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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

[12].

Symmetrical stretching Asymmetrical stretching Scissoring

Rocking Wagging Twisting

Fig. 1.2: Symmetric and asymmetric stretching, scissoring, rocking, wagging and

twisting vibrations.

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The normal coordinates, denoted as Q, refer to the positions of atoms away

from their equilibrium positions, with respect to a normal mode of vibration. Each

normal mode is assigned a single normal coordinate, and so the normal coordinate

refers to the “progress” along that normal mode at any given time. Formally, normal

modes are determined by solving a secular determinant, and then the normal

coordinates (over the normal modes) can be expressed as a summation over the

cartesian coordinates (over the atom positions). The advantage of working in normal

modes is that they diagonalize the matrix governing the molecular vibrations, so each

normal mode is an independent molecular vibration, associated with its own spectrum

of quantum mechanical states. If the molecule possesses symmetries, it will belong to

a point group, and the normal modes will "transform as" an irreducible representation

under that group. The normal modes can then be qualitatively determined by applying

group theory and projecting the irreducible representation onto the cartesian

coordinates.

1.13. VIBRATIONAL ASSIGNMENTS AND GROUP FREQUENCY

The vibrational motion of a molecule is quantized and the resulting energy

level spacings give rise to transitions in the mid-IR portion of the electromagnetic

spectrum (4000 to 400 cm-1

). As you know from study of the diatomic harmonic

oscillator, the energies (or wavenumber positions, cm-1

) of these transitions are related

to the bond strength (force constant), bond length, and atomic masses (reduced mass).

In polyatomic spectra, the positions and relative intensities of the vibrational modes

depend on the symmetry (i.e. shape or structure) of the molecule, as well as the bond

strengths and masses. For this reason, vibrational spectra (IR and Raman) can provide

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detailed structural information. This structural information is the objective of this lab,

and it is obtained by this analysis, or interpretation, of the infrared and Raman spectra.

In this experiment you will obtain infrared and Raman spectra of a polyatomic

molecule, predict the selection rules, assign vibrational modes, and then compare

these with the vibrational mode positions and intensities predicted for that molecule

using HyperChem. Using group theory, we shall predict the spectral selection rules,

i.e. predict the spectra for a particular structural model. Assignment of vibrational

modes in a spectrum involves relating the experimental spectrum and the predicted

spectrum so that each observed vibrational band is identified as to its theoretical

origin. A series of empirical rules is provided below to aid in this assignment. Also, a

chart defining the well-known positions of group frequencies will be available. (These

charts summarize the vast knowledge obtained from the extensive, experimental

spectral database that has been collected, literally, over the past 65 years.) Finally, the

results of the HyperChem calculation will be compared with the above. Because these

calculated normal mode positions will be harmonic frequencies, they must be

multiplied by a constant to relate them to the empirical, anharmonic band positions.

This constant depends upon the orbital basis set.

Factors influencing vibrational frequencies

Many factors influence the precise frequency of molecular vibrations, and it is

usually impossible to isolate one effect from another. Each molecular group is

influenced by the structure of the molecule or different electronic environments [56]. Some

of the important factors which are responsible for shifting the vibrational frequencies

of certain groups from their normal values are discussed below:

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Coupled Interactions

When bond oscillators share a common atom, they almost never behave as

individual oscillators unless the individual oscillation frequencies are quite different.

Mechanical coupling interaction between the oscillators is responsible for this

behavior. For example CO2, consists of two C=O bonds (O=C=O) with a common

carbon atom. Thus CO2 has two fundamental stretching vibrations. Labeling of

vibrations as symmetric or asymmetric is done with reference to an axis known as

axis of symmetry.

(a) Hydrogen bonding

Hydrogen bonding can occur on any system containing a proton donor group

(X-H) and a proton acceptor (Y), if the s-orbital of the proton can effectively overlap

the p or orbital of the acceptor group. Atoms X and Y are electronegative with Y

possessing lone pair of electrons. In organic molecules, the common proton donor

groups are carbonyl, hydroxyl amine or amide groups and common proton acceptor

atoms are oxygen, nitrogen and halogens. The strength of the hydrogen bond is at its

maximum, if the proton donor group and the axis of the lone pair orbital are collinear.

