Molecular Spectroscopy of The Triplet State

226 Pages·1969·20.592 MB·English

by  McGlynn S.

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Universi\?o.~~-;./7
S. P. McGlynn
OF CHEMISTRY, lOUISIANA STATE UNIVERSITY
T. Azumi
THE INSTITUTE FOR SOLID STATE PHYSICS, UNIVERSITY OF TOKYO
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M. Kinoshita
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DEPARTMENT OF CHEMISTRY, UNIVERSITY OF TOKYO
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PRENTICE-HAlL INTERNATIONAL SERIES IN CHEMISTRY f M O L E C U L A R SPECTROSCOPY
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Hildebrand and Scott REGULAR SOLUTIONS
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Janes ELEMENTARY COORDINATION CHEMISTRY
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Kiser INTRODUCTION TO MASS SPECTROSCOPY AND ITS APPLICATIONS
McGlynn, Azumi, and Kinoshita MOLECULAR SPECTROSCOPY OF THE TRIPLET STATE
Pasta and Johnson ORGANIC STRUCTURE DETERMINATION
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Simpson THEORIES OF ELECTRONS IN MOLECULES
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PREFACE
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@ 1969 by Prentice-Hall, Inc., Englewood Cliffs, N.J. The development of the triplet state electronic spectroscopy of organic
' materials ranks as one of the more important advances of chemical physics
'. of the last two decades. Knowledge of this area appears to be of vital concern
All rights reserved. No part of this book to biology, biophysics, and chemistry. In view of this, it seems strange that
•
may be reproduced in any form no text devoted to triplet state spectroscopy is available. This book con
or by any means without permission
stitutes an effort to fill this gap.
in writing from the publisher. The book attempts to serve two functions: a pedagogic function and
a research function. The pedagogic aims are particularly manifest in the
first five chapters; these chapters are written at the senior undergraduate
Current printing !last digiti : 10 9 8 7 6 5 4 3 2 ' level in physical chemistry. On the other hand, we have been loath to let
oversimplicity dull the research edge of the book; for this reason, we have
Library of Congress Catalog Card Number : 69-1 0922 ntoo tt hhee srietaseteadrc thoe rc,o wmep ihlea vdea tnao at nedv ardefeedr ednicsecsu swsihoinc ho wf ea rceoans swidheer rteo obnee ugsueefussl
is as good as another, and we have not allowed inherent difficulty of the
Prentice-Hal/ International, Inc., London textual matter to preclude its consideration. Thus, Chapters 7, 9, and 10
Prentice-Hal/ of Australia, Pty. Ltd., Sydney are written at a slightly higher level, the senior undergraduate-beginning
Prentice-Hal/ of Canada, Ltd., Toronto I graduate student level in physical chemistry. The general readership level
Prentice-Hall of India Private Ltd., New Delhi would then be as follows: senior undergraduate to beginning graduate
Prentice-Hal/ of Japan, Inc., Tokyo student level in chemistry and biophysics; graduate student level in biology
and biochemistry.
The division of textual matter may be viewed in the following way:
Printed in the United States of America Chapters 1 and 2, introductory; Chapters 3 and 4, energy; Chapters 5 to 8,
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VI PREFACE
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spinorbit coupling; Chapters 9 to 11, spin-spin coupling. We have made \' /"v\ . (~ .
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an attempt throughout the text to juxtapose experiment and theory. We ' '.: :,: ..--
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have assumed the primacy of theory because we believe that it is in this :::, IJ.lil MICA 0
vein that the material can best be grasped and remembered. We have not 0' \I F/SlCA :":..'
concentrated on details of experimental methodology, but have merely noted ' S- ~
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the results and pondered their rationale. , ~- ~;;:,<~o
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There are some aspects of the triplet state that are not covered in the '
/J'Versi\<~\ /
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present volume. Limitations of space and consistency of textual level have --~
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necessitated, for example, exclusion of any specific discussion of molecular
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phosphorescence and energy transfer. These topics will be discussed in 'i
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another text, now in preparation, tentatively entitled: Luminescence. Its •'• CONTENTS
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issuance will be largely determined by the reception accorded to the present [
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work.
