinguished from
F1(,,,).Finally, the calculation gives:
0,
={
In a search for errors not only the spectrum but also the
interferogram should be thoroughly and precisely inspected.
Differentiation of the various types of error (e. g. electronic
disturbances, wrongly chosen instrumental parameters, unsuitable preparation of the sample) is often only possible by
checking the interferogram alone (“Qualitative Interferogram
Evaluation”)[82’.
+
(2n 2)Fm,,- F 1
2n 0,,,+0,
If it is not certain that all the wave trains with F>Dmax are
excluded by optical or electrical filtering, then the intensity
measured for O,<Fmax may arise wholly or partially from
intensity contributions with 2 P m , , ~ 0 1 40,,,+01,
,
... efc., the
so-called false light contributions.
The problem of false light contributions arises not only
for the Fourier method but also in conventional dispersive
spectroscopy. Here the unambiguity of the assignment (5a)
can be safeguarded only by optical filtering, which is most
efficiently achieved with double or triple monochromators.
The false light (also misleadingly called stray light) that has
to be filtered out arises mainly from interfering grating orders.
Example I
Figure 11 shows that a slightly structured, continuous
intensity distribution I(?) provides an interferogram function
F ( x )that is dependent on the optical path difference .x over
only a relatively narrow region (Fig. I l a ) . On the other
hand, the optical path difference at which the interferogram function becomes constant (e.g. identical to zero) is
the larger, the sharper are the spectral lines present in the
intensity distribution I,,, (Fig. 11b, rotational transitions of
water vapor).
Interterogram
Spectrum
500
rn
1
I
1
400
300
200
t_
100
I
20
-0 1
0
I
I
I
0.1
02
0.3
Optical path diflerence [cm-’]
W a v e number [cm-’l
--is
Fig. 11. Comparison of the interferogram and the spectrum in the cases o l ( a ) continuous. and (b) discrete spectral intensity
distributions.
A further contribution is provided by light that passes through
the monochromator by routes deviating from the prescribed
beam path.
5. Simple Examples of the Interpretation of Interferograms
T o obtain a spectrum on a Fourier spectrophotometer the
Fourier transformation must in principle be carried out quantitatively. This is possible only with the aid of data-processing
machines, except for strictly monochromatic radiation (Fig.
5, lower part) or for polychromatic radiation that contains
only a few, strictly monochromatic, components, neither of
which are of practical interest. After some practice, however
valuable qualitative information can be extracted from the
interferogram without a quantitative Fourier transformation.
The labor of qualitatively interpreting interferograms will
materially assist the beginner in appreciating the principle of
the Fourier method.
36
The explanation of this follows from the Heisenberg uncertainty principle (Section 4.3), which provides a connection
between the coherence length of a light wave and the half-width
of the corresponding spectral lines or bands. Thus, one can
infer from the interferogram function alone whether there
are more or less sharp emission or absorption areas in the
intensity distribution studied.
Example 2
The periods of the harmonic functions that form the interferogram function are the larger, the longer are the wavelengths
of the light studied. This can be seen in Figure 12.
The figure shows two intensity distributions-one mainly
short-wave with a mean wavelength of about 26 pm (386 cm- ’)
and a second, mainly long-wave, with a mean wavelength
of about 155 pm (65 cm- ‘)-together with the corresponding
interferogram functions. The ratio of the mean wavelengths
is about I:6 and the same ratio is found again in the separations of the two central minima in the corresponding interferoAngen. Chern. Int. E d . Engl. J Vol. 15 ( 1 9 7 6 ) N o . I
Spectrum
-
Wavenumber [cm-’l
lnterierogram
Optical path diflerence
[cm-’]
+
Fig. 12. Comparison of the interferogram and the spectrum for mainly shortwave (a) and mainly long-wave light (b)
gram functions. The other minima in the interferogram function corresponding to the shorter-wave radiation likewise follow one another more closely than in those corresponding
to the longer-wave radiation. Thus, from the interferogram
function alone one can decide whether mainly short-wave
or mainly long-wave light is concerned. In this way one can
e. g. determine whether the attempts t o exclude light-scattering
effects during the preparation of the sample were successful.
Example 3
Periodic interference of the FIR spectrum prejudicial to
the substance-specific character of the information obtained
is often observed; this can have various causes, which can
be unambiguously identified from the interferogram function:
- Disturbing impulses in the interferogram function (Fig. 13a);
they are caused by electrical or mechanical interferences
and are not symmetrical about the position x=O.
