1 1.1. INTRODUCTION Spectroscopy is a technique that uses the interaction of energy with a sample to perform an analysis and studying the properties of matter through its interaction with different frequency components of the electromagnetic spectrum. In general, spectroscopy is classified into two types: 1. Emission spectroscopy 2. Absorption spectroscopy In emission spectroscopy the radiation is emitted, whereas in absorption spectroscopy the radiation is absorbed. Atoms produce line spectra, whereas molecules produce band spectra. It is the most powerful tool available to the scientist for probing the microscopic world of atoms and molecules [1]. It - determines molecular structure - monitors and study molecular events - examines transition state of chemical reaction - enables calculations of many thermodynamic quantities. Molecular spectroscopy can be used to identify compounds, to measure how much of a compound is present, and to determine molecular properties. Absorption of energy can only take place when the energy of the radiation exactly matches the difference between molecular energy levels. The electromagnetic spectrum contains radiation with a large range of energies that can interact with various processes within molecules [2].
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1.1. INTRODUCTION
Spectroscopy is a technique that uses the interaction of energy with a sample
to perform an analysis and studying the properties of matter through its interaction
with different frequency components of the electromagnetic spectrum. In general,
spectroscopy is classified into two types:
1. Emission spectroscopy
2. Absorption spectroscopy
In emission spectroscopy the radiation is emitted, whereas in absorption
spectroscopy the radiation is absorbed. Atoms produce line spectra, whereas
molecules produce band spectra. It is the most powerful tool available to the scientist
for probing the microscopic world of atoms and molecules [1]. It
- determines molecular structure
- monitors and study molecular events
- examines transition state of chemical reaction
- enables calculations of many thermodynamic quantities.
Molecular spectroscopy can be used to identify compounds, to measure how
much of a compound is present, and to determine molecular properties. Absorption of
energy can only take place when the energy of the radiation exactly matches the
difference between molecular energy levels. The electromagnetic spectrum contains
radiation with a large range of energies that can interact with various processes within
molecules [2].
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Vibrational spectroscopy is the collective term used to describe two analytical
techniques–infrared and Raman spectroscopy. Infrared (IR) and Raman spectroscopy
are non–destructive, non–invasive tools that provide information about the molecular
composition, structure and interactions within a sample. These techniques measure
vibrational energy levels which are associated with the chemical bonds in the sample.
The sample spectrum is unique, like a fingerprint, and vibrational spectroscopy is
used for identification, characterisation, structure elucidation, reaction monitoring,
quality control, and quality assurance [3,4]. Vibrational spectroscopy encompasses the
techniques of infrared (IR) spectroscopy and Raman spectroscopy. Both IR and
Raman produce a spectrum which reflects the vibrational modes of the sample and is
therefore characteristic of its molecular structure. The information contained in the
spectra can be used for both qualitative and quantitative purposes. However, because
of differing quantum mechanical selection rules IR and Raman spectra are not
identical, but are said to be complementary. IR spectra tend to emphasize vibrations
involving polar groups (e.g. O-H, C-H, N-H, C=O etc) while Raman spectra tend to
emphasize the non-polar symmetric vibrations such as C=C and C-C stretches, and
aromatic ring breathing vibrations. IR and Raman spectra are collected in quite
different ways by very different spectrometers [5].
1.2. INFRARED SPECTROSCOPY
The spectral range for FT-IR spectra used by most chemists is approximately
4000–400 cm-1
. This range is now called the mid-IR and because it contains the
fundamental vibrational modes it is mostly useful for qualitative purposes, but it is
also much used for quantitative analysis. Now, mid-IR spectrometers have been based
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on an interferometer that produces an interferogram of the sample from which the
absorbance spectrum can be calculated. These spectrometers are known as Fourier
transform infrared (FT-IR) spectrometers. The FT-IR approach has a number of
advantages in terms of speed, accuracy, reproducibility and sensitivity. FT-IR has
revolutionized IR spectroscopy by allowing a range of sampling techniques to be
used, many of which are wasteful of energy, so that a useful and reproducible
spectrum of almost any sample can be obtained with relative ease. This made FT-IR
an extremely versatile technique [6].