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All of our efforts during preparation of this book have been supported
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by the United States Atomic Energy Commission Biology Branch. We are
very grateful to this agency. The manuscript was prepared while all of us
were employed at the Louisiana State University. We are thankful for the '
many considerations tendered us during the course of our residency there .
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The number of persons to whom we are indebted is large. Among these
l.
we list our teachers: M. Kasha, W. T. Simpson, I. G. Ross, T. Dillon, and THE DISPOSITION OF ENERGY IN ISOLATED MOLECULES 1
H. Akamatu. The typing was the work of Judy Brignac; it is a pleasure to 2. •
I. AN ENERGY LEVEL DIAGRAM. 1 VIBRATIONAL-ELECTRONIC
acknowledge the skillful manner in which she deciphered and ordered our TRANSITIONS. 3 3. HOT BANDS, 6 4. RESONANCE RADIATION, 6
initial handwritten drafts. The illustrations were prepared by Eva Jungreis 5. KASHA'S RULE, 7 6. QUANTUM YIELDS. 9 7. INTERNAL CONVERSION. 10
and (unwittingly) by Dick Hoffmann; their patience and their willingness 8. INTERSYSTEM CROSSING, 13 9. TRANSITION PROBABILITY OF RADIATIVE
to redraw is much appreciated. We are also grateful to Tony Trozzolo, TRANSITIONS, 17 10. VIBRATIONAL RELAXATION, 20 II. FLUORESCENCE, 21
Danny Carroll, Errol McCoy, and Edel Wasserman for suggestions con 12. PHOSPHORESCENCE, 23 13. DELAYED THERMAL FLUORESCENCE, 27
cerning Chapters 1 to 3. Luc Vanquickenborne and Carl Ballhausen read the REFERENCES. 29
entire book and made many important and constructive suggestions; we are
deeply obligated to them. The subject index was prepared in collaboration 2. THE TRIPLET NATURE OF THE PHOSPHORESCENT STATE 33
with B. N. Srinivasan; his help made an onerous task less burdensome. Bert
I.
N. Zelman of Prentice-Hall guided this work through all its stages from INTRODUCTION, 33 2. PARAMAGNETIC SUSCEPTIBILITY, 35 3, ELECTRIC
manuscript to book; it was our good fortune to have been associated with DIPOLE NATURE OF EMISSION, 36 4. DIRECT ABSORPTION TO THE
him. PHOSPHORESCENT STATE, 36 5. HEAVY-ATOM EFFECTS, 40 6. TRIPLET
We hope that our book will be helpful to both students and research TRIPLET ABSORPTION, 43 7. PARAMAGNETIC RESONANCE ABSORPTION OF
THE P STATE, 46 8.
workers. All comments concerning improvements will be very much appreci MAGNETIC ROTATION SPECTRA. 51 9. MAGNETIC
CIRCULAR DICHROISM, 56 10. ZEEMAN EFFECT. 56 II. ELECTRON IMPACT
ated. We shall consider all suggestions.
SPECTROSCOPY, 60 12. CONCLUSIONS, 62 REFERENCES, 62
We dedicate this book to our families: wives, mothers, fathers, and chil
dren. We hope it conveys some small token of the regard in which we hold
3.
67
them all. ENERGY OF THE LOWEST TRIPLET STATE
I. THE ORIGIN OF SINGLET-TRIPLET SPLITTING$, 68 2. A CORRELATION WITH
S. P. McGlynn
EXPERIMENT. 75 3. THE EFFECTS OF CHEMICAL SUBSTITUTION ON THE T
T. Azumi 1
4.
STATE, 92 TRIPLET GROUND STATE MOLECULES, 97 5. TRIPLET STATES
M. Kinoshita
AND BIRADICALS, 105 REFERENCES, 112
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VII
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CONTENTS IX
•••
CONTENTS
VIII
8.
THEORETICAL DISCUSSION OF
STRONG CHARGE-TRANSFER COMPLEXING, 321
4.
