SENGAMALA THHAYAAR EDUCATIONAL TRUST WOMEN’S COLLEGE SUNDARAKKOTTAI, MANNARGUDI - 614016.
(Accredited with A grade by NAAC) (An ISO 9001:2015 Certified Institution)
DEPARTMENT OF CHEMISTRY
ACADEMIC YEAR: 2020-2021 (Odd SEMESTER)
Name : Ms. T.Vimala, Assistant Professor.
Unit : I (Photochemistry and Group theory)
Class : III B.Sc., Chemistry
Subject Name : Physical Chemistry – I
Subject Code : 16SCCCH7
SEMESTER V CORE COURSE VII Hours/Week: 6
Credits: 5 PHYSICAL CHEMISTRY I
OBJECTIVES
1. To know the various concepts of photochemistry and group theory. 2. To learn the second law of thermodynamics, carnot cycle, carnot theorem, entropy, free energy
and Maxwell’s relations. 3. To learn the third law of thermodynamics, Van’t Hoff isotherm, Clausius – Clapeyron equation
and Nernst heat theorem. 4. To understand the laws and properties of solutions. 5. To learn the fundamental concepts of phase rule and its applications to one, two and three
component systems.
UNIT I PHOTOCHEMISTRY AND GROUP THEORY
1.1. Consequences of light absorption- Jablonski diagram- radiative and non-radiative transitions.
Lambert’s Beer law, quantum efficiency. 1.2. Photochemical reactions-Comparison between thermal and photochemical reactions.
Photosensitization and quenching. Fluorescence, phosphorescence and chemiluminescence. Laser
and uses of lasers. 1.3. Group theory – symmetry elements and symmetry operation- group postulates and types of
groups- abelian and non abelian – symmetry operation of H2O molecule. 1.4. Illustration of group postulates using symmetry operations of H2O molecule - construction of
multiplication table for the operation of H2O molecule – point group- definition- elements
(symmetry operations) of the following molecules- H2O, BF3 and NH3.
UNIT II THERMODYNAMICS II
2.1.Second law of thermodynamics – need for the law- different statements of the law-Carnot’s cycle
and efficiency of heat engine- Carnot’s theorem- thermodynamic scale of temperature. 2.2. Concept of entropy- definition and physical significance of entropy- entropy as a function of P, V
and T – entropy changes during phase changes- entropy of mixing – entropy criterion for spontaneous and equilibrium processes in isolated system. 2.3. Gibb’s free
energy (G) and Helmholtz free energy(A) – variation of A and G with P, V and T- Gibb’s – Helmholtz equation and its applications.
2.4. Thermodynamic equation of state, Maxwell’s relations- A and G as criteria for spontaneity and
equilibrium.
UNIT III THERMODYNAMICS III
3.1. Equilibrium constant and free energy change- thermodynamic derivation of law of mass action-
equilibrium constants in terms of pressure and concentration – NH3, PCl5 and CaCO3. 3.2. Thermodynamic interpretation of Lechatelier’s principle (Concentration, temperature, pressure
and addition of inert gases). 3.3. Systems variable composition- partial molar quantities- chemical potential – variation of chemical
potential with T, P and X (mole fraction) – Gibb’s Duhem equation. Van’t Hoff’s reaction
isotherm- van’t Hoff’s isochore. Clapeyron equation and Clausius – Clapeyron equation-
applications.
3.4. Third law of thermodynamics- Nernst heat theorem. Statement of III law and concept of
residual entropy – evaluation of absolute entropy from heat capacity data.
UNIT IV SOLUTIONS
4.1. Raoult’s law, Henry’s law, Ideal and non-ideal solutions, completely miscible liquid systems-
benzene and toluene. Deviation from Raoult’s law and Henry’ law. Duhem-Margules equation.
Theory of fractional distillation. Azeotropes- HCl – water and ethanol- water system. 4.2. Partially miscible liquids- phenol- water, triethylamine- water and nicotine- water systems.
Lower and upper CSTs – effect of impurities on CST.Completely immiscible liquids- principle
and applications of steam distillation. Nernst distribution law – derivation. 4.3. Dilute solutions- colligative properties, relative lowering of vapour pressure, osmosis, law of
osmotic pressure, derivation of elevation of boiling point and depression in freezing point. 4.4. Determination of molecular masses using colligative properties. Abnormal molecular masses,
molecular dissociation- degree of dissociation- molecular association.
