Fundamentals of photochemistry 0470265477, 9780470265475

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K K Rohatgi-AAukherj

UNIVERSITY

L U •

INDIA

•

Ti^~ Sc^^^-^

FUNDAMENTALS OF PHOTOCHEM.STRY

nuBims of

KK

Rohatgi-Mukherjee

Jadavpur University, Calcutta

WILEY EASTERN New

Delhi

•

LIMITED

Bangalore

•

Bombay

©

Copyright

1978,

Wiley Eastern Limiteo

This book or any part thereof

reproduced

in

may

not be

any form without the written

permission of the publisher

This book

is

not to be sold outside

the country to which

it is consigned by Wiley Eastern Limited

This book has been subsidized by the Government of India, through the National Book Trust, India,

for the benefit of students

Price:

ISBN

Published by Vinod

Safdarjang

Enclave,

Kumar

New

Krishna Avtar Rastogi at Grounds, Meerut 250 002.

Rs 22 00 85226 784

for

3

Wiley Eastern Limited,

Delhi 110 016

Prabhat

Press,

AB

8

and printed by 20/1 Nauchandi Printed in India.

To

FATHER who cared for education

MOTHER who

still

encourages

Foreword

Not many

years ago photochemistry was a flimsy subject, devoid

Theory now provides an effective way of understanding the interaction of light with atoms and molecules, and measuring devices of extremely high sensitivity and accuracy are now available. New light sources, photomultipliers, electronics, chromatography, etc. have entirely

of system and ill-equipped with apparatus.

transformed the subject.

The molecular bases of plant growth, and upper air chemistry are some

vision, photobiological effects

of the areas

now

being rapidly explored.

fields

find photochemistry essential

gives

an overall description of the

been built up to aid to students,

its

present state.

lecturers

It

in their

subject,

Specialists

work.

showing how

March 1977

it

has

to

form a

field.

E.J.

Oxford

many

should prove an invaluable

and researchers who wish

coherent understanding of the whole

in

This book

Bowen

Preface

"TST *1i: BJJT 9«ai: l" »> c\ Ck (All that exists

was born from the Sun) —Brhad-devata, I: 61

In the last ten years photochemistry has seen a tremendous upsurge of interest

and

activity.

excited states has

A

come

great deal of fundamental knowledge about the to light as a result of the advent of tunable

high intensity laser beams.

The

field is

ledge gained becomes outdated before

circumstances, perhaps another textbook

and

developing so fast that any knowit

is

fully

comprehended.

In the

\

is justified.

This book is written as a university level textbook, suitable for graduate, postgraduate and research students in the field of photochemistry, photophysics and

photobiology.

During the long years of teaching photolevels, I have always found it

chemistry at the graduate and postgraduate difficult

recommend a

to

textbook to

single

the students.

My

first

introduction to photochemistry was through Bowen's Chemical Aspects of Light which very lucidly explained the interactions between radiation and

matter and their consequences and which has influenced me the most although photochemistry has travelled a long way since then. I have

books and monographs which are now available subject. All these books are listed in the beginning of the bibliography. J.B. Birks' Photophysics of Aromatic Molecules, N.J. Turro's Molecular Photochemistry, J.P. Simons' Photochemistry and Spectroscopy and A.A. Lamola and N.J. Turro (ed) Organic Photochemistry and Energy Transfer are some of the books from which I have drawn heavily. To these should be added the many review articles which have been of great help. I have adapted diagrams from some of these articles which have been

freely taken the help of

on the

acknowledged.

As

the

title

photochemistry.

implies, the

The

first

book emphasizes

the relevance of photochemistry. is

the fundamental aspects of

section introduces the subject by enumerating

Since the vocabulary of photochemistry

that of spectroscopy, the second section in which

schemes and symmetry properties,

level

third section detail

mechanism of

like

light

is

discussed energy

a refresher course. absorption

is

In the

taken up in

because the probability of absorption forms the basis of photo-

chemistry.

can

the actual

is

A proper understanding

appreciate

photochemistry.

of the process

The next

three

is

essential before

sections

one

present the

X

PREFACE

properties

of the electronically excited states and the fundamentals of

photophysical processes.

The primary photochemical

processes form a

separate section because chemical reactions in the excited states present certain

new

concepts.

The

rest of the

book

application of the knowledge so gained to

is

mainly concerned with the typical photochemical

some

Some current topics which are being actively pursued and are of great relevance have been presented in section nine. The last section

reactions.

discusses the latest tools

and techniques

for the determination of various

photophysical and photochemical parameters.

An

attempt has been made,

as far as possible, to explain the concepts by simple examples. is

given at the end of each of the

first six

sections

A

summary

which deal mainly with the

fundamental aspects. My thanks are due to the University Grants Commission for approving the project for writing this book and for providing necessary funds and I facilities, and to the National Book Trust for subsidizing the book. take this opportunity to acknowledge with thanks the help and suggestions that I have received from various quarters. I am deeply indebted to my teacher Dr. E.J. Bowen, FRS, Oxford University, for going through the entire manuscript with a 'fine-toothed comb' as he puts it, for suggestions and criticisms and for writing a Foreword to this book. Only because of his encouragement could I confidently embark upon a project of such

C.N.R. Rao, M.R. Padhye and Mention must be made of S.K. Chakraborty, A.K. Gupta, P.K. Bhattacharya, S.K. Ash, U. Samanta, To S. Basu and Shyamsree Gupta, who have helped me in various ways. the scholar-poet professor P. Lai I owe a special debt for suggesting a beautiful couplet from the Vedas, pronouncing the glory of the Sun the magnitude.

I

also

thank professors

H.J. Arnikar for their valuable comments.

—

soul of the world.

Words fail to express the patience with which my husband, Dr. S.K. Mukherjee bore my writing bouts at the cost of my household duties. His constant encouragement gave me the moral and mental support which I needed in large measure in course of this arduous task.

Calcutta

K.K. Rohatgi-Mukherjee

Contents

1

.

Introducing Photochemistry

1

1

1.2

2.

1

.

1

.

1

.5

Importance of photochemistry Laws of photochemistry Photochemistry and spectroscopy Units and dimensions Thermal emission and photoluminescence

1

3

6 7 9

Nature of Light and Nature of Matter 2.1

Interaction between light

2.2

Wave

and matter

nature of radiation

12 14

2.3

Particle nature of radiation

2.4

Dual nature of matter

16

2.5

Electronic energy states of atoms

18

2.6

The

2 7

Diatomic and polyatomic molecules

16

|

.

27

selection rule

2 8

Spectroscopic terms for electronic states

2.9

Orbital symmetry

2. 10

Notation for excited

.

and molecular symmetry states of organic molecules

2.11 Energy levels for inorganic complexes

27 3

34 38

42

CONTENTS

Xll

Mechanism of Absorption and Emission

3

of Radiation

of Photochemical Interest 3

1

48

Electric dipole transitions

and emission

3.2

Einstein's treatment of absorption

phenomena

50

3 3

Time-dependent Schrodinger equation Time-dependent perturbation theory

53

Correlation with experimental quantities

61

3 6

Intensity of electronic transitions

63

3

The

.

4 3.5 3

.

.

.

7

rules governing the transition

55

between two

energy states

65

3 8

Directional nature of light absorption

3.9

Life times of excited electronic states of

.

76

atoms and

molecules

77

3.10 Types of electronic transitions in organic molecules 3.11 Two-photon absorption spectroscopy

4.

4

.

4 5 .

4 6 .

Nature of changes on electronic excitation and rotational energies Potential energy diagram Shapes of absorption band and Franck-Condon

90

principle

94

Emission spectra Environmental effect on absorption and emission

99

Electronic, vibrational

spectra

91

92

101

moment

4.7 4.8

Excited state acidity constants

4 9

Excited state redox potential

.

Excited state dipole

103

—pK*

values

4.10 Emission of polarized luminescence

106 111

113

4.11 Geometry of some electronically excited molecules

121

4.12 Wigner's spin conservation rule 4. 13 Study of excited states by flash photolysis experiments

122

and

.

87

Physical Properties of the Electronically Excited Molecules

4.2 4.3 4.4

5

81

laser

beams

123

Photophysical Processes in Electronically Excited Molecules 5.

Types of photophysical pathways

5.2

Radiationless transition

126

— internal conversion and

intersystem crossing

129

5.3

Fluorescence emission

137

5.4

Fluorescence and structure

140

CONTENTS Triplet states

144

5.6

and phosphorescence emission Emission property and the electronic configuration

5.7

Photophysical kinetics of unimolecular processes

151

5.8

State diagrams

154

5.9

Delayed fluorescence

156

5. 10

The

160

5.5

6

.

