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A noninteractive model for dual phosphorescence in aromatic carbonyls
Volume 34, number2
CHEMICAL
15 Jlily 1975
PHYSICS LETTERS
:
A NONiNTERACTIVE
MODEL FOR DUAL PHOSPHORESCENCE IN AROMATIC CARBONYLS*~
San-Yan CI-IU* and Lionel GOODMAN Wright and Rieman Labontoties School of Chemistry, Rutgers University. 77i.e Srate Univnir’ersiryofNsru fersey. ~Vew Brunsrvick. New Jersey 08903, USA
Received 9 hfay 1975
A non-interactive density of states model is presented to explain the observed anomalous dual phosphorescences of certain aromatic carbonyl compounds. Although the experiments are in rigid media the model is in terms of the free molecule. The phenomenon of dual phosphorescence in a large molecule violates the well-known Kasha rule: emission can occur only from the lowest excited electronic state of a given multiplicity. For a small energy gap between the second triplet state (Tz) and the first triplet state (iI), the sparse density of TI vibronic levels isoenergetic with the T2 vibrationless level leads to a slow T2 --+ T, radiationless process which is unable to quench the Tz emission completely. Two cases: T1 = 3nn*, Tz = 3nrr*; and T1 = 3rrnf, Tz = 3 nrr” are discussed at both low and high temperature limits. An impcrtant result is that raising the tsmperature in the former case is predicted to incxase the intensity cf the T, emission at the expense of the T2 emission, and conversely for ihe latler case. According to the model dual phosphorescence should also be observable in certain azines.
the emission be observed,
1. Introduction. In the study
of emission
spectra
of large polyatom-
ic molecu!es, the emission
from the second or higher state of a given multiplicity is rarely observed.
excited This result, that in a polyatomic molecule there is only a single emission form the lowest excited electronic state of a given mu!tiplicity, is known as !&ha’s rule
PI Kasha’s rule can be interpreted as a limiting case where the radiationless decay rate, k,,, from the second excited electromc state, $z, to the first excited electronic state, Q1 , is much faster than the emission rate, k,, from #2 to the ground state, QO. Thus the radiationless process quenches the emission from the higher electronic excited state. This is generally true for a large molecule. In the other extreme case of a small molecule, where k, is much smaller than k,, l
Supported by National Science Council of Republic of
China and National Sciance Foundation Grant MPS 7103359 A03. T Unfortunately, a preliminary version of this paper [ 1 ] containing certain errors and omissions was submitted for publication. The complete paper is printed here. * Resent address: Department of Chemistry, Nntiond Tsing Hua University, Hsirkhu, Taiwan.
from the second excited state can often in addition to the lowest energy emission
131 -
Recently, exceptions to Kasha’s rule have been reported for aromatic carbonyls. For example, Yang and Murov observed 1 and 200 ms-lived triplet emissions from 1 -indanone in EPA at 77 K [4] . Pownall reported
short and long-lived triplet emissions from xanthone [5] in 3.methylpentane at 77 K. The Rutgers group reported two triplet emissions from acetophenone in n-pentane media [6] and from p-chlorobenzaldehyde in nlethylcyclohexane [7], both at 4.2 K and at lower temperatures. In this paper, we try to understand dual emission in aromatic carbonyls utilizing the radiative !ifetimes of assumed non-interactive 3nn* and 3~z* states present in these molecules. The starting point is a single ground state molecular ensemble. It shculd be noted that the reported dual emissions are not unambivalently all from excitation of a single
molecular ensemble in the ground state. Photochemistry may account for the I-indanone observation [S] , aggregates for acetophenone [9], and different sites for xanthone [5].