UNIT V PHASE CHANGES
5.1. Definitions of terms in the phase rule- derivation and application to one component system –
water and sulphur- super cooling, sublimation. 5.2. Two-component systems-solid liquid equilibria, simple eutectic (lead- silver, Bi-Cd),
desilverisation of lead. 5.3. Compound formation with congruent melting point (Mg-Zn) and incongruent melting point (Na-
K). 5.4. Solid Solutions-(Ag-Au)-fractional crystallization, freezing mixtures- FeCl3-H2O systems,
CuSO4-H2O system.
REFERENCES
1. Gurdeep Chatwal R, Photochemistry, Good publishing House. 2. Raman, K. (1990), Group theory and its application to Chemistry, New Delhi: Tata McGraw-
Hill. 3. Samuel Glasstone (1974), Thermodynamics for Chemists (3rd printing), East- West Edn.
4. Rajaram J. and Kuriacose, J.C. (1986) Thermodynamics for students of Chemistry, New Delhi:
Lal Nagin Chand.
5. Puri B.R., Sharma L.R. and Pathania M.S. (2013), Principles of Physical Chemistry, (35th
edition),New Delhi: Shoban Lal Nagin Chand and Co. 6. Glasstone S. and Lewis D., Elements of Physical Chemistry, London, Mac Millan & Co Ltd. 7. Atkins P.W. (1994), Physical chemistry, (5th edition), Oxford University press. 8. Sangaranarayanan, M.V., Mahadevan, V., Text Book of Physical Chemistry, 2nd Edition,
Hyderabad, Universities Press, (India) 2011.
*****
Photochemistry
Photochemistry is the study of the interaction of electromagnetic radiation with
matter resulting into a physical change or into a chemical reaction.
Primary Processes
One molecule is excited into an electronically excited state by absorption of a
photon, it can undergo a number of different primary processes.
Photochemical processes are those in which the excited speciedissociates,
isomerizes, rearranges, or react with another molecule.
Photo physical processes include radiative transitions in which the excited
molecule emits light in the form of fluorescence or phosphorescence and
returns to the ground state, and intramolecular non-radiative transitions in
which some or all of the energy of the absorbed photon is ultimately converted
to heat.
Laws Governing Absorption Of Light
Lambert’s Law: This law states that decrease in the intensity of monochromatic light
with the thickness of the absorbing medium is proportional to the intensity of incident
light.
-dI/dx ∞I
-dI/dx=KI,
on integration changes to
I=I0 e-Kx
Where , I0 = intensity of incident light.
I=intensity of transmitted light.
K= absorption coefficient
Beer’s Law :
It states that decrease in the intensity of monochromatic light with the thickness of the
solution is not only proportional to the intensity of the incident light but also to the
concentration ‘c’ of the solution.
Mathematically, -dI/dx ∞ Ic
-dI/dx = Є Ic
on integration I=I0 e- ЄCX
Where,
Є = molar absorption coefficient or molar extinction coefficient Numerical value
of Einstein In CGS Units
E=2.86/λ(cm) cal per mole
or
=2.86X105 / λ(A
0) K cal per mole
In SI units
E=0.1197/λ(m)J mol -1
GrotthuSs-Draper Law(First Law of Photochemistry):
Only the light which is absorbed by a molecule can be effective in
producing photochemical changes in the molecule.
Stark-Einstein’s Law ( Second Law of Photochemistry):
It states that for each photon of light absorbed by a chemical system, only one
molecule is activated for a photochemical reaction.
The energy absorbed by one mole of the reacting molecules is E=Nhv.
This energy is called one einstein.
Or
11.97X10-5
/λ(m)KJ mol-1
Processes of photochemical reactions
1. Primary Process: Atoms or molecules activated by actual absorption of
radiation.
Or, the excitation of the species from the ground electronic state to excited
state.
2. Secondary process: Activated species undergoes chemical reaction.
---Does not involve the absorption of light.
