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Franck-Condon factors in intermolecular intersystem crossing
Volume 11, numbor 5
CHEMlCAL PHYSKS
~RANCK-CANYON
FACTORS
IN I~TER~~~LECULAR
Recently, Baessler et al. [I] have shown that trapping of triplet excitons in ~nthr~cene mixed crystals is not necessarily a diffusion-limited process in the sense that each excitor which encounters art acccptor molecule gets trapped. In particular it was found that the rate constant k,,, for triplet exciton transfer between neigtibourine h&t and guest molecules - and. concomitantly, the trapping probability - decreases as the energy gap AE bet%Jeen host and guest triplet levels increases, folIowin& approsimately kk = khh exp(-AE/E$
LEl-TERS
.
k, is the reciprocal trip!9 exciton hopping time in the host lattice and E. is an empirical energy parameter. This result suggests that conversion of the electronic excess energy U’ into vibrational energy determines the raze of the energy transfer process. The ratio kllg/khh was therefore associated with the Franck-Condon factor for intermolecular triplet energy transfer, which is nothing &se but a radiationiess transition. One objective of ;he present work was to ascertain this assignment by studying singlet-triplet intersystern crossing (EC) between different molecules, a process which has been discovered recently t2.33. Since overlap of the vibrational wavefunctions is vir-
1.5 Nowmbcr
INTERSYSIE3f
IY7I
CROSSIKG
tuaIIy independent of electronic excitation. a similar fuitctional dependence as is observed for X;,(AEl is to be expected irir the KC-rate constant k+..iS,uT,J fM3, where M no\-’ stands for the chergy difference between donor singlet and acceptor triptet level. The rsperimental technique is described cisewh~re [2 j . It is based ‘311 a ~le3s~re~len t of spectraif- isolated delayed hcst tluoresccnce resulting from excitation of the lowest singlet state of guest maiecuies embedded in a mono.crystalline anthrncene f.4) or &rysene (Ch) matrix. Tetracene (Tj, pcntzcene (PC)and peryfene (Py} were chosen as guest substances. hfised crystals were grown from solution. The relative gucsr concentration was determined spectroscopically and varied between 1O1.6 and 3 X .1W5. Corttinuous Ar and Kr lasers were used as excitation sourcesI providing 17 lines of adjustable intensity in rhe wavtc-riengtit range 450 to 68G nrn. The relevant spectroscopic energy data are: El,&Aj = 1.83 eV, ETfChj = 2.43 eS [41, ES,g(A:Py) = 2.70 eV_f, +(Pyf = 1.72 eV [s”l) .E&(A:Pc) = 2.04 eV*,&+(Pcf = 1.0 eV [51 ,A !&,,(A:T) = 2.54 eV?, Es,(Ch:TI = 2.57 eY +) ET(T) = 1.25 eV {S] . ? This work.
Volume 11, number 5
CHEMICAL PHYSICS LY’ITERS
15 November 1971
Indices S, T, h. g refer to singlet, triplet, host and guest respectively. In the mixed crystal systems: A:T, A:Pc, and Ch:T the guest triplet level is located at ieast 0.6 eV below the host triplet level. Consequentiy thermai release of t_raDDed triplet eucitons, gene;zted by i;!terrystem L. crossing within -he guest molccu!es, to the host trip!:i level can !I,- ignored even at 293°K. The A:Py mixed crystal was cooled down to about iGO”K to meet this condition. Therei’ore only two pathways have to be considered for pcpulation of the host triplet ieve: i5 the e;rcitation wavelength is below the singlet absorption band of the host: (1) S,-,h -f Tl,h excitation and (2) S,,g + St,, excitation followed by intermolecular intersystem crossing
[rhj is the concentration of host triplet excitons, the incident photon flux, crT I1 is the host singlet-
I !s
triplet absorption cocfficieni? crss is the guest singlet absorption coefficient, c is the relative molar guest concentration, rs,g is the guest singlet 1ifc:ime and &.c& is the rate constant for guest-host intersystem crossing. At moderate light intensities monomolecuJar exciton kinetics apply yielding f~ = 2. The experimental procedure is as follows: The mixed crysta! is excited at a photon energy ES,, > E&i > ET,k where a?$ is known. /(I) denotes the inter&y necessary to produce a certain emission signal. Subsequently the intensity It21 is measured at variable photon energy Ec&&) >Cuss which produces the same emi+ sio’n signil?.c., the same host triplet concentration. Assuming klsoh < r$? it foliows from eq. (1 j that c
(2) The advantage of the method is that trapping effects involving both triplet and singlet host excitons cancel out. Fig. 1 shows the “excitation spectrum” of delayed host fluarcscence of n chrysene crystal doped with tetracenc. The inverse relationship to the tetracene absorption spectrum is evident. With various doping levels the linear concentration dependence predicted 614
(nm)
Fig. 1. “Er;citation spectrum” of delayed host fluorescence of a chrysene uys!al@~lopcd with 3 X 10” and l 4 X 10” mcfc,‘moIc tttraccne (temperature: 100°K). Plotted is the ex-
citation intensity ncuessary IO produce a constant DF output sign.31.Open cfclcs r.:fcr to an undoped crystal, th2 values are normalized to Ch:T data obtain& at photon energies E,,c > ES p. Dashed curvz: icciprocllcvtinction coefficient of tetra9, me in benzene solution.