Volume 34, number 1 2. Radiationls
15 July 197s
CHEMICAL PHYSICS L&ERS
process
In order to understand the emission properties of excited electronic states, it is necessary to consider the coupling among thkse states. This coupling process is known as a radiationiess transition. Its rate can be given as [lo] knr(i 4 f) a C (~ila/aQl~~2(x,la/aQlxi;~2. k
(1)
The radiationless transition is caused by vibrational-electronic coupling via normal mode Q between initial (upper) electronic state pi at zero-point vibrational level x0, and final (lower) electronic state Of with vibrational excited manifold &}. The summation in the expression is understood to include only those levels QTxk whose total energy (electronic energy f vibrational energy) is isoenergetic to the initial state QiXo. Usually eq. (1) is further simplified to a golden rule expression knr 0: @,l~ldQif@L+p,,
(2)
by use of an averaged Franck-Condon Factor, W’.), and the density of states, pf. For a simple aromatic hydrocarbon, pf can be as high as lo3 states/cm-l _ For a small molecule, it can resch Q 1. The great difference in vibrational density between large and small molecules is accounted for by: (a) The existence of low frequency modes in large molecules. For example, a 40 cm-l COCH, torsional mode has been assigned in acetophenone [6] . (b) The large number of different vibrational modes in complex molecules, since the total number of mode is equal to 3N - 6. Both (a) and (b) are helpful in building up vibrational level density with consequent faster radiationless processes for large molecules. Eq. (2), thus provides an exp!anation for Kasha’s rule. For a complex molecule, k,, is large enough to quench the emission from the second excited state due to a relztively high PfWe assume that for a qualitative interpretation of the ar?omalous dual emission, it is sufficient to concentrate on the vibrational density factor, or in the rate expression for the radiationless process. Then
km = Pf' For a small AE, there are few combinations
of vi-
brational quanta to satisfy the conservation of the total energy for the electronic-vibrational energy conversion: 3N-6 AE= c “++. (4) i This suggests that a necessary condition for dud emission in a large molecule is 2 small energy gap between the emitting states. In fact this is just the situation found fo; many aromatic carbonyls: the separation of the emissions is 46 cm-l in p-chlorobenzaldehyde in methylcyclohexane [7] , 140 cm-t for acetoph:none in rl-pentane [6] j 180 cm-l for xanthone in 3-methylpentane [S] , and = 200 cm-’ for 1 -hdanone in EPA [4] . It also gives 2 reason why appropriate solvents are needed in order to observe dual emission in these molecules, since a well known property of carbony1 3nn* and S,n* excited states is the different sign of the energy shift with respect to solvent polarity.
3. Intersystem
crossing
and vibration
relaxation
In the following we provide the background for a simple model for dual phosphorescence in terms of 3 nir” and 3nsi* states. The populated 3n~* 2nd 3nii* vibrationless levels are taken from three sequential steps with the starting state taken as ’ nli*. Srep A. Intersystem crossing from l nn* to viironic manifold of the triplet: from spin-crbital symmetry cocsiderations 111x*3,,* intersystem crossing is far more efficient than 1nlr * h-, 3n,s [I I] _The former can proceed by direct spin-oibital coupling, whereas the latter is a spin-orbitai forbidden process which can proceed only by second-order effects such 2s vibrationally induced spin-orbital coupling [ 131 . Step B. internal conversion from T? vibronic manifold to T1 vibronic manifold: this step is of importance especially when 3~7~~ is T7 and 3nrr* is T,.From the work by Heller et al. on benzene, the radiationless rate increases with increasing vibrational quanta in the initial state [I 31 _Thus, when T$ is cascading down from vibrational level k, intemd conversion to T, becomes progressively less efficient. This can readily be rationalized from eq. (3) since for a lower vibrational level k, Ts faces a less dense vibrational manifold of Tt , i.e., a smaller value ofp, in the radiationless rate expression. Step E actually competes with a fast vibrational 233
Volume
34, number
CHbhiICA~ PHYSICS LETTERS
2
15 July 197s
I RYr *
tiepA-
=
s&z--
(A)
Fig. lj Non-interactive density of states3model for f;ur cases involving S~(rm*) and cl;ssiy space$tripIet states: (A) Tz = 3~~t, Ts,= m-r*, 10: temperature; (4.‘) TZ = TT~*, Tj = nrr*, high temperature;(B) T2 = nir*, T1 = IT-K*, low temperature; (B’) Tz = nr;*, T1 = TTTT*,high temperature. ( denotes radiationless process, and +-+ forhidden radiationless process. 4 and .$f and 5 denote n shor:-, medium-, and long-lived emission, respectively). Steps A, B and C in (A) are discussed in section 3. A = X-T.
relaxation
process
within T;! itself_ conversion from the vibrationless T, to T, vibronic mTMfold: when the ener,gy gap betweet. T, and T, is small enough there are only two or threeiibroaic states, Tf which can be nearly isoenergetic to the vibrationless l’~. In this important case step B is dominant. Step C should be most important when T2 is a long-lived emitting state like 3~.rr*. Sfep C. Internal
triplet states. Alternative and iemperature effects is assumed to be na*.