Xlll

of temperature on emission processes

effect

Photophysical Kinetics of Bimolecular Processes 6.1

Kinetic collisions and optical collision

6 2

Bimolecular collisions in gases and vapours and the

.

mechanism of fluorescence quenching

1

Collisions in solution

169

6.4

Kinetics of collisional quenching: Stern-Volmer

6.5

Concentration dependence of quenching and excimer

6.6

171

formation

175

Quenching by foreign substances

182

21

7 3

Classification of photochemical reactions Rate constants and lifetimes of reactive energy states Effect of light intensity on the rate of photochemical

reactions

217

7.4

Types of photochemical reactions

218

7 2 .

.

Some Aspects

21

of Organic and Inorganic Photochemistry

8.1

Photoreduction and related reactions

235

8.2 8.3

Photooxidation and photooxygenation Cycloaddition reactions

253

8.4

Woodward-Hoffman

8.5

Chemiluminescence Transition metal complexes

8.6

9.

66

Photochemical Primary Processes 7.1

8.

165

6.3

equation

7.

147

Some Current Topics

in

rule of electrocyclic reactions

243

256 265 268

Photochemistry

9.1

Origin of

9 2

Mutagenic

9.3

Photosynthesis

280

9.4 9.5

Photoelectrochemistiy of excited state redox reaction

286

Solar energy conversion and storage

290

.

278

life

effect

of radiation

279

CONTENTS

XIV

10

Tools and Techniques

.

10,

Light sources and their standardization

298

10.

Measurement of emission characteristics: fluorescence, phosphorescence and chemiluminescence

302

10.3

Techniques for study of transient species in photochemical reactions

311

10.4

Lasers in photochemical kinetics

317

Appendix

I:

Appendix

II

Appendix

111

Mathmatical equation for the combination of two plane polarized radiation

322

Low

325

temperature glasses

Photokinetic scheme for determination of

quantum

yields

327

Bibliography

329

Index

339

ONE

Introducing

Photochemistry

1.1

IMPORTANCE OF PHOTOCHEMISTRY Photochemistry

with reactions which

concerned

are initiated by Such molecules are produced by the absorption of suitable radiation in the visible and near ultraviolet region of the spectrum. Photochemistry is basic to the world we live in. With sun as the central figure, the origin of life itself must have been a photochemical act. In the primitive earth conditions radiation from the sun was the only source of energy. Simple gaseous molecules like carbon ammonia and dioxide must have reacted photochemicaliy methane, organic like proteins and nucleic acids. to synthesize complex molecules Through the ages, nature has perfected her machinery for the utilization of solar radiant energy for all photobiological phenomena and providing food for the propagation of life itself. Photobiology, the photochemistry of biological reactions, is a rapidly developing subject and helps the is

electronically excited

understanding

molecules.

of phenomena

like

periodism, photodynamic action, In doing so

it

tries

to

integrate

photosynthesis,

phototaxis,

photo-

and mutagenic effects of light. knowledge of physics, chemistry and vision

biology.

in

The relevance of photochemistry also lies in its varied applications and technology. Synthetic organic photochemistry has pr

-

science

vided methods for the manufacture of 1(45-78/1977)

many

chemicals

which could not

FUNDAMENTALS OF PHOTOCHEMISTRY

2

be produced by dark reactions. vity

of these

selecti-

be mentioned here:

D

syntheses

from ergosterol

2

of cubanes

synthesis

and

may

photochemical

synthesis of vitamin

(ii)

efficiency

Some examples of

viable

industrially (i)

Moreover, greater

methods have an added advantage.

which

are

isolated

antiviral

from certain

agents,

yeasts,

industrial

(iii)

monomer for Nylon 6, (iv) manufacture of cleaning solvents, insecticides and halogenated aromatics (used as synthetic

synthesis of caprolactam, the

photochlorination, and

by

intermediates)

of antioxidants

(v) synthesis

by photosulphonation. polymerization and

Photoinitiated

photopolymerization are

used in

and manufacture of printed circuits for the electronic industry. The deleterious effect of sunlight on coloured cotton fabrics is of everyday experience, the worst sufferers being window curtains. The light absorbed by dyes used for colouring the fabric initiates oxidative photography,

lithoprinting

chain reaction in cellulose

This causes the tendering of cotton.

fibres.

Similar depolymerizing action

is

observed in plastic materials.

are going on to find suitable colourless

dyed materials or it

over the excitation

plastics will take

Researches

when added to energy and divert

chemicals which

These are known as energy degraders or o-hydroxybenzophenones.

to nondestructive pathways.

photostabilizers, e.g.,

The photophysical phenomena of

and phosphorescence tube lights, X-ray and TV have found varied applications screens, as luminescent dials for watches, as 'optical brighteners' in white dress materials, as paints in advertisement hoardings which show enhanced brilliance by utilizing fluorescence, for detection of cracks in metal work, fluorescence

in fluorescent

for tracing the course of river through

caves,

as microanalytical reagents,

and so on. Certain

chemicals

characteristics,

source

irradiation

A

materials.

change their colour,

when exposed well

is

that

is,

their

absorption

and reverse when the known as photochromic

to suitable radiation

removed.

These

known example

is

are

the spiropyrans.

Their use

in

photochromic sunglasses is obvious. But they have found application in information storage and self-developing self-erasing films in digital computers also. It is said that a company experimenting on such photochromic

memory used it

and blue

UV

light for writing the information, green light for reading

light for erasing

it.

Unfortunately organic substances usually

lack the stability for very large numbers of reversals.

Another revolutionary application of

electronically excited molecular

of monochromatic and coherent radiation. From their early development in 1960 they have found wide fields of application. They have provided powerful tools for the study of diverse phenomena ranging from moonquakes to picosystems

is

in laser technology. Lasers are intense sources

second processes of nonradiative decay of excitational energy in molecules. The intense and powerful beam of coherent radiation capable of concentra-

INTRODUCING PHOTOCHEMISTRY tion

to

point

a tiny

diamonds,

as military

is

3

used for eye surgery, cutting metals, boring many such finders and detectors, and

range

The advent of tunable dye lasers has increased the and technology.

applications.

possibility

of their application in science

A

to the study of photochemical reaction has been crisis. This has initiated researches into the the by energy provided of solar storage energy, and processes which plants carry out conversion

so

further impetus

Solar energy provides a readily available source of energy,

efficiently.

especially in those countries

is

which

between the tropics of cancer and

lie

In these areas, the daily incident energy per square kilometre

Capricorn.

equivalent to 3000 tonnes of coal.

If suitable

and devices for proper

photochemical reactions

of this abundant source problem might be solved. Solar batteries working on the principle of photovoltaic effects is one such device. For basic researches in these fields, the understanding of The various photophysical and photochemical processes is essential. fundamental study of excited states of molecules is exciting by itself. Short-lived energy states with nano and pico-second reaction kinetics have are discovered

of energy perfected,

half the

utilization

world's energy

led to the proper understanding of chemical

transfer

and the

intricate

pulsed laser photolysis states.

Now

it is

cally substituted

dye

1.2

structure

of

reactions,

matter.

are newer tools

for

the

modes of energy

Flash photolysis and study of higher energy

possible to excite individual vibronic levels

or isotopi-

compounds by using appropriate beams from tunable

lasers.

LAWS OF PHOTOCHEMISTRY Prior to 1817, photochemical changes

such as photofading of coloured of silver halides, etc. was

materials, photosynthesis in plants, blackening

observed and studied qualitatively.

The

quantitative approach to photo-

chemistry was initiated by Grotthus and Draper in the beginning of the

was

was not and the first law of photochemistry, now known as Grotthus-Draper law was formulated: nineteenth century.

effective

Only

in

bringing

It

about

that light which is

realized that

a

all

the

incident light

chemical change

absorbed by a system can cause chemical change.

The probability or rate of absorption is given by the Lambert-Beer Law. The Lambert law states that the fraction of incident radiation absorbed by a transparent medium is independent of the intensity of incident radiation and that each successive layer of the medium absorbs an equal fraction of incident radiation. The Beer law states that the amount of radiation absorbed is proportional to the number of molecules absorbing the radiation, that is the concentration C of the absorbing species. The two are combined and expressed as

FUNDAMENTALS OF PHOTOCHEMISTRY

y=a where a v

is

amount of

v

O//

(1.1)

The quantity

the proportionality constant.

Cell,

measures the

solute per unit area of the layer, dl being the thickness of the

Since

layer.

C=

x

area

thickness

mole

Cdl

Therefore,

mole

mole volume

area

On (i) /

integrating equation (1.1) within the

= / w hen = 0,

and

/

,

(ii)

/

=

when

7,

=

ln^ av

known

,

as absorption coefficient,

The

length of radiation.

final

form

log? where

€v

=a

v /2.303,

called

is

boundary conditions, we get

=

I

/,

we have

a v C7 is

a function of frequency or wave-

expressed in the decadic logarithm,

is

=c

(1.2)

v

C7

the molar

(1.3) extinction coefficient

and

expressed in moles

is

per

a

function of frequency

v,

and

The SI units of c, I and e are mol and respectively. 7 and / are the incident JI is log respectively (Figure 1.1). The quantity I

/

dm~ 3

,

is

and

nPmoh

commonly known (or

litre

1

as the optical density

logarithm) vs

its

absorption bands.