The force constant of both the group X and Y is altered as a result of hydrogen

bonding [8]. Hence frequencies of both stretching as well as bending vibrations are

altered because of hydrogen bonding. The X-H stretching bands move to lower

frequencies usually with increased intensity and band widening. The H-X bending

vibration usually shifts to higher frequencies or shorter wavelength when bonding

occurs. Thus hydrogen bonding changes the position and shape of an infrared

absorption band.

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Intermolecular hydrogen bonding involves association of two or more

molecules of the same or different compounds, and it may result in dimmer molecules

as in carboxylic acids. Intramolecular hydrogen bonds are formed when proton donor

and acceptor are present in a single molecule under special conditions that allow the

required overlap of orbital e.g., formation of a 5 or 6 membered ring. The extent of

both intramolecular and intermolecular hydrogen bonding depends upon the

temperature. In general intermolecular hydrogen bonds give rise to broad bands, while

intramolecular hydrogen bonds give sharp and well defined bands.

(b) Fermi Resonance

The Fermi resonance effect usually leads to two bands appearing close

together when only one is expected. When an overtone or a combination band has the

same frequency as, or a similar frequency to, a fundamental, two bands appear, split

either side of the expected value and are of about equal intensity. The effect is greater

when the frequencies match, but it is also present when there is a mismatch of a few

tens of wave numbers. The two bands are referred to as a Fermi doublet.

(c) Electronic effects

Apart from external factors such as hydrogen bonding and molecular

association, various internal factors may affect the electronic structured of the

carbonyl group. The nature of the substituent group X in carbonyl compounds of the

formula RCOX may influence the frequency of C=O stretching by inductive and

mesomeric effects. Inductive effect arises due to the different electro negativities of

the carbonyl carbon and of the substituent in compounds of the type RCOX. It

involves the electrons in the sigma bonds. The mesomeric effect involves the

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electrons in the and nonbonding orbitals and it operates in general opposite to the

inductive effect. These effects cannot be isolated from one another and the

contribution of one of them can only be estimated approximately. Electron

withdrawing groups (such as chloro and nitro) suppress the polar contribution with an

effective increase in the double bond character and consequently an increase in the

force constant of the C=O bond. In other words, the inductive effect reduces the

length of the C=O bond and thus increases its force constant and consequently the

frequency of absorption. Electron releasing groups, such as amino and methyl,

attached to the carbonyl group tend to favour the polar contribution by mesomeric

effect and thus lower the force constant of the C=O bond and consequently resulting

in a decrease of the carbonyl stretching frequency. In Introduction of alkyl group

causes+1 effect, which results in weakening of the bond and hence the force constant

is lowered and wave number of absorption decreases. The introduction of an

electronegative atom (or) group causes-I effect, which results in the bond order to

increase. Thus, the force constant increases and hence the wavenumber of absorption

rises. In most of the cases, mesomeric effect works along with inductive effect and

cannot be ignored. It is important to note that only inductive effect is considered when

the compound in meta substituted. In para substitution, both inductive and mesomeric

effects become important and the domination of one over the other will decide the

wavenumber of the absorption. In ortho substitution, inductive effect, mesomeric

effect along with steric effect is considered. In ortho substituted compounds, the lone

pairs of electrons on two atoms influence each other through space interactions and

change the vibrational frequencies of both the groups. This effect is called field effect.

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1.14. OTHER MOLECULAR PROPERTIES

1.14.1. Molecular orbitals

Molecular orbitals; both the highest occupied molecular orbital (HOMO) and

the lowest unoccupied molecular orbital (LUMO) and their properties such as energy

are very useful for physicists and chemists. These are the main orbitals taking part in

chemical reaction. While the energy of the HOMO is directly related to the ionization

potential, LUMO energy is directly related to the electron affinity. This is also used

by the frontier electron density for predicting the most reactive position in -electron

systems and also explains several types of reaction in conjugated system. The

conjugated molecules are characterized by a small HOMO-LUMO separation, which

is the result of a significant degree of intramolecular charge transfer from the end-

capping electron-donor groups to the efficient electron-acceptor group through

-conjugated path.