Eg., Photochemical combination of Cl2 and H2 (It is chain mechanism)
a. Primary Process
Cl2 + hv----- 2Cl. Chain Initiation step
Photochemical equivalence is applicable to this step
b. Secondary process
Propagation reaction and Chain terminating step
Utility of the Laws
1. Calculation of the rates of formation of reactive intermediates in photochemical
reactions
2. The study of the mechanisms of photochemical reactions .
Interpretation of Einstein’s Law
In terms of Quantum efficiency:
Quantum Efficieny
ф= No. of molecules reacting in a given time
No.of quantas of light absorbed in the same time
Experimentally,
Ф = rate of chemical reaction quanta
absorbed per second.
Quantum efficiency :
It expresses the efficiency of a photochemical reaction.
A photochemical reaction strictly obey the laws of photochemical equivalence Ф
should be unity.
Because the ratio between the reacting molecules & no. of quanta absorbed =1:1
Only few reactions,
Ф =1
eg.
SO2 + Cl2
SO2 Cl2
But in major cases,
Ф ≠ 1
Quantum Yield
In the photolysis of Cl2 and H2, HCl can be as high as 1 million.
Cl2 + hv- 2Cl .
Cl . + H2 HCl + H (exothermic)
H + Cl2 - HCl +Cl .
In the photolysis of Br2 and H2, HBr is very low i.e about 0.01 Br2 + hv- 2Br
Br+ H2 -HBr+ H (endothermic)
H + Br2 --HBr + Br
The hydrogen- chlorine reaction
We are considering the photolysis of Cl2 and H2
H2(g) + Cl2(g) -2HCl(g)(radiation,λ=4800A0)
Its quantum yield =104 to 10
6 ,because it is a chain reaction
Chain reaction : A chain reaction is one in which a single photoactivated molecule
sets off a sequence of reactions so that a very large number of reactant molecule react
through a chain reaction.
Primary process, involve the decomposition of chlorine molecule into chlorine
radicals.
Cl2 + hv--2Cl. (1) Chain Initiation step
In secondary process - propagate the chain by their continued reaction gives a
large no. of HCl molecules.
Cl. + H2 -- HCl + H
.
H. + Cl2 - HCl + Cl
. Propagation reaction
Exothermic and low activation energy hence large no. of HCl molecule is formed before
terminating the reaction.
Hence the no of Cl2 molecules that undergoes reaction per each quantum of
radiation absorbed is very large, ie, 104 to 106 .
So the reaction has very high quantum yield.
The chain is finally terminated by the combination of chlorine radicals on the
walls of the vessels or in gas phase.
Cl. + Cl. -- Cl2 (Chain terminating step)
potosensitization
Photosensitized reactions:An electronically excited molecule can transfer its
energy to a second species which then undergoes a photochemical process even
though it was not itself directly excited.
eg, 1. Mercury acting as a photosensitizer:
Hg+hv → Hg*
Hg*+H2 → H2* + Hg
H2* → 2H.
2. Chlorophyll acting as a photosensitizer
Chlorophyll +hv → Chlorophyll *
6CO2+6H2O+ Chlorophyll *→ C6H12O6 + 6O2 + Chlorophyll
3 Chlorine photosenstizes the reaction of ozone to oxygen.
Cl2 +hv →Cl2*
Cl2* + O3 → Cl2 + O2+ O
O+O3 → 2O2
Luminescence
The glow produced in the body by methods other than action of heat i.e. the
production of cold light is called Luminescence.
It is of three types,
1. Chemiluminescence: The emission of light in chemical reaction at ordinary
temperature is called Chemiluminescence
e.g. The light emitted by glow-worms
2. Fluorescence: Certain substances when exposed to light or certain other
radiations absorb the energy and then immediately start re-emitting the energy.
Such substances are called fluorescent substances and the phenomenon is
called fluorescence .
e.g Organic dyes such as eosin,fluorescein etc.
vapour of sodium,mercury,iodine etc.
3. Phosphorescence: There are certain substances which continue to glow for some
time even after the external light is cut off.
Thus, phosphorescence is a slow fluorescence.
Fluorescence and phosphorescence in terms of excitation of electrons
Singlet ground
state So
Singlet excited state
S1
( pair of electrons with
Opposite spins but
each
in different
orbital)
Triplet excited state
T1 (pair of electrons with
parallel spins in different
Orbital’s)
The excited species can return to the ground state by losing all of its excess energy by
any one of the paths shown in Jablonski diagram.