A GENERAL DISCUSSION OF THE ENERGIES OF SPINORBIT COUPLING INDUCED BY CHARGE-TRANSFER COMPLEXING WITH ELECTRON
ACCEPTORS WHICH DO NOT CONTAIN HEAVY ATOMS, 323 REFERENCES, 325
TRIPLET STATES 119
1. MOLECULAR ENERGY LEVELS, 119 2. THE ETHYLENE MOLECULE, 127
9.
ELECTRON PARAMAGNETIC RESONANCE SPECTROSCOPY 329
4.
3, ACETYLENE AND POLYACETYLENES, 139 BENZENE, 141
6.
5. ALTERNANT HYDROCARBONS, 151 AZA-AROMATICS. 162
1. THE EFFECT OF SPIN-SPIN DIPOLE INTERACTION ON ZFS PARAMETERS, 330
7. 8.
MOLECULES CONTAINING THE CARBONYL GROUP, 166 ORGANIC
2. THE EPR ABSORPTION PATTERN, 334 3. EVALUATION OF THE PARAMETERS
DYESTUFFS, 171 REFERENCES, 176
4.
D AND E. 336 THE EFFECTS OF SPINORBIT INTERACTION ON ZFS
PARAMETERS, 345 REFERENCES, 348
5.
SPINORBIT COUPLING 183
JO.
EXTRACTION OF ZERO-FIELD SPLITTING PARAMETERS
1. A PRIMITIVE MODEL, 183 2. THE MIXING OF STATES OF DIFFERENT
350
FROM EXPERIMENT
MULTIPLICITIES, 189 3. PROBABILITIES OF MOLECULAR INTERCOMBINATION
4.
TRANSITIONS, 198 THE USE OF GROUP THEORY, 201 5. A PERSPECTIVE,
1. BASIC EQUATIONS, 351 2. ORIENTED TRIPLET STATES. 353
205 REFERENCES, 207
3. 4.
RANDOMLY ORIENTED TRIPLET STATES. 359 THE METHOD OF
REFERENCES. 367
MAGNETOPHOTOSELECTION, 364
6.
SPINORBIT COUPLING: A CORRELATION OF THEORY
Jl.
AND EXPERIMENT 209
APPLICATIONS OF TRIPLET STATE ELECTRON PARAMAGNETIC
369
' ' RESONANCE SPECTROSCOPY
1. A RESUME, 209 2. SPINORBIT COUPLING IN 3 1'n~• STATES OF AZINES, 212
3. SPINORBIT COUPLING IN 31u• STATES OF AZINES, 217 4. SPINORBIT
1. 2.
THE LIFETIME OF THE TRIPLET STATE, 370 TRIPLET-TRIPLET ENERGY
!',.,..
COUPLING IN 3 STATES OF BENZENE. 225 5. SPINORBIT COUPLING IN
TRANSFER. 372 3. SENSITIZED SOLVENT DECOMPOSITION. 376 4. EXCITON
3 l'u• STATES OF PLANAR POLYACENES, 237 6. SPINORBIT COUPLING IN 31n,.•
MOTION WITHIN A MOLECULE, 378 5. EXCITON MOTION IN A CRYSTAL. 382
STATES OF CARBONYLS, 241 7. SPINORBIT COUPLING IN 31u• STATES OF
6. 7.
TWO-QUANTUM TRANSITION. 385 ORBITALLY DEGENERATE EXCITED
CARBONYLS. 245 8. THE EXPERIMENTAl DISTINCTION BETWEEN 31 u• AND
8.
TRIPLET STATES. 386 DINEGATIVE IONS OF AROMATIC COMPOUNDS, 389
3 9.
1'n,.• STATES OF AN AZINE OR CARBONYL, 246 AROMATIC AMINES, 247
9. 70.
THE ION-RADICAL PAIR. 391 IONIC MOLECULAR CRYSTALS. 392
10. AROMATIC NITRO COMPOUNDS, 251 REFERENCES, 257
11. BIOLOGICAL APPLICATIONS 397 REFERENCES, 398
7.