The frontier orbital gap helps to characterize the chemical reactivity and

kinetic stability of the molecules. The hardness which is a key descriptor for reactivity

is related to the HOMO-LUMO energy difference. A ‘‘hard’’ molecule thus has a

large HOMO-LUMO gap, and is expected to be chemically less reactive, i.e. hardness

is related to chemical stability. A small HOMO-LUMO gap, on the other hand,

indicates a ‘‘soft’’ molecule. Examining molecular orbitals and the spatial distribution

of other molecular properties is useful for many purposes. Molecular orbitals can

provide important insight into bonding and other chemical properties. The HOMO is

an electron donor and the LUMO is electron acceptor. The HOMO-LUMO energy

gap explains the charge transfer interaction within the molecules. As the energy gap

between the LUMO and HOMO decreases, it is easier for the HOMO electrons to be

excited.

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1.14.2. Non-linear optical property

Non-linear optical (NLO) effects arise from the interactions of electromagnetic

fields in various media to produce new fields altered in phase, frequency, amplitude

or other propagation characteristics from the incident fields. NLO is at the forefront of

current research because of its importance in providing the key functions of frequency

shifting, optical modulation, optical switching, optical logic, and optical memory for

the emerging technologies in areas such as telecommunications, signal processing,

and optical interconnections. Organic molecules that exhibit extended conjugation,

in particular, show enhanced second order NLO properties.

1.14.3. Natural bond orbital analysis

Natural bond orbital (NBO) analysis provides an efficient method for studying

intra- and intermolecular bonding and interaction among bonds, and also provides a

convenient basis for investigating charge transfer or conjugative interaction in

molecular systems. The larger the hyperconjugative energy E(2) value, the more

intensive is the interaction between electron donors and electron acceptors, i.e. the

more donating tendency from electron donors to electron acceptors and the greater the

extent of conjugation of the whole system.

In the NBO analysis, in order to compute the span of the valence space, each

valence bonding NBO (AB) must be paired with a corresponding valence anti-

bonding NBO (*

AB). The NBO analyses of the molecules could be used to estimate

the delocalization of electron density between occupied Lewis-type orbitals (bond or

lone pair) and formally unoccupied non-Lewis NBOs (antibonding or Rydberg),

which corresponds to a stabilizing donor–acceptor interaction. The energy of these

interactions can be estimated by the second order perturbation theory.

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1.14.4. Mulliken population analysis

Mulliken atomic charge calculation has an important role in the application of

quantum chemical calculation to molecular system due to atomic charge effect, dipole

moment, molecular polarizability, electronic structure and lot of properties of

molecular systems. The definition of Mulliken’s charges is based on population

analysis. The Mulliken population analysis provides a partitioning of either the total

charge density or an orbital density. In Mulliken analysis, half the overlap population

is assigned to each contributing orbital, giving the total population of each atomic

orbital. Summing over all the atomic orbitals on a specific atom gives us the gross

atomic population. The sum of all net and overlap populations equals the total number

of electron in the molecule.

1.14.5. Molecular electrostatic potential

The Molecular electrostatic potential (MESP) is a plot of electrostatic potential

mapped onto the constant electron density surface. The MESP superimposed on top of

the total energy density as a shell. Because of the usefulness feature to study reactivity

given that an approaching electrophile must be attracted to negative regions (where

the electron distribution effect is dominant). In the majority of the MESP, while the

maximum negative region which preferred site for electrophilic attack indications as

red color, the maximum positive region which preferred site for nucleophilic attack

symptoms as blue color. The importance of MESP lies in the fact that it simultaneously

displays molecular size, shape as well as positive, negative and neutral electrostatic

potential regions in terms of color grading and is very useful in research of molecular

structure with its physicochemical property relationship. The different values of the

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electrostatic potential at the surface are exemplified by different colors in the map of

MESP. The potential increases in the order from red to blue color. The MESP is best

suited for identifying sites for intra- and intermolecular interactions. When an

intramolecular interaction takes place the electrostatic potential of the negative atom

becomes less negative and the positive region on the other atom becomes less

positive.