- Internal reflection in a plane-parallel layer (e.g. in the cell,
in the sample carrier, or in the sample itself18’.821);figure
13b illustrates this case: the spectral intensity distribution
corresponds to the apparatus characteristic of a Michelson
interferometer where a plane-parallel almost absorption-free
paraffin wax film about 100pm thick has been introduced
into the path of the beam. The internal reflection in a
single plane-parallel layer produces in the interferogram
two side-burst peaks arranged symmetrically around x = O
(arrows in Fig. 13b). They are converted by the Fourier
transformation into the periodic interference observed
in the spectrum (“channel spectra”). If we use for the Fourier
transformation only that part of the interferogram function
that lies between these two maxima, the interference in the
spectrum disappears; admittedly, in certain circumstances
the resolving power is then too small for the determination
of the true band form (see Section 4.3 : cf. Fig. 1 3 b and 13c,
absorption band at 72cm- ’). The plane-parallelism between the relevant surfaces must then be destroyed in some
other way; in the present example this was done with the
Angen,. CArm. I n t . E d Engl. j Vol. 15 ( 1 9 7 6 ) No. I
KTZD
c
Wave number [ c m - l l
Fig. 13. Causes of periodic interference of the FIR Fourier spectrum (for
explanation see text).
37
-
paraffin wax film (wedge shaped), which finally gave the
interferogram and the spectrum shown in Figure 13d.
Overlapping ofa boxcar function (error in the determination
of the interferogram function from the interferogram) or
a triangular function (so-called drift in the interferogram)
on the interferogram function used for the Fourier transformation[' 21.
6. Concluding Remarks
Introduction of the Fourier method into FIR spectroscopy
has not only led to a considerable facilitation of work and
an improvement in the quality of the spectra, but has also
fostered interest in the FIR region. This is the case especially
for the introduction of FIR spectroscopy into organic chemistry. Owing to the absence of heavy bonded atoms in organic
molecules, the information content of the FIR spectrum was
long underestimated. It followed that the demands on finance
and time made by the measurement of FIR spectra by the
conventional dispersive method were rightly assessed as too
great. The introduction of the Fourier apparatus has certainly
not eased the financial burden, or at the most slightly so
in isolated cases; but its efficiency-greater than that of the
conventional dispersive apparatus-has
encouraged attack
on, and indeed in some cases the solution of, the problems
set out in Sections 2 and 3. The region below 100cm-',
which is especially important for the study of weak intermolecular interactions, would certainly have remained inaccessible
had it not been for the Fourier apparatus, and the expansion
of collections of spectra far into the FIR regionLs4]would
presumably never have happened without the Fourier apparatus.
In recent years the Fourier method has received recognition
and more extended use in NMR spectroscopy[65.8 5 - 8 8 1, as
it has in FIR spectroscopy. In particular, 3C-NMR spectroscopy owes its present importance as an analytical tool exclusively to the Fourier method.
This progress report is based on five years experience in
thefield o f F I R Fourier spectroscopy which the author collected
in the Anwendungstechnik and Training Department at Beckman
Instruments GmbH in Miinchen (Germany). Opportunity is
taken here to express thankful recognition of the possibilities
ofered by the firm Beckman to carry out relevant scientific
work-particularly
in the field of molecular spectroscopy.
Thanksaredue to Prof. Dr. B. Schrader (Universitat Dortmund)
and Priv. Doz. Dr. P. Bleckmann (Universitat Dortmund) for
valuable suggestions and e.\-pert opinion on parts of' the Iwnuscript, and to Grad. Ing. K . Dabelstein (Beckmann Instruments)
for help with the measurements necessary for this work.
Received: August 4, 1975 [A 92 IE]
[I]
[2]
13)
[4]
[S]
38
B . Schrader, Angew. Chem. 85, 925 (1973); Angew. Chem. Int. Ed.
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A. Finch, P. N . Gores, K . Radclige, F . N . Dickson, and F . F. Benrley.
Chemical Applications of Far Infrared Spectroscopy. Academic Press,
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R . J . Bell Introductory Fourier Transform Spectroscopy. Academic
Press, New York 1973.
F . Winflier, Z . Naturforsch. 28a, 1179 (1973).