Although the mid-IR is the most important spectral region for most chemists,
other regions are also significant. The near-IR (approximately 15000–4000 cm-1
) has
become important for quantitative work and for remote spectroscopy using fibre
optics. The far-IR (approx. 400–50 cm-1
) may be used to measure vibrations involving
metal atoms, for example in minerals and in organometallic compounds. Both near-IR
and far-IR can be accessed with an FT-IR spectrometers by utilizing appropriate
sources, beamsplitters and detectors.
1.3. RAMAN SPECTROSCOPY
When a beam of light is passed through a transparent substance, a small
amount of the radiation energy is scattered, even if all dust particles are rigorously
excluded from the substances. If monochromatic radiation of a very narrow frequency
band is used the scattered energy will consist almost entirely of radiation of the
incident frequency (the so-called Rayleigh scattering) but, in addition, certain discrete
frequencies above and below that of the incident beam will be scattered, which is
referred to as Raman scattering [7-10].
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1.4. APPLICATIONS OF VIBRATIONAL SPECTROSCOPY
The applications of vibrational spectroscopy are extremely diverse and the
techniques are making a contribution to many areas of science. Perhaps the most
interesting areas are in material science and in biomedical research where the early
detection of cancer in human tissues is a goal. Industrial applications, both on- and
off-line are also becoming important [11]. The use of chemometrics (statistical data
processing techniques) has become a standard method for extracting maximum
information from vibrational spectroscopic data.
1.5. SELECTION RULES FOR INFRARED AND RAMAN SPECTRA
Both Raman spectroscopy and infrared spectroscopy provide a unique spectral
fingerprint of a material. The patterns of the spectra are caused by molecular or lattice
vibrations. Although the spectral features of Raman and infrared spectra can be
interpreted in a similar way the spectra look slightly different. The whole vibrational
picture of a material is given by the complementary information of both Raman and
infrared spectra.
Using selection rules, it can be predicted whether a molecular vibration is
Raman or infrared active. During the interaction between a molecule and a photon the
total angular momentum in the electronic ground state has to be conserved. As a
consequence of this requirement only specific vibrational transitions are possible.
(a) Rule of mutual exclusion
In general, molecular vibrations symmetric with regard to the centre of
symmetry are forbidden in the infrared spectrum, whereas molecular vibrations which
are antisymmetric to the centre of symmetry are forbidden in the Raman spectrum.
This is known as the rule of mutual exclusion [10].
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(b) Selection rules for an infrared absorption and for Raman scattering
Infrared absorption can be detected if the dipole momentum µ in a molecule is
changed during the normal vibration. The intensity of an infrared absorption band IIR
depends on the change of the dipole moment µ during this vibration:
2
IR
0
�I µ
q
� �∂� �
∂� �
where q is the normal coordinate.
A Raman active vibration can be detected if the polarizability α in a molecule
is changed during the normal vibration. The intensity of a Raman active band
IRaman depends on the change of polarizability α during this vibration:
2
Raman
0
�I µ
q
� �∂� �
∂� �
As a consequence of the selection rules, infrared spectroscopy provides
detailed information about functional groups and Raman spectroscopy especially
contributes to the characterization of the carbon backbone of organic substances or
polymers [12].
Vibrational transitions may also be observed using IR or Raman spectroscopy.
For an IR absorption to be allowed between two vibrational levels, a change in dipole
moment (�) must occur as the atoms move, and �� must equal + 1. To be Raman
active (i.e. allowed), there must be a change in polarizability (�ij) during the vibration
and �� must equal ± 1. This polarizability can be better understood as an induced
dipole. A fundamental vibrational mode will involve a transition from the � = 0 level
to the � = 1 level. The selection rules for IR and for Raman spectra differ so that the
two techniques provide complementary information, not redundant information.
Therefore, the Raman spectrum provides significant new structural information, in
addition to that of IR spectrum.