.

or absorbance A.

wavelength or wavenumber

A

plot of

gives rise to familiar

10-*vC7

(1.4)

^^

LS 1

OD

Since

/=/

Figure

is

the optical path length in cm.

mm

transmitted intensity

c«

the concentration

a photochemical reaction by a collimated of cross-sectional area A. LS=light source, L=lens, F=filter, S=collimating shield, C= reaction cell, l=optical path length, Io=incident light intensity, I=transmitted light

Optical arrangement

beam

of

intensity.

radiation

for

INTRODUCING PHOTOCHEMISTRY the

amount of

light

absorbed /a

I fl ,

by the system

=/ -/ = /u -/

=/

is

10- € vC/

(l-10- e vC7)

(1>5)

For more than one absorbing components,

optical

density

is

Icv^C/, i

where € V| is the molar absorptivity at frequency v/ for the /th component whose concentration is C/, assuming path length to be unity. Hence the measured OD is

OD = OD + OD + OD + 2

1

3

.

(1.6)

.

The second law of photochemistry was first enunciated by Stark (1908) and later by Einstein (1912). The Stark-Einstein law states that:

One quantum of

light is

absorbed per molecule of absorbing and reacting

substance that disappears.

Work

by Warburg and Bodenstein (1912-1925) clarified earlier confusions between photon absorption and observed chemical change. Molecules which absorb photons become physically 'excited', and this must be distinguished

from becoming chemically

'active'.

Excited molecules

may

nonchemical ways, or alternatively may trigger off

lose their energy in

thermal reactions of large chemical yield.

The

socalled 'law', therefore,

rarely holds in its strict sense, but rather provides essential information

about the primary photochemical

To

act.

express the efficiency of a photochemical reaction, the quantity

quantum

efficiency

is

defined as

_ number

^ reactlon ~

of molecules decomposed or formed number of quanta absorbed

_ {i

'

,}

yield or quantum efficiency was first Because of the frequent complexity of photoreactions, quantum yields as observed vary from a million to a very small When high intensity light sources as from flash lamps fraction of unity. or lasers are used 'bi photonic' photochemical effects may occur which modify the application of the Einstein law. At very high intensities a

The

concept

of

quantum

introduced by Einstein.

simultaneously; a more common effect, photon of longer wavelength to be absorbed by a metastable (triplet or radical) species produced by the action of the first photon. The nature of the photo-products and the quantumyields are here dependent on the light intensity. The concept of quantum yield can be extended to any act, physical or chemical, following light absorption. It provides a mode of account-keeping for partition of absorbed quanta into

molecule

may absorb two photons

however,

is

for a second

various pathways.

FUNDAMENTALS OF PHOTOCHEMISTRY

_ number of molecules undergoing that process number of quanta absorbed

>proce8 8

_

""

1.3

rate

o f the process

rate of absorption

'

'

PHOTOCHEMISTRY AND SPECTROSCOPY Since the primary photoprocess

is

absorption of a photon to create a

photoexcited molecule, photochemistry and spectroscopy are intimately related.

Quantum mechanics

has played a

vital

part in describing the

energy states of molecules.

For any chemical reaction, energy is required in two ways: (i) as energy of activation A£ and (ii) as enthalpy or heat of reaction A//. The need for energy of activation arises because on close approach, the charge clouds of the two reacting partners repel each other. The reactants must ha\e sufficient energy to overcome this energy barrier for fruitful interaction. The enthalpy of reaction is the net heat change associated with the breaking and making of bonds leading to reaction products. In thermal or dark reactions, the energy of activation is supplied as heat energy. In photochemical reactions, the energy barrier is bypassed due to electronic excitation and one of the products may appear in the excited state. The bond dissociation energy per mole for most of the molecules lie between 150 kJ and 600 kJ. These energies are available from Avogadro's number of photons of wavelengths lying between 800 nm and 200 nm respectively, which correspond to the visible and near ultraviolet regions of the electromagnetic spectrum. The same range of energies is required for electronic transitions in most atoms and molecules. For example, anthracene has an absorption band with a maximum at wavelength 365 nm. This signifies that a photon of this wavelength is absorbed by the anthracene molecule to promote it from the ground energy state Ely to upper energy state £2 From Bohr's relationship, the energy equivalent of a photon of this wavelength is calculated as fl ,

.

£s65=£2 -£i where, h

When

=

Planck's constant and

v is

=

(1-9)

/'v

the frequency of absorbed radiation.

expressed in waven umber in reciprocal centimetre (cm -1 ) or wave-

length in nanometre (nm) and substituting the values for h and c (the velocity of light),

we

get

E3t6 = hv = hcv

=Y =

(v=cv)

(1.10)

(v"=lA)

(l.H)

6.62 x 10- 27 ergs X 3.00 x 10 10 365 x 10~ 7 cm

= 5.44 x

10- 12 erg photon- 1

cm

s" 1

INTRODUCING PHOTOCHEMISTRY

7

UNITS AND DIMENSIONS

1.4

According

modern

the

to

measurable

convention,

expressed in SI (System Internationale)

quantities are

and replace the centimetre-

units

gram-second (cgs) system. In this system, the unit of length is a metre the unit of mass is kilogram (kg) and the unit of time is second (s). All the other units are derived from these fundamental units. The unit of thermal energy, calorie, is replaced by joule (1 J = 10 7 erg) to rationalize the definition of thermal energy. Thus, Planck's constant

(m\

h=

10- 34 Js;

X

6.62

velocity of light

= 3.00x Wins-

c

the wavelength of radiation \

1 ;

expressed in nanometres

is

(1

nm = lO^m).

Therefore in the SI units

6.62

365

~ = 5.44

x

This quantum of energy

An Avogadro number

0- 34

X 3.00 X 365 x 10- 9 m

1

10 8

J s

m

s- 1

x

10- 19 J photon- 1 .

is

contained in a photon of wavelength 365 nm.

of photons

is

called an

einstein.

The amount of

energy absorbed to promote one mole of anthracene molecules to

the

excited electronic state will be

first

= 5.44 X 10- J photon= 3.27 x 10 J moh = 327 kJ (kilojoule) mol -1 19

1

5

This amount of energy

x 6.02 x

10 23 photon

moH

1

is

contained in one mole or one einstein of photons

of wavelength 365 nm. in

The energy of an einstein of nm) can be calculated from the

108

x

1.196

radiation

=-

Rate of absorption

is

.

Ia

cm -1

=

1.196 x 10 8 =r—

,

is

is

per mole (kcal/mole),

the unit

of wavenumber

tionality constant

lie, is

implied

quite

Some

.

,_

.

g% (1.12)

.

_

,

.

.„ #1 (113)

.

einstein irr 2 s- 1

often

terms of kiloSometimes, merely

expressed in

= 4- 186 J).

(1

calorie

is

used to express energy.

therein.

used for single atom or molecule

volt signifies

.

4 1 kJT einstein-

expressed in einstein per unit area per second

The energy of radiation calorie

of wavelength X (expressed

simplified expression

The

events.

A

The proporof electron-volt (eV) chemical potential of one

unit

an energy of one electron volt per molecule.

values for the energy of radiation in

regions are given in Table 1.1.

the visible

and

ultraviolet

FUNDAMENTALS OF PHOTOCHEMISTRY

TABLE Energy of electromagnetic photon

1.1 in the visible

and uv regions

expressed in different units

Approx. wavelength range

Region

Energy

mob 1

eV

nm

Wavenumber cm- 1

200

50,000

598

142.9

6.20

400

25,000

299

71.4

3.10

450

22,222

266

63.5

2.76

500

20,000

239

57.1

2.48

570

17,544

209

49.9

2.16

590

16,949

203

48.5

2.10

620

16,129

192

45.9

2.0

750

13,333

159

38.0

1.6

in general

defined

kJ

kcal

Ultraviolet

Violet

Blue

Green Yellow

Orange

Red

=-=

A (nm) v '

4- cm" 1

v

m

10~ 9

= 4.186 J eV= 1.6 x 10- J cm- mol- = 2.859 cal mol" = 0.0135 kJmoleV mol- = 23 .06 kcal mol= 96.39 kJ molcal

1

19

1

1

=

v

1

1

1

1

1

1

1

1

The

from

intensity of incident flux

light sources

is

=

_1 J s ). Since of power, i.e watt per unit cross-section (watt power is energy per unit time and each photon has energy associated with We have, of quanta m~ 2 sr 1 it, intensity / can be expressed in number

in terms

.

