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Bimolecular radiationless transitions in crystalline tetracene
Received
Bimolecular fluorescence
27 July 1968
decay of an excited singlet exciton into two triplet excitons is suggested to be an imporchannel in crystailinc tetracene and its corresponding rate is estimated to orocess is tentatively proposed to account for the observed reJ.ative efficiencies of anthracene, tetracene and pentacene.
Recent experiments by Kazzaz and Zahlan [l] have shown that the quantum yield for fluorescence for crystalline tetracene exhibits a large temperature dependence (- a factor of 30 or more under slow cooling from room temperature to 85’K) in direct contrast to its homologs, crystalline naphthalene and anthracene [2]. The authors tentatively interpreted this as arising from competition between emission from the O-O level and radiationless transitions from the O-O + 1400 cm-l level with the Iarge difference in radiationless transition rates qualitatively accounted for by the Dexter-Fowler mode1 [3]_ It is our purpose here to point out the possibility of an additional, and possibly the dominant quenching channel for fluorescence in tetracene, namely correlative bimolecular decay of an excited singlet exciton into two triplet excitons and estimate its corresponding probability [4]. Although the decay of the lowest vibrationally relaxed singlet exciton into two triplet excitons in tetracene crystals is energetically impossible it is nevertheless possible from the first excited vibronic state. The necessity for the system to use thermal energy to * Research supported in part by the US Army Research Office (Durham), under Grant DA-ARO-D-31-124-G, 828, University of Rochester, and in part by Contract DA-ARO-D-31-124-G, 873, University of Illinois. ** Present address: Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois, USA.
activate this decay &annel leads naturaLly to the observed temperature dependence_ Specificafly, 2E(T) - 20 500 cm-l and E(s) - 19 800 cm-1 where E(T) and E(S) are the energies of the =relaxed” triplet and singlet excitons respectively [5,6]. To simplify our presentation we do not consider the symmetry of the intramolecular mode operative and disregard small energy discrepancies and corrections arising from triplettriplet exciton binding energy due to the uncertainties in the experimental value of E(T). We introduce our calculation in terms of Localized excitons and single out any two nearest neighbor molecules writing the states of the eiectrons thereon as 1(YB). Neglecting anisotropy and writing Vas the intermolecular Coulomb interaction and iY as the total crystal Hamiltonian the time-independent expression for transition proba-, bility is k =yl(GS]
V]TT)+
((CT)]B]GS}((CT)f AE
VjTT)
2 IP-
Here 1(C’J?)} represents a localized charge-transfer exciton, AE the energy difference between the relaxed singlet and the lowest charge-transEer band, G, S and T refer respectively to the ground, singlet and triplet states, p is an =effectivem density of states (a product of Franck-Condon factors) and 2 is a geometrical factor representing the number of possible nearest neighbor pairs. For our case Z = 9. 327
Volume 2, number 5
CHEMICAL PHYSICS LETTERS
A numerical vahte for k may be estimated as follows. From the estimate of Geacintov et al. [‘7] of the rate of transition kli (- lo12 see-1) from a vibrational level of the singlet state to ionized states we infer that {(CT) ]I?(GS) - 10-3 eV, a value not inconsistent with similar matrix elements computed by Choi et al. 181. The matrix element {GSI VITT) has been considered in other contexts (for anthracene) by various authors; Jortner et al. [S] estimate it as 10-3 to 10m4 eV, while Sternlicht et al. l_YO]use 100 cm-1 (0.012 eV). Hence an estimate of (SG] V/TT} - 2 x 10-3 eV is justifiable whereas the matrix elements ((CT) 1VI TT) are known [ 111 to be - 10-2 eV. Using the value of Pope et al. [12J for the energy of the CT excitons (AE - 3 600 cm-l) and adopting the reasonable value (see ref. [ll]) of 0.5 states/ eV for the “effective” density of states we obtain k - 4 x 1010 to 1012 sec’l, a value several orders of magnitude larger than that of the usual channels. Note that for naphthalene and anthracene the rat* would be reduced several orders of magnitude due to the large vibrational energies involved. A value of (1 to 5) X 10-3 eP for the transition amplitude is not unreasonable and in any case it is unlikely that k is less than 1010 set-1 or greater than lo13 and is thus comparable to the rate of degradation of vibrational energy. An over-simplified mode?, which approximates the temperature dependence reported by Kazzaz and Zahlan with the assumption that bimolecular deca is the only channel, requires k to be - 1013 set’ P. The mechanism discussed here should be readily discernible from the tunneling mechanism since the latter process is strongly influenced by deuteration whereas the former is relatively insensitive. Besides explaining why the lifetime of tetracene singlet exciton is 500 times shorter than its anthracene counterpart and thus tetracene’s low quantum efficiency, this mechanism interprets the strong fluorescence of tetracene dissolved in
328
September 1968
anthracene crystals as arising from the inoperativeness of the bimolecular quenching channel. Similar processes should occur in pentacene crystals (2,?(T) - 1.90 eV, well below the first excited singlet at 2.16 eV) [13] as well as in crystalline anthracene [14]. Correlative bimolecular decay may be viewed as an environmental electronic Fermi resonance, and in general whenever 2E(T) is within several; hundred cm-l of E(S) we may expect the molecular crystal to exhibit a low quantum efficiency for fluorescence with a pronounced temperature dependence.