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1.6. QUANTUM THEORY OF RAMAN EFFECT
Quantum mechanics gives a qualitative description of the phenomenon of
Raman Effect. A schematic energy level in Raman and Rayleigh scattering diagram is
shown in Fig.1.1.The Raman effect is the inelastic scattering of a photon. It was
discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa
Krishnan in liquids, [13] and by Grigory Landsberg and Leonid Mandelstam in
crystals [14,15]. When photons are scattered from an atom or molecule, most photons
are elastically scattered (Rayleigh scattering), such that the scattered photons have the
same kinetic energy (frequency) and wavelength as the incident photons. However, a
small fraction of the scattered photons (approximately 1 in 10 million) are scattered
by an excitation, with the scattered photons having a frequency different from, and
usually lower than, that of the incident photons [16]. In a gas, Raman scattering can
occur with a change in energy of a molecule due to a transition (see energy level).
Chemists are concerned primarily with such transitional Raman effects.
The different possibilities of visual light scattering: Rayleigh scattering (no
exchange of energy so the incident and emitted photons have the same energy),
Stokes scattering (the atom or molecule absorbs energy and the emitted photon has
less energy than the absorbed photon) and anti-Stokes scattering (the atom or
molecule loses energy and the emitted photon has more energy than the absorbed
photon) .The Raman Effect corresponds, in perturbation theory, to the absorption and
subsequent emission of a photon via an intermediate quantum state of a material. The
intermediate state can be either a “real”, i.e., stationary state or a virtual state. The
Raman interaction leads to two possible outcomes:
Fig. 1.1: Energy levels involved in Raman and Rayleigh Scattering
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• the material absorbs energy and the emitted photon has a lower energy
than the absorbed photon. This outcome is labeled Stokes Raman
scattering.
• the material loses energy and the emitted photon has a higher energy than
the absorbed photon. This outcome is labeled anti-Stokes Raman
scattering.
The energy difference between the absorbed and emitted photon corresponds
to the energy difference between two resonant states of the material and is
independent of the absolute energy of the photon. The spectrum of the emitted
photons is termed the Raman spectrum, and it is typically displayed according to the
energy difference with the absorbed photons. The stokes and anti-stokes spectra form
a symmetric pattern above and below the absorbed photon energy. The frequency
shifts are symmetric because they correspond to the energy difference between the
same upper and lower resonant states. The intensities of the pairs of features will
typically differ; the intensity depends on the population of the initial state of the
material. At thermodynamic equilibrium, the upper state will have a lower or
equivalent population and the corresponding anti-Stokes spectrum will be less intense.
1.7. MOLECULAR FORCE CONSTANT AND ITS SIGNIFICANCE
The force constant is defined as the resistive or restoring force per unit
displacement (stretching or bending) i.e. the force which restores the molecule to its
equilibrium configuration. The changes in the energy of the electrons binding the
nuclei together give the “Force Field”. Hence the force constant gives a measure of
the strength of the chemical bonding between the atoms.
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Since the force constants of a molecule and its isotopic analogues have almost
the same set of force constants, it is possible to deduce the fundamental wave
numbers of the isotopic substitutes when the force field of the molecule is known.
Since the force constants are the characteristic of certain group vibrations, they can be
transferred from molecule to molecule. Hence we can suggest the nature of force
fields in large molecules from those of smaller ones.
The force constant depends on the bond order and the mass of atoms. The
variation of force constants with bond order indicate that the force constants yield
information regarding the valence state of atoms in the molecule. Force field helps to
know normal coordinates associated with each vibrational frequency essential for the
absolute intensity studies. Infrared and Raman intensities have been used along with
the force constants successfully to obtain the bond dipole moments, polarizabilities
and their derivatives [17].
1.8. MOLECULAR FORCE FIELDS
In the context of molecular modeling, a force field refers to the form and
parameters of mathematical functions used to describe the potential energy of a
system of particles (typically molecules and atoms). Force field functions and
parameter sets are derived from both experimental work and high-level quantum
mechanical calculations. “All-atom” force fields provide parameters for every type of
atom in a system, including hydrogen, while "united-atom" force fields treat the
hydrogen and carbon atoms in methyl and methylene groups as a single interaction
center. “Coarse-grained” force fields, which are frequently used in long-time
simulations of proteins, provide even more crude representations for increased
computational efficiency.
