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Analysis of singlet-triplet absorption profiles in carbonyl molecular crystals
Joumai of Molecular Shucture, Q Else&r S&nGfic Publishing
ANALYSIS
OF SINGLET-TRIPLET
P. PERETTI,
351-357 Amsterdam
ABSORPTION
PRORLES
351 -
Printed in The Netherlands
MOIJXULAR
IN CARBONYL
CRYSTAIS
P. RANSON
Ddpartement Laboratoire
47 (1978) Company,
de Rechercfies
Physiques,
UnivasitL
P. et M.
Curie,
associ6 au C. N.R.S.
4, Place Juzsieu - Tour 22-23,
2bme &age
- 75230 PARIS Cedex
The present paper reports the results of an experimental
06, France
investigation
of the temperature
widths and profiles of the phooonlerJ lines and phonon lines in the ?;+so dichl~~emophenone~
The experimenral
results are interpreted
dependences
of the
absorption spectrum of 4 - 4’
on the basis of tbe theory of exciton - pbonon
interaction.
The study of the interaction has been undertaken is small
compared
between
collective
on 44’ dichlorcbemophenone
to the optical
the resonance coupling
between
electronic
study this problem we have investigated
and collective
(44’ DCBP) a material
phonon frequencies. molecules
excitations
the T1 -SO
deformation
excitations
in which the triplet exciton band width
The excitcm-phonon
and to a lattice
vibrationJ
coupling
leads to a modification
about an excited
spectra of crystalline
molecule
(1).
of
To
44’ DCBP as a function of
temperature.
The crystal face cleavage
are monoclinic
with two molecules
on which the b axis could be easily located.
same region as benzophenone
At low temperhues
(T
(
at 4124,6
i
is atso a series of peaks corresponding
T
15 K transftions appear below
energies
at half
above the free excitor matimum
unit ceil(Z).
The singIe crystals
44’ DCBP has its low energy nw*
displayed
an ab
states in tbe
(3).
60 K) we find fine structure with the characterist%e very sharp zero p;honon line Sk = 0).
There >
per primitive
to two particle
transitions of an exciton and a photon.
the opricaf exciton Ievel (hot bands).
energy band and more rapidly
of the 0 - 0 line is about 1 cm
-1
when
The intensity decreases slowly at
at energies below.
At T = 4,2 K the halfwidth
. The 0 - 0 lines are nearly of lorentzian shape at all tempe-
ratures between I ,5 and 60 K. We have not observed Davydw splitting, tbe apparatus slit function being about -1 of the pbononless iincs were measured as a function of the temperature T as we 0,7cm . The linewidth can see in the b-polarized
spectra (Fig.3
). The temperature
dependence
may be simulated
in a
model without dispersion by a number (4). For low tern-at-
2 n(qr) + 1 r-e,
temperature dependence where @qs) is tbe meati phcmonoccupatkm
the agreement of this model with experimental data is not good. It is
impaaible COmake any ldnd of fit including phomm frequencies. The exciton bandwidth being much.sm$k
than the o@cg
phonon energies we PUS take into acc_m
second otder effects and t&i crystal is to be viewed as a Iarge number of equivalent trapping sites (5). Seff trapping can occurs if the resonance transfer is slow compared with local lattice relaxation, as is true of triplet excitons especially in carbonyl compounds. Thus we have used to explain the variation of the halfGdth of the zero phonan line a theory precedently developped for impurity host coupling in mixed crystals (6). If the density of states is assumed to follow the Debye diskibutkm, at low temperatmes .!$lr)s given by : ta/,
44’DCBP
+
exp_
0 talc.
20
Q FIGURE
1
.4-o
I-K
Experimental (+) and tbeoreticlI (0) temperatuxe dependencas of the width at balf’maximmn of the zerophoapn line of 44’ dicbkxobemepbone. caicufated adng equation 1 and @ 5: 8OK.
The circlesrepresent tbemetioal depmdrnces
(T]
353
mm-11 A
6C b-
44’DMBP 5c )-
4c b-
+
talc.