by eq. (2) is veriikd, indicating the absence of cluster formation between guest molecules which should reduce the effective concentration at higher doping Ieveis. This result unambiguously confirms the previous conclusion that ISC between the lowest guest singlet 2nd the host triplet state takes place. The principal features of the delayed fluorescence excitation spectra are the same with all mixed crystals studied so far. Thera is, however, a significant dependence of the mlmerical kj,,g_,7S,g-vah_!es, caiculated from cq. (2). on the energy gap LW = Es,~-E~_~ (see fig. 2). Since 1io.m the similarity of the oscillator strengths it can be conclude@ that the singlet lifetimes of terrscene, pentacene and perylene do not differ by much more than a factor of 2 (T~,~ * 10B8 set), this dependence must be attributed to a decrease of kjsc;& with increasing rZ. ISC is a radiationless transition, its rate constant being Cisc = kisc &A,!?) [7]. The Franck-Condon factor F(E) is !=Imeasure of the rate at which the excess electronic energy AL is converted into vibrational dnergy. A theoretical calculation for the! function
Volume 1i, number 5
CHEMICAL PHYSICS LEM%RS 0.1 I5 k 0.01 cV derived from studies on triplet cx-ci-
ton transfer between host and guest mufecuIcs in similar systems [I 1 corrohorateR those resufcs and the statement that triplet energy transfer is aIso H radia- ‘-. tionless transition depending on Fran&-Condon fatt0Ci.
Nevertheless, it is a surprising fact that. within the experimental accuracy, F&E) c: F(,ctEj, because in a two-molecular system the excess electronic energy could be used to excite moleculzx vibrations in both n~olocules participating in tile &CtiWtiC transitio? Thus one mighr expect that F&L&E) equaIs the product F(AEgjF(AE-i!d$j of the Franck-Condon factors of the individual molecules, A!?, being the energy dissipated within the guest moIccu!e. However, under the assumption ilE; = i(U) the dotted curve in fig. 1 is calculated for F&L&l. which displays too smaII a variation with &E to account for thz &E-dependence Of ki%gh. Therefore it is conc!uded that the excess energy &Y is distributed asymmetricntlp between the molecules,
Fig. 2. Dependence of kjsfrS,g-V3lUCS OCI thC cncrgy gap L%!?. -With anthracenc as a host, data ace crlculatcd nccurding to cq. (2) assuming a maximum singlet-triplet absorption cucfficient ah max(A) - 3.4 X IO” cm-l (61. The large error indicated fdr CfxT is due to the hck of data for aI&Ch). The falue is c&x&ted assuming that near an energy 0.1 cV nbovt: the Q-O transition singlet-triplet absarption coefficients for anthracene and chryscne are the same (= lCld cm-‘). ---: Fran&-Condon factor for intramoleci;hr ISC in aystallinc
factor for intr~mole~u~ anthraccne 19 1. .... Franck-Condon transitions caIcufated from F&tif = [F($fG3]‘.