E = nhtc

and

Power

=

watt

m'

E 1

m

2

J

m

2

s

J

hvc m's

s

-4- = 5.03 = watt

x

10 24

x A(nm) x power

(watt)

/jcv

Also

/

= ejnstein_ = 8 nr

#

36

x

A (nm)

x power

(watt)

s

W

8 at For example, a helium-argon laser with a power of 2 x 10~ 2 8 1 2 15 1 632 8 nm will emit 6 37 x 10 quanta s" m~ or 1 66 X 10" einstein s- m~ .

.

.

.

£

INTRODUCING PHOTOCHEMISTRY If the area

of the reaction vessel exposed to the radiation

incidence

gi\en as the intensity / times the area A.

is

Atoms and molecules absorb only by

dictated

their

one which absorbs

all

A

When

called a black body.

Under

with

suitable

absorber

perfect

the radiation falling

conditions, emits all frequencies

frequencies of radiation

specific

configurations.

electronic

they also emit some of these frequencies.

is

A, the rate of

THERMAL EMISSION AND PHOTOLUMINESCENCE

1.5

as

is

on

is

defined

is

and, under steady state

it

Such an absorber

unit efficiency.

a system

conditions

thermal equilibrium with

in

its

environment rates of absorption and emission are equal (Kirchhoff's law). This equilibrium is disturbed if energy from another source flows in. Molecules electronically excited by light are not in thermal equilibrium with their neighbours.

The total energy E, of all wavelengths radiated per m 2 per second by black body at temperature TK is given by the Stefan-Boltzmann law

£ = cr

1

a

(1.14)

where the Stefan's constant a

From

=

5.

699

lO" 8 J

x

m" 2

deg"4 s" 1

m

Planck's radiation law, the energy per

tion density p in

3

of radiation or radia-

an enclosure having wavelength between A and \

+ dh

is

px d\, that is

dX \ d\ C { n Snhc Px^=-5j5c *c,x*r_i= x5^xi--iJ s

C =

where

mann

x

4.992

constant

=

1

x

x 10~ 24 Jm- 1 C2 = 1 .439 X .38 x 10~ 23 J molecule -1 ,




energy terms (//)

is

proportional to the square of the electric

Interaction between

h= and £ = 3,2,1 1

p and d /2

=2

electron

field strength.

NATURE OF LIGHT AND NATURE OF MATTER

25

V

'S

M«0 /

I I i

/ / / i / / i

2s + /

1

singlet

I

level

/

»

\

/

M-l

; /

/ i

i

i

/

/

'p

:

/ ;

2s

i

'

\

level

,

3

\\

triplet

/

/

V

t 1

+1

P,

'

M

o

!

h

M-o

n a u \i

t

No

s, s 2

electronic interaction

/,

t

Magnetic

L S coupling

2

coupling

coupling

field present (2| + 1) levels

Energy

Figure 2.6

configuration (np) 2 , e.g. carbon, coupling and Hund's rules. (Adapted from Eyring, Walter and Kimball, Quantum Chemistry, Wiley, New York, levels

for

the electron

illustrating spin-orbit

1946.)

S=l,0 J (Hi)

=

4, 3, 2,

/i

S / r/7£'

d

=3

=

1

and S =

1

and S

electrons

= 2,/ = 2 2

L=4,

(iv)

when L

Interaction between two

3, 2, 1,

= 1,0 = 5, 4,

3,

when L

=4

3

In rare earths or lanthanide energy levels of rare earth ions La *. is being gradually built up. The number of/

ions, the /electronic shell

electrons for the

first

Ce 3+ No. of/ electrons

nine

members of the

Nd 3+ Pm3+

series

Sm s+

is

given as:

Eu 3+

Gd s+ Tb3+

Dy 3+

123456 789 Pr»+

FUNDAMENTALS OF PHOTOCHEMISTRY

26

An 0,

The values of m are Eu 3+ and Tb 3+ on either side of

/shell (/=3) can accommodate 14 electrons.

±1, ±2, ±3.

Gd 3+

Let us take the cases of

which the subshells are just half-filled. For europium ion in the ground state, 6 electrons occupy separate m states all with spins parallel: in

t

t

+3

+2

+

0-1

1

= 3, L 3; therefore, the ground state = = 1 3; therefore, maximum multiplicity (2 7 = 3 + 3, 3 + 3-1, ..., 3-3 = 6,5,4,3,2,1,0

Zmi

i.e.,

is

z

'5

And

-2 is

an

x

F-state.

3 -f 1)

= 7.

3+ is 7 Fj. The lowest level of the multiplet Hence, the ground state of Eu 3+ with 7 For, Hund's rule. Tb to 8 electrons the ground according is F 7 subshell is But since the Fj. more than half-filled, inverted is again state 7

multiplets are obtained, the lowest level being

6

.

Figure 2.7 gives the

•»|

28 H £6

84

F

'0, -

22

CO

Q 7/2

^3/2 a 5/2

H .3/2 12

•p

tft

* w S/2

10

"7/2

8

H

n/« •ftfe

ia/2

V«

6

V2 13/2

•13/2

11/2

9/2 7/2

"&'2

Sm

Figure 2.7

6

o

t3 Eu

+3

Tb

+ 3

—

(A.P.B. Sinha "Fluorescence and Laser Action in Rare Earth Chelates" in Spectroscopy in Inorganic Chemistry Ed. Rao and JR Ferraro.)

Energy

levels

of trivalent rare earth ions.

CNR

27

NATURE OF LIGHT AND NATURE OF MATTER energy level schemes

for

Sm 3+ Eu 3+ ,

and Tb 3+

These ions are para-

.

magnetic.

2.5.2

Inverted Multiplets

Oxygen atom with p A effective electron configuration has terms similar 2 But since the subshell to those of carbon with p effective configuration. 3 P2 is more than half-filled for oxygen, the multiplet manifold is inverted 2 2 3 P1? 3 P For sodium atom, 3 P 1/2 level lies below 3 P2f2 but for chlorine atom the order is reversed. The case for Tb 3+ is already mentioned above. ,

.

2.6

THE SELECTION RULE

governed by certain selection rules initially derived empirically. These are: In an electronic transition any value (i) there is no restriction on changes in n; A« (ii) S can combine with its own value; AS =

The

transition between the possible electronic energy states

is

=

(iii)

L

(iv)

/can

can vary by vary by

transition

is

or

±

or

±1

1

unit;

AL = 0, ±

except that

not allowed;

A/ =

0,

1

J=

±1

to

/

(except

=

0— /-* 0)

A basis for these empirical observations is provided by quantum mechanics according to which an odd term can combine with an even term and vice versa. This selection rule is known as Laportes rule. Quantum mechanical justification for this A convenient mode of representing these diagram for the energy is

states of

rule

an atom.

is

given in the next chapter. the

Grotian

Such a diagram for

Hg atom

selection

rules

is

given in Figure 2.8.

The allowed transitions are between adjacent columns of energy states. The singlet and triplet manifolds are separated as they are forbidden by Under certain conditions they do occur with reduced spin selection rules. 3 efficiency, as for example, the transitions between 6 S and 6 P states of mercury. They are indicated by dashed lines in the diagram. The l

wavelength associated with each transition

2.7

is

indicated in

A

units.

DIATOMIC AND POLYATOMIC MOLECILES Molecules

differ

from atoms

in

more than one nuclei. These and can also rotate around and rotational energies are also

having

nuclei can vibrate with respect to each other

the molecular axes.

quantized, they give

Since vibrational rise to discrete

energy levels which can be calculated

from the Schrodinger equation. The differences in quantized energy levels for vibrational energy and those for rotational energy are respectively smaller by nearly 10 2 and 10* times than those for the electronic energy

28

FUNDAMENTALS OF PHOTOCHEMISTRY

F.

5-0

Figure 2.8

-

Grotian diagram for

Hg

atom.

Wavelengths are

in

A

units.

NATURE OF LIGHT AND NATURE OF MATTFR

29

Therefore, the changes associated with rotational transitions only

levels.

are observed

the far

in

infrared region and

The

rotation in the near infrared.

those with

electronic

and

vibration

require energies

transitions

and ultraviolet regions of the electromagnetic radiation and accompanied by simultaneous changes in the vibrational and rotational

in the visible

are

quantum numbers. In principle,

should be possible to obtain the electronic energy

it

of the molecules

of the Schrodinger

a solution

as

and internuclear cross-coulombic terms

electronic

if

But the can be broken up into equations which

it

A

variable at a time. larger

simplifying feature

interin

the

can be solved of one

functions

are

much

because of the

that

is

levels

if

included

are

equation

potential energy for the Hamiltonian.

only

equation,

mass of the nucleus the motion of the electrons can be treated

independent of that of the nucleus. heimer approximation.