orderings of 3n7r* and 3rrn*, are considered. As before S,
Case (A): T2 = 3rrrr*, T1 = 3nz*, low temperature (fig. 1A). Intersystem crossing from ’ nr;* populates 3rm* only (step A). 3nrr* can also be populated by the intemal conversion from the vibronic manifold of 3m-r* (step B). However, internal conversion from the vibra-
4. Dual phosphorescence
tior\less 3;1~* to 3 nrr* (step C) is not important because of the low density of coupling 3n~* vibronic levels iso-
‘.
energetic with %sr* for a small’energy gap. According to the model the two states can emit independently
In this section, we propose a dual phosphorescence model in terms of the relative importance of steps A, B and C-in. terms oftwo cio;;ely spaced non-inteiactive
_,
.’
-
234.,..
..
:.
from their separate vibrationless levels with different
Volume 34, number
lifetimes. aldehyde
This seems to be the case for p-chlorobenzin methylcyclohexme media at 4.2 K where ‘Lheenergy gap between thekmission origins is only 46 cm-l [7], but see section 5. Case (A’): T, = 3~~*, T, = 3nrrTT”,high temperature
(fig. 1A’). Intersystem crossing from ‘I-W* initially populates 3rn* only (step A). Internal conversion from vibrationally excited 3nrr* to 3nrr* (step S) is enhanced by a thermal population step within the 31;~” vibronic manifold. Thermal pumping increases the number of levels satisfying eq. (4) by increasing dE. Consequently a decrease in T2 emission intensity is predicted. The lower energy emission in pchlorobenzaldehyde has a 1 ms lifetime, the upper energy one a 12 ms lifetime. At 77 K, the lower energy emission from 3n~* grows stronger at the expnse of the higher energy emission from 3nz* [7]. This observation is expected from the model. Case (B): T, = 3n+, (fig. 1B). Intersystem
T, = 3xx,
low temperature
from lnir* can populate only cases. However, internal conversion from the vibronic manifold of 3nn* to 3nir* (step ES), in the present case, is considered to be unimportant, since the vibronic manifold for T, is denser than for T-, at any given total vibronic energy. The internal co&rsion process is important only in the direction from a sparse to a dense manifold. Thus, a vanishingly small 3 n+ population and only a single long-lived emission from 3z, (T, ) is expected. This probably the common case for aromatic carbonyl compounds in strongly polar media where 3nx* is frequantly shifted to T2 [ 141 _ 3
15
CHEMICAL PHYSICS LEFI-ERS
2
crossing
S~ST*(step A) as in the previous
Case (B’): T, = 3nrr*, T, = 3rrrr*, high temperature (fig. IB’). The dual phosphorescence, in this case activated by thermal energy, is commonly known as thermally repopulated phosphorescence [I 51. The process is expected to be important when there is a long-lived T, (3?m*), such that the thermally populated T, vibrational levels can convert into a short-lived Tz (3n.*). Migirdicyan seems to have been the fast to observe this phenomenon in durene aldehyde [I63 . Other examples are provided by Hayashi and Nagakura’s studies
JdY
1975
ofp-substituted zldehydes in polu environments [ 171. In the limit of fast thermal equilibrium with a 2O@ cm-l enerw gap between T, and T, , and KT = 50 cm-l at 77 K, the Boltzman factor exp(-AEIK7) gives a fractional occupancy for T, of 0.02. The observed life time 7obs [IS] can be expressed as ‘/‘ohs
= 0.98/r,,,,,
f 0.02/T,,*.
(5)
On the basis of experience T”+ = IW%,,t for aromatic carbonyls [18]‘? hence a medium-lived emission life time robs which is about one-third of ;iin* is expected for the total emission. Numerous observations of medium lifetime aromatic carbonyl emissions have been reported 77 K [1gY20] _ The example given in eq. (5) corresponds to S-methyl-l-indanone in fz-hexane observed by Long and Lim [20], and MBCN in ethanolmethanol observed by J_outfy and Morris [13]. The discussions in the previous four cases are based
on the assumption that S, is IV?. If S, is assumed to be ZIP;, then intersystem crossing will populate the short-lived 3n~* state. Provided that k, is fast enough the model predicts a single emission of short life time which is hardly modified by either temperature or enerw ordering relative to 3rr~*. Aromatic carboxylic acids satisfy this energy sequence. However, the lowest triplet states are we!1 spaced with the TI - Tt energy gap exceeding IO3 cm-l. Thus phosphorescence is uniquely observed frcm T, , which is always 3n~f [21]. The hypothetical carbonyl with both St = lx,* and a small T2 - T, en-
ergy gap is unknolwn because of the constancy of the nli* singlet-triplet
5.