F(AIZ) has been presented by Siebrand [S] . Numerical data for the S, -+ T, transitjor~ in cryMlinc an-
thracene recentIy published by Swenberg and Stacy [9],were used to construct theF(dE)-plot shown in fig. 2. Apparently the functional dependences of both&U?} agree reasonably weil. Therefore we and k+J.hE) must conclude that the Franck-Condon factor Fgh(AE) describing irrtermolecular radiationless transitions is to a good ap~rox~nla~ion at least proportion.a1 to the Franck-Condon factor F(LL) for irrrrumofecular vibrational overlap. For &E > 0.4 CV an F,,(M) a exp(-AE/EO) dependence is fulfilled with E, = 0.13 + O.G2 eV. The good agreement with E, =
the essentia!
portion
be&; dissipated
with-
in the acceptor which i;? the presertz case is a host molecule. This indicates that the primary step in radiation&s transitions involving two motecutes is an adiabatic transfer of vibronic energy frsin.the donor to the acceptor moiecute FolIowed by the cooling off of the vibrationally excited acceptor 7. For further expcrimental verification of this point it wocld be desirabk to have kixgh data available for systems in which either guest or host or both are deuterated. Knowledge of F,,,, ailows comparison oftltc kc 0 -values for 1SC processes opcrating on a sir&molecular and a ~vo.n~o~ecular level. From ki,,(S1+ T2) = 4 X IO7 set-k (at ti = 0.1 ev) me3sured in pure crystalline anthracenc [IOj and k~~z.Y~~l = 106 sec- 1 (at A.E = 0.1 eV) it foltoivs that f iatte: process is by a factor of 40 less efficient. tv_itd should be correct
at least within
one order or‘magni-
tude.) This must be due to the fact that ovcrkp between o:bitals ofdifferent nlu[tip~icity beiongti‘lg to different molecuies is much weaker than overlap within the same molecule. The referee of this paper has suggested art altcrna?fThis conclusion does not rem LOhokJ for radhtionIitss transitions when the electronic matrix ekmcat isdetrrmincd b> dipole-dipole
ratI:er than electron cxchz.r.ge intcrxtion. 615
Volume 11, number 5
CHEMICAL PHYSICS LETTERS
tive way of interpreting ?he observation of delayed hG
is of the order
1 O-l1
to 10-l
2 XL‘. p‘ denotes
ET h-Ei cvalues decrease in the series Ch:T (1.1 P eV), i:Pc ‘(0.87 eV), A:T (0.6 eV), A:Py (0.11 eV). (On the other hand ES,g-ET, h -values increase in the same series.) Consequently F(E~_t,-.Er,s) and, concomitantly, A-shou!d i;:crease in the same sense, contrary to what has been observed. (Differences in kisc,z cannot account for the discrepancy.) Therefore we conclude that the present experimental determina!ion of the energy-gap-relationship rules out the “exciton-transfer model” and !et!ds support to the interpretation in terms of intermolecular intersystem crossing giver? in the present ptiper. thr Frnnck-Condon
616
factor.
Howeve!,
the
15 November 1971
One of us (C.V.) gratefully acknowledges the continuous interest of Professor H. Gerischer in this work. We arc indebted to the referee of this paper for making a valuable comment.
References [I ] H. Bacsslcr, G. Vaubel and H. KaIImann, I. Chcm. Phys.
53 (1970) 370. (21 G. Vaubel, Chem. Phys. Lcttcrs 9 (1971) 51. [3] V.L. Ermolaev and E.B. SvcshnikovqOpt. Spectry. 28 (1969) 324. [4] 51. Kinoshita nnd S.P. hld;Iynn, MoL Cryst. 4 (1968) 23!. [5] S.P. FiGlynn, T. Azumi and bl. Kinoshitn, hiokcular spectia~ulpy of the triplet state (Prentice&IL, En&wood Cliffs, !?69). [6] P. Avrlkian an2 R.E. irlcrrifield, Mol. Cryst. 5 (1968) 37. 17 ] G.W. Robinson and R.P. Frosch, J. Chcm. Phys. 38 (1963) 1187. [8] \V. Siebrnr?d, J. Chem. Phys. 46 (1967) 440; 47 (1967) 2411. i9] W.T. Sincy and C.E. Swenberg, J. Chem. Phys. 52 (19701 1962. [IO] J. Adolph and D.F. WiIIiams, J. Chem. Phyr. 46 (1967) 4248. [ 11 1 G. hlnirr, U. Xleberkin and H.C. Wolf, Phys. Lcrtcrs 25A (1967) 323.