0
exp.
3cI-
2( I-
1cI-
0 FIGURE 2
5 Experimental of
(+) and theoretical
4 - 4’ dimethylbemophenone.
10
15
(0) temperature dependences
20 TK
of the width of the zeropbonon line
44’DCBP exp. results
e.___
16
K
---36K -- 54K
FIGURE 3
Experimental band profiles of 44’ DCBP fa b polarized
light incident on the a - b face of
single cristal at different temperatures.
@
is the Debye temperature and
a coupling parameter_ Assumiag that 0 is 80 em X none crystals, a feast squares fit of the theoretical expression yields $ = 17.5cm -I_ Fig_ ‘: where
that
the agreement with expaimentlf
data is very good.
was subtracted from all widths measured
A similar
study
has
been
made
for
The residuJ
j.
Fig. 2
In order COanalyze tbe compkte
ShoWS
width at the lowest remperature me-d
at higher temperatures.
4.4’ dimetFlyll*enzophenone
(4
- 4’
temperature T was found to be the same. The corresponding valoe of one ( 1( = 8800 cm-l
as for benzophe-
DMM’).
21
The
bebavicxrr
with
the
is greater than the 4 - 4’ DCSP
absorption spectrum‘of 44’ DCBP we have used the theoreticll’results
of
355 Craig and Dissadobythe prcfiles
can be simulated
an effect
in a model
3S, 37, 39, 41, 43 cm ( i(
= IS cm-f).
Fig.
+$-
width of tbe fines the values of r weuld be necessary value of the average
A similar
to take into coupling
-1
dependence
Thetemperahue
aftbe
with only one optical torsional mode (39 cm-*).
of dispersiorr in the pbonon spectrum,
fret+ncics coupling
Green fmnction method(7).
the pbonous are divided
. To each of t&se
groqs
calculated.
spectra obtained
For a best agreement
account more than one optical
constant g (g = 0.9) defining
into five frequeucy
is assigned the same value
shows the theoretical
greceodtly
phonoo.
groups with of the dispersion
when we have given for the with erpesimental
results
it
From these results we can deduced
the strength of the excitou
study has been made for the 44’ DMBP crystal.(Fig.ti).
abso@onband
To take into account
1x1theoretical
a
- phonou interaction.
resufts we have taken a
44’DCBP theor. results
. ..___ I6K
-----
-50 FIGURE 4
0 T%retieal
pbonon is 39 cm these frequencies
+lOO
+5U
Baud profiles of 44’ DCBP at different -1
_
mth
ailowance
foe dispersion.
temperatures. (35,
WC
rrl--I
The energy of optScal coupling
37, 39, 4f,
is assigned the same value of the coupling
36K 54K
43 cm
-2
1. To each of
function (15 cm-‘).
356
357 model without dispersion with five optical phonon frequencies deduced from inspectioo of the excitor band -1 structure (38, 55, 78, 95, 106 cm ). The correspondiag dispersion coupling values are =40, 60, loo, x -1 70cm . Thus the average coupling constant g is 4.9 which indkates a strong coupling.
R!zxmxENcE.s
(I)
A.S.
Theory of Mcdeculzr excitons
DAWWV
Plenum
(2)
J. TOUSSAINr
Re?ss New York 1971
Bulletin de&x Socicltk! Royale
des Sciences de Liege
17, !0(1948)
(3)
R.M.
HOCHSTRASSER
amf J.W. MICHALUK
J. Mel,
(4) L.A.
DISSADO Chem. Phys.
(51 D.P.
CRAIG,
L.A.
Spectrosc. 42, I97 (1972)
8, 289 (1975)
DISSADO, S.H. WALMSLEY Cbem.
(6) for example J. L. RICHARDS
Phys. Letters, 46, 191(1977)
am3 S. A. RICE
1. Chem.
(7)
D.P.
CRAIG,
L.A.