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The basic functional form of a force field encapsulates both bonded terms
relating to atoms that are linked by covalent bonds, and nonbonded (also called
“noncovalent”) terms describing the long-range electrostatic and van der Waals
forces. The specific decomposition of the terms depends on the force field, but a
general form for the total energy in an additive force field can be written as
total bonded nonbondedE = E + E where the components of the covalent and noncovalent
contributions are given by the following summations:
bonded bond angle dihedralE = E + E + E ... (1.1)
nonbonded electrostatic vander WaalsE = E + E ... (1.2)
The bond and angle terms are usually modeled as harmonic oscillators in force
fields that do not allow bond breaking. A more realistic description of a covalent bond
at higher stretching is provided by the more expensive Morse potential. The
functional form for the rest of the bonded terms is highly variable. Proper dihedral
potentials are usually included. Additionally, “improper torsional” terms may be
added to enforce the planarity of aromatic rings and other conjugated systems, and
"cross-terms" that describe coupling of different internal variables, such as angles and
bond lengths. Some force fields also include explicit terms for hydrogen bonds.
The nonbonded terms are most computationally intensive because they include
many more interactions per atom. A popular choice is to limit interactions to pair wise
energies. The Vander Waals term is usually computed with a Lennard-Jones potential
and the electrostatic term with Coulomb's law, although both can be buffered or
scaled by a constant factor to account for electronic polarizability and produce better
agreement with experimental observations.
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1.9. TYPES OF FORCE FIELDS
1.9.1. Central Force Field (CFF)
A force whose line of action is always directed toward a fixed point. The
central force may attract or repel. The point towards or from which the force acts is
called the center of force. If the central force attracts a material particle, the path of
the particle is a curve concave toward the center of force; if the central force repels
the particle, its orbit is convex to the center of force. Undisturbed orbital motion under
the influence of a central force satisfies Kepler's law of areas.
1.9.2. Simple Valence Force Field (SVFF)
Simple valence force field developed by Bjerrum [18] involves a restoring
force in the line of every valence bond; if the distance between the two bonded atoms
is changed and restoring force opposing the change of the angle between two valence
bonds connecting one atom with two others. In this force field, the potential function
includes terms involving changes in interatomic distances and also changes in angles
between two valence bonds. But this force excludes the forces between non-bonded
atoms.
The potential energy function under this model is expressed as
� �i i
2 2
r i � ii
1 1V f (r ) + f (� )
2 2= �
� � � � �
... (1.3)
where r and � are the changes in bond lengths and bond angles respectively, fr and f�
are the respective stretching and bending force constants.
Shimanonchi et al., [19] have applied this model successfully to a number of
molecules containing hydrogen atoms and a single heavy atom such as H 20, NH3 and
CH4. However, this model is not suitable for molecules having more than one heavy
atom. This force field is superior to the central force field and chemically more
meaningful, yet often fails to reproduce the observed frequencies.
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1.9.3. General Valence Force Field (GVFF)
The simple valence force field potential functions can be modified in order to
get more accurate description of the vibrational frequencies, by introducing some
judiciously chosen interaction constants. In this model the potential energy function,
which includes all interaction terms in addition to the valence forces is given
expression (1.3). It is expressed in its most general form as,
� �i j i j i j
2 2
r i � i r r i j � � i j r�i¹j
1 1 1V f (r ) + f (� ) + f (r r ) + f (� � ) + f (r�)
2 2 2= � � � � �
�
... (1.4)
where r and � are the changes in bond lengths and bond angles, respectively.
In the expression (1.4), the force constants fr, and f� refer to principal
stretching and bending force constants respectively and frr, and f�� and fr� refer
respectively to stretch-stretch, bend-bend and stretch-bend interactions. This is a
convenient force field from practical point of view since the force constants can be
straight forwardly transferred from one molecule to other.
1.9.4. Urey-Bradley Force Field (UBFF)
The Urey-Bradley force field [20] is a combination of central force field and
valence force field. The UBFF adds interactions terms between nonbonded atoms to
the simple valence force field. It includes the bond stretching force constants K, angle
bending force constants H, torsional force constants Y and repulsive force constants
F. The potential energy function under this model is written as [21].
( ) ( ) ( )2 2
2
ij ij ijk ijk ijk ij ij
1 1 1 1V r ( ) Y t F R
2 2 2 2= ΣΚ + ΣΗ α + Σ + Σ ... (1.5)
where r, �, t and R are the changes in bond lengths, bond angles, angle of internal
rotation and distance between non-bonded atom pairs, respectively.