CHEMlCAL PHYSKS
~RANCK-CANYON
FACTORS
IN I~TER~~~LECULAR
Recently, Baessler et al. [I] have shown that trapping of triplet excitons in ~nthr~cene mixed crystals is not necessarily a diffusion-limited process in the sense that each excitor which encounters art acccptor molecule gets trapped. In particular it was found that the rate constant k,,, for triplet exciton transfer between neigtibourine h&t and guest molecules - and. concomitantly, the trapping probability - decreases as the energy gap AE bet%Jeen host and guest triplet levels increases, folIowin& approsimately kk = khh exp(-AE/E$
LEl-TERS
.
k, is the reciprocal trip!9 exciton hopping time in the host lattice and E. is an empirical energy parameter. This result suggests that conversion of the electronic excess energy U’ into vibrational energy determines the raze of the energy transfer process. The ratio kllg/khh was therefore associated with the Franck-Condon factor for intermolecular triplet energy transfer, which is nothing &se but a radiationiess transition. One objective of ;he present work was to ascertain this assignment by studying singlet-triplet intersystern crossing (EC) between different molecules, a process which has been discovered recently t2.33. Since overlap of the vibrational wavefunctions is vir-
1.5 Nowmbcr
INTERSYSIE3f
IY7I
CROSSIKG
tuaIIy independent of electronic excitation. a similar fuitctional dependence as is observed for X;,(AEl is to be expected irir the KC-rate constant k+..iS,uT,J fM3, where M no\-’ stands for the chergy difference between donor singlet and acceptor triptet level. The rsperimental technique is described cisewh~re [2 j . It is based ‘311 a ~le3s~re~len t of spectraif- isolated delayed hcst tluoresccnce resulting from excitation of the lowest singlet state of guest maiecuies embedded in a mono.crystalline anthrncene f.4) or &rysene (Ch) matrix. Tetracene (Tj, pcntzcene (PC)and peryfene (Py} were chosen as guest substances. hfised crystals were grown from solution. The relative gucsr concentration was determined spectroscopically and varied between 1O1.6 and 3 X .1W5. Corttinuous Ar and Kr lasers were used as excitation sourcesI providing 17 lines of adjustable intensity in rhe wavtc-riengtit range 450 to 68G nrn. The relevant spectroscopic energy data are: El,&Aj = 1.83 eV, ETfChj = 2.43 eS [41, ES,g(A:Py) = 2.70 eV_f, +(Pyf = 1.72 eV [s”l) .E&(A:Pc) = 2.04 eV*,&+(Pcf = 1.0 eV [51 ,A !&,,(A:T) = 2.54 eV?, Es,(Ch:TI = 2.57 eY +) ET(T) = 1.25 eV {S] . ? This work.
Volume 11, number 5
CHEMICAL PHYSICS LY’ITERS
15 November 1971
Indices S, T, h. g refer to singlet, triplet, host and guest respectively. In the mixed crystal systems: A:T, A:Pc, and Ch:T the guest triplet level is located at ieast 0.6 eV below the host triplet level. Consequentiy thermai release of t_raDDed triplet eucitons, gene;zted by i;!terrystem L. crossing within -he guest molccu!es, to the host trip!:i level can !I,- ignored even at 293°K. The A:Py mixed crystal was cooled down to about iGO”K to meet this condition. Therei’ore only two pathways have to be considered for pcpulation of the host triplet ieve: i5 the e;rcitation wavelength is below the singlet absorption band of the host: (1) S,-,h -f Tl,h excitation and (2) S,,g + St,, excitation followed by intermolecular intersystem crossing
[rhj is the concentration of host triplet excitons, the incident photon flux, crT I1 is the host singlet-
I !s
triplet absorption cocfficieni? crss is the guest singlet absorption coefficient, c is the relative molar guest concentration, rs,g is the guest singlet 1ifc:ime and &.c& is the rate constant for guest-host intersystem crossing. At moderate light intensities monomolecuJar exciton kinetics apply yielding f~ = 2. The experimental procedure is as follows: The mixed crysta! is excited at a photon energy ES,, > E&i > ET,k where a?$ is known. /(I) denotes the inter&y necessary to produce a certain emission signal. Subsequently the intensity It21 is measured at variable photon energy Ec&&) >Cuss which produces the same emi+ sio’n signil?.c., the same host triplet concentration. Assuming klsoh < r$? it foliows from eq. (1 j that c
(2) The advantage of the method is that trapping effects involving both triplet and singlet host excitons cancel out. Fig. 1 shows the “excitation spectrum” of delayed host fluarcscence of n chrysene crystal doped with tetracenc. The inverse relationship to the tetracene absorption spectrum is evident. With various doping levels the linear concentration dependence predicted 614
(nm)
Fig. 1. “Er;citation spectrum” of delayed host fluorescence of a chrysene uys!al@~lopcd with 3 X 10” and l 4 X 10” mcfc,‘moIc tttraccne (temperature: 100°K). Plotted is the ex-
citation intensity ncuessary IO produce a constant DF output sign.31.Open cfclcs r.:fcr to an undoped crystal, th2 values are normalized to Ch:T data obtain& at photon energies E,,c > ES p. Dashed curvz: icciprocllcvtinction coefficient of tetra9, me in benzene solution.