Even with

has been

the

possible for

molecule ion,

H

2

+

only,

This

this

known

is

solution

the exact

simplification,

of molecules, that

simplest

as

as the Born-Oppen-

the hydrogen

is,

and with some approximations for the

H

2

molecule.

The

on approach of two atoms form a diatomic molecule when plotted as a function

variation of total energy of the system

towards each other to

of internuclear distance

At

the repulsion terms.

is

given in Figure 2.9.

diagram.

If

no

the electrostatic attraction terms balance

and the curve

attractive interaction

is

is

identified as the

is

known

then no bond formation

possible,

for the molecular systems

of the atomic orbitals of the

MOs

atomic orbitals method)

(LCAO)

summation or

with suitable

^Mo=C where Cv is the by the function

1

(\sa 8 y (\sa u ) 2 (2sa g f

Mulliken notation:

2.8

K

K

za

t

antibonding

r (2sa u f (2pa 8 ) 2 (2p x y iz u Y ,

yol

xa]

(2p x y n 8 )* ,

._-'

H'tt:

v-

SPECTROSCOPIC TERMS FOR ELECTRONIC STATES The spectroscopic term symbols

for the molecular case can be obtained,

J

FUNDAMENTALS OF PHOTOCHEMISTRY

32 as in

by the summation of

the case of atoms,

all A's

to give

the

total

momentum number in the direction of the bond axis, A = 2a,- and the total spin angular momentum number S = 2s/. The two quantities combine vectorially to give resultant angular momentum number £1 = A + S\ The angular

.

|

total multiplicity

±2,

is

again given by (2S

respectively

etc.

are 2,

A,

IT,

The term symbols for A = 0, ±1, and the spectroscopic terms are

1).

-f-

etc.,

represented as 2S + ,

For

example,

A = 2A/ = 0,

term

and the

resultant angular

symbol for

= Zs, = £,

configuration

electronic

electrons

the

and S

is

momentum

Is

electron

For the

2.

in 2

H+

with

A=±l

and

spin value can only

inner

electrons in the

momentum

A=

2A/

from

be

vectors

= 0, ± 2

same

state exists.

orbital possible.

principle

and a doubly degenerate

.

1

1

A

sign

indicates that the

respect to the operation of reflection axis whereas the

(— )

the spectro-

combination («- ->),

the

destroyed by interaction to give 2 + and 2"

is

(+)

more than For the

momentum When A = 2, the total

l

degeneracy of the state

antibonding

are

t

spates respectively.

the shell

according as the

direction.

Pauli's

half-filled

this

When A = 0, S = 2s can be or 1 giving When a 2 state is obtained from scopic terms 2 g and 3 2 g - 1 (-> «-) or A = - 1 + of A > 0, for example, \ = + \g

= 0,

because they form the completed subshell.

two p

vectors are in opposite or in the

1

A

with

molecule,

the nonbonding

above,

Because of the degeneracy of

important.

electron,




OlV^Ol'S) Schurr,ann-R unge

continuum

Schumann-Runge bands

Herzbcrg bands

Atraospherjc

bands

infrared atrtospheric banc

i

Figure 2.11

in

A

Potential energy diagrams for molecular states

oxygen electronic energy and the absorption spectrum of oxygen molecule.

ORBITAL SYMMETRY AND MOLECULAR SYMMETRY

2.9

As already evident from the previous

symmetry properties of a its chemical and in general, behaviour and spectroscopy and photochemistry in physical selection rules which The govern particular. the transition between the energy states of atoms and molecules can be established from considerations of the behaviour of atoms or molecules under certain symmetry operations. For each type of symmetry, there is a group of operations and, therefore, section,

molecule are of utmost importance in understanding

they can be treated by group theory, a branch of mathematics.

A symmetry

operation

is

one which leaves the framework of a molecule

unchanged, such that an observer who has not watched the operation cannot tell that an operation has been carried out on the molecule (of course one presupposes the structure of the molecule from other experimental sources).

The geometry of the molecule

is

governed by the geometry of There

the orbitals used by the constituent atoms to form the molecule. are five kinds

of symmetry operations which are necessary for classifying

a point group.

Cp

(i)

Rotations about an axis of symmetry

(ii)

Reflection in a plane of symmetry: o.

(iii)

Inversion through a centre of symmetry: i. Rotation about an axis followed by reflection

(iv)

cular to

it

(also called

:

.

improper rotation):

S.

in a

plane perpendi-

NATURE OF LIGHT AND NATURE OF MATTER

35

Identity operation or leaving the molecule unchanged:

(v)

/.

and centre of symmetry are known as the elements of one point, the centre of gravity of the molecule, which does not change during these operations. Hence the designation point symmetry, in contrast to translational symmetry

The

axes, planes

symmetry.

All these elements intersect at

observed in crystals. Let us take the simple molecule, say, water to understand some of these terminologies (Figure 2.12).

Figure 2.12

Elements of symmetry for

The water molecule has a two-fold (p = z-direction.

On

complete rotation

H2

2)

molecule.

rotation

axis

along the

of the molecule through 360°, the

molecule has indistinguishable geometry at two positions, 360°/2 and 360°. has two planes of mirror symmetry, Gyz passing through the plane of

It

the molecule

and the other aX2

three operations

group

C2V

together with

,

bisecting the

the

identity

HOH

bond

angle.

These

operation / form the point

to which the water molecule belongs.

In the molecular

the symmetry

theory and electronic spectroscopy we are wave functions of the molecules. Since each of

orbital

interested in the electronic

operations of the point group carries

physically equivalent

the molecule into a

configuration, any physically observable property of

the molecule must remain unchanged by the symmetry operation.

Energy one such property and the Hamiltonian must be unchanged by any symmetry operation of the point group. This is only possible if the symmetry operator has values ± 1. Hence, the only possible wave functions of the molecules are those which are either symmetric or antisymmetric towards the symmetry operations of the of the molecule

is

FUNDAMENTALS OF PHOTOCHEMISTRY

36

group, provided the wave functions are nondegenerate. The symmetric and antisymmetric behaviours are usually denoted by -f 1 and — 1 respectively, and are called the character of the motion with respect to the symmetry operation. Let us examine the behaviour of p y orbital in water under the symmetry operation of the point group C 2V (Figure 2.13a). Rotation around the z-axis changes sign of the wave function, hence under d, p y orbital is

Y

(a)

X 2

*P*

(1/2)

*p9

(l/2)(*i-*4)

*Pz

(l/2)(* 5

4>3

4>4

a tg

4>6

(^-fa)

-* 6

1 tlu

3

)

(-*! -4> 2 -4> 3

3dz *

(1/12)

3dx *-y*

(1/4) (*!

M

The

has a lg symmetry.

5-orbital

-* 4

—* — 5

4>

6)

«0

+ +!— ^3 + **)

i

—

vx

i

— —

M„ ldzx

hi j

Summary 1

atoms are expressed in terms of four quantum numbers n, quantum number; /, the azimuthal quantum number; m, the magnetic quantum number and ms or s, the spin quantum number. According

The energy

states of

:

the principal

to Pauli's exclusion principle,

the four 2.

no two electrons can have the same values

for all

quantum numbers.

Electromagnetic radiation is an oscillating electric field E in space which is propagated with the velocity of light. The idea of field is wholly derived from its measurable physical effects; the additional concept of 'aether is valueless and unnecessary.

3.

Electromagnetic radiation consists of an electric vector E directed along the displacement direction of the wave. The associated magnetic field vector H, lies perpendicular to the electric vector and perpendicular to the direction of propagation.

The

oscillations of the

Ew = E Hz = H

two

fields are

Sin

2tt (vf

Sin

2tt (vf

given by

— kx) - kx)

45

NATURE OF LIGHT AND NATURE OF MATTER

V

6

9+

Bil E

-JO

•IS

° S E 2

©

n —£ 5

/

A6j3U3

46

FUNDAMENTALS OF PHOTOCHEMISTRY and EqIH

= VfVc

fx

€ Ar

= magnetic permeability = dielectric constant = 1/A

4.

Electromagnetic waves behave like particles in photoelectric effect, Compton effect and phenomena of absorption and emission. The quantum of energy, E = //v, is called a photon. Photons travel with the speed of light c, and possess a

momentum

5.

Matter

classically particulate in nature, but

6.

Av/c.

it also manifests wave character. The wave property of matter is related to its particle nature by de Broglie's relation X = hip, where A is known as the de Broglie wave length. Our understanding of the interaction between light and matter is governed and

is

limited by the Heisenberg uncertainty principle which

A*- &p^h;A 7.

8.