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The general validity of this type of field has been demonstrated by
Shimanouchi [21]. In this model, the VFF is supplemented by forces between non-bonded
nuclei. The advantages of this force field are:
• It requires only a few parameters to describe the potential energy completely.
• Force constants of similar bonds can be transferred from related molecules.
• Determination of force constants of complex molecules is also possible.
It has its own limitations. Sometimes the force constants may not give a good
estimate of the frequencies for certain types of vibrations, such as vibrations involving
hydrogen atoms. In such cases, modifications have been suggested [22-30]. The
resulting force field is known as Modified Urey- Bradley Force Field (MUBFF).
1.9.5. Orbital Valence Force Field (OVFF)
This force field is a modified form of valance force field devised by Health
and Linnet [31]. OVFF eliminates the difficulty of introducing separate angle bending
constants for the out-of-plane vibrations and makes use of the same constants as those
used for in-plane vibrations and strictly in accordance with modern theory of direct
valency [32]. In this field, it is assumed that the bond forming orbitals of an atom X
are at definite angles to each other and a most stable bond is formed when one of
these orbitals overlaps the bond forming orbitals of another atom Y to the maximum
extent possible. If now Y is displaced perpendicular to the bond, a force will be set up
tending to restore it to the most stable position. The potential energy function is
expressed as,
( ) ( ) ( ) ( ) ( )22 2' '
i � i jk jk i
jk jk
1V = K r + K � + A R B R + B r
2−� � � � � … (1.6)�
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Where r and R are the changes in bond lengths and the distance between non-
bonded atom pairs, respectively, the �i is the angular displacement. The symbol K,
K'�, B and A stands for the stretching, bending and non-bonding repulsion force
constants respectively. This model was shown by Health and Linnet [31] to be a very
satisfactory one for tetrahedral XY4 and planar XY3 types of molecules and ions.
Later on, it has been shown by Kim et al., [33] and Rai et al., [34] to be a superior
model to the usual one using interbond angles for a series of octahedral hexahalides.
Considerable attention has been focused in recent years on the application of this
model to different types of systems [35-42]. A modified form of OVFF known as
modified orbital valence force filed has been successfully applied to octahedral
systems [43-45].
1.9.6. Hybrid Orbital Force Field (HOFF)
Mills [46] proposed this model by incorporating the idea of changes in the
hybridization orbitals because it attributes the molecular deformation to changes in
bond angles. Therefore, it accounts for the stretch-bend interactions. The relation
between stretching force constants under this model is given by [46]
i iij ii
i j
�R ��F = F
�� ��
� �− � �� �
� � ... (1.7)
Hence Ri, �j refer to internal stretching and bending coordinates, respectively,
and �i is the hybridization parameter associated with Ri. The HOFF has been applied
successfully by several workers [47-51] to a variety of compounds. It is evident that
the simplified force fields cited above are essential when one has to evaluate the force
constants from frequency data alone. The approximation involved in framing the
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models are arbitrary and empirical, though the degree to which they are so is varied.
Different groups of molecules or ions are found to obey different force fields,
depending on how perfectly the assumptions made correspond to the actual state of
affairs.
1.10. MOLECULAR SYMMETRY AND POINT GROUPS�
The aim of this study is to provide a systematic treatment of symmetry in
chemical systems within the mathematical framework known as group theory (the
reason for the name will become apparent later on). Once we have classified the
symmetry of a molecule, group theory provides a powerful set of tools that provide us
with considerable insight into many of its chemical and physical properties. Some
applications of group theory that will be covered in this study include:
i) Predicting whether a given molecule will be chiral, or polar.
ii) Examining chemical bonding and visualising molecular orbitals.
iii) Predicting whether a molecule may absorb light of a given polarisation,
which spectroscopic transitions may be excited if it does.
iv) Investigating the vibrational motions of the molecule.