Jablonski Diagram for various photophysical processes
Allowed singlet states:
Forbidden triplet states
due to spin conversion
Explanation of Jablonski Diagram
First step: is the transition from higher excited singlet states (S2, S3, …) to the lowest
excited singlet state S1.This is called internal conversion (IC).
It is a non-radiative process and occurs in less than 10-11 second.
Now from S1 the molecule returns to ground state by any of the following paths.
Path I : The molecule may lose rest of the energy also in the form of heat so that the
complete path is non-radiative or radiation less transitions.
Path II: Molecule releases energy in the form of light or uv radiation. This is called
Fluorescence
Path III : Some energy may be lost in transfer from S1 to T1 in the form of heat. It is
called intersystem crossing (ISC).
This process involves transition between states of different spins (parallel to
antiparallel), ie, different multiplicity.
This path is non-radiative.
Path IV : After ISC, the molecule may lose energy in the form of light in going
from the excited triplet state to the ground state. This is called phosphorescence.
Chemical reaction
The activated molecule loses energy by undergoing chemical reaction.
Since the molecules in singlet excited sates returns quickly to the G.S, it gets no chance to react
chemically.
However the molecules in the triplet state returns to the G.S. slowly, has a opportunity to the
activated molecule undergoes chemical reaction.
i.e., the molecule which undergoes chemical reaction is one which is previously present in a triplet
state.
Chemiluminescence
Chemiluminescence: The emission of light in chemical reaction at ordinary temperature is
called Chemiluminescence
e.g. The light emitted by glow-worms.
It is the reverse of a chemical reaction. Chemical reaction—results from the absorption of light
Chemiluminescence— emission of light from a chemical reaction.
Quantum Efficieny (ф)=
No. of photons emitted in a given time
No. of molecules of the reactant consumed in the same time
ф is less than 1. Explanation
Excited products undergoes deactivation and the excess energy is emitted as
radiation
If the wavelength of the emitted light falls in the visible region,
Chemiluminscence is observed.
A→ B* →B+hv
The exothermic reaction can produce one of the product to the electronically excited state, it
shows chemilumincescence.
Examples:
1. Phosphorus glows in air with faint greenish colour due to its oxidation.
P oxidizes to phosphorus trioxide (P2O3 exists as dimer
P4O6) oxidises to phosphorus pentoxide(P2O5 exists as dimer
P4O10)
4P+3O2 → P4O6* →P4O6+hv
P4O6* +2O2 → P4O10
* → P4O10 +hv
Natural Example:
Photosensitization is that by chlorophyll in the
Photosynthesis of carbohydrates in plants.
Chlorophyll +hv → Chlorophyll*
6CO2+6H2O+Chlorophyll * → C6H12O6+O2 + Chlorophyll
Bioluminescence
Emission of visible light accompanies a chemical reaction that occurs in the
living organism.
Or it is the chemiluminescence from a biological system. egs: Glow of
fire files
Emission of light results from the oxidation of a protein called luciferin in
their body by atmospheric oxygen in the presence of enzyme luciferase.
LASER
A laser is a device that emits light through a process of optical amplification based
on the stimulated emission of electromagnetic radiation.
LASER: light amplification by stimulated emission of radiation
Principle of Emission of Radiations
Difference between Spontaneous and Stimulated Emission
Spontaneous emission: Electron drops from an excited state to a lower state
(no outside mechanism) - emitting a photon.
Stimulated emission (lasers): Stimulated emission is
the process by which an atomic electron (or an excited molecular state)
interacting with an electromagnetic wave of a certain frequency may drop to
a lower energy level, transferring its energy to that field. A new photon
created in this manner has the same phase, frequency, polarization, and
direction of travel as the photons of the incident wave.
This is in contrast to spontaneous emission which
occurs without regard to the ambient electromagnetic field.
Types of LASER
Lasers are classified into 4 types based on the type of laser medium used:
Solid-state laser
Gas laser
Liquid laser
Semiconductor laser
Applications of LASER
1.Thousands of highly varied applications in every section of modern society,
2. including consumer electronics, information technology, science, medicine,
industry, law enforcement, entertainment, and the military.