interval
near 2 000 cm-l _
Conclusions
The lack of explicit inclusion: of the environment except through its perturbation on energy levels, T$ - T< interactions, z_nd the Franck-Condon factor are inadequacies in the non-interactive free molecule model. E.g., there is evidence that the upper state phosphorescence from pchlorobenz2ldehyde in methylcyclohexane is from a state which foLrrns through interactian
of the 3~rr* vibrationiess level with the 3nr*-CH0
tor-
1 ‘l-his is based on cases with subshntial
tferzberg-Teller cou-2 s). In benzoic acp!@ between 3nn* snd 3nn (rfiITf = 10 id the Henbeig-Teiler effect is weaker (rm* = 1 s [22]).
235
Volumc~34, nur+r
2
sional level. These effects have been discussed to some extent previously [22] ; in terms of dynamical interactions dong with environment perturbations for small T, - T, energy gaps. This approach has led to an interactive model highly sensitive to the environmental potential where the environment along with pseudoJahn-Telier distortion perturbs the potential surface into excited state confornlers [22]. hother objection is t&the golden rule conclusion that at a small energy gap the low state density factor
results in slow radiationless rate. In fact, in the low density case, the concepts of density of state: and average Fran&-Concon factor are no longer valid. This objection may be by-passed by regarding radiationless processes between two closely spaced states in a large molecule; as a kind of small molecule limit be-
cause of the very few available fiial vibronic levels. Thus whatever can happen in a small molecule (like dual emission phenomena) is also expected in a large molecule with a small ener,gy gap. In the limit of small interactions this may be a reasonable view of the dual emission phenomenon. The cases discussed in section 4 require a small enerw gap: selective intersy:;tem crossing, and a large difference in radiative lifetimes between T1 and T2. It is unlikely that the latter condition can be satisfied when both TI and T2 are iv+. It can be for a n~i*, nsr* pair. Such pairs are not limited to aromatic carbony!s and dual phosphorescence should be observable in aza compounds with small T - Tz energy gaps. However, the radiative lifetime of 1 nn* states in azines exceeds that in aromatic carbonyls by at least 10’ _Although no ex-
ample has been reported, dual phosphorescerlce should be possible for the case (A) triplet sequence with S, = mr*. Because of the slow kr, dul phosphorescence might also be possible in azines for case (B) ordering
of triplets, when S, is TIT*.
Acknowledgement Dr. 0mar.S.
15 July 1975
CHEMICAL PHYSICS LETTERS
Ichalil and Mr. Ilker Ozkan have con-
tributed to the ideas in this paper by many critical cussions.
dis-
References Chem. Phys. Letters 32 (197.5) 24. 121 hf. Kasha, Discussions Faraday Sot. 9 (1950) 14. 13.1P.J. Gardner and hi. Kasha, J. Chcm. Phss. 50 (19693 1543. I41 N.C. Yang and S. hlurov, J. Chem. Phys. 45 (1966) 4358. 151 H.J. Pownall, R.E. Connors and J.R. Huber. Chem. Phys. Letters 22 (1973) 403. 161 hf. Koyanagi. R.J. Zwarich and L. GoodmEn, J. Chem. Phys. 56 (1972) 3044. [71 O.S. Khalil and L. Goodman, J. Am. Chem. Sot., to be published. [81 N.Y. Chu and D.R. Kearns, J. Am. Chem. Sot. 94 (1972) 2619. 191 N. Kanamaru, M.E. Long and EC. Lim, Chem. Phys.
III
S.Y. Chu and L. Goodman,
Letters
26 (1974)
1.