E.

may

be stated as

A t±h

We

cannot extrapolate our knowledge of everyday macroscopic world to the world of subatomic dimensions. The Heisenberg uncertainty principle, the wave character of particle motion and quantization of energy become important when the masses of the particles become comparable to Planck's constant /;. For multielectron atoms, the term symbol for an energy state is represented as

where S

is

the total spin angular

addition of the spins of

all

momentum component

obtained by the vector

the valence shell electrons and (2S

multiplicity of the given energy state;

L

is

+

1)

the total orbital angular

is

the total

momentum

component obtained by the vector addition rules; and / is the total angular momentum quantum number, obtained by L = S or Russell Saunder's coupling 9.

scheme. The molecular orbitals (MOs) are formed by the linear combination of atomic orbitals (LCAO-MO method). For diatomic molecules, the component of the angular momentum (X) in the direction of the bond axis is now important. The energy states are expressed by the symbol

where

25-j-i

SA/

obtained by vectorial addition of A and S. states of an atom or a molecule are obtained by considering the properties of all the electrons in all the orbitals. The properties of the electrons

and 10.

A=

£1 is

Electronic

in the unfilled shells are the

main contributors.

It is useful to classify electronic

terms of their symmetry properties as defined by the group operations Mulliken's terminology is based pertinent to that particular molecular species. on the following rules (small letters are used for one electron orbitals and states in

capital letters for molecular states) (i)

species as (ii)

E and

triply

A

or B; doubly degenerate

degenerate as T.

Nondegenerate species which are symmetric (character, + 1) with respect to rotation about the principal axis C„ are designated as A; those which are antisymmetric (character, — 1) to this operation are designated as B (operation

(iii)

:

All nondegenerate species are designated as

If

CJ

the species

).

is

symmetric with respect to a

C2

operation perpendicular to

NATURE OF LIGHT AND NATURE OF MATTER the principal axis then subscript

1

47

(symmetric) or subscript 2 (antisymmetric)

added to A and B (operation C\ v ). Single primes and double primes are added to A and B when the species is symmetric or antisymmetric respectively to reflection in a plane perpendicular to the principal axis of symmetry (operation a h ). For centrosymmetric molecules with a centre of inversion subscripts g and u are added if the species is symmetric or antisymmetric respectively to the is

(iv)

(v)

/',

operation of inversion through this centre (operation 11.

In saturated

and unsaturated organic molecules,

are conveniently designated as

singlet

1 (rr, tt*), *(tz, tt*),

i).

and

i(w, tt*),

triplet

\n,

energy states according

tt*) etc.

as they are generated by (ir-*.n*) transition or (n -> n*) transition.

common

terminology,

S

,

S lt S2

,

.

.

.

and

7\,

T2 T3 ,

,

etc. are

For most

used for singlet and

triplet states.

12.

For inorganic complex compounds, group theoretical nomenclatures are used.

THREE

Mechanism of Absorption and Emission of Radiation of Photochemical Interest

3.1

ELECTRIC DIPOLE TRANSITIONS When

electromagnetic

electric field

atom or the molecule. particle composed of electric field.

radiation

falls

on an atom or

a molecule, the

of the radiation tends to disturb the charge cloud around the

When

U

The

situation

positive

the

field

U

LJ

is

analogous to the case when a

and negative charges is brought near an is applied from the upper side (Figure 3.1), Matter

Radiation

OOP

n n n la)

Figure 3.1

(b)

Creation of an oscillating dipole by interaction between the charge cloud of an atom, (a) an oscillating electric field; (b) electromagnetic radiation wave.

the positive charge density

is

attracted

density repelled, generating a dipole field is

towards

moment

it

and the negative charge

in the

particle.

applied from the lower side, the direction of the dipole

If is

now

the

reversed.

49

MECHANISM OF ABSORP1ION OF RADIATION

between the upper and the lower positions, the induced The also oscillate with the frequency of oscillation of the field.

If the field oscillates

dipole will oscillating

fashion

which

electric

electromagnetic radiation acts in a similar

of the

fiel0

an oscillating dipole in the atom or the molecule with The dipole is generated in the direction of the interacting.

to create it

is

electric vector

From

of the incident radiation.

we know

when

a positive and a negative becomes a source of electromagnetic radiation. The radiation emanating from the source is propagated A similar situation in all directions like a sound wave from a ringing bell. applies to the present case. The disturbed molecub becomes a source of electromagnetic radiation of the same frequency as the frequency of the incident radiation. This is the mechanism of scattering of radiation by a particle of molecular dimensions. The secondary radiation thus scattered uniformly in all directions interferes with the primary incident radiation. As a result, radiation waves are cancelled out by destructive interference

electrodynamics,

that

charge oscillate with respect to each other,

in all directions except that

As long

it

of reflection or refraction.

as the frequency of incident radiation

the natural frequency

v„

v,

is

of the molecule as given by

not close to that of its

energy

states, the

forced distortion of the molecule by the electro-

due to But when v, v„, and a resonance condition is established between the two interacting partners (the photon and the molecule), the oscillations

are

s

magnetic wave.

become

oscillations classically

radiation or a photon it

to a higher energy

is

'free'. Under this condition a quantum of absorbed by the atom or the molecule, promoting

An

state.

the product of charge e times

dipole

oscillating

moment

of separation

the distance

jj.

r

(defined by between the

and negative charges) is created and designated moment. The mechanism can be illustrated as follows for the case of a hydrogen atom (Figure 3.2). The electric vector of the centres of gravity of positive as the transition

plane its

polarized

incident radiation

spherically symmetric s state to

direction of the vector

field.

H(1

Figure 3.2

4(45-78/1977)

distorts the

Obviously

S

)

normal hydrogen atom

a state which creates

*

it is

H (2 p

in

a dipole in the

a p state with a nodal plane

)

Mechanism of absorption of radiation by

H

atom.

FUNDAMENTALS OF PHOTOCHEMISTRY

50 perpendicular to the electric

promotion to the upper This

radiation.

known

is

absorption

with

occurs

of appropriate

electric dipole transition.

TREATMENT OF ABSORPTION AND EMISSION

EINSTEIN'S

3.2

an

as

Under the resonance condition,

vector.

state

PHENOMENA According to the classical electromagnetic theory, a system of accelecharged particles emits radiant energy. When exposed to thermal The rates of radiation at temperature T it also absorbs radiant energy. absorption and emission are given by the classical laws. These opposing rated

9

processes are expected to lead to a state of equilibrium. treated the

corresponding problem for

and molecules

in 1916

Einstein

quantized systems such as atoms

in the following way.

Let us consider two system, with energy values

nondegenerate

Em

and

En

stationary

where

Em >

theory, the frequency of the absorbed radiation Vm/i

=

Let us assume that the system

is

states

m

and n of a

According to Bohr's given by E„.

~ h is

(3.1)

in the

lower state n and

exposed to a

radiation of density p (v) defined as the energy of radiation per unit volume between the frequencies v and v -f- dv. The probability per unit time that

absorb the radiation and

will

it

m

is

9

proportional

density of radiation

will

Bnm

coefficient

is

N

n in

the state n

and the

.

Rate of absorption

where

thereby be raised to the upper state

number of particles of frequency v mn Hence to the

the proportionality

= B„ m Nn

p (v„«)

and

constant

(3.2)

known

is

as

Einstein's

of absorption.

m to n consists of two parts, one which spontaneous and hence independent of radiation density and the other proportional to it. If m be the number of particles in the upper state m at any time t, then The

probability of return from

is

N

Rate of emission

where

Bmn

A mn

is

known

coefficient

Bnm Nn

On

rearranging,

we

? (Vnm)

Nm ratio of the

(3 3) .

= A mn Nm + Bm

n

Nm

At

equilibrium, the

p iymn)

and two

(3.4)

get

Nn

The

9 iy mn )

as Einstein's coefficient of spontaneous emission

of induced emission. be equal and we have

as Einstein's

rates will

= A mn Nm + Bmn Nm

number of

_ A mn + Bmn p

{v mn )

( (J 5) '

Bnm9(?nm) particles in the

states n

and

m with energy En

MECHANISM OF ABSORPTION OF RADIATION

Em

and

can also be obtained from the Boltzmann distribution

respectively,

,

51

law:

_

NjL

e -{E n -Em)lkT _, e h»lkT

Nm Solving for

p (v flm)

and

N /Nm

for

substituting

n

,

^.6)

from (3.5) and

(3.6),

we

have P (v " ffl)

On

the other hand,

body radiation

and

(3 .7)

J?- Bmn

Bnm

(3 7 > '

from Planck's derivation of energy density for a

T (Sec.

at temperature

(^«)= -2-r

9

Comparing

=

(3 8), .

we

Bn-+m

1

.4),

\e

we know

black

that (3

hvjkT_\)

-

8)

find

= Bm-+n

\* •')

h

8tu

Bm +n

c*

(3.10)

Probability of Induced Emission and Its Application to Lasers

3.2.1

From emission,

the condition of equilibrium between the rates of absorption and

we have from equations

(3

Nn

A mn -f Bmn

Nm

Bnm

.

and

5)

(3 6) .