3. The first use of lasers in the daily lives of the general population was the
supermarket barcode scanner
4.The compact disc player was the first laser-equipped device
5.Communications: Lasers are used for free-space optical communication, including
laser communication in space
Applications of LASER: Medicine
Lasers have many uses in medicine
1. laser surgery (particularly eye surgery), laser healing, kidney stone treatment,
ophthalmoscopy, and cosmetic skin treatments such as acne treatment, cellulite and
striae reduction, and hair removal.
2. To treat cancer by shrinking or destroying tumors or precancerous growths
Laser therapy is often combined with other treatments such as surgery, chemotherapy,
or radiation therapy
3. Cancer: Basal cell skin cancer like cervical, penile, vaginal, vulvar, and non-small cell
lung cancer.
4.Laser Therapy: Surgery, chemotherapy, or radiation therapy.
5.Laser-induced interstitial thermotherapy (LITT), or interstitial laser
photocoagulation, uses lasers to treat some cancers using hyperthermia, which uses heat
to shrink tumors by damaging or killing cancer cells.
Applications of LASER: Medicine
1.Cosmic Surgery: Removing tattoos, scars, stretch marks, sunspots, wrinkles,
birthmarks, and hairs
2.Eye surgery and refractive surgery
3.Laser scalpel (General surgery, gynecological, urology, laparoscopic)
4.Photo bio modulation (i.e. laser therapy)
5."No-Touch" removal of tumors, especially of the brain and spinal cord.
6.Intelligent laser speckle classification for skin health assessments (especially regarding
damage caused through ageing)
7.In dentistry for caries removal, endodontic/periodontic procedures, tooth whitening,
and oral surgery
Applications of LASER
1.Industry: cutting, welding, material heat treatment, marking parts, non-contact
measurement of parts.
2.Military: marking targets, guiding munitions, missile defense, electro-optical counter
measures (EOCM), lidar, blinding troops.
3.Law enforcement: LIDAR traffic enforcement. Lasers are used for latent fingerprint
detection in the forensic identification field[64][65]
4.Research: spectroscopy, laser ablation, laser annealing, laser scattering, laser
interferometry, lidar, laser capture microdissection, fluorescence microscopy,
metrology.
5.Commercial products: laser printers, barcode scanners, thermometers, laser pointers,
holograms, bubblegrams.
6.Entertainment: optical discs, laser lighting displays
SYMMETRY & GROUP THEORY IN CHEMISTRY
INTRODUCTION
Group Theory is a mathematical method by which aspects of a molecules symmetry can
be determined. The symmetry of a molecule reveals information about its properties (i.e.,
structure, spectra, polarity, chirality, etc…).
Group theory can be considered the study of symmetry: the collection of symmetries of
some object preserving some of its structure forms a group; in some sense all groups
arise this way.
It can be grouped into three categories:
Getting to know groups — It helps to group theory and contain explicit
definitions and examples of groups; Group applications — It helps to understand the applications of group
theory. The mathematical descriptions here are mostly intuitive, so no
previous knowledge is needed. Group history — It focuses on the history of group theory, from its
beginnings to recent breakthroughs.
Electromagnetic Radiations are the radiations having electric field as well as magnetic
field both are perpendicular to each other & are also perpendicular to the line of
propogation. There are various electromagnetic radiations like radiowaves,
microwaves, x-rays, uv-rays cosmic rays etc. Theses when interact with matter give rise
to various different phenomenons like diffraction, interference, absorbtion, emission
depending on the type of EMR & matter (energy).
1.1 - OBJECTIVES
By studying this unit we come across many of the things which you are not aware of :
Є The significance of group theory for chemistry is that molecules can be
categorized on the basis of their symmetry properties, which allow the
prediction of many molecular properties. Є The process of placing a molecule into a symmetry category involves identifying
all of the lines, points, and planes of symmetry that it possesses; the symmetry
categories the molecules may be assigned to are known as point groups. Є It allows you to determine that Which vibrational transitions are
allowed or forbidden on the basis of symmetry. Є How EMR interact to show different phenomenons like polarization,
Dispersion, Refraction etc. Є What is Transition & transition probability.