IlO1 K.F. Freed, Topics Current Chem. 31 (1972) 105. 1111 hl.A. El-Sayed, J. Chem. Pnys. 36 (1963) 2834. 1121 A.C. Albrecht, J. C’hcm. Phys. 33 (1960) 169. [I31 D.F. Hekr,
K.F. Freed and WM. Gelbart, J. Chem. Phys. 56 (197’) 2309. [I41 L. Goodman and h1. koyanagi, MO!. Photochem. 4 (1972) 369. 1151 E.W. Schlag, S. Schneider and S.F. Fisher, Ann. Rev. Phys. Chem. 22 (1972) 46.5. (161 E. Sfigirdicyan, Chem. Phys. Letters 12 (1972) 473. ii. Hayashi and S. Nagakura, Chem. Phys. Letters 15 iI71 (1973) 63; Mol. Phys. 27 (1974) 969. P.J. Wagner, h1.J. May, A. Haung and D.R. Grabcr, J. 1181 Am. Chem. Sot. 92 (1970) 5269. R.C. Loutfy and J.M. Morris, Chem. Phys. Letters 22 1191 (1973) 584. 1201 ME. Long and E.C. Lim, Chem. Phys. Letters 20 (1973) 413. [21] H. Baba and hi. Kitzmurn, J. Mol. Spectry. 41 (1972) 302. (211 A.J. Duben, L. Goodman and hf. Koyanagi, in: Excited states, ed. E.C. Lim (Academic Press, New York, 1974) p. 235.
CHEMICAL
15 Jlily 1975
PHYSICS LETTERS
:
A NONiNTERACTIVE
MODEL FOR DUAL PHOSPHORESCENCE IN AROMATIC CARBONYLS*~
San-Yan CI-IU* and Lionel GOODMAN Wright and Rieman Labontoties School of Chemistry, Rutgers University. 77i.e Srate Univnir’ersiryofNsru fersey. ~Vew Brunsrvick. New Jersey 08903, USA
Received 9 hfay 1975
A non-interactive density of states model is presented to explain the observed anomalous dual phosphorescences of certain aromatic carbonyl compounds. Although the experiments are in rigid media the model is in terms of the free molecule. The phenomenon of dual phosphorescence in a large molecule violates the well-known Kasha rule: emission can occur only from the lowest excited electronic state of a given multiplicity. For a small energy gap between the second triplet state (Tz) and the first triplet state (iI), the sparse density of TI vibronic levels isoenergetic with the T2 vibrationless level leads to a slow T2 --+ T, radiationless process which is unable to quench the Tz emission completely. Two cases: T1 = 3nn*, Tz = 3nrr*; and T1 = 3rrnf, Tz = 3 nrr” are discussed at both low and high temperature limits. An impcrtant result is that raising the tsmperature in the former case is predicted to incxase the intensity cf the T, emission at the expense of the T2 emission, and conversely for ihe latler case. According to the model dual phosphorescence should also be observable in certain azines.
the emission be observed,
1. Introduction. In the study
of emission
spectra
of large polyatom-
ic molecu!es, the emission
from the second or higher state of a given multiplicity is rarely observed.
excited This result, that in a polyatomic molecule there is only a single emission form the lowest excited electronic state of a given mu!tiplicity, is known as !&ha’s rule
PI Kasha’s rule can be interpreted as a limiting case where the radiationless decay rate, k,,, from the second excited electromc state, $z, to the first excited electronic state, Q1 , is much faster than the emission rate, k,, from #2 to the ground state, QO. Thus the radiationless process quenches the emission from the higher electronic excited state. This is generally true for a large molecule. In the other extreme case of a small molecule, where k, is much smaller than k,, l
Supported by National Science Council of Republic of
China and National Sciance Foundation Grant MPS 7103359 A03. T Unfortunately, a preliminary version of this paper [ 1 ] containing certain errors and omissions was submitted for publication. The complete paper is printed here. * Resent address: Department of Chemistry, Nntiond Tsing Hua University, Hsirkhu, Taiwan.
from the second excited state can often in addition to the lowest energy emission
131 -
Recently, exceptions to Kasha’s rule have been reported for aromatic carbonyls. For example, Yang and Murov observed 1 and 200 ms-lived triplet emissions from 1 -indanone in EPA at 77 K [4] . Pownall reported
short and long-lived triplet emissions from xanthone [5] in 3.methylpentane at 77 K. The Rutgers group reported two triplet emissions from acetophenone in n-pentane media [6] and from p-chlorobenzaldehyde in nlethylcyclohexane [7], both at 4.2 K and at lower temperatures. In this paper, we try to understand dual emission in aromatic carbonyls utilizing the radiative !ifetimes of assumed non-interactive 3nn* and 3~z* states present in these molecules. The starting point is a single ground state molecular ensemble. It shculd be noted that the reported dual emissions are not unambivalently all from excitation of a single
molecular ensemble in the ground state. Photochemistry may account for the I-indanone observation [S] , aggregates for acetophenone [9], and different sites for xanthone [5].