Phys. 54,
2014 (1971)
DISSADO Chem.
Phys. 14,
69 (f976)
60,
ANALYSIS
OF SINGLET-TRIPLET
P. PERETTI,
351-357 Amsterdam
ABSORPTION
PRORLES
351 -
Printed in The Netherlands
MOIJXULAR
IN CARBONYL
CRYSTAIS
P. RANSON
Ddpartement Laboratoire
47 (1978) Company,
de Rechercfies
Physiques,
UnivasitL
P. et M.
Curie,
associ6 au C. N.R.S.
4, Place Juzsieu - Tour 22-23,
2bme &age
- 75230 PARIS Cedex
The present paper reports the results of an experimental
06, France
investigation
of the temperature
widths and profiles of the phooonlerJ lines and phonon lines in the ?;+so dichl~~emophenone~
The experimenral
results are interpreted
dependences
of the
absorption spectrum of 4 - 4’
on the basis of tbe theory of exciton - pbonon
interaction.
The study of the interaction has been undertaken is small
compared
between
collective
on 44’ dichlorcbemophenone
to the optical
the resonance coupling
between
electronic
study this problem we have investigated
and collective
(44’ DCBP) a material
phonon frequencies. molecules
excitations
the T1 -SO
deformation
excitations
in which the triplet exciton band width
The excitcm-phonon
and to a lattice
vibrationJ
coupling
leads to a modification
about an excited
spectra of crystalline
molecule
(1).
of
To
44’ DCBP as a function of
temperature.
The crystal face cleavage
are monoclinic
with two molecules
on which the b axis could be easily located.
same region as benzophenone
At low temperhues
(T
(
at 4124,6
i
is atso a series of peaks corresponding
T
15 K transftions appear below
energies
at half
above the free excitor matimum
unit ceil(Z).
The singIe crystals
44’ DCBP has its low energy nw*
displayed
an ab
states in tbe
(3).
60 K) we find fine structure with the characterist%e very sharp zero p;honon line Sk = 0).
There >
per primitive
to two particle
transitions of an exciton and a photon.
the opricaf exciton Ievel (hot bands).
energy band and more rapidly
of the 0 - 0 line is about 1 cm
-1
when
The intensity decreases slowly at
at energies below.
At T = 4,2 K the halfwidth
. The 0 - 0 lines are nearly of lorentzian shape at all tempe-
ratures between I ,5 and 60 K. We have not observed Davydw splitting, tbe apparatus slit function being about -1 of the pbononless iincs were measured as a function of the temperature T as we 0,7cm . The linewidth can see in the b-polarized
spectra (Fig.3
). The temperature
dependence
may be simulated
in a
model without dispersion by a number (4). For low tern-at-
2 n(qr) + 1 r-e,
temperature dependence where @qs) is tbe meati phcmonoccupatkm
the agreement of this model with experimental data is not good. It is
impaaible COmake any ldnd of fit including phomm frequencies. The exciton bandwidth being much.sm$k
than the o@cg
phonon energies we PUS take into acc_m
second otder effects and t&i crystal is to be viewed as a Iarge number of equivalent trapping sites (5). Seff trapping can occurs if the resonance transfer is slow compared with local lattice relaxation, as is true of triplet excitons especially in carbonyl compounds. Thus we have used to explain the variation of the halfGdth of the zero phonan line a theory precedently developped for impurity host coupling in mixed crystals (6). If the density of states is assumed to follow the Debye diskibutkm, at low temperatmes .!$lr)s given by : ta/,
44’DCBP
+
exp_
0 talc.
20
Q FIGURE
1
.4-o
I-K
Experimental (+) and tbeoreticlI (0) temperatuxe dependencas of the width at balf’maximmn of the zerophoapn line of 44’ dicbkxobemepbone. caicufated adng equation 1 and @ 5: 8OK.
The circlesrepresent tbemetioal depmdrnces
(T]
353
mm-11 A
6C b-
44’DMBP 5c )-
4c b-
+
talc.