9 (v mn )

p \y n m)

Amn Bmn P (ymn)

f

(assuming Bmn

1

= Bnm

)

s ehvlkT Hence,

when

/iv

" m"

_

,

Bmn

> kT,

1

= e»" kT -

(3.11)

1

9 (Vm „) is

Therefore, at high

negligible in

comparison to

eh, l kT 9

and A mn

> i?m«

p (v).

frequency regions such as visible and near ultraviolet,

spontaneous emission has a large probability but that of induced emission very small. On the other hand, when /?v

Figure 3.3

To

(a)

(b)

Radiation from a normal source— incoherent beam, (b) Radiation from a laser source— coherent beam.

obtain the laser action or light amplification by stimulated emission

of radiation, the probability of induced emission in the visible region must

be increased. The probability of induced emission is given as B mn Nm p iy m „). When Bmn is small, the rate of such emission is expected to be small since

Nm

the population increase

probability

Bmn

low,

is

is

somehow

to

whether absorption

will take place or

to

even when the emission

increase the

—N

on the

One way

in general small.

is

For any given value of

in the higher energy state.

B nmi

m

of the upper state

the rate of phase-coherent emission,

number of

particles

Bmn which ,

is

Nm

equal to

emission stimulated, depends

N

difference (Mi m ), where N„ and m are the populations of the energy states n and m, respectively. In the absence of a radiation field,

the

numbers are governed by the Boltzmann distribution

electronic

ground

energy states at ordinary

state

impinge on

is

such

The population of is

temperatures,

practieally

For

only the

stream of photons is allowed to absorption is preferred because N„ is large. starts building up and after a time, the rate of a

a system,

state

absorption becomes equilibrium

When

populated.

law.

m

equal

established.

to

the

As long

rate of emission.

A

photostationary

as the irradiation source

is

maintained

two energy levels remain constant. On the other hand, if by some means the population of the excited state is increased, the impinging photon is more likely to encounter an excited particle than an unexcited one, thereby stimulating emission of a

the populations of the

MECHANISM OF ABSORPTION OF RADIATION photon rather than

its

system, an extra photon

emitted

absorption. is

53

To each photon impinging on

added to the beam.

the

Under the circumstances

be larger than the incident intensity.

This is important aspect of laser system is the inherent possibility of bringing about population inversion. The radiation which promotes the molecules to upper energy state is the

known

intensity will

the

as

laser

Therefore,

action.

the

known as pump radiation and the radiation which stimulates emission is known as laser radiation (Figure 3.4). The photon thus induced to be emitted has the same phase relationinducing photon. Further amplification of this coherent brought about in a resonant optical cavity containing two highly reflecting mirrors, one of which allows the amplified beam to come out, either through a pin-hole or by a little transmission (Section 10.4). ship as the

emission

is

TIME-DEPENDENT SCHRODINGER EQUATION

3.3

The phenomena of absorption and emission can be handled mathematically

by

the

Schrodinger

time-dependent

equation

only.

It

is

represented in one dimension as

// T( ,

or,

where

¥

is

+

dx'

fifth

>0=

y ( x)

Y » -2«i

(3,I3) dt

dY(x,t) _____ h

, ... (3 .14)

a function of position coordinate x, and time

/,

and (— hflvi)

quantum mechanical operator for the total energy E in a nonconservative system. If we denote ty(x) as a function of x only and

(d/dt)

(t)

the

is

as a function of

/

only, then

Substituting

On

separation rf variables,

L4.^ + KM*W.^i-^ w W

* (x)

Each E, and

we have

side

we

8ic«/w

*

ft?

2wi

must be equal to a constant which

is

4>

(t)

dt

identified

(3 K

15) '

>

with energy

have,

-^^

)

+ rx°v:

jr

simplifying and rearranging (3.26),

space, equation (3.27)

to satisfy

get

9

n

V

Substituting (3.24)

T^

(3.26)

we have

and integrating over the

entire configuration

becomes

-^-^^^^d^la^^M-^di

(3.28)

MECHANISM OF ABSORPTION OF RADIATION All terms

on the

57

vanish except that for n

left

=m

due to orthogonality

property of wave functions and from the conditions of normalization,

dam (t) d This If

(329)

r*-™**®!**-******

a set of simultaneous differential equations in the function a m

is

we consider

two

consisting of only

the simple case

states n

and

{t).

m

then

on expanding

= -T L *w/v; ^"« r. ,

Since initially the system a„

=

1

and am

= 0.

is

in the

*- ? T-«"(')/'r; *'*:*

lower energy state

w,

we have

p

at

Therefore, the final term will not contribute

/

3 °)

= 0,

initially,

and we have

>>

(331)

-tt/t:**'*;*

This equation gives the rate at which a system changes from one stationary state to

the molecule

The

The

another under the perturbing influence of the radiation.

oscillating electric field of the

and causes

rate with

which the

it

radiation

to escape

potential energy of

disturbs the

from

stationary

initial

its

coefficient am increases

state n.

corresponds to the rate with

T W

which the description of the system changes from to m To evaluate the equation, we must find out the nature of perturbation imposed on a system of molecules when the electromagnetic radiation falls

on

When

the oscillating

electric field

interacts with the molecules

composed of

it.

.

of the electromagnetic radiation positive

and negative charges

the electric vector of the incident radiation induces a dipole the molecule along

its

direction (Sec. 3.1).

moment

The perturbation energy along

the x-axis as given by the perturbing Hamiltonian Si'

is

JC = Ex lej Xi Ex

;

er in

(3.32)

in x-direction and ej represents the x-component of the displacement for the yth particle of the system. The expression I ej xj is known as the component of the electric dipole moment of the system along the x-axis and is represented by

where

is

charge and

[i x .

When

the electric field strength

x;, the

of the

the time variation

field

is

introduced (Section 3.2).

Si' becomes

SC = E x (v) Substituting the value of

-"*— - -

SC

TJ T

u


|fdeal

2

|

2

/,/

w

_

M„ m

|

2

,

M„ m

sometimes written as

is

|

R„ m

|

|

matrix element of the electric dipole

moment

8* 2 Att V»m C

3A?

2

OT

65

2

-.

,

*"*

(i

-

'

2

/! '

(3.72)

|

where

,

M

'

|

|

R nm

moment and has

|

the

known

is

as the

same meaning

as

There are a few other related quantities the strength of an electronic transition. expressing for used which are

the transition

integral.

Dipole strength of transition

D=\M nm Q=

where,

The concept of

«

r

|

ty

or

|

m dx

R nm

= dipole

related to the

It is

2 |

=eQ 2

2

(3 73) .

length

(3 74) .

strength was

oscillator

theory of dispersion.

2 |

developed from the classical molar refraction R of a substance

by

M n _ fmn *~7 *T2-3^n S ^37, -

2

where

M

is

Ne 2

1

(3 75) -

molecular weight of the substance, d the density, n the refrac-

tive index, v the

frequency

of the radiation

and

field

fmn

the oscillator

m

which absorbs a The summation is over all the binds or frequency corresponding to v flm energy states to which the transition can take place from the ground state n, including the continuum. transitions

for

strength

between the

states

n and

.

THE RULES GOVERNING THE TRANSITION BETWEEN TWO ENERGY STATES

3.7

The Basis of Selection Rules

3.7.1

As already

discussed, the interaction of electromagnetic

matter leads to absorption only

if

a dipole

moment

is

radiation with

created as a result

of such interaction. During the process of emission the dipole This

may

be stated symbolically as d^jdt

The strength or of transition

D

is

intensity of absorption

or square of the transition

expressed in terms of oscillator strength

/

positive is

and

is

destroyed.

d^dt 2 ^

0.

related to the dipole strength

moment

integral

|

M nm

2 ,

and

is

|

or integrated molar extinction

dv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational Some are forbidden which can become states are not equally permitted. allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection

J €v

rules.

For atomic energy

levels, these selection rules

have been empirically

obtained from a comparison between the number of 5(45-78/1977)

lines

theoretically

FUNDAMENTALS OF PHOTOCHEMISTRY

66

expected in the spectrum of a given atom and those experimentally obtained The rules so derived state: Am (vide Section 2.6). and 0,

=

=±

±1

where m and / are magnetic and orbital annglar momentum quantum numbers, respectively. There is no such restriction imposed These selection rules can be justified from the mechanics of for/*. A/

1

interaction between matter

When

a plane

along z-axis

and

radiation.

polarized radiation

with the electric vector directed

imposed on a hydrogen atom

is

in

its

ground

state (/

= 0),

the radiation distorts the molecule in z direction such that an oscillating dipole

is

necessarily created as

the radiation

the radiation

shown diagrammatically

in Figure 3.2.

If

of a frequency in resonance with the transition \s->2p z

is

is

absorbed.