Volume 34, number 1 2. Radiationls
15 July 197s
CHEMICAL PHYSICS L&ERS
process
In order to understand the emission properties of excited electronic states, it is necessary to consider the coupling among thkse states. This coupling process is known as a radiationiess transition. Its rate can be given as [lo] knr(i 4 f) a C (~ila/aQl~~2(x,la/aQlxi;~2. k
(1)
The radiationless transition is caused by vibrational-electronic coupling via normal mode Q between initial (upper) electronic state pi at zero-point vibrational level x0, and final (lower) electronic state Of with vibrational excited manifold &}. The summation in the expression is understood to include only those levels QTxk whose total energy (electronic energy f vibrational energy) is isoenergetic to the initial state QiXo. Usually eq. (1) is further simplified to a golden rule expression knr 0: @,l~ldQif@L+p,,
(2)
by use of an averaged Franck-Condon Factor, W’.), and the density of states, pf. For a simple aromatic hydrocarbon, pf can be as high as lo3 states/cm-l _ For a small molecule, it can resch Q 1. The great difference in vibrational density between large and small molecules is accounted for by: (a) The existence of low frequency modes in large molecules. For example, a 40 cm-l COCH, torsional mode has been assigned in acetophenone [6] . (b) The large number of different vibrational modes in complex molecules, since the total number of mode is equal to 3N - 6. Both (a) and (b) are helpful in building up vibrational level density with consequent faster radiationless processes for large molecules. Eq. (2), thus provides an exp!anation for Kasha’s rule. For a complex molecule, k,, is large enough to quench the emission from the second excited state due to a relztively high PfWe assume that for a qualitative interpretation of the ar?omalous dual emission, it is sufficient to concentrate on the vibrational density factor, or in the rate expression for the radiationless process. Then
km = Pf' For a small AE, there are few combinations
of vi-
brational quanta to satisfy the conservation of the total energy for the electronic-vibrational energy conversion: 3N-6 AE= c “++. (4) i This suggests that a necessary condition for dud emission in a large molecule is 2 small energy gap between the emitting states. In fact this is just the situation found fo; many aromatic carbonyls: the separation of the emissions is 46 cm-l in p-chlorobenzaldehyde in methylcyclohexane [7] , 140 cm-t for acetoph:none in rl-pentane [6] j 180 cm-l for xanthone in 3-methylpentane [S] , and = 200 cm-’ for 1 -hdanone in EPA [4] . It also gives 2 reason why appropriate solvents are needed in order to observe dual emission in these molecules, since a well known property of carbony1 3nn* and S,n* excited states is the different sign of the energy shift with respect to solvent polarity.
3. Intersystem
crossing
and vibration
relaxation
In the following we provide the background for a simple model for dual phosphorescence in terms of 3 nir” and 3nsi* states. The populated 3n~* 2nd 3nii* vibrationless levels are taken from three sequential steps with the starting state taken as ’ nli*. Srep A. Intersystem crossing from l nn* to viironic manifold of the triplet: from spin-crbital symmetry cocsiderations 111x*3,,* intersystem crossing is far more efficient than 1nlr * h-, 3n,s [I I] _The former can proceed by direct spin-oibital coupling, whereas the latter is a spin-orbitai forbidden process which can proceed only by second-order effects such 2s vibrationally induced spin-orbital coupling [ 131 . Step B. internal conversion from T? vibronic manifold to T1 vibronic manifold: this step is of importance especially when 3~7~~ is T7 and 3nrr* is T,.From the work by Heller et al. on benzene, the radiationless rate increases with increasing vibrational quanta in the initial state [I 31 _Thus, when T$ is cascading down from vibrational level k, intemd conversion to T, becomes progressively less efficient. This can readily be rationalized from eq. (3) since for a lower vibrational level k, Ts faces a less dense vibrational manifold of Tt , i.e., a smaller value ofp, in the radiationless rate expression. Step E actually competes with a fast vibrational 233
Volume
34, number
CHbhiICA~ PHYSICS LETTERS
2
15 July 197s
I RYr *
tiepA-
=
s&z--
(A)
Fig. lj Non-interactive density of states3model for f;ur cases involving S~(rm*) and cl;ssiy space$tripIet states: (A) Tz = 3~~t, Ts,= m-r*, 10: temperature; (4.‘) TZ = TT~*, Tj = nrr*, high temperature;(B) T2 = nir*, T1 = IT-K*, low temperature; (B’) Tz = nr;*, T1 = TTTT*,high temperature. ( denotes radiationless process, and +-+ forhidden radiationless process. 4 and .$f and 5 denote n shor:-, medium-, and long-lived emission, respectively). Steps A, B and C in (A) are discussed in section 3. A = X-T.