by eq. (2) is veriikd, indicating the absence of cluster formation between guest molecules which should reduce the effective concentration at higher doping Ieveis. This result unambiguously confirms the previous conclusion that ISC between the lowest guest singlet 2nd the host triplet state takes place. The principal features of the delayed fluorescence excitation spectra are the same with all mixed crystals studied so far. Thera is, however, a significant dependence of the mlmerical kj,,g_,7S,g-vah_!es, caiculated from cq. (2). on the energy gap LW = Es,~-E~_~ (see fig. 2). Since 1io.m the similarity of the oscillator strengths it can be conclude@ that the singlet lifetimes of terrscene, pentacene and perylene do not differ by much more than a factor of 2 (T~,~ * 10B8 set), this dependence must be attributed to a decrease of kjsc;& with increasing rZ. ISC is a radiationless transition, its rate constant being Cisc = kisc &A,!?) [7]. The Franck-Condon factor F(E) is !=Imeasure of the rate at which the excess electronic energy AL is converted into vibrational dnergy. A theoretical calculation for the! function
Volume 1i, number 5
CHEMICAL PHYSICS LEM%RS 0.1 I5 k 0.01 cV derived from studies on triplet cx-ci-
ton transfer between host and guest mufecuIcs in similar systems [I 1 corrohorateR those resufcs and the statement that triplet energy transfer is aIso H radia- ‘-. tionless transition depending on Fran&-Condon fatt0Ci.
Nevertheless, it is a surprising fact that. within the experimental accuracy, F&E) c: F(,ctEj, because in a two-molecular system the excess electronic energy could be used to excite moleculzx vibrations in both n~olocules participating in tile &CtiWtiC transitio? Thus one mighr expect that F&L&E) equaIs the product F(AEgjF(AE-i!d$j of the Franck-Condon factors of the individual molecules, A!?, being the energy dissipated within the guest moIccu!e. However, under the assumption ilE; = i(U) the dotted curve in fig. 1 is calculated for F&L&l. which displays too smaII a variation with &E to account for thz &E-dependence Of ki%gh. Therefore it is conc!uded that the excess energy &Y is distributed asymmetricntlp between the molecules,
Fig. 2. Dependence of kjsfrS,g-V3lUCS OCI thC cncrgy gap L%!?. -With anthracenc as a host, data ace crlculatcd nccurding to cq. (2) assuming a maximum singlet-triplet absorption cucfficient ah max(A) - 3.4 X IO” cm-l (61. The large error indicated fdr CfxT is due to the hck of data for aI&Ch). The falue is c&x&ted assuming that near an energy 0.1 cV nbovt: the Q-O transition singlet-triplet absarption coefficients for anthracene and chryscne are the same (= lCld cm-‘). ---: Fran&-Condon factor for intramoleci;hr ISC in aystallinc
factor for intr~mole~u~ anthraccne 19 1. .... Franck-Condon transitions caIcufated from F&tif = [F($fG3]‘.