REFERENCES 111A.A. Kazzaz and A-B. Zahlan. J. Chem.Phys. 48 (1968) 1242. [Z] G. T. Wright, Proc. Phys. Sot. (London) A68 (1955) 701. [3] D. L. Dexter and B. W. Fowler. J. Chem. Phys. 47 (1967) 1379. 141 Experimental evidence for this process in anthracene has been reported by S. Singh, W. cT.Jones, W. Siebrand, B. .??.Stoicheff and W. G. Schneider, J. Chem. Phys. 42 (1965) 330. [5] J_ Tanaka, Chem. Sot. Japan Bull. 38 (1965) 86. 161 R. EKeHogg and H. C. Wyeth, J_ Chem.Phys. 45 (1966) 3156. [7J N. Geacintov, M. Pope and H. Kallmann, J. Chem. Phys. 45 (1966) 2639. [8] S. Choi, J.Jortner, S.A. Rice and R.Silbey, J. Chem.Phys. 41 (1964) 3294. [9] J. Jortner, S.A.Rice and J. L.Katz, J. Chem.Phys. 42 (1965) 309. [lo] H. Ster&ht, G. C.Nieman and G. W. Robinson, J. Chem.Phvs. 38 (1963) 1326: 39 (19631 1298. [ZIJ C. E.Swenberg. Ph.D. Thesis, University of Rochester. 1967. to be published. [I4 Af. Pope, J. Burgos and J. Giachino, J. Chem. Phys. 43 (1965) 3367. [13] E. J. Bowen, Advan. Photochem. 1 (1963) 27. [l-i] D. C. Northrop and 0. Simpson, Proc. Roy. Sot. (London) A234 (1956) 324.
Bimolecular fluorescence
27 July 1968
decay of an excited singlet exciton into two triplet excitons is suggested to be an imporchannel in crystailinc tetracene and its corresponding rate is estimated to orocess is tentatively proposed to account for the observed reJ.ative efficiencies of anthracene, tetracene and pentacene.
Recent experiments by Kazzaz and Zahlan [l] have shown that the quantum yield for fluorescence for crystalline tetracene exhibits a large temperature dependence (- a factor of 30 or more under slow cooling from room temperature to 85’K) in direct contrast to its homologs, crystalline naphthalene and anthracene [2]. The authors tentatively interpreted this as arising from competition between emission from the O-O level and radiationless transitions from the O-O + 1400 cm-l level with the Iarge difference in radiationless transition rates qualitatively accounted for by the Dexter-Fowler mode1 [3]_ It is our purpose here to point out the possibility of an additional, and possibly the dominant quenching channel for fluorescence in tetracene, namely correlative bimolecular decay of an excited singlet exciton into two triplet excitons and estimate its corresponding probability [4]. Although the decay of the lowest vibrationally relaxed singlet exciton into two triplet excitons in tetracene crystals is energetically impossible it is nevertheless possible from the first excited vibronic state. The necessity for the system to use thermal energy to * Research supported in part by the US Army Research Office (Durham), under Grant DA-ARO-D-31-124-G, 828, University of Rochester, and in part by Contract DA-ARO-D-31-124-G, 873, University of Illinois. ** Present address: Department of Physics and Materials Research Laboratory, University of Illinois, Urbana, Illinois, USA.