0
exp.
3cI-
2( I-
1cI-
0 FIGURE 2
5 Experimental of
(+) and theoretical
4 - 4’ dimethylbemophenone.
10
15
(0) temperature dependences
20 TK
of the width of the zeropbonon line
44’DCBP exp. results
e.___
16
K
---36K -- 54K
FIGURE 3
Experimental band profiles of 44’ DCBP fa b polarized
light incident on the a - b face of
single cristal at different temperatures.
@
is the Debye temperature and
a coupling parameter_ Assumiag that 0 is 80 em X none crystals, a feast squares fit of the theoretical expression yields $ = 17.5cm -I_ Fig_ ‘: where
that
the agreement with expaimentlf
data is very good.
was subtracted from all widths measured
A similar
study
has
been
made
for
The residuJ
j.
Fig. 2
In order COanalyze tbe compkte
ShoWS
width at the lowest remperature me-d
at higher temperatures.
4.4’ dimetFlyll*enzophenone
(4
- 4’
temperature T was found to be the same. The corresponding valoe of one ( 1( = 8800 cm-l
as for benzophe-
DMM’).
21
The
bebavicxrr
with
the
is greater than the 4 - 4’ DCSP
absorption spectrum‘of 44’ DCBP we have used the theoreticll’results
of
355 Craig and Dissadobythe prcfiles
can be simulated
an effect
in a model
3S, 37, 39, 41, 43 cm ( i(
= IS cm-f).
Fig.
+$-
width of tbe fines the values of r weuld be necessary value of the average
A similar
to take into coupling
-1
dependence
Thetemperahue
aftbe
with only one optical torsional mode (39 cm-*).
of dispersiorr in the pbonon spectrum,
fret+ncics coupling
Green fmnction method(7).
the pbonous are divided
. To each of t&se
groqs
calculated.
spectra obtained
For a best agreement
account more than one optical
constant g (g = 0.9) defining
into five frequeucy
is assigned the same value
shows the theoretical
greceodtly
phonoo.
groups with of the dispersion
when we have given for the with erpesimental
results
it
From these results we can deduced
the strength of the excitou
study has been made for the 44’ DMBP crystal.(Fig.ti).
abso@onband
To take into account
1x1theoretical
a
- phonou interaction.
resufts we have taken a
44’DCBP theor. results
. ..___ I6K
-----
-50 FIGURE 4
0 T%retieal
pbonon is 39 cm these frequencies
+lOO
+5U
Baud profiles of 44’ DCBP at different -1
_
mth
ailowance
foe dispersion.
temperatures. (35,
WC
rrl--I
The energy of optScal coupling
37, 39, 4f,
is assigned the same value of the coupling
36K 54K
43 cm
-2
1. To each of
function (15 cm-‘).
356
357 model without dispersion with five optical phonon frequencies deduced from inspectioo of the excitor band -1 structure (38, 55, 78, 95, 106 cm ). The correspondiag dispersion coupling values are =40, 60, loo, x -1 70cm . Thus the average coupling constant g is 4.9 which indkates a strong coupling.
R!zxmxENcE.s
(I)
A.S.
Theory of Mcdeculzr excitons
DAWWV
Plenum
(2)
J. TOUSSAINr
Re?ss New York 1971
Bulletin de&x Socicltk! Royale
des Sciences de Liege
17, !0(1948)
(3)
R.M.
HOCHSTRASSER
amf J.W. MICHALUK
J. Mel,
(4) L.A.
DISSADO Chem. Phys.
(51 D.P.
CRAIG,
L.A.
Spectrosc. 42, I97 (1972)
8, 289 (1975)
DISSADO, S.H. WALMSLEY Cbem.
(6) for example J. L. RICHARDS
Phys. Letters, 46, 191(1977)
am3 S. A. RICE
1. Chem.
(7)
D.P.
CRAIG,
L.A.
Phys. 54,
2014 (1971)
DISSADO Chem.
Phys. 14,
69 (f976)
60,