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-