'
[6] R. B. Sanderson and H. E . Scort, Appl. Opt. 10, 1097 (1971).
[7] A. R . H . Coirand F. R. Hoiiry, Appl. Opt. 10. 1581 (1971).
[8] H . A. Sraub' Einfiihrung in die theoretische organische Chemie Verlag
Chemie, Weinheim 1970, p. 194.
[Y] J . F.Ferraro: Low-Frequency VibrationsofInorganicand Coordination
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C 0 M M U N I CAT1 0 N S
Treatment of P,N4F,(NHJ2 ( 1 ) with SOCl, afforded
P,N,F,(NSO), (2). In the presence of pyridine, (2) eliminates
sulfur dioxide to give a low yield of 1,5,7,7,1O,lO-hexafluoro3h4-thia-2,4,6,8,9,1 I-hexaaza-I h5,5h5,7h5,1OA'-tetraphosphabicycle[ 3.3.3]undeca-2,3,5.7.9(l),lO-hexaene ( 3 ) .
Compound ( 3 ) is a yellowish crystalline solid which sublimes at 25"C/0.5 torr and melts at 57°C. Its composition
is proved by complete elemental analysis, and its monomeric
structure in the liquid and gaseous state follows from the
molecular weight (exp. 350, cryoscopic in C,H,) and the mass
spectrum [ M + : m/e 354 (48"/,)]. In the '"F-NMR spectrum
two multipletsappear in the intensity ratio of 1 :2, their centers
of gravity lying at SF= 59.8 ppm and 66.2 ppm. The spectrum
is independent of temperature, an argument strongly supporting the proposed structure ( 3 ) .
Procedure.
A Cyclophosphazene Spanned by a Sulfur Diimido
Group[**]
By Herbert M.: Roeskj and Enno JanssenF*]
Although the chemistry of fluorinated cyclophosphazenes
has been actively studied in recent years"], derivatives having
inorganic ring bridges have nevertheless remained unknown.
Consideration of a model of P,N4FR revealed that a central
bridge of this kind would have to have at least three members.
P1N,F6(NSO),['1 (4.2g, 0.01 mol) is heated in the presence
of a catalytic amount of pyridine (2 drops) on a water bath
for 7 d. Sublimation of the reaction product affords ( 3 ) (0.28 g,
8 "/,). This compound is also formed in low yield during the
preparation of P,N,F,(NSCI,), by heating of P+,N,F,(NHz)z
and sulfinyl chloride with elimination of SO, and HCI.
Received: August 21, 1975 [Z 323 IE]
German version: Angew. Chem. 88. 24 (1976)
-
[I]
[2]
f
1. Haiiluic The Chemistry of Inorganic Ring Systems. Wiley. New York
1970; S. Punrel and M Beckr-Gorhvirig: Sechs- und achtgliedrige Ringsysteme In der Phosphor-Stickstoff-Chemie. Sprineer. Berlin 1969.
H . M! Rouslj. and E . Junasrti, to be published.
2 S0Cll
- 4 HCI
Tellurium(1v) Iodide: Tetrameric Te41 Molecules in
the Solid[*']
By Volker Pauiat and Bernt Krebs[*l
The structures of chalcogen(rv) halides investigated up to
now are determined largely by the stereochemical activity
of the S'", Se'", and Telv nonbonding electron pairs. Gaseous
SF, and SeF, (also TeCI, in the gas phase)"] have the monomeric C,, structure predicted by the VSEPR theory"]; in
solid TeF,, on the other hand, square-pyramidal TeF, groups
are linked uin corners to form chains, the localized lone pair
(E) completing octahedral TeF5E c~ordination'~].
The structures of solid TeCI,'"J, TeBr,"], and SeC1,[61contain tetrameric
- -.
~
.~
[*] Prof'. Dr. H. W. Roesky and Di-. E. Janssen
[*] Prof. Dr. B. Krebs and DipLChem. V. Paulat
Anorganisch-chemisches Institut I der Universitit
6 Fi-ankfurt am Main SO, Niederurseler Hang (Germany)
[**I
This work was supported by the Deutsche Forschungsgemeinschaft
and the Fonds der Chemischen Industrie.
Fakultit fur Chemie der Universitit
48 Bielefeld, Universititsstrasse (Germany)
[**I
This work was supported by the Land Nordrhein-Westfalen and by
the Fonds der Chemischen Industrie.
39
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