Symmetry Elements & symmetry operation -
The term symmetry implies a structure in which the parts are in harmony with each other, as
well as to the whole structure i;e the structure is proportional as well as balanced.
Clearly, the symmetry of the linear molecule A-B-A is different from A-A-B. In A-B-A the A-B
bonds are equivalent, but in A-A-B they are not. However, important aspects of the symmetry
of H2O and CF2Cl2 are the same. This is not obvious without Group theory.
Symmetry Elements - These are the geometrical elements like line, plane with respect to which
one or more symmetric operations are carried out.
The symmetry of a molecule can be described by 5 types of symmetry elements.
Symmetry
axis: an axis around which a rotation by results in a molecule indistinguishable
from the original. This is also called an n-fold rotational axis and abbreviated Cn.
Examples are the C 2 in water and the C3 in ammonia. A molecule can have
more than one symmetry axis; the one with the highest n is called the principal
axis, and by convention is assigned the z-axis in a Cartesian coordinate system.
Plane of symmetry: a plane of reflection through which an identical copy of the
original molecule is given. This is also called a mirror plane and abbreviated ζ.
Water has two of them: one in the plane of the molecule itself and one
perpendicular to it. A symmetry plane parallel with the principal axis is dubbed
vertical (ζv) and one perpendicular to it horizontal (ζh). A third type of symmetry plane
exists: if a vertical symmetry plane additionally bisects the angle between two 2-fold
rotation axes perpendicular to the principal axis, the plane is dubbed dihedral (ζd). A
symmetry plane can also be identified by its Cartesian orientation, e.g., (xz) or (yz).
Centre of symmetry or inversion center, i. A molecule has a center of symmetry when,
for any atom in the molecule, an identical atom exists diametrically opposite this center
an equal distance from it. There may or may not be an atom at the center. Examples
are xenon tetrafluoride (XeF4) where the inversion cente is at the Xe atom, and
benzene (C6H6) where the inversion center is at the center of the ring.
Rotation-reflection axis: an axis around which a rotation by , followed by a
reflection in a plane perpendicular to it, leaves the molecule unchanged. Also called an
n-fold improper rotation axis, it is abbreviated Sn, with n necessarily even. Examples
are present in tetrahedral silicon tetrafluoride, with three S4 axes, and the staggered
conformation of ethane with one S6 axis.
Identity, abbreviated to E, from the German 'Einheit' meaning Unity. This symmetry
element simply consists of no change: every molecule has this element. It is analogous to
multiplying by one (unity).
Symmetry Operations/Elements
A molecule or object is said to possess a particular operation if that operation when applied
leaves the molecule unchanged. Each operation is performed relative to a point, line, or plane -
called a symmetry element. There are 5 kinds of operations - Identity
n-Fold Rotations
Reflection
Inversion
Improper n-Fold Rotation
Identity is indicated as E
does nothing, has no effect i;e this operation brings back the molecule to the original orientation
all molecules/objects possess the identity operation, i.e., posses E. E has the same importance as the number 1 does in multiplication (E is needed in
order to define inverses).
n-Fold Rotations: Cn, where n is an integer, rotation by 360°/n about a particular axis
defined as the n-fold rotation axis.
C2 = 180° rotation, C3 = 120° rotation, C4 = 90° rotation, C5 = 72° rotation, C6 = 60°
rotation, etc. Rotation of H2O about the axis shown by 180° (C2) gives the same molecule back. Therefore H2O possess the C2 symmetry element.
However, rotation by 90° about the same axis does not give back the identical
molecule Therefore H2O does not possess a C4 symmetry axis.
BF3 posses a C3 rotation axis of symmetry
This triangle does not posses a C3 rotation axis of symmetry.
XeF4 is square planar. It has four DIFFERENT C2 axes . It also has a C4 axis coming out of the
page called the principle axis because it has the largest n. By convention, the principle axis is in
the z-direction
Reflection: ζ (the symmetry element is called a mirror plane or plane of symmetry) If reflection about a mirror plane gives the same molecule/object back than there is a plane of symmetry (ζ).