relaxation
process
within T;! itself_ conversion from the vibrationless T, to T, vibronic mTMfold: when the ener,gy gap betweet. T, and T, is small enough there are only two or threeiibroaic states, Tf which can be nearly isoenergetic to the vibrationless l’~. In this important case step B is dominant. Step C should be most important when T2 is a long-lived emitting state like 3~.rr*. Sfep C. Internal
triplet states. Alternative and iemperature effects is assumed to be na*.
orderings of 3n7r* and 3rrn*, are considered. As before S,
Case (A): T2 = 3rrrr*, T1 = 3nz*, low temperature (fig. 1A). Intersystem crossing from ’ nr;* populates 3rm* only (step A). 3nrr* can also be populated by the intemal conversion from the vibronic manifold of 3m-r* (step B). However, internal conversion from the vibra-
4. Dual phosphorescence
tior\less 3;1~* to 3 nrr* (step C) is not important because of the low density of coupling 3n~* vibronic levels iso-
‘.
energetic with %sr* for a small’energy gap. According to the model the two states can emit independently
In this section, we propose a dual phosphorescence model in terms of the relative importance of steps A, B and C-in. terms oftwo cio;;ely spaced non-inteiactive
_,
.’
-
234.,..
..
:.
from their separate vibrationless levels with different
Volume 34, number
lifetimes. aldehyde
This seems to be the case for p-chlorobenzin methylcyclohexme media at 4.2 K where ‘Lheenergy gap between thekmission origins is only 46 cm-l [7], but see section 5. Case (A’): T, = 3~~*, T, = 3nrrTT”,high temperature
(fig. 1A’). Intersystem crossing from ‘I-W* initially populates 3rn* only (step A). Internal conversion from vibrationally excited 3nrr* to 3nrr* (step S) is enhanced by a thermal population step within the 31;~” vibronic manifold. Thermal pumping increases the number of levels satisfying eq. (4) by increasing dE. Consequently a decrease in T2 emission intensity is predicted. The lower energy emission in pchlorobenzaldehyde has a 1 ms lifetime, the upper energy one a 12 ms lifetime. At 77 K, the lower energy emission from 3n~* grows stronger at the expnse of the higher energy emission from 3nz* [7]. This observation is expected from the model. Case (B): T, = 3n+, (fig. 1B). Intersystem
T, = 3xx,
low temperature
from lnir* can populate only cases. However, internal conversion from the vibronic manifold of 3nn* to 3nir* (step ES), in the present case, is considered to be unimportant, since the vibronic manifold for T, is denser than for T-, at any given total vibronic energy. The internal co&rsion process is important only in the direction from a sparse to a dense manifold. Thus, a vanishingly small 3 n+ population and only a single long-lived emission from 3z, (T, ) is expected. This probably the common case for aromatic carbonyl compounds in strongly polar media where 3nx* is frequantly shifted to T2 [ 141 _ 3
15
CHEMICAL PHYSICS LEFI-ERS
2
crossing
S~ST*(step A) as in the previous
Case (B’): T, = 3nrr*, T, = 3rrrr*, high temperature (fig. IB’). The dual phosphorescence, in this case activated by thermal energy, is commonly known as thermally repopulated phosphorescence [I 51. The process is expected to be important when there is a long-lived T, (3?m*), such that the thermally populated T, vibrational levels can convert into a short-lived Tz (3n.*). Migirdicyan seems to have been the fast to observe this phenomenon in durene aldehyde [I63 . Other examples are provided by Hayashi and Nagakura’s studies
JdY
1975
ofp-substituted zldehydes in polu environments [ 171. In the limit of fast thermal equilibrium with a 2O@ cm-l enerw gap between T, and T, , and KT = 50 cm-l at 77 K, the Boltzman factor exp(-AEIK7) gives a fractional occupancy for T, of 0.02. The observed life time 7obs [IS] can be expressed as ‘/‘ohs
= 0.98/r,,,,,
f 0.02/T,,*.