INTERNAL HEAVY-ATOM SPINORBIT COUPLING EFFECTS 261 Appendix 1: THE SPINORBIT COUPLING HAMILTONIAN, 403
Appendix 2: THE ONE-ELECTRON SPINORBIT COUPLING OPERATOR IN
1. 2.
PHOSPHORESCENCE LIFETIMES. 263 LUMINESCENCE POLARIZATION
CYLINDRICAL COORDINATES, 406
STUDIES OF THE INTERNAL HEAVY-ATOM EFFECT, 267 3. INTERSYSTEM
Appendix 3: VIBRONIC.SPINORBIT COUPLING, 409
4.
CROSSING 5 VV'Y> T 270 INTRA-ANNULAR INTERNAL HEAVY-ATOM
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EFFECTS, 275 5. INTERNAL HEAVY-ATOM EFFECTS ON n* n TRANSITIONS SUBJECT INDEX, 423
<-- AUTHOR INDEX, 412
OF CARBONYL$, 276 6, USES OF INTERNAL HEAVY-ATOM EFFECT. 277
,,....,---~~
REFERENCES, 281 -
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EXTERNAL SPINORBIT COUPLING EFFECTS 284 --...
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1. OXYGEN EFFECTS. 285 2. NITRIC OXIDE EFFECTS. 293 ro
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3. PARAMAGNETIC METAL ION EFFECTS, 294 4. A THEORETICAL DISCUSSION 00 \ ~
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MOLECULES, 297 5. EXTERNAL HEAVY-ATOM EFFECTS, 307 6. THEORETICAL
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C O M P E N D I U M O F N O T A T I O N S
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The contents of this book are quite diversified and, as a result, a multiplicity
of notational requirements are imposed. The compendium of notations which
follows represents that which we have tried to retain invariant throughout
the text. However, all other notations used, as well as a few of those in this
•
compendium, must serve double duty.
Wavefunctions
an atomic orbital (AO); AO subscripts: fl-, v, p, [_;", 7J
X
a molecular orbital (MO): MO subscripts occa
t:p
sionally a, b, c, d; often r, s, t, u; seldom v, w
one-electron spin wavefunctions
a,(3
a one-electron molecular spinorbital
cpa = cp; t:p(3 = 'P
many-electron spin wavefunction: S, total spin
SsMs
quantum number; M total spin component quan-
,
8
tum number
cfJ, many-electron orbital wavefunction corresponding
to ith state
+
many-electron spinorbital wavefunction: 2S I,
• 2S+l'IJ.fMs = cfl,SSMs
spin multiplicity
Tfs an abbreviation of 3'l'f•: i = I, 2, . . . is a serializa
tion in order of increasing energy
•
XI
.....
000
COMPENDIUM OF NOTATIONS XIII
0 0
XII COMPENDIUM OF NOTATIONS
General
S; an abbreviation of 1'JI'fs; Ms 0
=
Qf:s an abbreviation of 5'¥f: s H magnetic field
® vibrational wavefunction (Chapter 4 only) E electrical field
zero-field splitting parameters
D, E; D*; H; X, Y, Z
spinorbit coupling factor
S
nr
Particles
Bohr magneton
(3
Numbering of nuclei K, L, M, N, P; occasionally A, B, C, D dipole moment
fL
Electron numbering usually i, j, k, l
Operators
£' hamiltonian
£;: electronic hamiltonian to Born-Oppenheimer approxi
mation
£'N nuclear hamiltonian to Born-Oppenheimer approxima
tion
£'' or )I • s spinorbit coupling hamiltonian
~(r
£:ss spin-spin dipolar interaction operator in an explicit form
£:s spin-spin dipolar interaction operator in the form of the
spin hamiltonian
One-electron spin angular momentum operators
S, Sx, Sy, Sz
Total spin angular momentum operators S, S,
Sx, Sy,
One-electron orbital angular momentum operators I,
fx, fy, /z
Total orbital angular momentum operators L, Lx, Ly, L,
•
One;: electron angular momentum operators • • •
J,]n]y,]z
Dipolar interaction operators A, 6'
§J,
'
Kinetic Parameters
kF intrinsic fluorescence decay constant; kF 1/-r'i.-
=
rate constant for internal conversion, usually for S S
kQF ~
1 0
k sc intersystem crossing rate constant for S T
~
1
1
1
kr intrinsic phosphorescence decay constant; kr
=
Ijr~
kQP rate constant for the intersystem crossing process T S
~
1 0
rate constant for vibrational relaxation
kv&
+ +
fluorescence lifetime; 1/(kF kQF)
Tp Tp = kiSc
r'ic
intrinsic fluorescence lifetime
+
phosphorescence lifetime; Tr I/(kr kQr)
=
Tr
intrinsic phosphorescence lifetime
r~
q.. quantum yield
THE DISPOSITION OF ENERGY
I N ISOLATED MOLECULES
•
We will describe here the manner in which electronic excitation energy is
shuttled between and partitioned among the various molecular energy levels.