,

Thus, a dipolar radiation can bring about

changes only from s->p, or p ->d or d^-f. Each transition involves the creation of a node at right angles to the direction of polarization of the vector,

electric

A/=lin

and the change

When

each case.

p -> s, A /

=—

in angular

the

atom

For an s->d

momentum quantum number

reverts

to

its

energy

original

quadrupole radiation is required since two nodal planes have to be created by the incident radiaSuch transitions have very low probabilities, since the intention field. state

sity

1.

transition, a

of electric quadrupole component in the radiation

field is

x

only 5

10~ 6

of that of the dipole component.

Also ls-*2.s, or 2p -+ 3p transitions are forbidden, as no transition moment is created or destroyed conforming to the selection rule

A

/

^ 0.

The same conclusions can be

drawn from the quantum mechanical

condition that the square of the transition

moment

integral

|Mnw

2 |

must

be nonzero for a transition to be induced by electromagnetic radiation.

That

is

M,nm

where rules

fx

nW

is

we have

the dipole

= | Vn^nm^mdT^O

(3.76)

moment operator. To understand the selection symmery properties of the three functions

to consider the

and ty m within the limits of integration. A qualitative picture of problem can be obtained if we consider one electron wave functions to be located with the nucleus as the centre and work out the symmetry of each function, in terms of odd and even character. For a one-dimensional case in the x direction, an odd function changes sign on changing the coordinate from x to — x. With this criterion, the dipole moment vector is always odd since it changes sign at the origin. The one electron wave functions are either odd (— ) or even (-f ). Let us consider two types of possible transitions, Is -+2s and ls-+2p, by pictorial representation of s and p one-electron orbital functions (Figure 3.6). For convenience, we divide the configuration space into +n

,

the

V-nm

MECHANISM OF ABSORPTION OF RADIATION

67

1-^.2 s s

^37 -

+

p

y -X.

+ X

+

+\.

- x

x

•

(B) (A) Graphical integration of transition moment for transition to emphasize the selection rule:

Figure 3.6

H

|

M

ls-*2s and Is -* 2p ^ for an allowed

|

transition.

+a (A) Is-* 2s:

|\W*|=

-x

sdx= | v*(ex); 2 J

+

J

J

(

+ )(-)(+)

-a

-a (

+ )( + )(+) +

[ (+)( + )(-)

= + )+(-) + (+) + (-)=0;(B)ls-*2p: M„ mx (

|

+x

o

+a

+a Y9. J

(+)(-)(-) +

-a

-a

+x

o

V*(ex)^ 2p

dx=

|

(

+ )(-)(+) +

— oo to and two parts moment can be written as

to

:

J

+

(

+ )(+)(_)«(_) + (_) ^0

oo.

The expression

for

transition

+oo

|[W|=[

i>n

{ex)

i>

m dx

+

I

ty n

(ex)ty m

dx

(3.77)

— oo

With reference to Figure 3.6, the integral can be further subdivided for point by point multiplication of odd and even functions. It is observed that a nonzero value of transition moment is obtained only when an even atomic wave function s, combines with an odd function p. Besides establishing the

selection

rule

A/=l,

it

also

says

that a transition

between a g state and an u state only. The transition g-+g is forbidden. These two statements are symbolically written as g->« (allowed), g—/->g (forbidden) and are applicable for systems with a centre of symmetry. These observations can be further generalized. The atomic wave is

allowed

functions

s,

p, d,f, etc. are alternatively symmetric (S)

and antisymmetric

FUNDAMENTALS OF PHOTOCHEMISTRY

68 (A) with respect to the operation system.

The

of inversion about the origin of the

operator

electric dipole

antisymmetric (A) with respect to

is

The

quadrupole operator is the product function in the expression for transition moment is symmetric for electric dipole radiation and antisymmetric for electric quadrupole radiation. inversion at

point of symmetry.

R

A

inversion symmetric (S).

For

transition

is

electric

allowed

if

electric dipole radiation,

Is -+2p,

5d

\s ->3d, Ad,

electric

t

5/,

6/

-> Aft

5/,

6/ is forbidden, since A. A. A.

is

=A

quadrupole radiation, Is ->

2/7, 3/7, 4/7 is

Is -> 3J, Ad,

3.7.2

is

3d->Af 2/7

For

=S forbidden, since S.A.S. = A allowed, since S.A.A. = S allowed, since S.A.A.

3/7, 4/? is

5d

is

forbidden, since S.S.A. allowed, since S.A.A.

=A

=S

Selection Rules for Molecular Transitions

For molecules, the

rules governing the

transition between

two given

energy states are (i)

AA=0,±1

:

changes in the component of the total in the direction of the molecular

allowed

momentum

orbital angular axis, (ii)

AS=

(iii)

Symmetry

:

the spin conservation rule. properties of the energy states must be conserved.

wave function

one electron orbital

()

is

out from the vibrational function (X) and the spin function

(S),

we

If in the total

( '

;

/=0.01,

€ max

=il0 3

;

so on.

Modification of Selection Rules

The

rule governing the transition between the most stringently obeyed. Transitions between states are strictly forbidden. But such transitions

Spin-orbital interaction.

states

;

(3.80)

for the dye molecules,

as observed

^-4i™0^

Av

of like multiplicities

ideal singlet

and

triplet

is

FUNDAMENTALS OF PHOTOCHEMISTR

70

do occur under

and intermolecular per and pure triplet states. These perturbations are functions of the magnetic field near the nucleus and are therefore a function of atomic mass (heavy atom effect). The Hamiltonian operator which causes the mixing of states of unlike multiplicities is influence of intramolecular

the

which can mix pure

turbations

singlet

expressed as

= Kl{L-S)

J(,

where £ is a function which depends on the scalar product of orbital and spin angular

(L*S =

ol

cos

0,

(3.82)

field

of the nucleus, (L'S)

momentum

the

is

vectors respectively

two vectors) and AT is a The wave function obtained on such spin-orbit which cause mixing of the pure triplet T°r and pure

where

the angle between the

is

constant for the molecule.

coupling interactions singlet V's

expressed as

is

Tso-yr + AVj where A indicates the degree of mixing and

,_rv°s

M

x

so

VT

\Es-ET Es

and

Vso is

is

ET

is

(3.83)

given by Vso

clx

(3 84)

-\Es-Et

\

are the energies of the singlet

and

'

\

triplet states respectively,

the interaction energy which flips the electronic spin.

the energy gap between singlet

V so

coefficient A.

will

and

be large also

triplet states, the larger is the

if

the molecule

is

for transition

from

singlet

ground

state to a

mixing

paramagnetic.

Therefore, under spin-orbital coupling interaction the transition

|M|

and

Thus, smaller

mixed excited

moment state

is

given as

M\

= ^V so ^V u h i

= Jt^T^t + A

JYstVidT:

(forbidden)

For the

(3.85)

(allowed)

ground state, the first term is zero but the second term The transition intensity is proportional to A. From 82) and (3 84)

singlet

contributes.

expression (3

.

.

'*'« and is seen to be directly between the singlet and

\Es-ET

related to £

and

\.

^

inversely to the energy separation

5 is a function of the potential near a nucleus and has a high value for an orbital which can penetrate close to the nucleus of a heavy atom such as iodine. The values for several triplet states.

field

atoms have been calculated from atomic spectral data and are presented in the Table 3.1.

MECHANISM OF ABSORPTION OF RADIATION

TABLE Values of

71

3.1

atoms obtained from spectral data

\ for

Atom

3 P t transition in illustrated in Figure 3.7. The heavy atom Hg has consider-

linear correlation with the

Gr

II

atoms

is

The S-»T

able intensity for intercombination transitions. said to

borrow

intensity

from S-^ S

transition is

transition.

I

4

I.S

1.6

log .(atomic numbers!

Spin-orbit coupling.

Figure 3.7

ratio of intensities iS

(After

R.H.

Linear relation between atomic number Zand iP 2 and iS -* *P transitions in Gr II atoms.

+

X

Hocstrasser,

Behaviour of Electrons

in

Atoms,

New

York: W.A.Benjamin, 1964)

The

effect

is

observed when the

heavy atom

heavy atom

is substituted in the the molecule collides with a containing perturber (intermolecular or external effect). The

molecule (intramolecular dramatic enhancement intermolecular heavy

effect) as also

of S

—T

when

transition

atom perturbations

due to intramolecular and

are respectively

shown in Figure 3.8 for chloronaphthalenes in ethyl iodide and other perturbants. Molecular oxygen has a perturbing effect on S T absorption spectra of organic molecules in solution. Under a pressure of 100 atm of O well defined a

-

,

72

FUNDAMENTALS OF PHOTOCHEMISTRY

£ 3 S

s

a | Sua

"Sf

si 3S.2 « A — co

J*

£ g »