F(AIZ) has been presented by Siebrand [S] . Numerical data for the S, -+ T, transitjor~ in cryMlinc an-
thracene recentIy published by Swenberg and Stacy [9],were used to construct theF(dE)-plot shown in fig. 2. Apparently the functional dependences of both&U?} agree reasonably weil. Therefore we and k+J.hE) must conclude that the Franck-Condon factor Fgh(AE) describing irrtermolecular radiationless transitions is to a good ap~rox~nla~ion at least proportion.a1 to the Franck-Condon factor F(LL) for irrrrumofecular vibrational overlap. For &E > 0.4 CV an F,,(M) a exp(-AE/EO) dependence is fulfilled with E, = 0.13 + O.G2 eV. The good agreement with E, =
the essentia!
portion
be&; dissipated
with-
in the acceptor which i;? the presertz case is a host molecule. This indicates that the primary step in radiation&s transitions involving two motecutes is an adiabatic transfer of vibronic energy frsin.the donor to the acceptor moiecute FolIowed by the cooling off of the vibrationally excited acceptor 7. For further expcrimental verification of this point it wocld be desirabk to have kixgh data available for systems in which either guest or host or both are deuterated. Knowledge of F,,,, ailows comparison oftltc kc 0 -values for 1SC processes opcrating on a sir&molecular and a ~vo.n~o~ecular level. From ki,,(S1+ T2) = 4 X IO7 set-k (at ti = 0.1 ev) me3sured in pure crystalline anthracenc [IOj and k~~z.Y~~l = 106 sec- 1 (at A.E = 0.1 eV) it foltoivs that f iatte: process is by a factor of 40 less efficient. tv_itd should be correct
at least within
one order or‘magni-
tude.) This must be due to the fact that ovcrkp between o:bitals ofdifferent nlu[tip~icity beiongti‘lg to different molecuies is much weaker than overlap within the same molecule. The referee of this paper has suggested art altcrna?fThis conclusion does not rem LOhokJ for radhtionIitss transitions when the electronic matrix ekmcat isdetrrmincd b> dipole-dipole
ratI:er than electron cxchz.r.ge intcrxtion. 615
Volume 11, number 5
CHEMICAL PHYSICS LETTERS
tive way of interpreting ?he observation of delayed hG
is of the order
1 O-l1
to 10-l
2 XL‘. p‘ denotes
ET h-Ei cvalues decrease in the series Ch:T (1.1 P eV), i:Pc ‘(0.87 eV), A:T (0.6 eV), A:Py (0.11 eV). (On the other hand ES,g-ET, h -values increase in the same series.) Consequently F(E~_t,-.Er,s) and, concomitantly, A-shou!d i;:crease in the same sense, contrary to what has been observed. (Differences in kisc,z cannot account for the discrepancy.) Therefore we conclude that the present experimental determina!ion of the energy-gap-relationship rules out the “exciton-transfer model” and !et!ds support to the interpretation in terms of intermolecular intersystem crossing giver? in the present ptiper. thr Frnnck-Condon
616
factor.
Howeve!,
the
15 November 1971
One of us (C.V.) gratefully acknowledges the continuous interest of Professor H. Gerischer in this work. We arc indebted to the referee of this paper for making a valuable comment.
References [I ] H. Bacsslcr, G. Vaubel and H. KaIImann, I. Chcm. Phys.
53 (1970) 370. (21 G. Vaubel, Chem. Phys. Lcttcrs 9 (1971) 51. [3] V.L. Ermolaev and E.B. SvcshnikovqOpt. Spectry. 28 (1969) 324. [4] 51. Kinoshita nnd S.P. hld;Iynn, MoL Cryst. 4 (1968) 23!. [5] S.P. FiGlynn, T. Azumi and bl. Kinoshitn, hiokcular spectia~ulpy of the triplet state (Prentice&IL, En&wood Cliffs, !?69). [6] P. Avrlkian an2 R.E. irlcrrifield, Mol. Cryst. 5 (1968) 37. 17 ] G.W. Robinson and R.P. Frosch, J. Chcm. Phys. 38 (1963) 1187. [8] \V. Siebrnr?d, J. Chem. Phys. 46 (1967) 440; 47 (1967) 2411. i9] W.T. Sincy and C.E. Swenberg, J. Chem. Phys. 52 (19701 1962. [IO] J. Adolph and D.F. WiIIiams, J. Chem. Phyr. 46 (1967) 4248. [ 11 1 G. hlnirr, U. Xleberkin and H.C. Wolf, Phys. Lcrtcrs 25A (1967) 323.