Our discussion will be confined to intramolecular processes, and we will not
concern ourselves presently with intermolecular events such as energy transfer
from molecule to molecule, or exciton-exciton annihilation processes. ft is
well to remember that many of the processes which will be described here
as intramolecular are, at best, only nominally so, and that we may have to
broaden our attitudes somewhat in subsequent discussion.
A primary purpose of this chapter is a precise specification of termi
nology. An effort is made to keep the discussion non mathematical; we feel
this to be appropriate, because all the topics touched on here will be dis
cussed in considerable detail in following chapters.
l. AN ENERGY LEVEL DIAGRAM
Figure 1.1 is an attempt to illustrate the various intramolecular processes
initiated by photon absorption. The large box beside any one electronic
energy level indicates the molecular orbital (MO) electron configuration
which best describes that level; the spin-components of the two highest
energy electrons of the molecule are also shown. The sub-boxes within any
one large box are the MO's; of these we show only three or, in one case,
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2 DISPOSITION OF ENERGY IN ISOLATED MOLECULES Chap. 1 Sec. 2 DISPOSITION OF ENERGY IN ISOLATED MOLECULES
'
f_
'
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• • : the singlet level, Sk; they differ only in the relative spin-axis orientations of
'
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the two electrons. The triplet level is always drawn lower in energy than the
• '
•
singlet level of the same MO configuration; this arrangement is correct for
si 7j
the lower excited energy levels of most organic molecules, and is a conse
•
•
•
• quence of Hund's rule (1). Quintet states are not shown; to do so would
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• '
'
require an illustration of the relative spin-axis orientations of four electrons
'
' and would complicate Fig. 1.1 severely. Quintet states do exist, they are
'
52 almost certainly spectroscopically accessible, and they may be of some
•
c photochemical importance. The first identification of a quintet state of a
- 0
o·v;
72
c._ relatively complex molecule was made in 1967 (6a).
·-·-
'-<1>
c
<1>> - The "pure" electronic energy levels are shown as heavy horizontal lines
- c
0
·-
Eo
-ri u a.... in Fig. 1.1. It is well to emphasize that if the molecule is complex the "pure"
I I I J
St
Intersystem 0
If) electronic level consists of considerable vibrational energy (i.e., the sum
..c
-------•- ---~
cross1ng <(
of zero-point vibrational energies of all normal modes) in addition to elec
f.-
r,
tronic energy. Actually, the heavy horizontal lines represent potential energy
~
Intersystem
hypersurfaces in a multidimensional space; each such potential energy hyper
~--------
•
c "' cross1ng 1 l t r
u
I I
·-0- c I I 1 surface may intersect every other potential energy hypersurface of the
I I I "'
g
... Q) I I I c
a. I I I
u
1 I I ., I I I o molecule; the intersection of any two such surfaces will itself be a hyper
I.f.).