(5)
On the basis of experience T”+ = IW%,,t for aromatic carbonyls [18]‘? hence a medium-lived emission life time robs which is about one-third of ;iin* is expected for the total emission. Numerous observations of medium lifetime aromatic carbonyl emissions have been reported 77 K [1gY20] _ The example given in eq. (5) corresponds to S-methyl-l-indanone in fz-hexane observed by Long and Lim [20], and MBCN in ethanolmethanol observed by J_outfy and Morris [13]. The discussions in the previous four cases are based
on the assumption that S, is IV?. If S, is assumed to be ZIP;, then intersystem crossing will populate the short-lived 3n~* state. Provided that k, is fast enough the model predicts a single emission of short life time which is hardly modified by either temperature or enerw ordering relative to 3rr~*. Aromatic carboxylic acids satisfy this energy sequence. However, the lowest triplet states are we!1 spaced with the TI - Tt energy gap exceeding IO3 cm-l. Thus phosphorescence is uniquely observed frcm T, , which is always 3n~f [21]. The hypothetical carbonyl with both St = lx,* and a small T2 - T, en-
ergy gap is unknolwn because of the constancy of the nli* singlet-triplet
5.
interval
near 2 000 cm-l _
Conclusions
The lack of explicit inclusion: of the environment except through its perturbation on energy levels, T$ - T< interactions, z_nd the Franck-Condon factor are inadequacies in the non-interactive free molecule model. E.g., there is evidence that the upper state phosphorescence from pchlorobenz2ldehyde in methylcyclohexane is from a state which foLrrns through interactian
of the 3~rr* vibrationiess level with the 3nr*-CH0
tor-
1 ‘l-his is based on cases with subshntial
tferzberg-Teller cou-2 s). In benzoic acp!@ between 3nn* snd 3nn (rfiITf = 10 id the Henbeig-Teiler effect is weaker (rm* = 1 s [22]).
235
Volumc~34, nur+r
2
sional level. These effects have been discussed to some extent previously [22] ; in terms of dynamical interactions dong with environment perturbations for small T, - T, energy gaps. This approach has led to an interactive model highly sensitive to the environmental potential where the environment along with pseudoJahn-Telier distortion perturbs the potential surface into excited state confornlers [22]. hother objection is t&the golden rule conclusion that at a small energy gap the low state density factor
results in slow radiationless rate. In fact, in the low density case, the concepts of density of state: and average Fran&-Concon factor are no longer valid. This objection may be by-passed by regarding radiationless processes between two closely spaced states in a large molecule; as a kind of small molecule limit be-
cause of the very few available fiial vibronic levels. Thus whatever can happen in a small molecule (like dual emission phenomena) is also expected in a large molecule with a small ener,gy gap. In the limit of small interactions this may be a reasonable view of the dual emission phenomenon. The cases discussed in section 4 require a small enerw gap: selective intersy:;tem crossing, and a large difference in radiative lifetimes between T1 and T2. It is unlikely that the latter condition can be satisfied when both TI and T2 are iv+. It can be for a n~i*, nsr* pair. Such pairs are not limited to aromatic carbony!s and dual phosphorescence should be observable in aza compounds with small T - Tz energy gaps. However, the radiative lifetime of 1 nn* states in azines exceeds that in aromatic carbonyls by at least 10’ _Although no ex-
ample has been reported, dual phosphorescerlce should be possible for the case (A) triplet sequence with S, = mr*. Because of the slow kr, dul phosphorescence might also be possible in azines for case (B) ordering
of triplets, when S, is TIT*.
Acknowledgement Dr. 0mar.S.
15 July 1975
CHEMICAL PHYSICS LETTERS
Ichalil and Mr. Ilker Ozkan have con-
tributed to the ideas in this paper by many critical cussions.
dis-
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