All the axes and planes of symmetry of a molecule must intersect at least at
one common point. Thus, the symmetry operation performed on molecule must leave
at least one point unaffected. Such groups of operations are called point groups. In a
point group, the symmetry of space about a point is uniquely described by a collection
of symmetry elements about that point. Point groups are used to describe the
symmetry of isolated molecules.
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1.11. GROUP THEORY AND MOLECULAR VIBRATIONS
Knowledge of the point group symmetry of a molecule and application of
group theory concept are useful in the classification of the normal vibrations,
determination of their normal vibrations and determination of their spectral activity.
Molecule of different symmetries has qualitatively different spectra [3,52,53].
A very important property of the normal vibrations is that they transform
according to the irreducible representations of the molecular point group. Because of
their relationship with the normal coordinates, the vibrational wave function
associated with the vibrational energy levels also behaves in the same way. Hence, the
normal coordinates and the vibrational wave functions can be classified according to
their symmetry properties.
1.12. NORMAL MODES OF VIBRATIONS
In general, a molecule with N atoms has 3N–6 normal modes of vibration, but
a linear molecule has 3N–5 such modes, as rotation about its molecular axis cannot be
observed [54]. A diatomic molecule has one normal mode of vibration. The normal
modes of vibration of polyatomic molecules are independent of each other but each
normal mode will involve simultaneous vibrations of different parts of the molecule
such as different chemical bonds.
A molecular vibration is excited when the molecule absorbs a quantum of
energy, E, corresponding to the vibration’s frequency, �, according to the relation E = h�
(where h is Planck’s constant). A fundamental vibration is excited when one such
quantum of energy is absorbed by the molecule in its ground state. When two quanta
are absorbed the first overtone is excited, and so on to higher overtones.
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To a first approximation, the motion in a normal vibration can be described as
a kind of simple harmonic motion. In this approximation, the vibrational energy is a
quadratic function (parabola) with respect to the atomic displacements and the first
overtone has twice the frequency of the fundamental. In reality, vibrations are
anharmonic and the first overtone has a frequency that is slightly lower than twice that
of the fundamental. Excitation of the higher overtones involves progressively less and
less additional energy and eventually leads to dissociation of the molecule, as the
potential energy of the molecule is more like a Morse potential.
The vibrational states of a molecule can be probed in a variety of ways. The
most direct way is through infrared spectroscopy, as vibrational transitions typically
require an amount of energy that corresponds to the infrared region of the spectrum.
Raman spectroscopy, which typically uses visible light, can also be used to measure
vibration frequencies directly. The two techniques are complementary and
comparison between the two can provide useful structural information such as in the
case of the rule of mutual exclusion for centrosymmetric molecules.
Vibrational excitation can occur in conjunction with electronic excitation
(vibronic transition), giving vibrational fine structure to electronic transitions,
particularly with molecules in the gas state.Simultaneous excitation of a vibration and
rotations gives rise to vibration-rotation spectra. The coordinate of a normal vibration
is a combination of changes in the positions of atoms in the molecule. When the
vibration is excited the coordinate changes sinusoidally with a frequency �, the
frequency of the vibration.
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Internal coordinates are of the following types:
• Stretching: a change in the length of a bond.
• Bending: a change in the angle between two bonds.
• Rocking: a change in angle between a group of atoms.
• Wagging: a change in angle between the plane of a group of atoms
• Twisting: a change in the angle between the planes of two groups of
atoms.
• Out-of-plane: a change in the angle between any one of the C-H bonds
and the plane defined by the remaining atoms .
In a rocking, wagging or twisting coordinate the bond lengths within the
groups involved do not change. The angles do. Rocking is distinguished from
wagging by the fact that the atoms in the group stay in the same plane. The atoms in a
CH2 group, commonly found in organic compounds, can vibrate in six different ways:
symmetric and asymmetric stretching, scissoring, rocking, wagging and twisting as
shown in Fig. 1.2.
(These figures do not represent the “recoil” of the C atoms, which, though
necessarily present to balance the overall movements of the molecule, are much
smaller than the movements of the lighter H atoms).
Symmetry-adapted coordinates may be created by applying a projection
operator to a set of internal coordinates [55]. The projection operator is constructed
with the aid of the character table of the molecular point group. Illustrations of
symmetry-adapted coordinates for most small molecules can be found in Nakamoto