0 I I ·.;::
"'
I l l " '
If) I I I a. surface which must be of smaller dimension than either of those which
;..C 0 I I I ~
6
<( I I I
-:::J
I I ( -g_
I I Ill"' intersected. The lighter, shorter horizontal lines of Fig. 1.1 are the vibra
lL
I I l..c
•
I ' "'
'I 0 I I I<( tional-electronic states; these states consist of one or more quanta of the
I I I I I I ! ' j
So :1: .r::. I I I So
a..
vibrational energy of one or many modes of vibration superposed on the
"pure" electronic energy level. Only one of the many modes of vibration is
A somewhat general schematic of the lower energy levels of represented in Fig. 1.1 ; 3n - 6 modes are possible in a nonlinear molecule
Fig. J.J
an organic molecule which contains an even number of electrons and which contains n atoms, and since any number of quanta of many of these
which exhibits no orbital degeneracy. normal modes may be coupled in a given vibrational-electronic state, a very
•
large number of such states is possible.
The energy within a given manifold of states increases with increasing
four. The lowest sub-box within any large box is the highest energy filled
numerical subscripting of states within that manifold; for example, the
MO of the ground singlet state, S the discussion is restricted to those
;
0
energies within the singlet manifold are S S,, S St, . . . , in order of
excited electronic levels which involve single electron depopulation of this , , ••• ,
0 2
increasing energy. In our notation, the lowest energy triplet state usually
MO. The energy of the MO's is supposed to increase vertically within any
one large box. Only two electrons are considered in Fig. 1.1; the others are will be a T, state.
supposed to constitute an even number and to be paired in such a way that
their total spin angular momentum is zero.
The levels on the left of Fig. 1.1 are seen to constitute a manifold of 2. VIBRATIONAL-ELECTRONIC TRANSITIONS
singlet states. The triplet manifold of states is displaced to the right, as is
also the practice (1) in atomic spectroscopy.t The notation used is such Inspection of the S, S fluorescence process and the reverse S, S 0
0
absorption process outlined in Fig. 1.1 indicates that the lowest energy
that the triplet level (or state), Tk> has the same electron configuration as
absorption line is of equal energy to the highest energy emission line. This
t A molecular electronic energy level diagram in which the triplet manifold is displaced line is called the 0, 0 line. These processes are abstracted from Fig. 1.1 and
to the right relative to the singlet manifold is commonly referred to as a Jablonski diagram. are shown more clearly in Fig. 1.2; S and S, are the two "pure" electronic
0
This name· derives in some obscure way from the early conventions used by Jablonski
energy levels and only one vibrational mode is shown coupling to either of
(2, 3). The spin multiplicity identifications (i.e., singlet, triplet, etc.) were first provided
these two states; the number of quanta of this vibrational mode which is
by the work of Terenin (4) and Lewis and Kasha (5, 6).
'
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Sec. 2 DISPOSITION OF ENERGY IN ISOLATED MOLECULES
Chap. 1
4 DISPOSITION OF ENERGY IN ISOLATED MOLECULES
contrary to the most commonly used convention (7) which dictates the writing
•
of the v" lower energy symbol in the leftmost position; this latter convention
•
•
is used in Fig. 1.2. However, this latter usage is incompatible with the
3
electronic convention (i.e., S, S etc.); thus, henceforth, we will write v'
,
s,
v'j2 0
in the leftmost position.
(iv) A further convention will be adopted in the diagrams: all transitions
between states of different spin multiplicity will be represented by dashed
lines. Thus, a wavy dashed vertical arrow represents a nonradiative event
between states of different multiplicity (i.e., a nonradiative intercombination);
a vertical dashed arrow represents a radiative intercombination event,
Absorption Emission
0 0 0 0 absorption or emission; a horizontal dashed arrow represents transfer of
o~Nr<J
+ t t t
H
t t
energy between equienergetic (or, better, quasi-degenerate) points in the
0 0 0 0 o~Nr<J
singlet and triplet manifolds.