If plane contains the principle rotation axis (i.e., parallel), it is a vertical plane (ζv)
If plane is perpendicular to the principle rotation axis, it is a horizontal plane (ζh)
If plane is parallel to the principle rotation axis, but bisects angle between 2 C2 axes, it is a
diagonal plane (ζd) H2O posses 2 ζv mirror planes of symmetry because they are both parallel to the principle
rotation axis (C2)
XeF4 has two planes of symmetry parallel to the principle rotation axis: ζv XeF4 has two planes of symmetry parallel to the principle rotation axis and bisecting the
angle between 2 C2 axes : ζd
XeF4 has one plane of symmetry perpendicular to the principle rotation axis: ζh
Inversion: i (the element that corresponds to this operation is a center of symmetry
or inversion center) .
The operation is to move every atom in the molecule in a straight line through the inversion
center to the opposite side of the molecule.
Therefore XeF4 posses an inversion center at the Xe atom.
Improper Rotations: Sn
n-fold rotation followed by reflection through mirror plane perpendicular to rotation axis
also known as Rotation Reflection axis. It is an imaginary axis passing through the molecule,
on which when the molecule is rotated by 2π/n angle & then reflected on a plane
perpendicular to the rotation axis then an equivalent orientation is observed.
Note: n is always 3 or larger because S1 = ζ and S2 = i.
These are different, therefore this molecule does not posses a C3 symmetry axis.
This molecule posses the following symmetry elements: C3, 3 ζd, i, 3 ┴ C2, S6. There is no C3 or
ζh.
Eclipsed ethane posses the following symmetry elements: C3, 3ζ v, 3 ┴ C2, S3, ζh. There is no S6
or i.
Compiling all the symmetry elements for staggered ethane yields a Symmetry Group called D3d.
Importance of symmetry-
It is an important concept in crystal morphology,crystal structure analysis.
It helps in the classification of electronic states in a molecule.
It is also useful in determining which atomic orbitals can combine to form molecules.
It can be used in predicting the no of d-d absorption bands that are observed in
coordination compounds.
Ligand theory also depends on concept of symmetry.
IR & Raman Spectroscopy used for structure illucidation also depends on symmetry.
Groups & Subgroups
Each molecule has a set of symmetry operations that describes the molecule's overall symmetry.
This set of operations define the group of the molecule.A group is a finite or infinite set of
elements together with a binary operation (called the group operation) that together satisfy the
four fundamental properties of closure, associativity, the identity property, and the inverse
property. The operation with respect to which a group is defined is often called the "group
operation," and a set is said to be a group "under" this operation.
The study of groups is known as group theory.
A group is a set of operations which satisfies the following requirements-
Any result of two or more operations must produce the same result as application of one
operation within the group.i.e., the group multiplication table must be closed
Consider H2O which has E, C2 and 2 ζv's.
i.e., of course etc…
The table is closed, i.e., the results of two operations is an operation in the group i;e the
elements are commutable.
2. Must have an identity ( ) such that AE = EA = A for any operation A in the group.
All elements must have an inverse i.e., for a given operation ( ) there must exist an operation
( )
such that or AA-1
= A-1
A = E
Each element has follows associative law
P(QR) = (PQ)R
example, the point group for the water molecule is C2v, with symmetry operations E, C2, ζv and
ζv'. Its order is thus 4. Each operation is its own inverse. As an example of closure, a C2
rotation followed by a ζv reflection is seen to be a ζ v' symmetry operation: ζv*C2 = ζv'.
The group multiplication table obtained is therefore for water molecule:
E C2 ζv ζ'v σv . σv = E
E E C2 ζv ζ'v C2 .σv=σ'v
C2 C2 E ζ'v
ζv
ζv ζv ζ'v E C2 C2.E=E C2= C2
ζ'v ζ'v ζv C2 E
C2 (σv.σ'v)=( C2 .σv )σ'v
Another example is the ammonia molecule, which is pyramidal and contains a three-fold
rotation axis as well as three mirror planes at an angle of 120° to each other. Each mirror
plane contains an N-H bond and bisects the H-N-H bond angle opposite to that bond. Thus
ammonia molecule belongs to the C3v point group which has order 6: an identity element E,
two rotation operations C3 and C32, and three mirror reflections ζv, ζv' and ζv".