activate this decay &annel leads naturaLly to the observed temperature dependence_ Specificafly, 2E(T) - 20 500 cm-l and E(s) - 19 800 cm-1 where E(T) and E(S) are the energies of the =relaxed” triplet and singlet excitons respectively [5,6]. To simplify our presentation we do not consider the symmetry of the intramolecular mode operative and disregard small energy discrepancies and corrections arising from triplettriplet exciton binding energy due to the uncertainties in the experimental value of E(T). We introduce our calculation in terms of Localized excitons and single out any two nearest neighbor molecules writing the states of the eiectrons thereon as 1(YB). Neglecting anisotropy and writing Vas the intermolecular Coulomb interaction and iY as the total crystal Hamiltonian the time-independent expression for transition proba-, bility is k =yl(GS]
V]TT)+
((CT)]B]GS}((CT)f AE
VjTT)
2 IP-
Here 1(C’J?)} represents a localized charge-transfer exciton, AE the energy difference between the relaxed singlet and the lowest charge-transEer band, G, S and T refer respectively to the ground, singlet and triplet states, p is an =effectivem density of states (a product of Franck-Condon factors) and 2 is a geometrical factor representing the number of possible nearest neighbor pairs. For our case Z = 9. 327
Volume 2, number 5
CHEMICAL PHYSICS LETTERS
A numerical vahte for k may be estimated as follows. From the estimate of Geacintov et al. [‘7] of the rate of transition kli (- lo12 see-1) from a vibrational level of the singlet state to ionized states we infer that {(CT) ]I?(GS) - 10-3 eV, a value not inconsistent with similar matrix elements computed by Choi et al. 181. The matrix element {GSI VITT) has been considered in other contexts (for anthracene) by various authors; Jortner et al. [S] estimate it as 10-3 to 10m4 eV, while Sternlicht et al. l_YO]use 100 cm-1 (0.012 eV). Hence an estimate of (SG] V/TT} - 2 x 10-3 eV is justifiable whereas the matrix elements ((CT) 1VI TT) are known [ 111 to be - 10-2 eV. Using the value of Pope et al. [12J for the energy of the CT excitons (AE - 3 600 cm-l) and adopting the reasonable value (see ref. [ll]) of 0.5 states/ eV for the “effective” density of states we obtain k - 4 x 1010 to 1012 sec’l, a value several orders of magnitude larger than that of the usual channels. Note that for naphthalene and anthracene the rat* would be reduced several orders of magnitude due to the large vibrational energies involved. A value of (1 to 5) X 10-3 eP for the transition amplitude is not unreasonable and in any case it is unlikely that k is less than 1010 set-1 or greater than lo13 and is thus comparable to the rate of degradation of vibrational energy. An over-simplified mode?, which approximates the temperature dependence reported by Kazzaz and Zahlan with the assumption that bimolecular deca is the only channel, requires k to be - 1013 set’ P. The mechanism discussed here should be readily discernible from the tunneling mechanism since the latter process is strongly influenced by deuteration whereas the former is relatively insensitive. Besides explaining why the lifetime of tetracene singlet exciton is 500 times shorter than its anthracene counterpart and thus tetracene’s low quantum efficiency, this mechanism interprets the strong fluorescence of tetracene dissolved in
328
September 1968
anthracene crystals as arising from the inoperativeness of the bimolecular quenching channel. Similar processes should occur in pentacene crystals (2,?(T) - 1.90 eV, well below the first excited singlet at 2.16 eV) [13] as well as in crystalline anthracene [14]. Correlative bimolecular decay may be viewed as an environmental electronic Fermi resonance, and in general whenever 2E(T) is within several; hundred cm-l of E(S) we may expect the molecular crystal to exhibit a low quantum efficiency for fluorescence with a pronounced temperature dependence.
REFERENCES 111A.A. Kazzaz and A-B. Zahlan. J. Chem.Phys. 48 (1968) 1242. [Z] G. T. Wright, Proc. Phys. Sot. (London) A68 (1955) 701. [3] D. L. Dexter and B. W. Fowler. J. Chem. Phys. 47 (1967) 1379. 141 Experimental evidence for this process in anthracene has been reported by S. Singh, W. cT.Jones, W. Siebrand, B. .??.Stoicheff and W. G. Schneider, J. Chem. Phys. 42 (1965) 330. [5] J_ Tanaka, Chem. Sot. Japan Bull. 38 (1965) 86. 161 R. EKeHogg and H. C. Wyeth, J_ Chem.Phys. 45 (1966) 3156. [7J N. Geacintov, M. Pope and H. Kallmann, J. Chem. Phys. 45 (1966) 2639. [8] S. Choi, J.Jortner, S.A. Rice and R.Silbey, J. Chem.Phys. 41 (1964) 3294. [9] J. Jortner, S.A.Rice and J. L.Katz, J. Chem.Phys. 42 (1965) 309. [lo] H. Ster&ht, G. C.Nieman and G. W. Robinson, J. Chem.Phvs. 38 (1963) 1326: 39 (19631 1298. [ZIJ C. E.Swenberg. Ph.D. Thesis, University of Rochester. 1967. to be published. [I4 Af. Pope, J. Burgos and J. Giachino, J. Chem. Phys. 43 (1965) 3367. [13] E. J. Bowen, Advan. Photochem. 1 (1963) 27. [l-i] D. C. Northrop and 0. Simpson, Proc. Roy. Sot. (London) A234 (1956) 324.