Suppose that emission and absorption processes initiate only in the
• levels v' 0 and v" 0, respectively, and that the vibrational frequencies
= =
•
• are identical in both electronic states (see Fig. 1.3); it follows that the emis-
•
.3
v \
2
1
8 lOr-
So
0 ~ -::/" ~
I~
I I
i\
C
I I ././ ././
~
Fig. 1.2 Vibrational-electronic transitions associated with S +--> S • I 1 I I
1 0 I 1 I 1
-
For conventions used, refer to Section 2, item (iii). I ' I I
I ' I '
I I
J?
I
I I I
61- ,I ,,
- t . 1 I I 1/1
\..\
f..::-
I I I \
J? - 5
coupled to the electronic energy is indicated by the quantum number v" 1 I I \
N r I I I
t
0
in the lower state and v' in the excited state. The various vibrational-electronic -rJ) - ,5\, I I, ,I \ II
I I I \ I I
\
)
L X I I
transitions possible may now be labeled as in Fig. 1.2. 1(1 I U I
/0
I "' II( II I I :
I
4 I I 1 I \
We shall henceforth adopt the following conventions in writing down -0 I I
I It \
I I
I 1 I
I 1
X
electronic transitions: I ' '
' I I r
"'
I t
L 1
I \ I I
(i) The highest energy electronic state will be denoted by the leftmost 0 1
I I I 1
I I I
symbol. Thus, the processes Tj T,, S, , __ S T, S etc., represent I I I \
, ,
0 0 2f- I I I 1
il
energy absorption events; the processes T, S0 , S, S 0 , Sj S 0 , etc., I \ • I II IV I 1I
I '
1'\ I I I /'""'
I I
represent luminescence events. II \.~,..I
I \ 1 I
E
\ I \ r\ D II I
I • W I
(ii) A nonradiative transition will be represented by a wavy arrow. For A I I B \ •v ,
•
J '
example, S, S S, T,, T, S etc., represent nonemissive energy 0
VvV> , VvV> VvV> ,
0 0 10:::-' 15 20 25 30 34
degrading events. The symbol S, T, implicit in Fig. 1.11 represents a
<I'M
10-3
i7
X
thermal (i.e., nonradiative) excitation event.
(iii) A specific vibrational-electronic transition will be written as S,(v')
1.3 Levshin mirror symmetry (or vibrational envelope inversion)
Fig.
,___ S (v"), T,(v') S (v"), etc., in absorption, or S (v') S (v"), etc., in
1 --+ 0 diagram for T S and for S S transitions: A is the phos
0 0 .__.., '
1 0 1 0
emission. If it is the nature of the vibrational excitation which is the quantity phorescence (lOa); B is the delayed fluorescence excitation spectrum
of interest, the above may be abbreviated t6 v' , v" or v' v" for emission (lOb); Cis the heavy-atom perturbed T S absorption (!Oc); D
, __
1 0
and absorption, respectively. This last convention, namely the writing of the and E are S 1 > S0 fluorescence and S 1 <---- S0 absorption spectra,
respectively.
v' symbol descriptive of the excited state in the leftmost position, is exactly
""
'
i, :
'
'·
L
•
'
I .
'
f
6 DISPOSITION OF ENERGY IN ISOLATED MOLECULES Chap. J t: 7
Sec. 5 DISPOSITION OF ENERGY IN ISOLATED MOLECULES
'
i
'
'
i ;
sion lines will be arranged to lower energy relative to the 0, 0 line in a
,
tiplicity; it will be most probable in dilute gas systems where the time
•
manner which is reflection symmetric to the arrangement of absorption lines
I .
between collisions is greater than the radiative lifetime of the state in ques
!··
to higher energy. It is not obvious from this discussion that the relative , f
tion; it will be least probable in condensed media where interactions and
•
;
intensity of emission lines should be reflection symmetric to the relative '
•
·collisions with surrounding molecules usually occur on a time scale short
',
intensity of absorption lines. In fact, such a mirror image relationship should
compared to 10-s sec (which can be considered an average radiative lifetime
never obtain except under the most freakish of circumstances: it is required
' for most S S transitions). Nonetheless, resonance radiation of long
i
1 0
that the two potential energy hypersurfaces be exactly identical and super •
lifetime (i.e., in the millisecond range) may be observed in the solid phase
'
posed one above the other such that they never intersect.t Now, the intensity
from some well-shielded electronic systems, for example UO,t+ (12).
v v
of emitted radiation is dependent on 4 (where is in wavenumbers) since
radiation is normally a spontaneous process; however, since absorption
v;
is a stimulated process, it has an intensity which is linearly dependent on
5. KASHA'S RULE
'
this different frequency dependence could vitiate the mirror-symmetry of
'
Inspection of Fig. 1.1 indicates that only two emission processes are shown
intensity expected when the transition is accompanied by no shape change.