Classification Of Group
1. Abelian Group – All elements are commutable. Example Water
2. Non Abelian Group- All elements do not commute with one another.
Example - Phosphine symmetry operations are E,C13, C3
4, ζv
1, ζv
2
C3 . ζv ≠ ζv.C3
3.Cyclic group- In cyclic group all the elements of a group can be generated from one element
.It is denoted by An. A represents identity element & n represents total no of elements & is
called as order of group. Each cyclic group is abelian but each abelian group is not cyclic.
Example Trans 1,2 dichlorocyclopropane.
Point Symmetry Groups - Each molecule has a set of symmetry operations that
describes the molecule's overall symmetry. This set of operations define the point group of the
molecule. Since all the elements of symmetry present in the molecule intersect at a common
point & this point remains fixed under all symmetry operations of the molecule and is known
as point symmetry groups.
Point Groups
Low Symmetry Groups
C1: only E
Cs: E and ζ only
Ci: E and i only
Cn, Cnv, Cnh Groups
Cn: E and Cn only C2:
C3:
Cnv: E and Cn and n v's
C2v: E, C2, 2 v H2O
C3v: E, C3, 3 v NH3
Cσ v: E, C , v HF, HCN
Cnh: E and Cn and h (and others as well)
C2h: E, C2, h, I
Dn, Dnv, Dnh Groups
Dn: E, Cn, n C2 axes to Cn
D3: E, C3, 3 C2
[Co(en)3]3+
Dnh: E, Cn, n C2 axes , ζh
D3h: E, C3, 3 C2, ζh
D3h: E, C3, 3 C2, ζh
eclipsed ethane
D6h: E, C6, 6 C2, ζh
D h: E, C , C2, ζh
H2
Dnd: E, Cn, n C2 axes + to Cn,
D3d: E, C3, 3 C2, 3 ζd
staggered ethane
Sn Group
S2n: E, Cn, S2n (no mirror planes)
S4, S6, S8, etc. (Note: never S3, S5, etc.)
S4: E, C2, S4
High Symmetry Cubic Groups, Td, Oh, Ih
Td: E, 8 C3, 3 C2, 6 S4, 6 ζd
Tetrahedral structures
No need to identify all the symmetry elements -
simply recognize Td shape.
methane, CH4
Oh: E, 8 C3, 6 C2, 6 C4, i, 6 S4, 8 S6, 3 ζh, 6 ζd
Octahedral structures
No need to identify all the symmetry elements -
simply recognize Oh shape.
Ih: E, 12 C5, 20 C3, 15 C2, i, 12 S10, 20 S6, 15 ζ
Icosahedron
Other rare high symmetry groups are T, Th, O, and I
Common point groups
Point
Symmetry elements group
C1 E
Cs E ζh
Ci E i
C∞v E 2C∞ ζv
D∞h E 2C∞ ∞ζi i 2S∞ ∞C2
C2 E C2
C3 E C3
C2h E C2 i ζh
C3h E C3 C32 ζh S3 S3
5
C2v E C2 ζv(xz) ζv'(yz)
C3v E 2C3 3ζv
C4v E 2C4 C2 2ζv 2ζd
Td E 8C3 3C2 6S4 6ζd
Oh
E 8C3 6C2 6C4 3C2 i 6S4
8S6
3ζh 6ζd
Ih
E 12C5 12C52 20C3 15C2 i
12S10 12S103 20S6 15ζ
Simple description,
chiral Illustrative species if applicable
no symmetry, chiral CFClBrH, lysergic acid
planar, no other
symmetry
thionyl chloride,
hypochlorous
acid
Inversion center anti-1,2-dichloro-1,2-
dibromoethane
Linear hydrogen chloride, dicarbon
monoxide
linear with inversion
dihydrogen, azide anion,
carbon
center dioxide
"open book geometry,"
hydrogen peroxide chiral
propeller, chiral triphenylphosphine
planar with inversion
trans-1,2-dichloroethylene center
Propeller Boric acid
angular (H2O) or see-saw water, sulfur tetrafluoride,
(SF4) sulfuryl fluoride
trigonal pyramidal ammonia, phosphorus
oxychloride
square pyramidal xenon oxytetrafluoride
tetrahedral
methane, phosphorus
pentoxide,
adamantane
octahedral or cubic cubane, sulfur hexafluoride
icosahedral C60, B12H122-