'
· to occur between different electronic states, whereas many different electronic
Nonetheless, an approximate mirror symmetry is often observed between
absorption processes may be observed. This behavior is a consequence of
corresponding emission and absorption processes and is usually associated
Kasha's rule (13) which may be stated as follows: In organic molecules in
with the name Levshin (8, 9). It is clear that the anthracene spectra (lOa,
condensed media, the emitting level of a given multiplicity is the lowest
b, c,) of Fig. 1.3 exhibit a very good Levshin mirror symmetry.t
'
excited level of that multiplicity. The state S is the lowest energy excited
'
' 1
}
singlet level; the emission S S is termed fluorescence. The state T is
1 0 1
'
I the lowest excited triplet level; the emission T S is termed phosphores
3.
HOT BANDS
' 1 0
'
' cence. This rule does not guarantee luminescence; it merely states that if
l
> '
Transitions which initiate in a vibrational level for which v" 0 are termed luminescence occurs it will initiatet in either S or T The only well-sub '
•
' 1 1
'
absorption hot bands. A decrease of temperature lowers the population of ; stantiated exception to this rule is azulene where the observed fluorescence
these vibrational levels and decreases the absorptivity due to them. Hot (14, 15) corresponds to S, S and not S S
•
0 1 0
bands may be responsible for many thermochromic and thermotropic In condensed media, interactions due to collisions or just simple proxim
>
effects. Transitions which initiate in a level v' 0, with the proviso that ity are significant and take place many times during the radiative lifetime
the molecules in the v' set of vibrational levels are thermally equilibrated of any given excited state. Through such interactions, energy may be trans
with respect to v' 0, are termed emission hot bands. ferred between different molecules; as previously noted (cf. Kasha's rule),
=
it is an empirical fact that the excitation energy of S,, or of any higher singlet
'
state, or of any excited vibrational level of will be rapidly lost in inelastic
S~>
collisions until the zero point level (v ' = 0) of S is achieved radiationlessly.
4. RESONANCE RADIATION
1
In like manner S may have its energy degraded to S it may also be de
;
0
1
If an absorption process terminates in the vibrational electronic level v' j,
= graded to T or it may emit fluorescence. It is an experimental fact that
;
1
and if it is followed by emission from that same level giving rise to the
S is degraded energetically in a much less efficient way than S, or S;, and
1
series oftransitionsj O,j l,j 2, ... , where the numeral is the value
it is by no means completely clear yet why this should be so.
-->
of v", these emissions are said to constitute a resonance radiation. Resonance
Kasha's rule is very simple and of very general applicability. However,
radiation will occur only when the time required for thermal equilibration
exceptions do exist. There has been much discussion of this rule in the
in the excited electronic state is greater than the radiative lifetime of the
literature of late: many examples of molecules which are purportedly
d~viant
vibrational-electronic level v' j. Resonance radiation will be more prob
= from the rule have been discussed (16, 17) and amendations to the rule
able between states of like multiplicity than between ones of different mul-
have even been suggested ( 16, 17). In view of this, we now proceed to a very
brief but highly critical evaluation of the existing literature:
tThis last requirement is fulfilled if the molecule suffers no change in its equilibrium
shape on going from one electronic state to the other.
tWe exclude quintet states, septet states, etc. from Kasha's rule for the simple reason
tKasha (II) prefers the more descriptive name of vibrational envelope inversion.
that no Q TJ> S processes have been located in reasonably complex molecules.
1 1
~
'
'
•
l'